My Nutty, Extremist Beliefs
In nearly twenty years of blogging, I’ve unfortunately felt more and more isolated and embattled. It now feels like anything I post earns severe blowback, from ridicule on Twitter, to pseudonymous comment trolls, to scary and aggressive email bullying campaigns. Reflecting on this, though, I came to see that such strong reactions are an understandable response to my extremist stances. When your beliefs smash the Overton Window into tiny shards like mine do, what do you expect? Just consider some of the intransigent, hard-line stances I’ve taken here on Shtetl-Optimized:
(1) US politics. I’m terrified of right-wing authoritarian populists and their threat to the Enlightenment. For that and many other reasons, I vote straight-ticket Democrat, donate to Democratic campaigns, and encourage everyone else to do likewise. But I also wish my fellow Democrats would rein in the woke stuff, stand up more courageously to the world’s autocrats, and study more economics, so they understand why rent control, price caps, and other harebrained interventions will always fail.
(2) Quantum computing. I’m excited about the prospects of QC, so much that I’ve devoted most of my career to that field. But I also think many of QC’s commercial applications have been wildly oversold to investors, funding agencies, and the press, and I haven’t been afraid to say so.
(3) AI. I think the spectacular progress of AI over the past few years raises scary questions about where we’re headed as a species. I’m neither in the camp that says “we’ll almost certainly die unless we shut down AI research,” nor the camp that says “the good guys need to race full-speed ahead to get AGI before the bad guys get it.” I’d like us to proceed in AI research with caution and guardrails and the best interests of humanity in mind, rather than the commercial interests of particular companies.
(4) Climate change. I think anthropogenic climate change is 100% real and one of the most urgent problems facing humanity, and those who deny this are being dishonest or willfully obtuse. But because I think that, I also think it’s way past time to explore technological solutions like modular nuclear reactors, carbon capture, and geoengineering. I think we can’t virtue-signal or kumbaya our way out of the climate crisis.
(5) Feminism and dating. I think the emancipation of women is one of the modern world’s greatest triumphs. I reserve a special hatred for misogynistic, bullying men. But I also believe, from experience, that many sensitive, nerdy guys severely overcorrected on feminist messaging, to the point that they became terrified of the tiniest bit of assertiveness or initiative in heterosexual courtship. I think this terror has led millions of them to become bitter “incels.” I want to figure out ways to disrupt the incel pipeline, by teaching shy nerdy guys to have healthy, confident dating lives, without thereby giving asshole guys license to be even bigger assholes.
(6) Israel/Palestine. I’m passionately in favor of Israel’s continued existence as a Jewish state, without which my wife’s family and many of my friends’ and colleagues’ families would have been exterminated. However, I also despise Bibi and the messianic settler movement to which he’s beholden. I pray for a two-state solution where Israelis and Palestinians will coexist in peace, free from their respective extremists.
(7) Platonism. I think that certain mathematical questions, like the Axiom of Choice or the Continuum Hypothesis, might not have any Platonic truth-value, there being no fact of the matter beyond what can be proven from various systems of axioms. But I also think, with Gödel, that statements of elementary arithmetic, like the Goldbach Conjecture or P≠NP, are just Platonically true or false independent of any axiom system.
(8) Science and religion. As a secular rationalist, I’m acutely aware that no ancient religion can be “true,” in the sense believed by either the ancients or modern fundamentalists. Still, the older I’ve gotten, the more I’ve come to see religions as vast storehouses containing (among much else) millennia of accumulated wisdom about how humans can or should live. As in the parable of Chesterton’s Fence, I think this wisdom is often far from obvious and nearly impossible to derive from first principles. So I think that, at the least, secularists will need to figure out their own long-term methods to encourage many of the same things that religion once did—such as stable families, childbirth, self-sacrifice and courage in defending one’s community, and credible game-theoretic commitments to keeping promises and various other behaviors.
(9) Foreign policy and immigration. I’d like the US to stand more courageously against evil regimes, such as those of China, Russia, and Iran. At the same time, I’d like the US to open our gates much wider to students, scientists, and dissidents from those nations who seek freedom in the West. I think our refusal to do enough of this is a world-historic self-own.
(10) Academia vs. industry. I think both have advantages and disadvantages for people in CS and other technical fields. At their best, they complement each other. When advising a student which path to pursue, I try to find out all I can about the student’s goals and personality.
(11) Population ethics. I’m worried about how the earth will support 9 or 10 billion people with first-world living standards, which is part of why I’d like career opportunities for women, girls’ education, contraception, and (early-term) abortion to become widely available everywhere on earth. All the same, I’m not an antinatalist. I think raising one or more children in a loving home should generally be celebrated as a positive contribution to the world.
(12) The mind-body problem. I think it’s possible that there’s something profound we don’t yet understand about consciousness and its relation to the physical world. At the same time, I think the burden is clearly on the mind-body dualists to articulate what that something might be, and how to reconcile it with the known laws of physics. I admire the audacity of Roger Penrose in tackling this question head-on, but I don’t think his solution works.
(13) COVID response. I think the countries that did best tended to be those that had some coherent stategy—whether that was “let the virus rip, keep schools open, quarantine only the old and sick,” or “aggressively quarantine everyone and wait for a vaccine.” I think countries torn between these strategies, like the US, tended to get the worst of all worlds. On the other hand, I think the US did one huge thing right, which was greatly to accelerate (by historical standards) the testing and distribution of the mRNA vaccines. For the sake of the millions who died and the billions who had their lives interrupted, I only wish we’d rushed the vaccines much more. We ought now to be spending trillions on a vaccine pipeline that’s ready to roll within weeks as soon as the next pandemic hits.
(14) P versus NP. From decades of intuition in math and theoretical computer science, I think we can be fairly confident of P≠NP—but I’d “only” give it, say, 97% odds. Here as elsewhere, we should be open to the possibility of world-changing surprises.
(15) Interpretation of QM. I get really annoyed by bad arguments against the Everett interpretation, which (contrary to a popular misconception) I understand to result from scientifically conservative choices. But I’m also not an Everettian diehard. I think that, if you push questions like “but is anyone home in the other branches?” hard enough, you arrive at questions about personal identity and consciousness that were profoundly confusing even before quantum mechanics. I hope we someday learn something new that clarifies the situation.
Anyway, with extremist, uncompromising views like those, is it any surprise that I get pilloried and denounced so often?
All the same, I sometimes ask myself: what was the point of becoming a professor, seeking and earning the hallowed protections of tenure, if I can’t then freely express radical, unbalanced, batshit-crazy convictions like the ones in this post?
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Comment #1 October 13th, 2024 at 7:59 pm
Scott,
Regarding (7), how do we split AC/CH from Goldbach and even the P vs. NP problem? What shaves one problem from being in the Aaronson-realm of being platonically true or false vs. outside of the platonic realm and being merely true, false, or undecidable from a given set of axioms?
I agree with your examples. But I don’t know how to articulate the separation.
Comment #2 October 13th, 2024 at 8:07 pm
Mark Spinelli #1: For me it’s simple. Arithmetical sentences (those expressible via first-order logic over the integers, or equivalently, the halting or non-halting of Turing machines with oracles for the halting problem with oracles for the etc.), must have definite truth-values independent of any axiom system, since otherwise, how did we even get started talking about math? Our stance is not reflectively stable.
Non-arithmetical sentences like AC or CH might or might not have such truth-values. You can confuse me by asking about intermediate cases (determinacy of various games, etc), but at least those extremes seem clear.
Comment #3 October 13th, 2024 at 8:51 pm
Why could it not be an absolute physical fact that any even positive which fits in our universe is the sum of at most two primes, or that any physical instantiation of a particular Turing machine does not halt before something (the heat death of the universe if nothing else) causes it to cease be a good instantiation of that Turing machine, but the truth value of any statement which claims to quantify over an infinity of inconceivably huge integers depends on the rules you choose to characterize those numbers? That way we get enough absolute truth to ground formal mathematical reasoning (as all of our formal mathematical reasoning takes place in our universe on our physical brains and computers) without any need to postulate a superfluous platonic realm.
Comment #4 October 13th, 2024 at 9:06 pm
Ben Goodman #3: I think treating numbers as well-defined only if they fit in the physical universe doesn’t work. Suppose, for example, that current cosmological observations suggest (as they seem to) that we’re limited to computations involving at most ~10122 bits or qubits in the reachable universe. And suppose I then ask: is there a mistake in the cosmologists’ data, that makes the real number closer to ~10123? Clearly I must be allowed to ask such questions if we’re going to do science! And yet equally clearly, in the course of asking them, I’ll slightly exceed whatever is the true bound on which numbers can fit in the universe. But if I can exceed it by a little, why not by a lot?
Comment #5 October 13th, 2024 at 9:52 pm
Scott #2: Would it be fair to summarize that distinction like this: “God created the integers; all else is the work of man.”? 😀
Comment #6 October 13th, 2024 at 10:28 pm
Ted #5: Well, Kronecker meant to heap scorn on Cantorian set theory with that saying, whereas I have no similar intention. I think it’s awe-inspiring that we can use finite sequences of symbols to reason validly about infinite sets. It’s just that we shouldn’t expect to settle every possible question.
Comment #7 October 13th, 2024 at 10:38 pm
RE: QM Interpretation. Are there any unique, measurable, and (most importantly) falsifiable claims made by any of the different QM interpretations? I occasionally hear physicists speak of their preferred interpretation in language that implies a lot of confidence in their assertions, but I’ve yet to encounter any one explaining how their favorite interpretation can ever be confirmed, or what unique predictions it makes about reality.
Is there a good summary somewhere that answers the above question? I would love to read it if it exists.
Comment #8 October 13th, 2024 at 10:52 pm
Some of these things are very strange. Not your opinion on them, but the way they are part of the discussion.
For example, as a EU-US dual-citizen, I see that in the window of Europe I am exposed to there is no debate wrt the truth value of climate change at the same (stupid, IMHO) level we see here in the USA. However people are more worried about the local pollutants and smog, which people in the USA seem to completely ignore, even thought they would be a low hanging fruit to reach common ground with the others (and have the climate advantages as a “side benefit”). I mean what are we arguing about, the science is so clear!
On abortion, which in Europe seems like a well-settled issue from the 70s, I am shocked how we continue to argue here in USA. I mean, even the Pope (who obviously opposes abortion), does not talk about it like many pro-life people here in the USA….
For Israel-Palestinian thing, I agree with your position, but I find many “devils in the details”, such as https://www.npr.org/2024/10/10/nx-s1-5106059/west-bank-gaza-israel-justice-department which I find discomforting (and it makes me sad that you don’t report them, even though I think I understand why).
For the scientific and technical issues, I totally agree with your positions, so I can hardly understand how these can be controversial…..
I guess good thing I don’t have a blog (or a Facebook, Twitter or any other social media account) so I’m spared of the attacks you receive….
Comment #9 October 13th, 2024 at 10:53 pm
Tim #7: If they made differing predictions for any experiment anyone could currently imagine, they wouldn’t be “interpretations”; they’d just be rival physical theories.
Comment #10 October 13th, 2024 at 11:03 pm
Scott #8: My takeaway then is that while QM interpretations could be an amusing conversation topic at a party, there’s not much to be gained though devoting any serious mental energy towards them.
Is that fair? Am I missing something? Why do people like Sean Carroll spend so much energy advocating for their preferred interpretation if none of the options make any actionable claims about reality? Is this just some way for atheists to exercise muscles that would otherwise be devoted towards religious thought?
Comment #11 October 13th, 2024 at 11:05 pm
Scott, I think you’re misinterpreting what’s happening. You aren’t getting blowback for your positions; you’re getting blowback because you are widely read. There are just too many people who get their jollies yelling at other people online. In today’s ecosystem, I’m pretty confident that if you chose any random topic and content—even, e.g. some text from a random wikipedia article—you’d get blowback.
Comment #12 October 13th, 2024 at 11:40 pm
Scott, I really wish you would be less vague about “the woke stuff”. For instance, I have a daughter that is a trans woman. I love her, and want to protect her. Because of her, I have met many other trans people. Mostly, they are people trying to do the best they can in a very unusual situation. Often they inspire me.
I would like to protect them from people who want to erase their existence. Who want to claim that they don’t exist, they are all faking it to get away with something. They are exercising a sexual kink. Who want to prohibit medical care being provided to them, even as every single treatment a trans child gets is given to cis children in much greater numbers already.
Is that “woke stuff” to you? Use of the phrase “Woke stuff” way too often comes off as “your causes are stupid”. That does not mix well with “my causes are vital”.
Generally, we are fellow travellers. You catch a lot of garbage these days for no better reason than you are a public figure.
It’s possible that you simply would like people to show more compassion in their dialog with one another. Me too. As long as we have social media that is a public square, you will get people trying to raise their status by dumping on a perceived enemy, or ferretting out a “hidden enemy”. Which is why I don’t really participate in unmoderated forums at all.
Comment #13 October 13th, 2024 at 11:44 pm
This is a fun topic!
Excellent views on pretty much everything that I know anything about. A few comments.
#14: Agree. However, we differ in that I think it probably don’t mean squat, you maintain that it does. I think the best you can say is that it MIGHT mean something, in which case we differ on the likelihood that it actually matters.
I regard the common assertion that P = NP would have some practical application to be every bit as much false advertising as the claim that QC will solve everything at once.
#15: No opinion. Although I got A’s and could solve all the problems in (early 70’s) grad level QM, I don’t know squat about “what QM really means”. And I get a headache whenever I think about it.
Comment #14 October 14th, 2024 at 12:12 am
The most confusing part for me is that those anodyne middle-of-the-road very cautious beliefs can be labeled as extremist. But apparently this is not just your sarcasm.
Comment #15 October 14th, 2024 at 12:19 am
You’re a monster! 🙂
I agree with most of your points, except:
3) As I’ve said many times, I want full speed ahead, not to race bad guys, just to get wherever we’re going without gatekeepers blocking the way. I don’t trust gatekeepers.
5) I think your own experience in this is misleading, and your particular situation is vanishingly rare. I don’t think I’ve ever heard of another man who was afraid to approach women because of feminist literature! I myself was cripplingly shy about dating and still would be if I had to do it again (I had a fortunate set-up and have been married for 27 years), but it wasn’t because of feminism, just lack of self-confidence, and I never blamed women for it or thought that they would see me as evil.
7) Agree. I believe the difference is that the universe is finite, so math related to infinities doesn’t have a physical model, whereas counting pebbles is pretty concrete.
12) Nah. Consciousness is “just” an emergent property of the operation of brain and body. It should be obvious, given the way that the passage of time or various insults to the brain alter the person that emerges.
15) Postulating production of infinities of inaccessible universes just to avoid the notion of true randomness is unappealing to me. I *like* a random and non-deterministic universe, and find many-worlds to be a pseudo-religious belief.
Comment #16 October 14th, 2024 at 1:09 am
Is the second part of #7 (about statements about elementary arithmetic) a belief that might be wrong, or basically more along the lines of “every mathematician would agree” with no disagreement among serious people?
Comment #17 October 14th, 2024 at 1:17 am
Scott,
Could you expand on the phrase “you arrive at questions about personal identity and consciousness that were profoundly confusing even before quantum mechanics”?
I’ve heard some critics of the Everett interpretation say that it fails in explaining why we perceive one branch, and we don’t instead perceive the entire system in superposition. But doesn’t classical mechanics fail in the same way at explaining why we perceive ourselves as the lump of matter that we label as “Scott” or “Liam”, instead of some smaller or bigger system?
Comment #18 October 14th, 2024 at 2:05 am
I love the fact that out of all of these batshit-crazy ideas of yours, it’s your semi-Platonism that immediately gets people going.
Comment #19 October 14th, 2024 at 2:45 am
Hi Scott, re number 4, climate change – if you think it’s way past time to explore technological solutions to solve the climate change problems, what would you say are the best things we should be doing?
Comment #20 October 14th, 2024 at 2:52 am
This must be scale dependent. From my perspective, irrespective of subtleties, this looks like the canonical set of beliefs for US Academia. I can’t imagine any of your colleagues would seriously question your bona fides based on this list so maybe strictly Twitterlike opposition?
Comment #21 October 14th, 2024 at 3:29 am
> Jay L Gischer #12
Are you sure that conditions of all these people have the same aetiology and require the same treatment? If yes, where this certainty comes from?
Comment #22 October 14th, 2024 at 3:40 am
Regarding (7): I’d love a comment about the question of the solvability of a Diophantine equation that encodes the Halting Problem. Do they have a definite truth value? Isn’t there a countable set of possible solutions that we could check?
Comment #23 October 14th, 2024 at 3:41 am
Tim #10:
My takeaway then is that while QM interpretations could be an amusing conversation topic at a party, there’s not much to be gained though devoting any serious mental energy towards them.
Is that fair? Am I missing something? Why do people like Sean Carroll spend so much energy advocating for their preferred interpretation if none of the options make any actionable claims about reality? Is this just some way for atheists to exercise muscles that would otherwise be devoted towards religious thought?
Those are good questions.
One answer that’s commonly given, for why to care about the interpretation of QM, is that thinking about Bohmian mechanics is what led Bell to the Bell inequality, while thinking about many-worlds is what led David Deutsch to quantum computing. Another answer is that if quantum mechanics is ever to be generalized or modified—e.g. in combining it with general relativity—different interpretations will suggest different possible modifications. (E.g., in Bohmian mechanics, one could initialize the hidden variables to a distribution slightly different from |ψ|2.) More generally, even theories that are mathematically equivalent to each other will make different extensions and questions seem “natural.”
Beyond that, though, I’d say that different interpretations follow naturally from different assumptions about metaphysics, epistemology, and the whole point of doing science. So often people who passionately argue about interpretations are “really” arguing about the latter issues by proxy. Read Eliezer Yudkowsky’s quantum physics sequence for a sense of what I mean. Like a lot of many-worlders, Eliezer regards MWI as so obviously correct that it serves as a calibration test for harder problems: if you can’t just “accept what the math is screaming” in that case, then you probably also won’t do so in the cases he cares about more, like the risk of AGI. (Needless to say, many others disagree.)
Comment #24 October 14th, 2024 at 3:51 am
Jay L Gischer #12: By “the woke stuff,” I centrally mean the ideology, originating at universities, that seeks to replaces the old morality of right and wrong, just and unjust actions, by a new morality of “powerful” and “powerless” identity groups, and that can justify nearly anything, including lying, public shaming, discrimination, suppression of ideas, and violence, so long as it’s aimed at redressing the imbalance between “the powerful” and “the powerless.”
To my mind, treating trans people respectfully, using their preferred pronouns, etc., is just a slam-dunk matter of basic human decency, fully justifiable under the old morality of right and wrong—so indeed that’s what I’ve always done with all the trans people I’ve known. Which sports they ought to compete in is a harder question, but there I’m helped by not really caring about sports! 🙂
Comment #25 October 14th, 2024 at 3:55 am
scott:
you ask: what was the point of becoming a professor, seeking and earning the hallowed protections of tenure, if I can’t then freely express radical, unbalanced, batshit-crazy convictions like the ones in this post?
there are other, academically valid, reasons for becoming a tenured professor. In my case, it allowed me to do several things:
(1) i refused, in keeping with my libertarian political beliefs to pursue or accept government funding to support my research.
(2) i changed my research doing analytical theoretical soft matter physics to programming computer simulations
(3) i took time to learn a new subject for research and teaching.
(4) i changed from doing only research to also writing textbooks.
Comment #26 October 14th, 2024 at 4:01 am
It’s somehow surprising to me that you suggest that tools like rent control and price caps will always fail (and that it suffices to study economics to be convinced of this fact), while at the same time sugesting such constraining tools to control the development of AI. If the free market cannot be constrained for all other aspects of life, I don’t see why AI should be an exception. Guardrails with the best interest of humanity in mind, and not just profit of individual people or companies, are exactly what rent control and price caps are about.
Comment #27 October 14th, 2024 at 4:05 am
Dmitri #16:
Is the second part of #7 (about statements about elementary arithmetic) a belief that might be wrong, or basically more along the lines of “every mathematician would agree” with no disagreement among serious people?
Since I limited myself to “obviously correct” opinions in this post, I’d like to say that there’s no serious disagreement among experts about any of them … but alas there is, about every single one of them! 😀
In particular: many people, including some who should “know better,” seem to have taken the lesson from Gödel’s theorem that there’s no “truth,” not even in elementary arithmetic, outside of specific axiomatic theories. Ironically, this is almost the opposite of the lesson that Gödel himself drew: namely that there is truth, certainly at least in arithmetic, and it’s not reducible to or identifiable with any specific axiomatic theory.
Comment #28 October 14th, 2024 at 4:05 am
Followed a link here from ACX, so apologies if I’m unfamiliar with the culture here. These are obviously mostly not extreme at all, but I have a few questions:
On 5, do you think encouraging monogamy, and discouraging shallowness, has a role to play in ameliorating these problems? It bothers me how few progressive or rationalist leaning people, even those with such visceral experiences of the problems in this area as you, are willing to question the hedonistic orthodoxy of our culture and the harm it does to so many.
On 1, is your position “vote straight D in the current political climate” (which I respect although I disagree with it) or “vote straight D always, no matter who the Rs nominate”? If the latter, not only is this extreme IMO, but it invites hatred from the right (obviously) and paradoxically also from the left, since “I will vote for you no matter how bad you treat me” is a great way to get treated like crap by your own party. And many Democrats openly boast of treating their moderate will-never-vote-Trump voters like this: “they HAVE to support us, so we can do whatever we want!”
(Not to mention a great message to Republicans not to bother nominating reasonable candidates, since you’ll never vote for them anyway.)
On 8, by “true” do you mean something closer to “God actually exists” or to six-day-literal-creation? There’s a huge worrying motte-and-bailey with these.
Finally, 13 seems quite literally “the extreme positions are the best” so I can’t be surprised you’re called extreme on that.
Most of the rest sounds highly reasonable to me.
Comment #29 October 14th, 2024 at 4:10 am
Liam #17:
Could you expand on the phrase “you arrive at questions about personal identity and consciousness that were profoundly confusing even before quantum mechanics”?
I’ve heard some critics of the Everett interpretation say that it fails in explaining why we perceive one branch, and we don’t instead perceive the entire system in superposition.
No, that’s one of the many bad criticisms of Everett, one that’s easily answered by QM itself.
But here’s a better question: the Everettians say the simplest assumption is that all branches that seem to contain observers are actually experienced. The Bohmians say the simplest assumption is that almost all branches are “ghost towns,” just unrealized hypotheticals, while one branch is actually experienced, picked according to some rule that agrees with |ψ|2 as far as the experiencers are concerned. Without knowing more about the nature of subjective experience and how it relates to the physical world, how could we possibly say who was right?
Comment #30 October 14th, 2024 at 4:11 am
Coln R. #18:
I love the fact that out of all of these batshit-crazy ideas of yours, it’s your semi-Platonism that immediately gets people going.
LOL, yes!
Comment #31 October 14th, 2024 at 4:24 am
Full support to your views from one individual here. I don’t think your views would be considered extreme at all among the people I relate and work with. They would rather be considered the sound of reason and common sense.
One of our politicians told in his memoirs that he decided to be completely honest expressing his views before elections, however unpopular the thought those would be. The landslide of votes he received, proved to him that the loudest voices (in media, social or the other kind) are not the majority of voices. They are just the loudest.
Then again that happened maybe a decade ago. Techniques and means to influence people must have developed a lot since.
Comment #32 October 14th, 2024 at 4:25 am
James Knight #19:
Hi Scott, re number 4, climate change – if you think it’s way past time to explore technological solutions to solve the climate change problems, what would you say are the best things we should be doing?
I’m not an expert, and quickly defer to experts on these matters whenever I see that one has shown up, but ideas that seem promising to me include:
– Building hundreds of new nuclear plants (and restarting shuttered ones, and keeping the existing ones); streamlining regulations and getting rid of the execrable “ALARA” standard to allow this to happen much faster
– Blanketing deserts with cheap solar panels, which won’t provide baseload power but will help when the sun is out
– Once carbon-free electricity is widely available, using it to pull CO2 out of the atmosphere
– Cooling the planet with sulfur dioxide
– Sequestering carbon in algae in the oceans
– Blanketing large parts of the planet with white reflective material
I’d like to see all of these ideas and many more pursued in parallel, with 100x or 1000x more funding, and rapid iteration and learning from experience, and protection against shutdown by ideologues on either side.
Comment #33 October 14th, 2024 at 4:27 am
OhMyGoodness #20:
From my perspective, irrespective of subtleties, this looks like the canonical set of beliefs for US Academia.
Well, they’re correct beliefs, so yes, they’re very common in those parts of academia that care about getting things right! 😀 But many are denounced with equal fervor in other parts of academia.
Comment #34 October 14th, 2024 at 4:34 am
Have you perchance looked into modern-day Stoicism? (It’s had quite a revival in recent years, with many adopting it as a life-approach or philosophy… or even religion.) So much of what you say strikes me as being ultimately of a Stoic nature, and in practice it is largely about how to deal better with the vicissitudes of life, relationships, and ‘blowback.’ 😉
Comment #35 October 14th, 2024 at 4:35 am
Denis #26:
It’s somehow surprising to me that you suggest that tools like rent control and price caps will always fail (and that it suffices to study economics to be convinced of this fact), while at the same time sugesting such constraining tools to control the development of AI. If the free market cannot be constrained for all other aspects of life, I don’t see why AI should be an exception.
It all depends on what your goal is. If you want housing to be widely available, get rid of rent control. If you want food to be widely available, get rid of price caps. And if you want AI to progress as quickly as possible, get rid of restrictions on AI.
The crux is, what if you don’t necessarily want AI to progress as quickly as possible, because you believe (for example) that it could soon let any random person create their own bioengineered pandemic or bring down the Internet, or even pursue its own goals that could lead to human extinction?
Comment #36 October 14th, 2024 at 4:46 am
ascend #28: Yes, I do think there’s value in encouraging long-term monogamous relationships, but in getting to know the Bay Area rationalists and associated weirdos, I’ve now also seen people who apparently make polyamory work well, including in raising kids. I’m a very live-and-let-live sort of person.
In my Never-Trump from Here to Eternity FAQ, I spelled out specific conditions that could someday cause me to vote for a Republican.
Comment #37 October 14th, 2024 at 5:34 am
Jay Gischer #12
Thank goodness we are all different in our own way. It’s not much but my best wishes to you and your daughter.
Scott #33
Your story about the History professor that was concerned Arabs hated Jewish people for the wrong historical reasons was very humorous and comes to mind now.
Comment #38 October 14th, 2024 at 6:25 am
Scott,
“ but I’d “only” give it, say, 97% odds.” ?? Only 97%??!! By far your most extreme position 😉
Comment #39 October 14th, 2024 at 6:53 am
> It now feels like anything I post earns severe blowback, from ridicule on Twitter, to pseudonymous comment trolls, to scary and aggressive email bullying campaigns.
The problem with using Internet is that you get three levels of negative selection:
* people who have no life can spend more time on Internet, those are usually not the ones you want to talk or listen to;
* people who spend less time thinking about what they write, can write much more comments per unit of time;
* people who disagree with you are much more likely to comment than people who agree.
Now put all these three together, and the average response you get on Internet becomes “you are an idiot and you should die”. That’s nothing personal; it’s just another law of thermodynamics.
On specific points:
1) In USA, whichever party you support, at least 50% of population will disagree with you. You should try living in a country with more than 2 parties, where usually there is a populist strongman you wouldn’t vote for who gets 20-40% of votes, and all the remaining parties are somewhere between 1% and 20% each. That means, between 80% and 99% of people around you believe that your choices are horrible.
6) I would phrase my opinion as “I support Israel’s existence, but I don’t support its further expansion, especially if no one can say where it will stop”. I guess that is kinda similar.
7) From my (Platonist) perspective, the problem with Axiom of Choice and Continuum Hypothesis is that when different people talk about “sets”, they really talk about different things (assuming they have a specific thing in mind at all). For some flavors of “sets”, AC or CH is true; for other flavors of “sets”, AC or CH is false. First-order logic can’t even specify integers unambiguously; it only gets more complicated with sets.
13) Also, if you adopt an extreme position on COVID, you will make half of your population angry; but if you adopt a lukewarm position, you will make everyone angry.
15) Ah… I see. You are a crackpot, and all the negative responses are fully justified.
Comment #40 October 14th, 2024 at 7:01 am
When did pragmatism turn into batshit crazy ideas. In the 90s and early 2000s this could be easily level headed argument. Post social media world of polarization has made any sane discourse look crazy. Even minor disagreements get blown out of proportion. No wonder any newborn AGI will have these traits to grow up with
Comment #41 October 14th, 2024 at 7:26 am
1, Woke) I’m torn on the phrase “rein in the woke stuff”. I want to see all minorities thrive, and a world free of discrimination. However, I’d like to focus more on *doing*, not *talking*. In the last 5 years, progressives have been too focused on the best way of saying things, vs material improvements for minorities. Part of this is because declaring that a word is “problematic” is easy, while actually fixing problems in our society is difficult.
Another part of this is, progressives thoroughly control some sectors of our society, while conservatives thoroughly control others. For example, good luck getting a plumber who would ever say the phrase “unhoused people!” Progressives are more often in jobs which involve writing and administration, so trying to change the world by declaring words problematic is a path of least resistance.
However, in defense of “woke”, at least they’re trying. Many of the actual conservatives seem intent on rolling the clock back as far as they can get away with.
2, QC) I wish the field the best, it’s fun, even though it doesn’t personally appeal to me as much as some other fields. It seems like there are enough smart people working on QC, and I wish them the best of luck.
3, AI) I’m much more afraid that AI will end up as an expensive dud, than it will end up producing harms that destroy the world. People worry a lot more about “what if AI destroys the world” than “what if AI never really gets any better and we spend so much energy on it that we cause more harm in global warming”. In my career, I have tried to stay as far away from these fields as possible. There are enough smart people already working on them. I’m equally worried that AI is a bubble, and that it isn’t. I’ve tried as hard as I can to avoid using AI in my personal life for similar ethical reasons to why I’m a vegetarian.
4, Climate change) I oppose geoengineering, but strongly support other technological solutions, and it’s frustrating to see the two conflated. If we don’t witness the harmful effects of global warming, we will not seriously engage with the tradeoffs of actually becoming a carbon negative or carbon neutral society. I view fighting climate change while maintaining an industrialized standard of living as the most important thing humans can do. I strongly support climate tech efforts to convert our existing economy to be green, and oppose degrowth efforts to try to end industrialized society. However, I wish people were more personally frugal with their energy use, as I try to be. Geoengineering will just mean that we keep emitting longer and avoid our reckoning – we need to stop doing bad things, instead of having them try to cancel out.
5 feminism and dating) As a shy nerdy guy who found a wife and got married, I can say that there’s a lot of advice I had wished I had read earlier. People write from their own perspective, and I don’t think you writing from yours is harmful. I can understand women who are drowning in unwanted attention *not* focusing on writing the “hey men, here’s a good way to approach women” guide.
One thing I want to see shouted in male nerds’ face: there are plenty of female nerds, and you should try dating them!
In addition, I think men are more amenable to a “guide” style of writing for dating. This might put women off as being creepy / PUA-adjacent. But, guides need to focus on determining interest and not being a “how to get any woman ever to sleep with you” guides.
Men need to be more focused on commitment and less on casual sex. It’s worth acknowledging that men are *really* horny, particularly teenagers, and this horniness is a powerful force that can be harnessed for good or evil.
Media aimed at boys depict relationships and saying far less than media aimed at girls. I knew that when I was a boy, I was actively uninterested in anything about dating. But, this lack of knowledge was harmful when I actually tried to date people, and led to mistakes which I could have hopefully addressed later on.
Finally, part of dating is *being* somebody who is dateable. Not every boy or man is dateable, and many of those who are sad about not being dateable, should focus their efforts on changing themselves, not some sort of strategy about how to get women. Being dateable involves some combination of having a personality that’s interesting *to women*, becoming more attractive via dress, grooming, and exercise, having an interesting life, and having prospects for the future such as education, a job, etc. Self improvement is just as important as “dating advice”
Comment #42 October 14th, 2024 at 7:31 am
6 Israel / Palestine) I would like Israel to continue to exist as a Jewish state within the 1948 borders, and I would like to see a Palestinian state in the rest. I’m not sure how to get here. I acknowledge that the Palestinians have a right to be mad about the nakba. I support at least a temporary pause of aid to Israel in the hope that current leadership changes. However, I’m deeply uncertain about what the best policy is today to achieve my desired goals of a peaceful, two state solution.
7, platonism) I’m a radical materialist
Comment #43 October 14th, 2024 at 7:59 am
On point 11, I think this problem evaporates if you assume the unsolved problem of how to raise an economy to developed status. I don’t think natural resources or physical space will be binding constraints on living standards in the foreseeable future.
Comment #44 October 14th, 2024 at 8:41 am
While I’ve posted my disagreements with you on topics relating to #6, I don’t disagree with anything you’ve written there. In fact, that list doesn’t look crazy at all!
Comment #45 October 14th, 2024 at 8:48 am
I totally admire Scott for presenting difficult and important issues and debating all takers. I do that a bit for a very limited audience, but lack the energy and toughness to do it often.
I also totally agree with David Karger in #11, and think that Scott too often gets upset by the attacks from EZBpI (extremists, zealots, button pushers, and idiots). It it often worthwhile to converse with the merely confused, but a waste of time and mental energy to debate the EZBpI and provide a platform for their BS.
As for attack postings, I recommend deleting them, ignoring them, or a brief reply such as: “sure”.
Comment #46 October 14th, 2024 at 9:03 am
Coln R #18:
Point 7 is getting a lot of comment because it is a topic that many of us have thought long and hard about in the past. It is also a topic that it is easy to briefly say something about.
Some of the other topic are murky and/or very complex, and would require a long and careful reply. For example, science WRT religion. Scott has been discussing these points for years, and has boiled down the concise summaries posted.
Comment #47 October 14th, 2024 at 9:23 am
#4: Climate change.
This is an awkward one. Many get pissed off when you point out that there is nothing that can be done that will make any actual difference. Sorry — don’t shoot the messenger.
Most of the proposed actions are obvious nonsense, although many will be happy to get research funding to explore them. For example, carbon capture: the idea is that fossil fuels are burned (converted from captured to free gas) to make energy, and then captured from the air and converted back into fuel, and you are going to come out ahead? Hello — check out the second law of theromdynamics.
The underlying driver of climate change is that there are way too many people on Earth, and the vast majority of them want to use more power, not less, and they are not about to use less. Sorry — not my fault.
On a related note, the once great magazine “Scientific American” is now a mix of the traditional excellent stuff and modern crap. The recent issue had a book review of a book belittling the “Population Bomb” book, and saying that none of this turned out to have happened. WTF? how about the climate change?
Comment #48 October 14th, 2024 at 10:10 am
Scott,
My crazy belief surface overlaps almost entirely with yours. You can imagine my dismay, then, that you did not include your craziest belief, which I am in most passionate agreement with.
Time: Different Than Space.
Comment #49 October 14th, 2024 at 10:24 am
Viliam #39:
I support Israel’s existence, but I don’t support its further expansion, especially if no one can say where it will stop
I mean, not even the most extreme messianists in Israel talk about expanding it beyond its ancient borders. When Israel has invaded Egypt and Lebanon, it was in order to stop attacks, and it later withdrew in exchange for peace (or in the case of Lebanon, in exchange for no peace).
I’m in the leftist camp that says that even within its ancient border, Israel needs to withdraw to somewhere near the 1948 border to make room for a Palestinian state. I think this should happen the moment there’s Palestinian leadership that’s both in firm control and genuinely interested in peace, rather than continuing to wage war to reverse the ‘Nakba’ and kill or exile all the Jews.
Comment #50 October 14th, 2024 at 10:28 am
Also Viliam #39: I’d say the big difference between integers and sets is that, even though no first-order axioms can prove all true statements about integers (or
equivalently,every set of axioms has “nonstandard models”)—still, any computer program that enumerates over integers, searching for counterexamples to Goldbach’s conjecture or whatever, has some determinate result. In other words, I’d say there Platonically just is a standard model for the positive integers. For sets, by contrast, I have no idea.Comment #51 October 14th, 2024 at 10:32 am
Scott #48
That is certainly wrong, unless I don’t understand what ‘ancient borders’ means. See for e.g. Smotrich
Also, Daniella Weiss in this interview with Isaac Chotiner
Question about P!=NP
As I recall, in your Democritus lectures, you say that this is connected with quantum mechanics being linear. So, would a proof for this be essentially along the lines of – if this were not true, the universe as we know it would not exist?
Comment #52 October 14th, 2024 at 10:35 am
Raoul Ohio #47:
Climate change.
This is an awkward one. Many get pissed off when you point out that there is nothing that can be done that will make any actual difference. Sorry — don’t shoot the messenger.
I don’t agree with that fatalism at all. We’re the ones who made the temperature rise, and there are many things we could do to lower the temperature, fully consistently with the laws of thermodynamics, and even while maintaining our current numbers and standard of living. I listed some. Many solutions are actually quite cheap compared to global GDP, and to the amount by which climate change will plausibly lower global GDP.
If indeed “nothing can be done,” that’s not because of physics or engineering, it’s just because humans were unable to solve the requisite coordination problems.
Comment #53 October 14th, 2024 at 10:40 am
This post is all about how reasonable your beliefs are. But in recent comments in other threads, you’ve advocated for aggressive “regime change” across the globe. This is always framed in terms of good vs evil, freedom and liberal values, etc, but curiously the list of “evil regimes” never includes US allies. You’ve also advocated for endless war in Afghanistan, a decidedly extreme position. Rather than being modest, middle-of-the-road beliefs, your foreign policy ideas are basically indistinguishable from neocon hawks like John Bolton.
None of this is in any way offset or moderated by being pro-immigration. I don’t understand why “foreign policy and immigration” are in the same bullet point, other than to create the illusion that there is a centrist position that reconciles two opposing sides.
(I broadly agree with the rest of the points, or at least I don’t disagree enough to bother quibbling!)
Comment #54 October 14th, 2024 at 10:58 am
Raoul Ohio #47:
You misunderstand the claims made about carbon capture. Nobody is suggesting it’s a perpetual motion machine! Much of the captured carbon dioxide is used to extract more oil, but the point isn’t to make a net energy gain; it’s to reduce the net energy cost. Proponents of carbon capture think it’s worthwhile because it reduces carbon dioxide emissions.
Comment #55 October 14th, 2024 at 11:04 am
“12 – The mind-body problem. I think it’s possible that there’s something profound we don’t yet understand about consciousness and its relation to the physical world.”
For me it’s really the “physical world problem”.
As sentient beings, we don’t directly ever experience the so-called physical world, the only bottom reality for us (that we can’t deny) is consciousness. We could be dreaming, we could be brains in vats, we could be living in simulations… in all those cases, consciousness is the one thing we can’t be confused about.
For example, we tend to consider our eyes as literal “windows” into the physical world, a bit as if “we”, the ego, is like a pilot/driver sitting in the middle of our head, looking out into the world… this common view has no explanation power since it’s just a recursive re-framing. Rather, the “external world” (as lumps of matter hanging in a 3D space) we think we directly perceive is a recreation/interpretation/simulation within our own head created from the limited data captured by our senses.
So I don’t think this “problem” will ever be solved, because all we can possibly observe and reason about are patterns, but since consciousness can’t be reduced (as an experience), there can’t be no explanation for it. We may one day understand how to turn it on/off at will (we kind of already do with anesthesia), but it still won’t tell us why there’s consciousness rather than nothing.
Comment #56 October 14th, 2024 at 11:25 am
Nick Drozd #52: I mean, I do think that the Russia / China / Iran / North Korea axis is the most evil force on earth right now—what else comes close? And I do pray for regime change in all four of those countries (and Venezuela too), both for the sake of their own billion+ oppressed people, and for the sake of all those in Ukraine, Eastern Europe, Taiwan, Israel, South Korea, and elsewhere who those regimes threaten.
But crucially, that doesn’t mean the US should declare war against those regimes right now—i.e., that such wars would be winnable at an acceptable cost! That would still be a huge question, even if the quagmires of Afghanistan and Iraq (and before that, Vietnam) hadn’t underlined the question of whether the US still has the abilities it had in WWII.
For now, I’d say for the US to “stand more courageously” would mean things like:
– Removing all restrictions on Ukraine’s use of American-made weapons to strike inside Russia (we already missed so many opportunities here by being overcautious; at least we can stop compounding the error)
– Providing more weapons and training to Taiwan; stating explicitly that we’ll defend Taiwan in the event of a Chinese invasion
– At the very least, not standing in Israel’s way if it chooses to take out Iran’s nuclear and/or oil facilities
– Funneling (more) money to the brave Russian and Iranian dissidents
– Actually enforcing oil embargoes, rather than letting “ghost tankers” evade them
Interestingly, while Republicans are now the more hawkish party on the Iran-related items, the Democrats are the more hawkish party on all the others. I’m just equally hawkish on all of them.
Comment #57 October 14th, 2024 at 11:26 am
Regarding climate change mitigation, while I’m solidly in the camp of reducing emissions, I am also realistic that this will likely not happen. We still derive 85% of our energy from fossil fuels and our emissions and energy usage continue to grow.
Comment #58 October 14th, 2024 at 11:28 am
A great list of hot topics!
I agree with most of the stances. Although, I am much less confident in Platonism and interpretations of QM.
For example, are you sure that there is no Turing machine whose non-halting cannot be proved without the Axiom of Choice or some alternative statement lacking a seeming Platonic value?
As for interpretations of QM, I think MWI is far from the answer, it simply sweeps all the hard questions (including the nature of consciousness) under one multidimensional carpet.
Just think of our memory. Today, most humans use both, their inner (biological) memory and outer digital devices to store information. To collect our data from external devices we have to interact with them, that is, to perform a measurement. How can you be sure that the result of the measurement is untampered? Naturally, we keep a kind of hashes of the external data in our inner memory, that’s how we verify it.
Now, there are two problems with this vision. Our inner memory is also a device, although with some different architecture. Do we measure it in some sense as we think? If yes, then we also operate under the laws of QM in our minds. Now there is the following problem. The unconditionally secure quantum bit commitment is impossible under the laws of QM (by the theorem of Mayers-Lo-Chau). This means we can’t use this hash verification technique for quantum data as we do for classical. But, if our mind is quantum and can’t securely memoize quantum data, then how can we securely operate with classical data, since it’s only a shadow of quantum?
Comment #59 October 14th, 2024 at 11:51 am
Scott,
I have a pedantic fact-check on something you said in the comments to your last post, but the comments had closed by the time I read them.
You wrote “Arabs study at all of Israel’s top universities and serve in the Knesset and the Supreme Court. Can you imagine Jews being suffered to do the same in Syria, Lebanon, Iran, or Gaza, without cracking up?” While your broader point is correct, there is in fact one reserved Jewish seat in the Iranian Parliament: https://en.wikipedia.org/wiki/Iranian_Parliament_religious_minority_reserved_seats.
Comment #60 October 14th, 2024 at 12:14 pm
Scott @51:
Of course I mean what humans will actually do, not what is physically possible.
Consider the significant and rapidly growing fraction of all power now going to bitcoin mining! Retired coal burning plants coming back on line to enable more crypto mining. Apparently AI will soon consume even more power than cryptomining. Who knows what is next? Maybe vacations on the moon for the morbidly rich?
Even if any of the schemes to slow global warming actually worked, future demands for power will dwarf any results. Probably Elon Musk can use it all single handedly! Sorry, but not looking so good.
Comment #61 October 14th, 2024 at 12:27 pm
Dylan #58
Also, check on whether Israeli Arabs have the freedom to marry someone in the West Bank and bring them over to Israel.
https://www.reuters.com/world/middle-east/israels-knesset-passes-law-barring-palestinian-spouses-2022-03-10/
Also, the nation-state law makes Israeli Arabs second-class citizens.
https://www.vox.com/world/2018/7/31/17623978/israel-jewish-nation-state-law-bill-explained-apartheid-netanyahu-democracy
Comment #62 October 14th, 2024 at 12:28 pm
RB #50: Wow, if those quotes are legit then I stand corrected! I guess it’s always a mistake to underestimate Smotrich’s level of crazy.
Certainly we can say that Judaism, in obvious contrast to both Christendom and Islam, never had any aspirations to conquer and convert the whole world. It’s always remained strikingly fixated on one tiny speck of the globe, never seeking to rule anywhere beyond that speck. But of course, it’s had a lot of trouble over the millennia maintaining an independent polity even in just that speck.
Regarding P vs NP and quantum mechanics: P vs NP is a purely mathematical question, whose answer has no dependence whatsoever on physics. But if P≠NP, one can then ask the further question of whether NP-complete problems are efficiently solvable in the physical world. And yes, Abrams and Lloyd pointed out in 1998 that if QM were nonlinear, then generically the answer would be “yes,” and that this could be taken as an additional piece of evidence that QM is exactly linear. Knowing that, maybe you could rephrase your question?
Comment #63 October 14th, 2024 at 12:29 pm
Scott #49
> any computer program that enumerates over integers, searching for counterexamples to Goldbach’s conjecture or whatever, has some determinate result.
Yeah, but that kinda just passes the buck. Remember the ancient curse: “May you live in nonstandard times”. 🙂
Comment #64 October 14th, 2024 at 12:35 pm
The most confusing part for me is that those anodyne middle-of-the-road very cautious beliefs can be labeled as extremist. But apparently this is not just your sarcasm.
Comment #65 October 14th, 2024 at 12:36 pm
Danylo Yakymenko #57:
For example, are you sure that there is no Turing machine whose non-halting cannot be proved without the Axiom of Choice or some alternative statement lacking a seeming Platonic value?
Yes. That’s the Shoenfield Absoluteness Theorem. Deserves to be much better known!
As for interpretations of QM, I think MWI is far from the answer, it simply sweeps all the hard questions (including the nature of consciousness) under one multidimensional carpet.
Oh I agree! The most I’ll say for MWI is that it’s “the worst interpretation apart from all other extant ones,” and “the clearly preferred interpretation if you regard subjective experience as a relatively unimportant epiphenomenon of physics.”
Comment #66 October 14th, 2024 at 1:00 pm
Scott #61,
You can find the interview with Daniella Weiss and the quote here
I did not realize that the first condition was P!=NP
But there still seems to be a connection with physics in the sense: If Quantum mechanics is non-linear, NP-complete problems can be solved in polynomial time which will allow us to transmit superluminal signals, violate the 2nd law etc
Since the latter are facts of our Universe, take away any leg and the other leg (with regards to efficiently solving NP-complete problems) also seems to go away.
Comment #67 October 14th, 2024 at 1:04 pm
Coln R. #18 and Raoul Ohio #46:
Indeed! I felt more comfortable with an opening comment speaking about, say, topic 7 precisely because as Raoul comments, although I haven’t really “thought long and hard about in the past,” it “is easy to briefly say something about.”
Scott #2:
I am fond of an extension of Chaitin’s work applied to the MRDP theorem, which goes something like “There are an even number (respectively, finite number) of solutions to a particular Diophantine equation if and only if the n’th bit of Omega is 1, otherwise there are an odd number (respectively, infinite number).” Surely any Diophantine equation either has an even number or an odd number of solutions? Or is this also an edge case akin to the (in)determinacy of various games?
Comment #68 October 14th, 2024 at 1:17 pm
Scott,
As others have observed, your beliefs are really very reasonable and only appear radical to you because crazies keep finding your blog. To help ground the discussion I’ve decided to share a list of my own radical ideas:
(1) The universe is lost in an Everettian cacophony of possible worlds, and America needs a strong man in power to raise one of them above all – even if that means collapse. On account of our strong commitment to a single basis vector, members of our movement call each other, “based.”
(2) Quantum computing will never work, but the research poured into reversible low-temperature computing will open the door to adiabatic zero-energy circuits which run past the end of the universe, making P=NP the practical reality of people alive in simulations at that time.
(3) Countries with successful AI policies must choose between the absolute equality of all human beings, and absolute dominance of the first intelligence to outgrow its ultrawealthy master. The United States will choose neither, somehow muddling through the apocalypse.
(4) The key to solving climate change is a revolution in the consciousness of all humankind.
(5) In the long run, population dynamics will overrun any problems people are having about the relationship between genders, at the expense of a few unhealthy cultures.
(6) The long-term future of Israel is basically the academia-versus-industry debate played out on a larger scale. In Israel, people tend to be studious, and it is possible for many to enjoy lifestyles where their minds set on things far from the material world, but everyone has to compete fiercely for a fixed amount of space that hasn’t increased since World War II. Furthermore, its existence is constantly threatened from the outside by religious conservatives who are critical of the beliefs people hold there. On the other hand, in the United States, your right to exist stems from your productivity, but by the same token most people are productive enough to thrive; and while much has been made over socialists’ desire to destroy it, it has never been in any real danger.
(7) While everyday boundaries like lane markings and fences exist in some sense, the reason more abstract divisions such as national borders are so often subject to dispute is that they do not. The solution to this problem is the appointment of philosopher kings that own nothing, and who would have no reason to argue over what land is “theirs;” a system referred to by many as Platonism.
(8) I have no opinion on this subject because the number of items was odd.
Comment #69 October 14th, 2024 at 1:25 pm
RB #66: No, I don’t know of any implication from solving NP-complete problems to violating the Second Law, and certainly not from solving NP-complete problems to sending superluminal signals. The situation is rather that if QM was nonlinear, then generically you could do all three of those things.
Comment #70 October 14th, 2024 at 1:27 pm
I have identified an important and fantastically curious truth-
The set of canonical beliefs of US Academia remains INVARIANT under ALL transformations of the real world no matter the variance of the set with that transformation! It will not change no matter the circumstances and so in some curious sense represents an ultimate belief system!
Comment #71 October 14th, 2024 at 1:27 pm
Mark Spinelli #67: Yes, of course you can construct Diophantine equations whose solutions encode the bits of Omega. That’s not an edge case for me: the bits of Omega are Platonically determined, because they just depend on whether various Turing machines halt.
Comment #72 October 14th, 2024 at 1:33 pm
OhMyGoodness #70: Failing to update one’s beliefs in light of new evidence seems like a general human failing, not specific to academia. In my own life, I’ve gravitated toward the academic STEM community and (later, to some extent) the rationalist community precisely because I’ve found them to do better in the updating department than most. Certainly covid and AI were gargantuan empirical updates for me just within the past five years.
Comment #73 October 14th, 2024 at 1:43 pm
Tim #7: That’s a more subtle question than people usually give it credit for.
The “textbook” definitions state that if two models of reality make different experimental predictions, then they constitute two different physical theories, while if they make the same experimental predictions, then they constitute two different interpretations of the same physical theory.
Those definitions are all nice on paper. But the reality is much messier, because it is often far from obvious whether or not two models of reality make the same experimental predictions. Before Bell discovered his theorem, the scientific community may well have considered standard QM and certain local-hidden-variables theories to be different interpretations of the same physical theory. But then Bell’s theorem showed that they are in fact experimentally distinguishable physical theories. Whether or not two models of reality are considered to be distinct theories can therefore depend on our current degree of understanding of the theories, and not just the basic content of the theories themselves.
Sean Carroll has explicitly said that he thinks that there could be some experiments that empirically distinguish between (what are now considered to be) different interpretations of QM – presumably by probing systems that are right at the “edge of decoherence”. He thinks that we don’t yet understand the different interpretations well enough to be able to figure out what those experiments would be – but what with some more research, we may be able to in the foreseeable future. So I think that he does indeed think that thinking about interpretations of QM is more than just armchair philosophizing.
Personally, I think that the best way to think about “theories” vs. “interpretations” is not as being an absolute binary, but as lying along more of a spectrum. Some “interpretations”, like GRW objective-collapse theory, are pretty far toward – or maybe all the way at – the end of being a distinct physical theory from the Copenhagen interpretation. Other interpretations, like the ensemble interpretation, are pretty far toward the end of being an alternate interpretation of the Copenhagen interpretation.
Comment #74 October 14th, 2024 at 1:53 pm
Scott #72
Yes, agreed that a more general human failing. I will take a more in depth look at the rationalist community. My very meager reading there suggested it was more a style of writing and argument but could have completely missed the truth.
Comment #75 October 14th, 2024 at 2:09 pm
The irony is too over the top to miss.
Embrace discomfort; it’s where truth lives.
Comment #76 October 14th, 2024 at 2:54 pm
Scott’s comment no 56
My personal belief is that most of the particular measures that you are advocating against the Russia / China / Iran / North Korea axis are not “courageous”, they are ill considered.
For example, allowing Ukraine to strike with US supplied weapons inside Russia. The Biden administration has refused to allow this because of the fear that this could result in the use by Russia of nuclear weapons. Without any of the privileged information available to Biden, you don’t seem to have a credible basis to disagree with that assessment? And I don’t think that you are willing to risk a potential nuclear exchange.
So I believe you underestimate risk. On the reward side, the argument is that, by playing a patient game, Russia and China may drop away from the axis, as there seems to be no ideology or long term strategic rationale for belonging to it.
Comment #77 October 14th, 2024 at 3:00 pm
Christopher P Silvia #41:
>One thing I want to see shouted in male nerds’ face: there are plenty of female nerds, and you should try dating them!
I’m not that young anymore and this is completely contrary to my own experience. The advice I would give to male nerds would be that there are probably about 20 male nerds per female nerd, all those male nerds want to date the female nerd, and even if she is interested in nerds (not a given) then chances are any particular nerd is not in the top 5%. Therefore, in order to date, one has to learn how to socialize with at least some “normies” and enjoy their company.
I’m genuinely curious about where you’re finding all the female nerds that you see. I’ve looked in physics, programming, and the sort of video games I play (e.g. Dwarf Fortress) and I haven’t found them there. I suspect that you might have a non-standard definition of “nerd”.
Comment #78 October 14th, 2024 at 3:16 pm
Scott #50
“no first-order axioms can prove all true statements about integers (or equivalently, every set of axioms has “nonstandard models”)”
Correct me if I’m wrong, but I don’t believe those two things actually are equivalent (except in the literal sense that every two true statements are equivalent). For example, Tarski’s first order axiomatisation of Euclidean geometry is complete in that the theory can prove or refute every sentence, but clearly has non-standard models by the upward Löwenheim–Skolem theorem.
“In other words, I’d say there Platonically just is a standard model for the positive integers. For sets, by contrast, I have no idea.”
Is that because you aren’t sure of the right way to think about this, or because we’re missing some knowledge? Or to put it differently, do you have any idea of what type of evidence may convincingly show there is in fact a canonical model for sets?
Comment #79 October 14th, 2024 at 3:33 pm
Great read 🙂 I’d add biodiversity/bioabundance loss to (4) climate. To my mind a very serious, very complex and very neglected problem. What are your views on the issue? Do you think we can avoid a sixth mass extinction within the framework of capitalism? Chances of AI productivity gains enabling an effective decoupling of material consumption from economic growth? (Just thought I’d ask a few easy ones lol)
Comment #80 October 14th, 2024 at 4:03 pm
Trevor Redding #76: I don’t think this depends on classified information. We’ve seen over the past couple years that the US did ultimately relent and allow Ukraine to cross one supposed “red line” after another, and nothing bad happened, because Putin had already been doing everything he plausibly could to destroy Ukraine. He knows that if he uses even a “tactical” nuclear weapon, he’ll lose the support of China. To me, this history strongly suggests that we should’ve just crossed the “red lines” (which only existed in our own heads) immediately, when Russia was less prepared and it would’ve made more difference.
Comment #81 October 14th, 2024 at 4:09 pm
flergalwit #78: Ok you’re right, the two notions are “equivalent” if we identify two models whenever they agree on all first-order sentences (i.e. if we ultimately only care which first-order sentences are true or false), but otherwise not.
No, I have no clue what sort of evidence would pick out a “Platonically true” model of set theory, or if such evidence could ever exist. Certainly one could imagine axioms that future mathematicians accept as “natural” and that settle CH (for example) one way or the other; that was Gödel’s hope and is still an active research program now.
Comment #82 October 14th, 2024 at 5:08 pm
Scott #80
I think you underestimate the “Great game” aspect of the situation. Were George W. Bush more interested in protecting democracy and freedom when he vowed to help Georgia and Ukraine to enter NATO in 2008, or fertilizing the apple of discord was also on the list?
Of course, it doesn’t absolve Putin from choosing violent means.
Comment #83 October 14th, 2024 at 5:27 pm
@Dr. Aaronson
First, thank you for the insightful reply in Comment 29 (and, equally so to the reader who elicited it).
With regard to mathematical platonism and your remarks in Comment #2, I am curious of how you understand first-order logic. Logicism, first-order semantics, and Herbrand semantics all share the same inference rules. On several occasions, Hilbert made the observation that first-order semantics (formal axiomatics) presupposes decidable equality. As observed by Burgess, reflexive equality in logicism is clearly metaphysical. Typically, reflexive equality in first-order semantics (justified with the incomprehensible “self-identity” claim) is ontological. Both logicism and first-order semantics are non-constructive. By contrast, Herbrand semantics is constructive.
Logic programmers are often confused by these distinctions (especially where Skolemization and equisatisfiability are involved). Relative to these distinctions, the typical interpretation given to Goedel’s incompleteness is that it shows how truth is different from provability.
Concerns over completed infinities led the Hilbert school to pursue finitary metamathematics. The underlying idea had been to “ground” the investigation upon the apparent concreteness of symbol shapes on a written page (a “concreteness” invalidated by the taking of equivalence classes).
Turing’s work had also been “grounded” upon the symbol manipulation used when mathematicians make hand calculations. In this respect, it is syntactic and constructive. Distinct from computability theory, this syntactic ground in Turing’s work admits its use for “formal systems” described using language signatures and structural recursion. This, of course, is why one speaks of how mathematicians can talk of infinity with only finite language resources. It is why advocates of first-order formal systems impose an arbitrary definition (a “gatekeeper definition”) that mathematics is delimited by recursively verifiable “spellings” of formal expressions.
However, when you do the bookkeeping between the constructive and non-constructive elements involved here, simple advocacy for first-order Peano arithmetic is not as simple as one might think. The use of infinitary axiom schemes is very different from the (apparently) categorical second-order Peano arithmetic usually associated with the usual mathematical pedagogy.
Computability, to me, appears to be fundamentally of a different character. The syntax generated for a system includes both meaningful and meaningless expressions. Typically, the meaningless expressions are collated into an equivalence class denoted with the symbol for an empty set (Moschovakis, for example). One sees similar reasoning in algebraic topology, although the ubiquity of category theory on the Internet has made showing the distinction between a quotient space and an identification space difficult. As I learned it, an identification space maps all elements of one subset to singletons and the elements of the complementary subset to a singleton. The example used in the accepted answer of the MSE link,
https://math.stackexchange.com/questions/366281/understanding-quotient-topology
corresponds to the definitions I learned.
Topologically, meaning point-set topology, the structure of this reasoning may be compared with the particular point topology or the exluded point topology (2-point Sierpinski spaces satisfy either).
In logic, this reasoning corresponds with a principle from negative free logic — the principle of indiscernibility of non-existents (As such, it also bears comparison with the Fregean semantics rejected by Russell as non-classical.).
So, I have difficulty with comparing computability with first-order Peano arithmetic.
Along similar lines, if such a comparison requires a hierarchy of oracles, I am not convinced that this is much different from a hierarchy of metalanguages required to explain truth in first-order set theory.
What appears to be the case is that naive intuitions of “truth” (truth simpliciter) involve completed infinities.
It is, therefore, not “an interpretation of Goedel” that is problematic.
Now, one must applaud Goedel for the effective notion of recursion he introduced with his work on incompleteness. But, with regard to the preceding, Skolem’s paper on arithmetic is more significant. Among other things, he rejects the Russellian interpretation for the sign of equality. This is largely lost in the historical development because the Hilbert school had only shown interest in the “quantifier-free” aspect of Skolem’s paper. Although rejecting Russell’s logicism, the Hilbert school adopted the same inference rules as logicism. Meanwhile, without analysis, Herbrand simply used Skolem’s phrase “descriptive function” when declaring “zero-place descriptive functions” to be the constant parameters of a signature. This is the foundation for “the eliminability of descriptions” found in Kleene (presumably, reproducing untranslated results from Hilbert and Bernays).
That the problem of “truth” appears bound to completed infinities seems to correspond with Willard’s work on self-verifying theories,
https://en.m.wikipedia.org/wiki/Self-verifying_theories
The diagonalization lemma is circumvented when multiplication is not total. Yet, one may still speak of provability.
Again, what I see here is that the very complaints against ineffective, non-constructive mathematics undermine the classical premises of platonism. One may retain classical bivalence using Markov’s “givenness” criterion for strengthened implication. It is, however, a simple matter to find authors disputing semantics based upon constructive bivalence.
Well, that is more than anyone cares to think about. I do not have knowledge of this content because I am a historian or a philosopher. I am interested in mathematics.
When I began, I did not know that everyone and their brother (or sister) disagreed over the answer to the question, “What is mathematics?” With arguments over the interpretation of quantum mechanics, I suspect physics is catching up.
Comment #84 October 14th, 2024 at 5:31 pm
@red75prime #21
No, all trans people are not the same. I cannot conceive of a reason, though, that some legislator should imagine that they know better than the person themselves, their parents and their doctors.
I’m sure there is someone, somewhere who is up to something under cover of being a trans person. I have yet to hear about that person, though, and I have met, seen, or read about lots of trans people at this point. It’s something that happens to people, and has been happening as long as there have been people. It’s not some new “fad”.
Comment #85 October 14th, 2024 at 5:36 pm
mls #83: Apologies, but do you think you could ask me your question in, like, one sentence?
Comment #86 October 14th, 2024 at 5:39 pm
Scott #24 Ok. Thanks for the clarification.
The “woke” analysis you refer to can put one off. I tend to view that analytic framework as just one of many ways to look at collective behavior. And yes, it is enjoying a season of favorability.
I think you will wreck yourself if you try to reject it wholesale. Bear in mind that the philosophical underpinnings of it reject any absolute framework. I am white, male, cisgendered and hetero. More than a few people have taken the attitude that if it pisses me off, it must be good.
This is, needless to say, really pretty empty as a guiding principle. Needlessly reactionary.
At the same time, there are some important and ideas coming from this examination. And it’s probably best not to lean into certain differences. The ideas in this space are not like the ideas in math and physics. There really isn’t a right answer, that can be proven or disproven.
So you can say, “That’s interesting” and drive on.
Comment #87 October 14th, 2024 at 5:44 pm
Very well said Scott, I agree fully with your positions as stated. It’s inspiring to have people like you stand up for common sense because I am afraid extremists on both sides are taking over.
Comment #88 October 14th, 2024 at 5:57 pm
Hey Scott,
I feel like you’re making the mistake of overgeneralizing your (quite niche?) experiences and projecting them onto other people in part 5. If you read their online forums, the vast majority of the incels are not just sensitive nerds who “overcorrected some feminist messages.” On the contrary, they obviously don’t care what feminists think of them, they curse them and threaten them and say horrible things to them. Nor does it seem that they would be anxious about making women uncomfortable—they openly fantasize about r*ping and killing women. If you want to understand the psychology of extreme violent misogynists on these online forums, it’s more useful to study serial killers than sensitive nerds.
Comment #89 October 14th, 2024 at 6:20 pm
@Dr. Aaronson #85
My apologies. I ought not have posted.
Why do you think computability and Peano arithmetic (first-order or second-order) are even logically compatible? That seems to be an underlying assumption in Comment 2.
I expect that you are invoking “pre-theoretic mathematical intuition.” Nevertheless, you are discriminating between “arithmetical formulas” and “non-arithmetical formulas.” That distinction is definitely “post-theoretic.”
In all likelihood, mathematics in the sense of symbols used for counting historically precedes general linguistic syntax. But, the “pre-theoretic” simultaneity of a plural is not linearly ordered.
I suppose my real consternation lies with the distinction between “How do we start calculating?” versus “How do we start mathematics?”
Once again, I apologize. I ought not have posted.
Comment #90 October 14th, 2024 at 8:29 pm
Clayton #88: By how many orders of magnitude would you imagine that the population of shy nerds exceeds the population of serial killers, morbidly fascinating though the latter might be?
Comment #91 October 14th, 2024 at 10:28 pm
Scott #80
I couldn’t tell you if this is right, but the usual geopolitical thinking is that spending a month 1% beyond the red line is what allows you to spend the next month 2% past it. By this line of thought, the pride of the leadership may have possibly been so wounded by arriving at the present day’s norms on the first day that the could have done something rash or inadvisable.
Comment #92 October 14th, 2024 at 10:33 pm
Mike #79.
Excellent question, but be aware that the irrelevant insertion of “capitalism” will cause many readers to tune you out.
Comment #93 October 14th, 2024 at 10:39 pm
Hope I got this comment in before you are burned at the stake 🙂
I probably only have well formed opinions on about 2/3 of these, but for those I tend to agree.
My own nutty extremist opinion is that U.S. style brewed coffee is better than most coffees you can get in Europe (except Italian espresso) and certainly better than any coffee drink that has milk in it.
Comment #94 October 14th, 2024 at 10:47 pm
mls #89
One of the issues logicians never seem to get away from is the assumption that a formalization of language A in formal language B is a faithful model of language A, when obviously that can’t be proven without formalizing them both in a third language, doubling the hydra. Even Godel’s formalization of PA in PA had a step that was supposed to be self-evidently true, where he used English to describe the 1:1 mapping between PA described in English and in arithmetic. So if you are asking whether PA is *really* expressed in programs, or if Turing machines are *really* formalized in PA, I think we just have to accept that they are. If that’s a flaw, it’s only a flaw in formalism conceived of as a total replacement for ordinary reasoning in mathematics.
Comment #95 October 14th, 2024 at 11:45 pm
Scott#90: While the number of mass murderers is “low” (I’m aware of 5), I don’t think shy, sensitive nerds are well-represented in the incel community.
The Internet Archive has some old versions of the /r/incels front page. I picked a random day in 2017, and found:
– Three posts referring to women as “femoids” or “roasties” (do yourself a favor and don’t look up the etymology of the latter if you happen to be eating anything).
– One post arguing that women shouldn’t be psychiatrists
– One post which claims that “women are truly evil,” because some women would rather get a divorce than stay in a loveless marriage for the sake of the children.
All of these posts had more upvotes than downvotes, and none of them strike me as the sort of thing you would write if you were recovering from an overscrupulous adherence to feminism.
It’s also worth noting that one of the earliest incel forums was PUAHate.com, a site dedicated to exposing pick-up artists and dating gurus for scamming lovelorn men with strategies that don’t work (say what you will about incels, but they are mostly correct about pick-up artists). If it were possible to measure this, I’d bet money that “guys with questionable attitudes toward women, who tried to be assertive Alpha Males and failed at it” outnumber “sensitive nerdy guys [who] overcorrected on feminist messaging” by at least a factor of 10.
That said, no one is born an incel, and I think a significant factor in their radicalization is that almost no one from the feminist side of the internet (or even, say, the not-horribly-misogynistic side) is willing to meet these guys where they’re at. I completely agree with you about the need to disrupt the incel pipeline, though I have no idea how anyone would reach these guys without getting drowned out by louder, angrier voices.
Comment #96 October 15th, 2024 at 1:34 am
Scott, If P = NP, it certainly has a proof. If P != NP, it’s possible that no proof exists in ZFC. Same thing can be said for Goldbach Conjecture. What probability would you assign to this scenario?
Comment #97 October 15th, 2024 at 2:45 am
What’s your AGI/ASI timeline (if you have one)? Because how a lot of your above concerns including domestic politics and geopolitics turn out will depend very much on that I think
Comment #98 October 15th, 2024 at 4:40 am
A student #96:
If P = NP, it certainly has a proof.
No, that’s not necessarily true! There could be a polynomial-time algorithm for 3SAT, but no proof that it’s correct or halts within the polynomial time bound on all inputs.
Anyway, if either P=NP or P≠NP were true but unprovable in ZFC, one could further ask whether the independence from ZFC was provable, and so on ad infinitum.
Maybe I’ll also give the independence scenario a ~3% probability, overlapping with my 3% probability for P=NP?
Comment #99 October 15th, 2024 at 4:44 am
Opt #97:
What’s your AGI/ASI timeline (if you have one)?
I don’t have a “timeline.” What I have are extremely wide error bars, but which now comfortably include the possibility that AI will outperform humans at basically all intellectual tasks within the next five years, which I’d say is more than enough to worry about catastrophic harms.
Comment #100 October 15th, 2024 at 5:03 am
When are you sleeping, man? Lately your comment sections have been updated around the clock, even at 4 or 5 in the morning.
Comment #101 October 15th, 2024 at 5:41 am
Clayton #100: LOL. I’m now at an AI workshop in Berkeley, sleeping in a hotel, which means that I can check my blog comments when I happen to be up in the middle of the night without waking up my wife, then go back to sleep, as I’ll try to do now.
Comment #102 October 15th, 2024 at 6:22 am
It must depend on the scale. From my point of view, regardless of the subtleties, it looks like a canonical set of beliefs for the American academy. I can’t imagine any of your colleagues seriously questioning your bona fides based on this list, so perhaps the opposition will be purely Twitter-based?
Comment #103 October 15th, 2024 at 7:14 am
So I guess Scott mainly wants to have fun with this post, just like in the good old days before Trump and Palestine solidarity.
So maybe I should try to have fun too, by writing something subjective about any of
(2) Quantum computing
(7) Platonism
(15) Interpretation of QM
Let’s see. I recently wondered whether I should buy the new book Building Quantum Computers, because the part of Mike & Ike which I enjoyed most was chapter “7 Quantum computers: physical realization”. And this new book seems to focus exactly on this part: “Instead the focus is on the computer’s elementary constituents for four different qubit modalities: nuclear spins, photons, trapped atomic ions, and superconducting circuits. Each type of qubit has its own fascinating story, told here expertly and with admirable clarity. … Various proposed quantum information processing platforms have characteristic strengths and weaknesses, which are clearly delineated in this book.”
I could write more, but this would just end in TLDR, and it would still remain a personal decision and personal question, which little interest to Scott. Of course, Scott does get such question, but he has the courage, honesty and decency to answer even such requests, even if he sometimes just answers: TLDR (in more polite words). And because this is so much more valuable than simply staying silent, I decided to write this comment here. It reminds me how happy I was, when Lienhard Pagel answered me after three month (without any ping from my side in between).
Appart from that, I also totally agree with David Karger in #11 and Raoul Ohio in #45: “you’re getting blowback because you are widely read”!
Comment #104 October 15th, 2024 at 7:53 am
What do you make of Goodstein’s, Paris-Harrington, and Kanamori–McAloon theorems? Do they hold in the Platonic “standard model for the positive integers” or not, and how can you tell?
Comment #105 October 15th, 2024 at 7:56 am
Regarding 1), US politics…
It’s incredible how the human mind normalizes things.
I would go back in time 20 years ago and tell myself Trump would get elected, impeached twice, try to rig the 2020 elections, insite a violent mob to siege congress and hang his own VP… then 4 years later, the Cheneys would back democracts against Trump, running again, this time with a new VP that referred to him as America’s Hitler, with backing of the supreme court and backing of assholes tech bros to the tune of hundreds of millions of dollars, and promising we won’t have to vote ever again, survive two assassination attempts, and ready to gleefully back two of his authoritarian friends into two regime change wars in eastern Europe and the middle east…
November election day won’t be about counting the votes and moving on, but the start of a civil war.
Comment #106 October 15th, 2024 at 10:06 am
Adam B #104: Of course those theorems hold for the standard integers. They can be proved using just a tiny amount of reasoning beyond Peano arithmetic, such as people would accept without controversy in other areas of math.
Comment #107 October 15th, 2024 at 10:36 am
Scott #56
Various factions oppose funding this or that conflict. In the end, they join hands in heartwarming bipartisan compromise and fund it all. Even amidst political dysfunction totally unprecedented in the modern era, they always find a way to give money to military industrial complex. It’s the fundamental plank in the uniparty platform. In this sense, your support of endless war and global American dominance is firmly “centrist”.
Comment #108 October 15th, 2024 at 11:35 am
In rel. to P vs NP, if 97% on nequal,
what is your percentage breakdown for Imapgliazzo’s 5 worlds?
Context: https://www.quantamagazine.org/which-computational-universe-do-we-live-in-20220418/
Comment #109 October 15th, 2024 at 11:40 am
Chinmay Nirkhe #108: Oof. Maybe I’ll put 87% probability on Cryptomania, with a fairly even split across the other four, except less on Pessiland?
Comment #110 October 15th, 2024 at 11:57 am
Nick Drozd #107: Sure, except I’d put a different gloss on the same observation. I’d say: it’s mostly on the two conspiracy-addled fringes that one finds ideas like, “what if Putin, Xi, Kim Jong, Maduro, and Khamenei are actually the good guys, pursuing justified grievances against the evil American hegemon?” And it’s mostly in the center that one finds the answer, “no they’re not. However much is broken right now about the liberal-democratic West, how much do you actually know, or care to know, about the alternatives?”
Comment #111 October 15th, 2024 at 12:06 pm
#5: I somewhat agree with those who wrote to disagree with Scott. The situation is slippery and poorly defined, and any advice is highly problematic (although I will offer some pointers in my next post)
Is there any reasonable definition of Nerds, Geeks, etc.? I think I have a decent idea, and know plenty, some of whom are women.
What are Incels? I can guess, but am not aware of knowing any.
I have a pretty good idea of what Feminists are, and in fact know plenty, lots of whom don’t hate men at all.
Etc.
Anyway, everybody is different, and this is such a complex, stressful, fraught with implications, etc., area that it is hard to nail down any concrete facts.
Comment #112 October 15th, 2024 at 12:45 pm
Scott #80
> [Putin] knows that if he uses even a “tactical” nuclear weapon, he’ll lose the support of China.
One problem. Right now he has targets on Russian territory. I hope that Chinese government won’t tolerate that too, but who knows.
Comment #113 October 15th, 2024 at 12:49 pm
#5 Advice for Shy men.
Probably most people are rather shy. I am kind of bipolar introvert/extrovert, which is think is not uncommon. I have had some modest success in meeting and hanging out with women. At the risk of looking like a doofus, I will offer a couple pointers which I hope some will find useful.
Having as many women friends as possible is a GOOD THING: you learn to be sensitive to women’s viewpoints, and you are around events with a lot of women. Women are vastly more likely then men to help relations along. I have had lots of girlfriends and one one wife in my 77 years, and many of these more or less resulted from being “fixed up” by women friends or sisters (never by guy friends or brothers).
I, like most men, have been very hesitant to “ask women out” for the good reason of fearing rejection. Try to get over this (wish I had been able to) and don’t let “no” ruin your whole day. Obviously low stress situations like “get a coffee” or lunch are a good starting point. Being with some other people usually takes some of the stress out of a “first whatever”.
A LOT of couples I know met through dating services (hey, this is 2024!) and should probably be considered. There are a wide variety of such sites. One dimension is “looking for longterm relation” vs. “quick hookup”, and many specializations (Christians, Jews, Farmers, Gays, … ). I think maybe OKCupid, Match, eHarmony, ???, are mainstream and widely used. I have zero personal experience (to shy? to old? whatever). Anyone with knowledge or advice please speak up.
Comment #114 October 15th, 2024 at 3:59 pm
You do have some crazy views, but they are not mentioned in the post. For example, you think that Robin Hanson has a valid argument that grabby aliens will devour the universe at a large fraction of the speed of light, and that this can be inferred from the fact that we don’t see them now: because if the aliens were moving slowly, we’d probably be someone else observing them at some point in the distant future of the universe.
Similarly, some people argue that we are simulated beings because otherwise we would probably be one of our own simulations. From what I see, you are not quite as enthusiastic about this idea as you are about these super-fast alien expansions, but you don’t seem to reject the argument either.
Usually there are some readers who point out the obvious absurdities of these arguments in the comments, but this is a futile exercise: a few months later you will be promoting this kind of stuff again.
Comment #115 October 15th, 2024 at 4:52 pm
Mika #114: LOL, I never expressed confidence in Robin’s solution to the Fermi Paradox, just said that it seemed about as plausible as any other proposed solution I’d heard. Unlike the simulation argument, grabby aliens is motivated by actual empirical facts: not only the Fermi Paradox, but also the Poisson-like spacing of the major transitions in the evolution of life on earth. But I think it’s best thought of as a disjunction: either there’s some bottleneck that makes intelligent life in our universe incredibly rare, or else there’s a selection effect that makes us early. The point is that the scenario where our past lightcone was already teeming with intelligent life, but for some reason none of it ever “went singular” and expanded at near-light-speed and prevented our own evolution, isn’t nearly as plausible as it might seem before you’ve spent a few minutes thinking about it.
Anyway, unless you show some curiosity/comprehension of what my actual view is, I won’t engage further.
Comment #116 October 15th, 2024 at 6:40 pm
Robin Hanson: “We do NOT assume aliens can expand at near the speed of light. We instead assume they expand at some speed, and then INFER a fast speed from the fact that we don’t now see them.” (https://scottaaronson.blog/?p=5253#comment-1877426)
Scott #115: Do you think this inference is valid? I think it’s crazy and I hope you’ll forgive me for saying this. All else being equal, a rapid spread of other civilizations would make our isolated existence here and now less likely, not more likely.
Comment #117 October 15th, 2024 at 7:00 pm
Mika #116: It’s valid given the particular background assumptions he’s making; otherwise not. If you condition on the fact of our existence (the anthropic principle) and you also condition on the fact that we don’t see them, and you hypothesize that they’re everywhere, then fast expansion makes sense but slow expansion does not.
Comment #118 October 15th, 2024 at 8:06 pm
Sad you feel isolated Scott. This is a great post, and I’d hope you focus on the many folks that continue to admire your work and character. You should host meetups when you visit various cities, and you’d see the vast extent of friends you have!
Comment #119 October 15th, 2024 at 9:54 pm
Hello Scott,
Wonderful post: fascinating topics and a very reasonable perspective on all of the major issues. I agree with most of your opinions. I respect the remaining opinions as rationally defensible and very respectable. This is great for readers like me.
Of course, I am naturally inclined to the point about Science and Religion. Which leads me to two questions.
(1) If you were to rewrite/make proper distinctions in Steven Weinberg’s famous quote, what would that look like? The quote: “Mark Twain described his mother as a genuinely good person, whose soft heart pitied even Satan, but who had no doubt about the legitimacy of slavery, because in years of living in antebellum Missouri she had never heard any sermon opposing slavery, but only countless sermons preaching that slavery was God’s will. With or without religion, good people can behave well and bad people can do evil; but for good people to do evil–that takes religion.”
For me, I would say for good people to do evil takes–perhaps, false moral beliefs in general? Or false beliefs about the nature of reason (‘rational favoring relations’) in general? Facts about divine agents may be neither a necessary nor a sufficient condition? A crude version of Divine Command Theory, which seems to be assumed by Mark Twain’s mother in the quote by Steven Weinberg, is obviously a false (but sadly, wildly popular) moral belief. But there are other false moral beliefs: like selfish hedonism, or utilitarianism, or a Nietzschian theory of evaluative superiority of Napoleon-like supergeniuses over regular people, or widespread pragmatic moral indifference (i.e. the theory that it does not matter to even try to discern the nature of moral truths). In general, false theories lead to evil, or if not evil, then at least bad consequences. But, just because there are false and bad theories about reason and morality (like, for example, popular fallacies of affirming the consequent, confirmation bias, postmodern critiques of reason as destructive, immoral normative systems that proclaim they are moral), does not mean that the correct theories would necessarily be bad. Many (or most?) Christian philosophers now accept that there are ethical truths independent of God’s nature or mental states, and that these are necessary and binding upon him (just like truths about mathematics). Surely in the space of theories about God, there is a subset in which God is bound by ethics (among them the best Enlightenment principles that you treasure), and does not punish innocent people in hell for being truthful about their convictions. What would be so evil about that? That could be motivating and liberating.
(2) Suppose you were a conscious being, that ‘woke up’ in a very different world than our own, with a certain regular and consistent mathematical structure based on constant theoretical principles governing its fundamental ontology and update rules. A priori, what *kind* of structure, deep principles, and update rules would convince you that the rules themselves were probably not brute facts, but perhaps derivative in nature, and had some kind of underlying cause? If you were a conscious being in, say, a physical manifestation of the Mandelbrot set? Or a conscious tile in a Penrose tiling or Escher painting? Or an element in a a universe whose entire physical structure was a Fibonacci sequence? Or (pick your favorite interesting mathematical object, principle, or favorite update rule, and then imagine ‘breathing fire’ into it, and sprinkling in consciousness)?
Are there any such ‘special’ rules or principles that could, even in principle, act as evidence to support a transcendent inference? I ask because I wonder (and this is a genuine question that is in your expertise, but not mine), how close does our world’s update rules get to the kind of rules that may make that inference rational? A priori, I would not expect ‘theoretical beauty’, and ‘interesting mathematical structure’, in a world that blind to value (if nothing else, aesthetic theoretical value), but I could be wrong.
Also, I acknowledge the problem of evil is a better and stronger argument than the direction I am leaning toward in the question above. Still, I am curious. This question is based on Philo’s remark in Hume: “If a voice from the sky were heard in every land, speaking to every person in their own language, and declaring the existence of a divine being, that might be evidence enough to convince me.” I am just asking for the mathematical physicist’s/theoretical computer scientists version of that quote, applied to the mathematical structure and basic physical principles of reality.
Thanks again for the post.
Comment #120 October 15th, 2024 at 10:16 pm
Scott #114:
Shouldn’t there be physical constraints to expanding at a large fraction of the speed of light? For one thing, traveling at that speed means every particle you run into is gonna be a non-trivial collision. Light is gonna be extremely blue shifted. Doesn’t sound like a pleasant environment even for non-carbon based life.
Comment #121 October 16th, 2024 at 4:58 am
(I made a previous comment which I think was swallowed by Internet goblins, in any case this comment is much better than the previous version.)
Regarding #7 (Platonism):
While I don’t have a confident position, I have a lot of sympathy towards the view that meaningful truths have to be in some sense testable, at least in principle. For example, the result of a finite computation is testable given a big enough computer. The fact that a Turing machine halts is “semitestable”: if it does halt then it is possible to know this, but if it doesn’t then we can never know for sure (but maybe we can become gradually more confident the more time we run the machine). Anything higher in the hierarchy (such as arbitrary sentences with two or more opposite quantifiers in Peano arithmetic) seems completely untestable.
Hence, I think it’s defensible to be Platonist w.r.t. e.g. primitive recursive arithmetic (PRA) but not Peano arithmetic. On this view, Goldbach’s conjecture is “fine”, but P=NP isn’t necessarily so. Of course there are propositions that imply either P=NP (e.g. this particular algorithm solves SAT in this particular polynomial time) or P=/=NP (e.g. this particular superpolynomial function is a lower bound on circuit size for SAT), which *can* be stated in PRA. And we can also consider propositions like “P=NP is provable (resp. refutable) in PA/ZFC/…”.
I’m curious what would Scott say to this position.
Comment #122 October 16th, 2024 at 5:38 am
Opt #120: Presumably the aliens would’ve long ago uploaded themselves, becoming error-corrected digital entities within the computronium sphere expanding at near light-speed, and won’t be bothered by such trivial inconveniences as whatever space rocks the sphere hits as its expands! 😉
Comment #123 October 16th, 2024 at 5:47 am
Vanessa Kosoy #121: My view is that, once you’ve decided to be a Platonist about the Pi1-sentences (those that assert that some Turing machine runs forever), you’re then almost forced to be a Platonist about the Pi2-sentences (like P≠NP), Pi3-sentences, and so on forever. Why? Because a Pi2-sentence is just a statement that a certain Turing machine with an oracle for Pi1-sentences runs forever. (For example, P≠NP says that if you enumerate over all algorithms together with polynomial time bounds, you’ll never hit one that correctly decides 3SAT.) And we’ve already admitted the Pi1-sentences as Platonic, and we’ve also already admitted the principle that every Turing machine Platonically either halts or runs forever!
In short, I have very much the same intuition as you—mathematical statements are Platonically determined so long as they’re ultimately grounded in “doable mathematical experiments”—but am willing to be liberal with the “ultimately” part.
Comment #124 October 16th, 2024 at 5:52 am
(12) The mind-body problem.
This mind-body framing is also called “dualistic view”, where supposedly there’s the observer on one side (the self, the mind), and the observed world on the other.
But this dualism is an illusion, and it can’t be otherwise, it’s an impossibility both logically and through direct observation of how our mind works: by definition everything that can observed can’t be the self, and then what’s left would be the self, which can’t be observed and has zero signature.
So all your thoughts, emotions, your sense of being in the middle of the head behind your eyes and between your ears, above your teeth and tongue, your sense of attention moving from one object to another, your sense of familiarity or unfamiliarity with things, your sense of agency, pain, pleasure, … all can be clearly seen as observable characteristics, with well defined signatures, so none of this can be “you”, which isn’t observable anywhere (a bit like a spherical mirror reflects the whole world, but can’t reflect itself), and what’s left when this wrong “duality” concept is lifted is the concept of “emptiness”, i.e. the self is nowhere to be found, there’s no “observer”, nothing at the center, and subjectivity is only a vast collection of temporary patterns of energy. rising and disappearing, which can’t be reduced further.
We’re just often confused about this because those appearances can sometime “curl” on themselves, creating feedback loops that are very strong, i.e. the “ego”.
Comment #125 October 16th, 2024 at 8:13 am
Scott #110
A common criticism of the endless war agenda is that it needs a constant supply of enemies to demonize. From that perspective, it makes no sense to invert the relationship so that America bad and enemies good; rather, the good vs evil framing is a stupid way of looking at the world to begin with.
Speaking of identifying enemies, remember when the “Axis of Evil” was Iraq, Iran, and North Korea? China and Russia are included in the latest axis du jour, but they weren’t included back then. Did they just become evil recently or what?
Comment #126 October 16th, 2024 at 8:22 am
Scott #123
I feel that you committed a sleight of hand when you went from “the Pi1-sentences as Platonic” and “every Turing machine Platonically either halts or runs forever” to “every Turing machines with a Pi1-oracle Platonically either halts or run forever”. Notice that the step from Delat1 to Pi1 is not costless: Delta1 sentences can be tested in finite time, whereas Pi1 sentences can only be tested asymptotically. Pi2 sentences cannot be tested even asymptotically: there is no way to computably assign credence to all such sentences that will converge to their putative truth values in the limit.
Certainly I don’t feel “forced” to be a Platonist about Pi2 sentences: it seems perfectly consistent to stick with PRA in which you cannot even state a Pi2 sentence.
But let me try another angle. Suppose that you meet an alien, and you try to explain to them the meaning of your mathematical notation. For e.g. primitive recursive functions, if you just show the alien enough examples of function values, they will eventually deduce the semantics of your notation: every other computable hypothesis consistent with the data will be much more complex than the truth. However, can you convey to them the meaning of truth in Peano Arithmetic? How can you ever know that when you say “phi is a true sentence” the alien doesn’t understand it to mean e.g. “phi holds in such-and-such model of ZFC”?
If the meaning of something is in general not possible to reliably convey to an intelligent alien, then maybe there is no well-defined meaning?
Comment #127 October 16th, 2024 at 8:49 am
Scott, any opinion on the Israeli attack on Lebanon? Necessary self-defence or wanton massacre?
Comment #128 October 16th, 2024 at 9:00 am
Nick Drozd #125:
As it turns out, China and Russia have become (or, been revealed to be) a lot more evil lately.
Consider following the news — much of it is a bummer, but it is entertaining, and it is all we have.
Comment #129 October 16th, 2024 at 9:16 am
https://www.csoonline.com/article/3562701/chinese-researchers-break-rsa-encryption-with-a-quantum-computer.html
They claim quantum computer factorization of a “22-bit RSA integer” (2,269,753 is in the abstract of the linked paper) using D-Wave Advantage.
Is this real? It doesn’t seem to be using Shor’s algorithm.
Comment #130 October 16th, 2024 at 9:19 am
“how the earth will support 9 or 10 billion people with first-world living standards”
If this first-world living standards = US, then we are doomed. A more frugal experience, like that found in many European countries, should suffice.
1) a family does not need 2-3 cars, when there are public transportation or bikes;
2) children don’t need a ton of action figures and gadgets;
3) homes don’t need to be massive and filled with unused rooms;
4) people should not consume tons of fast food, pre-packaged meals, and disposable items
5) why billionaires?
The constant push for bigger, newer, and more is creating a cycle of waste and stress to the planet, that is strongly correlated to your (4) item (Climate Change).
Comment #131 October 16th, 2024 at 9:49 am
Scott #123: Your argument assumes a specific reason why Vanessa or me decided to be “Platonist about the Pi1-sentences”. I guess our initial reason was simply that we were sufficiently sure about this type of “semitestable” sentences, but remained unsure about the non-semitestable Pi2-sentences. And I guess that our initial reason to be not convinced by your argument is simply that we don’t seem to lose much by remaining unsure about Pi2-sentences.
But you hope to gain something by convincing people to be Platonist about Pi2-sentences, namely that they would then agree that P≠NP is just Platonically true or false independent of any axiom system.
For me personally, my reasons to become absolutely sure about Pi1-sentences and even Delta2-sentences (while still remaining unsure about Pi2-sentences) were closely related to the model existence theorem and my belief in “conservation of difficulty”: There must be a reason why a theorem is provable or not, and theorems must have meaning beyond mere symbol manipulation. It turned out that the model existence theorem follows from accepting “computation in the limit”. And this is basically equivalent to be Platonist about Delta2-sentences.
But why is consistency of Peano arithmetic both unprovable and provable? It is provable, because it follows from the fact that epsilon_0 is well ordered (Platonically). And it is unprobable, because some “mathematical universes” don’t contain the subset which consists of exactly the Platonic natural numbers. Each Platonic natural number itself is included in such a “mathematical universe”, but if you (try to) form their union, you get a set which contains some additional “fake” natural numbers, for example the number of steps of some non-halting (Platonically) Turing machine.
Comment #132 October 16th, 2024 at 10:01 am
Why can’t the Fermi paradox be resolved by taking the probability of the evolution of intelligence -> 0 and the size of the universe -> infinity? I’ve always felt like that’s the simplest available answer in lieu of discovering any aliens (intelligent or otherwise) nearby. Grabby aliens doesn’t do much for the probability of us being born as evolved humans rather than as computronium residents. Our own population would unimaginably many orders of magnitude below theirs.
I offer another aliens story. It is easier to satisfy your wants and needs by changing them than by colonizing the galaxy. There is a Nash equilibrium of being required to join the sessile philosopher’s club: a defecting colonizer would be a danger to the tranquility of those who remained.
Isaac #130
Going by the relative prices of the things you listed, the energy and resource requirements of healthy food is higher than heavily processed cereal grains. The same goes for the relative prices of socializing enrichment and plastic toys. If everyone was to live a life of access to green space, proximity to work, play with friends, and organic vegetables, we would need a lot more energy and transportation. (That’s not unattainable, but it is a disconnect from the environmental narrative.)
Comment #133 October 16th, 2024 at 10:16 am
My current crude view on platonism is that primitive recursive things are the only “platonically true/false” things, (so that the e.g. excluded middle is not a “thing”), but assuming Excluded middle+ZFC+inaccessible cardinals is a useful fiction that allows you to “see farther ahead”, so they’re fine. However, by the same token, a lot of areas of mathematics like infinite combinatorics and what have you, lose their appeal to me/my own aesthetic preference/my excitement over them the farther away they are from “actual/computable” questions (i.e. questions of the form, “find an algorithm that solves this specific problem”). Presumably I could be convinced to use other axioms or even modes of reasoning if someone sufficiently demonstrates their usefulness to “platonically true” questions.
Comment #134 October 16th, 2024 at 10:18 am
For whatever record might care, if any, I find myself about 90-95% in agreement with those opinions, and the difference might be due to misinterpretation of nuances. I’ll just focus on the possible disagreements.
I think a lot of the ancient wisdoms in religion are ways for con-people to keep their marks baffled. One I see a lot is, if something good happens, religion gets automatic credit, e.g., we prayed for grandpa and so he was able to get into a good palliative-care home, but if something bad happens, e.g., grandpa has incurable intestinal cancer, that doesn’t get put on the scales. I think people working together to survive and thrive can mostly sort out human behavior without ancient wisdom, thanks to the fact that we evolved as pack creatures. Other pack-creatures do. (Not perfectly, of course.)
I haven’t been exposed to any “woke” oppression. What I have been exposed to, is people justifying their bad behavior as “anti-woke”. I don’t get out much, though.
To me, Amanda Marcotte, or whatever her name is, being a jerk is roughly the opposite of being woke, as the term is actually defined–or was when I first saw it and looked it up. It meant being aware of ongoing oppression, not being oppressive one’s self.
Thanks for the post, and keep up all the good work.
Comment #135 October 16th, 2024 at 10:36 am
Nick Drozd #125: Rather than discussing “war” as an abstract concept (presumably none of us is in favor), let’s look at the state of the world more concretely.
(1) Do you agree that we should be aiding Ukraine militarily, and just disagree about the extent? Or do you think we should let Putin help himself to Ukraine (and probably next the Baltic states)?
(2) In the likely event that China invades Taiwan, what should we do? Should we let China help themselves, or should we come to Taiwan’s defense?
(3) Was it a good idea, in 1938, to let Hitler help himself to Czechoslovakia? If not, was that a one-off freak event, or were there general lessons to be learned?
Comment #136 October 16th, 2024 at 10:41 am
Joseph Shipman #129: As far as anyone knows, factoring numbers using quantum annealing on a D-Wave machine offers no scaling advantage whatsoever over just factoring the numbers classically (indeed, the classical Number Field Sieve should have much better scaling than quantum annealing). It’s therefore not in any way a threat to RSA encryption, and presenting it that way is effectively a scientific fraud—but alas, a fraud that’s perenially popular, because people keep conflating this uninteresting thing with Shor’s algorithm, which one imagines was the intent.
Comment #137 October 16th, 2024 at 10:56 am
MK #127:
Scott, any opinion on the Israeli attack on Lebanon? Necessary self-defence or wanton massacre?
Well let’s see, Hezbollah has been firing thousands of missiles and drones into Israel for a year now. They started on October 8, in “solidarity” with Hamas’s genocidal invasion of Israel, unprovoked by anything Israel had done. They’ve killed people, including a dozen Druze children playing soccer. Over 70,000 Israelis, including some of my relatives-by-marriage, have been forced to flee their homes in the north, effectively shrinking Israel’s borders. Many more Israelis have had to run to missile shelters multiple times per day.
The UN has demonstrated a total, craven unwillingness to do anything to stop Hezbollah, in violation of its own resolution 1701 (indeed, its UNIFIL force is effectively complicit with Hezbollah). The government of Lebanon has also demonstrated total unwillingness to do anything to stop Hezbollah.
So what would you do in this situation? What would the US or any other country do? Just consent to have missiles rain down forever?
Of course Israel needs to cripple Hezbollah. It’s shocking that it took as long as it did, but I’m glad that there have now been some dramatic victories.
Of course I hope that innocent Lebanese will be harmed as little as possible in this war. But more than that, I hope the Lebanese people will seize this rare opportunity to free their own country from Hezbollah’s tyranny, make peace with Israel, and restore Lebanon to what it used to be.
Comment #138 October 16th, 2024 at 11:02 am
Vanessa Kosoy #126 and gentzen #131: At some point this just becomes a battle of intuitions, but let me try one more intuition on you for size—the one from Section 6 of my independence of P vs. NP survey from 2003. As I pointed out there, every Πk-sentence admits an “interactive proof system,” in which there’s a prover strategy that causes the verifier to run forever if and only if the sentence is true. And the existence or nonexistence of such a strategy seems to me like ultimately a “testable” question, and therefore Platonic.
Comment #139 October 16th, 2024 at 11:24 am
Scott #135
“and probably next the Baltic states”
Sorry, but I was expecting better from you. It’s as plausible as Putin starting throwing nukes left and right. Do you think NATO members will not invoke article 5?
Comment #140 October 16th, 2024 at 11:27 am
Scott #138
How would you test that?
Comment #141 October 16th, 2024 at 11:40 am
Scott #138: The existence of a winning strategy for the prover in the kind of interactive proof system that you’re thinking of is (naively) a Sigma^1_1 statement. Moreover, every Sigma^1_1 statement can be phrased in this way (i.e. as the existence of a winning strategy for the first player in an infinite game with computable rules where, if the game goes on forever, the first player wins). So it seems like you’re essentially saying that since Sigma^1_1 sentences clearly have truth values, so do arithmetic sentences.
I personally agree that Sigma^1_1 sentences have truth values, but once you’ve started quantifying over real numbers, where do you decide the draw the line? It is well known that there are natural statements with just slightly higher complexity which are not decided by ZFC (e.g. determinacy for games with Sigma^1_1 winning conditions).
Comment #142 October 16th, 2024 at 12:04 pm
Comments are probably biased towards critiques. I often refrain from lame “me too” remarks and criticism is more rewarding. If I’m right, then, wow, I win an argument against Scott (never happened). If I am wrong, then I learn something. You can chalk up as an agreement (if you care), if I don’t comment. In case you don’t want to count my no comments, my statistics indicate that I agree with about 95% of what you say.
You wondered some time ago, why the other Scott doesn’t get as much blowback as you. The reason is, that you engage much more in the discussion. ACX Scott sometimes collects the most interesting contributions in a separate post and adds his opinion, but that’s about it.
I have a question about the platonic truth of arithmetic statements. Is that another way of expressing a belief in the consistency of arithmetic? Say, you run a Turing machine searching for counter examples of Goldbachs conjecture. If arithmetic is inconsistent and the machine halts, then the found counter example might be wrong. The truth of the Goldbach conjecture seems muddled then. Does this make any sense?
Comment #143 October 16th, 2024 at 12:08 pm
What’s the update one’s beliefs on AGI/ASI timelines in light of this new evidence ?
“Nvidia CEO Jensen Huang says Elon Musk set up 100,000 Nvidia H200 GPUs in 19 days – a process normally takes 4 years”
Comment #144 October 16th, 2024 at 12:09 pm
Concerned #140: The “test” is just whether a prover can come along and win the game! Alas, it might be impossible to run the test in real life, because (1) a perfect prover doesn’t exist and (2) even if one did, it would take the prover infinite time to win. But crucially, unlike with AC, CH, or other statements about transfinite sets, there seems to be no doubt here about what the test means.
Comment #145 October 16th, 2024 at 12:16 pm
red75prime #139: If Trump wins a few weeks from now, then yes, I’d be shocked to see him invoke Article 5 under any circumstances. I think he’d pull the US out of NATO entirely if he could. Certainly people I know in the Baltics are pretty terrified.
Comment #146 October 16th, 2024 at 12:24 pm
Patrick #141: Yes, Σ11 sentences strike me as necessarily determinate, because of the “prover/verifier game” intuition, and the fact that the game halts in finite time if the prover is lying. Once you get to more general infinite games, I lose the intuition for determinacy at some point, and by the time you get to AC, CH, etc I’ve completely lost it. But all the way up the arithmetical hierarchy the intuition is clear.
Comment #147 October 16th, 2024 at 12:31 pm
Uspring #142:
I have a question about the platonic truth of arithmetic statements. Is that another way of expressing a belief in the consistency of arithmetic?
No, it isn’t. That’s a different, incomparable belief.
The key point is this: if some formal system like Peano Arithmetic turned out to be inconsistent, that would be Peano Arithmetic’s problem. It wouldn’t be a problem for the positive integers themselves, which “existed” before PA and will continue to exist after it. All the same statements about positive integers would still be true. A correct program to search for a counterexample to Goldbach’s conjecture would still halt if and only if such a counterexample actually existed. We’d just need to look for a different formal system with which to try to prove that such a program ran forever.
Comment #148 October 16th, 2024 at 12:55 pm
Scott #138
Thanks for this Scott!
For Pi2, your argument can be reformulated as follows. Consider a sentence phi of the form “forall x exists y: P(x,y)”. Suppose I assign this sentence the credence f(n), where n is minimal s.t. I currently don’t know an example of y with P(n,y), and f: N->(0,1) is some monotonically increasing function s.t. f(n) goes to 1 as n goes to infinity. Then, if phi is true, my credence in phi will eventually converge to 1. On the other hand, if phi is false, my credence in phi is bounded away from 1.
This means that sentences in Pi2 are indeed testable in some sense. Note, however, that this sense is weaker than the testability of Pi1: the credence convergences to 1 in one case, but doesn’t converge to 0 in the other case (it’s merely bounded away from 1). Again, going one step up in the hierarchy wasn’t costless. For Pi3, we don’t have even this weak form of testability.
But, you’re also suggesting an “interactive protocol” that’s applicable to any sentence. The “wizard” (prover) implements all the existential quantifiers, and infinite brute force search implements the universal quantifiers.
Is this procedure valid? If the entire universe consists of you and the wizard, it seems to work. But a valid method of reasoning should be applicable universally. Now, imagine what happens if several such wizards come into the fray, all of them trying to prove sentence psi.
First there are just two wizards. Both of their answers check out for the first 1000 tests. Things are going well. But, after test 1001, wizard #1 turns out to be a fraud! Perhaps this harms your credence in psi a little. On the other hand, wizard #2 is still doing great. More wizards join the game, so now there are 4. When you reach 10^6 tests, wizard #2 turns out to be a fraud as well. But, wizards #3 and #4 are still solid. And also, wizards #5-8 come in.
My claim is the following: no matter which computable procedure you are using to assign a credence to psi, as a function of the wizard-evidence you saw so far, you cannot simultaneously ensure
(i) Completeness: If a true wizards shows up eventually, your credence in psi will converge to 1.
(ii) Soundness: If psi is false, then your credence in psi will not converge to 1, no matter which shenanigans the fake wizards pull.
Comment #149 October 16th, 2024 at 1:36 pm
Scott #138: “… battle of intuitions, but let me try one more intuition on you for size—the one from Section 6 …”. I read Section 6 completely now. Here is the part which fails to convince me:
The issue for me is that the wizard can lie to me by taking forever to describe the SAT instance. And if I interrupt him, and ask him to tell me the size of the SAT instance first, then he either lies again by taking forever to describe that size, or else uses an encoding of that size that I cannot check, for example as the number of steps of some Turing machine that he claims will halt.
Scott #146:
As I explained above, I am convinced that this claim is false, and not just a battle of intuitions.
Comment #150 October 16th, 2024 at 1:55 pm
Scott #137
“I hope the Lebanese people will seize this rare opportunity to free their own country from Hezbollah’s tyranny, make peace with Israel, and restore Lebanon to what it used to be.”
I hope the Israeli people also seize the opportunity to free their own country from the clutch of Bibi and his far-right extremists and restore Israel to the democracy it used to be.
Not holding my breath though since over a year of wide protests prior to the October 7th attacks did jack-shit to deter Bibi from his authoritarian trajectory, and there’s no October 7th investigation in sight, and a Trump victory will only consolidate this.
Comment #151 October 16th, 2024 at 2:18 pm
fred #150:
Not holding my breath though since over a year of wide protests prior to the October 7th attacks did jack-shit to deter Bibi from his authoritarian trajectory
Look, I want Bibi gone too, but you show a total misunderstanding of Israeli reaction to the protesters, who’ve become increasingly open and explicit about their desire to see Israel completely eradicated, and who celebrate violent “resistance” against Israeli civilians and Jews all over the world until that happens. To Israelis—even relatively liberal ones—this simply confirms the theory that the world is full of fanatical Jew-haters who will denounce Israel as long as it exists, so therefore Israel might as well crush its enemies while ignoring the antisemitic mobs who will cheer for Hamas and Hezbollah no matter what.
A message that could push Israel to the left might look like: unequivocal affirmation of Israel’s continued existence as a Jewish state, unequivocal condemnation of the October 7 mass-murders, coupled with denunciation of Bibi for his failure to protect Israel and failure to bring the hostages home, and ironclad security guarantees for Israel in exchange for such-and-such concessions.
Comment #152 October 16th, 2024 at 2:24 pm
Scott #151
I know you’re laser focused on the anti-Israel campus protests, but I wrote
“since over a year of wide protests prior to the October 7th attacks did jack-shit to deter Bibi from his authoritarian trajectory”
referring to the internal protests in Israel against Bibi’s judiciary reforms, supposedly a huge existential threat to democracy in Israel.
Comment #153 October 16th, 2024 at 2:30 pm
gentzen #149: Note that your objection, if upheld, would apply even to Π1-sentences. E.g., someone could claim that Goldbach’s Conjecture is false, but then take forever to specify the alleged counterexample as a string of bits (which is directly related to the “counterexamples” that exist in nonstandard models of PA).
So, this is irrelevant to the commenters above who are willing to be Platonists about Π1-sentences, but who draw the line at Π2-sentences. Those commenters presumably already accepted “specifying a positive integer” as a primitive action.
And to anyone who’s unwilling to be Platonist about Π1-sentences: come on! 🙂 If there’s a counterexample to Goldbach, that seems like a finitary fact as clear and unalterable as 7 being prime. And if there’s not a counterexample to Goldbach—well, that’s what it means for Goldbach to be true.
Comment #154 October 16th, 2024 at 2:31 pm
fred #152: Oops, sorry, missed the word “prior”!
Comment #155 October 16th, 2024 at 3:11 pm
Scott #153: The difference is that I don’t need to rely on anybody else for Π1-sentences. I can just check for myself.
If somebody tries to help me by telling me a counterexample, he can speed up the checking for me to some extent, but not without limits.
Let me remind you that I am one of those commenters. I am willing to be Platonists about Π1-sentences, because “computation in the limit” makes sense to me: It is a typical mathematical idealization that captures something which happens in the real world, i.e. the way human societies acquire knowledge by some sort of “trial and error procedure”.
I am unsure about Π2-sentences, but that doesn’t mean that I couldn’t be convinced to be Platonist about them too. After I wrote #131, I wondered whether one could use the (Platonic) well-order of epsilon_0 in an extension of the model existence theorem to actually ensure the existence of models with subsets for all arithmetic sentences.
Comment #156 October 16th, 2024 at 3:40 pm
Scott #145
“Certainly people I know in the Baltics are pretty terrified.”
I’m sure they are. My condolences to them. The history repeats itself. Berlin Crisis of 1961. Walls. The cold war. And I feel that potential for wider confrontation is roughly the same (that is high, but not extremely high).
To me Putin doesn’t seem to be completely bonkers. He plays a geopolitical game, like the one in Brzezinski’s “The Grand Chessboard: American Primacy and Its Geostrategic Imperatives.” But unlike the book he plays clumsy and rough.
America makes a move and tries to expand her influence by inviting countries into NATO (or so he thinks)? OK. Let’s support their separatists, incite violence and, if it is not working, invade under a pretext of helping/peacekeeping to scare the bejesus out of their politicians.
It had worked in Georgia.
It hadn’t worked in Ukraine. 2022 peace talks that began 4 days after invasion had gone nowhere. And then Bucha massacre and Ukrainian military successes has ended all hopes of “a short, victorious war” (as it was most likely envisaged).
That’s my reading of the situation. I haven’t heard Putin going all “let’s restore USSR”, his ramblings about Ukraine has a clear political goal of “legitimizing” specifically that invasion, he wasn’t extending them onto Lithuania, Latvia or Estonia. Clumsy and immoral meddler in the Great Game? Yes. Would-be-emperor with delusions of grandeur? Hardly.
Comment #157 October 16th, 2024 at 3:42 pm
While we are expected to unequivocally state a bunch of things, let’s not forget what has been happening before October 7 .
Comment #158 October 16th, 2024 at 4:03 pm
I agree with it all, Scott, but Israel’s heavy handedness (for want of a better word) in Gaza and Lebanon I cannot agree with.
Comment #159 October 16th, 2024 at 4:47 pm
I know you closed the comments of the previous thread a little before I could solidify my opinion on the specific proposal, but hopefully it is still ok to share it here. I was somehow not comfortable with a unilateral request for help, I think a gesture of friendship requires reciprocation. That said, I’d be more than happy to see a bill that allows Israelis free citizenship into my country in case of catastrophic collapse, in exchange for free citizenship for my countrymen in case of a catastrophic collapse of my own country (in my case a Venezuela style collapse is the more likely scenario). No doubt Israelis will be unlikely to agree to such a thing, as there certainly is the risk of non-jews like me going to Israel and voting for the holocaust 2.0, but then again this same risk also makes even an unilateral offer of help pointless in the first place. Given this unfortunate state of affairs, I’d prefer to support Israel as long as they’re at a healthy arm’s length from me (and by extension, as long as it doesn’t cost me much). I don’t want to be caught up with your people’s existential struggle. That said, for whatever it is worth, and as a counterweight to the mean comments you seem to despair at finding online, I do share your dream of a state of Israel and a state of Palestine, both of them democratic, secular, prosperous, and living side by side in peace, with a border that is about as important as the border between Norway and Sweden.
Comment #160 October 16th, 2024 at 4:54 pm
Scott #153
Some people are willing to be Platonist about the falsehood of Π1-sentences with counterexamples, but not the truth of some Π1-sentences with no counterexamples. If you made me decide right now (my true feelings towards metaphysics is to postpone all questions for an infinite amount of consideration) I would given any N say that n+1>n is Platonically true for natural numbers less than N, but only true in the ordinary sense for all n. I think it’s okay to believe in infinitary statements, but wish to reserve a prestigious tier of realness for finitary ones, as a stepping stone towards the best real estate, for necessarily finitary statements about things that may occur.
Comment #161 October 16th, 2024 at 5:14 pm
Concerned #160: Then that’s a crux, because I’m very, very big on the Law of the Excluded Middle. If for every n, it’s not true that n is a counterexample, then for me it’s true full stop that no n is a counterexample.
Comment #162 October 16th, 2024 at 5:28 pm
anton #159: I didn’t know that there was any great number of neither-Jews-nor-Palestinians who’d want to live in Israel. (Note that, as we saw on October 7, Hamas will happily murder non-Jewish and even Muslim Israelis right alongside Jews.)
I mostly had in mind large countries like the US or UK, which could easily absorb Israel’s population although not conversely. If you think your country should negotiate a bilateral freedom-of-movement treaty with Israel … well, that’s between your country and the Israelis, but if both parties favor it then so do I! 😀
Comment #163 October 16th, 2024 at 5:50 pm
Scott #161
I wouldn’t give a better metaphysical rating to “for all x, P(x)” than “there is no x such that not P(x)”. What I meant was, if you give me a specific N, I can compute P(x) for numbers up to N and return an A-grade truth certification, whereas if you want me to tell you what I would do for any N, like I did in the previous sentence, I have to assume that my axiom system is consistent, then answer with a B-grade truth certification. The former case is one where I trust my computation, the latter where I trust both my formal system and my computation.
Scott #162
I heard somewhere that a lot of people from Thailand want to move to Israel. While fact checking that, I discovered that a lot of people from Israel are moving to Thailand. People’s motivations can be diverse, but I am sure it helps that Israel offers rule of law, private property, and work to do.
Comment #164 October 16th, 2024 at 6:02 pm
Concerned #163:
I certainly agree that our knowledge of statements universally quantified over integers, can be less secure than our knowledge of computations involving specific integers, since the former will depend on the consistency of a formal system like PA with an induction schema. But I’d still say that the universally-quantified statement is either “grade-A true” or else “grade-A false,” even if I’ll never know which.
Yes, there’s a significant number of Thai guest workers in Israel; they were (alas) among the murdered on October 7. But I don’t know how many want to stay in Israel permanently versus return to Thailand; does anyone else? Conversely, there are many Israelis who tour Thailand after their army service.
Comment #165 October 16th, 2024 at 6:09 pm
Scott #164
Isn’t decoupling what we may know from what is true the error that leads to the expectation that hidden variables theories would be possible?
You can chalk this one up to the “every country is the same,” law of nature:
> Large numbers of asylum seekers and refugees arrived in Israel between the years 2007 –
2012. Israel took a number of steps to stem the tide and reduce the number of new arrivals,
including construction of a border fence with Egypt. These efforts have proven highly effective
and no new asylum seekers entered Israel via Egypt in 2017. Today this population numbers
approximately 38,000, most of whom are Eritrean and Sudanese nationals who illegally crossed
the Egyptian-Israeli border.
https://cdn.fedweb.org/fed-42/2212/Migrants%2520to%2520Israel%2520-%2520Full%2520Background%2520Briefing%2520February%25209%25202018.pdf
Comment #166 October 16th, 2024 at 6:35 pm
Concerned #165: Hidden-variable theories (like Bohmian mechanics) are possible; they just don’t make predictions that differ from the predictions of standard QM.
Local hidden-variable theories are ruled out, but by Bell’s Theorem, not some a-priori philosophical consideration.
Comment #167 October 16th, 2024 at 6:40 pm
If you’re placing percentage bets on complexity classes and computational worlds, I’m very curious what odds you’d put on NP \in BQP? Not high, but would you guess more than the 3% you give P=NP?
Comment #168 October 16th, 2024 at 8:01 pm
Eliot K #167: 4%? 5%?
Comment #169 October 16th, 2024 at 8:45 pm
Scott #166
Well, okay, I don’t mean “possible.” Thanks for keeping me honest. 🙂 I really mean the sense in which we all write them off as untrue – like the way you separated it from standard QM when the predictions are identical.
Bohmian mechanics is local, and the same as ordinary QM, everywhere except for measurement. If you take computer simulations of quantum systems, they are Bohmian in the sense that a definite state (the wavefunction) evolves over time according to local equations until it is interrupted by nonlocal projective measurements. That the result of the measurement is read out of a PRNG instead of the distant decimal places of the Bohm-particle’s initial conditions is not such a big difference, especially given that they both get their characteristic unpredictability from chaotic deterministic behavior. The property of preserving locality in measurement is ancillary because the physics that we can observe to be local must be local in any interpretation.
We have to ask why we prefer local nonrealism in interpretation over the nonlocal realism we adopt when doing calculations. I think the answer is that, as much as we want answers to questions like “is the spin_x of a spin_z=+1/2 electron” to have a grade-A true answer, it is too anti-positivistic to imagine that there is an enormous amount of unknowable information stored somewhere in reality’s PRNG just for the purpose of collapsing wavefunctions.
Comment #170 October 16th, 2024 at 8:50 pm
Fair enough! I’ve often thought if we see a paper that rigorously proves NP \in BQP, we’ll see a surge of work trying to prove P = NP (both through trying to dequantize whatever algorithm succeeds, and a kitchen sink array of other methods) in the years that follow it. My guess is a lot of people probably share your instincts here, as those relative probabilities would imply P = NP needing to be taken much more seriously as a possibility if NP \in BQP.
Comment #171 October 16th, 2024 at 10:59 pm
Concerned #169: I think I now understand what you’re driving at, and here’s my reply. Saying that the electron has a definite position before I measure it is, in physics, a totally superfluous assumption: I could just as well have said that the complete underlying reality before measurement was the wavefunction. It’s arguably only “classical prejudice” that makes some people (eg the Bohmiams) insist on a reality that also involves a specific (x,y,z) coordinate.
By contrast, saying for example that a given Turing machine either halts or doesn’t halt, even if none of our current formal systems prove which, seems to me like a minimum commitment for talking sensibly about math at all. I see nothing superfluous there. Unlike in the electron example, there’s no “wavefunction” to fall back on as the true underlying reality: what else could the underlying reality be, other than the machine actually halting or actually running forever? (I mean in the usual integers; I don’t care what happens in nonstandard models.)
Comment #172 October 17th, 2024 at 12:13 am
Scott #117: For the argument to work, you need a lot more than the fact that we exist and don’t see them. You have to postulate that the fraction of civilizations of all time that don’t see aliens when they reach our level of development cannot be small. At first glance, this may seem plausible, but in reality it is quite arbitrary. You could just as well choose narrower or broader reference classes, or assume other seemingly plausible things in addition. Ultimately, it is a variant of the Self-Sampling Assumption that you rejected earlier – or at least did not accept as a reliable scientific principle: https://scottaaronson.blog/?p=79
In any case, the inference is clearly invalid. Suppose we observe an alien bubble somewhere in the sky. Suppose this just happened and we have not yet been able to measure its expansion speed. What should we expect? Hanson would update to a lower speed. (Remember his words: “We … INFER a fast speed from the fact that we don’t now see them.” So if we see them, the inference is no longer possible.) But a low speed makes the appearance of aliens within our horizon at our time less likely rather than more likely. Updating from an observation to an assumption that makes the observation less likely rather than more likely is unscientific.
Comment #173 October 17th, 2024 at 12:56 am
Nr 8) We should remember that not all ancient religions had much to do with proper behavior. Gods did not neccessarily punish bad behavior. Plus there were supposedly a few secular societies, like Eskimoo Greenland.
There is an argument that Christianity specifically created a lot of the focus on human rights we have today, and that might need to be replaced in the West, but I think that a lot of day-to-day behavior can be perfectly adequately incentivized without religion.
Comment #174 October 17th, 2024 at 1:45 am
Scott,
In regards to QM interpretations I think MWI is not as “obviously correct” as Eliezer claims. Please take a look at this paper:
Locality in the Everett Interpretation of Heisenberg-Picture Quantum Mechanics
Mark A. Rubin
https://arxiv.org/pdf/quant-ph/0103079
In order for MWI to be local (which is mostly why it is so popular) one has to accept that each particle has a sort of memory (label) of its past interactions, so that each copy of particle A knows with which copy of particle B it is supposed to interact. Rubin writes:
“Entanglement via the introduction of nontrivial “label” factors is not limited to interactions between two or three particles; each particle of matter is labeled, for eternity, by all the particles with which it has ever interacted.”
The amount of information here is huge. After all, an electron does interact to some extent with all electrons in the universe. We arrive at the conclusion that each particle carries with it a copy of the entire universe. Rubin asks:
“What is the physical mechanism by means of which all of this information is stored?”
Then he proposes that this could be answered in quantum field theory and so on. Still, the issue is complicated and I don’t think it is well understood by most MWI supporters.
Comment #175 October 17th, 2024 at 3:50 am
Re (15): Glad to see the fact of Everett being fundamentally a *conservative* choice pointed out. As I’ve often said, it is the interpretation favoured by Occam’s Razor, resting one fewer postulate!
That said I was recently fascinated with Carlo Rovelli’s alternative interpretation of Everettian mechanics, which he calls the relational interpretation. Any thoughts on this?
(The fact that I had randomly *just* finished reading Zen and the Art of Motorcycle Maintenance for the first time, whose central claim is that the subject/object divide at the root of western philosophy is fundamentally flawed, and that Rovelli’s interpretation reaches *precisely the same conclusion*, may have contributed to my conversion. And then both books draw the connection to Zen philosophy (while steering clear of the pseudoscience), and suddenly we’re in point (8) and (12) territory too, if not even point (7)…)
Tl;dr: I read Rovelli’s “Helgoland”, and I thoroughly enjoyed it, being the first in a decade to make me question my Everettian convictions. Highly recommended!
Comment #176 October 17th, 2024 at 6:16 am
I mean, you actually explained yourself, right here, why people are so frustrated with you. It’s because you always take the most boring, popular, establishment position on every issue. You gravitate towards whatever position is most popular—in your social circle, or academia, or the mainstream media. Hence why you oppose Russia (“everybody does”), why you support Israel (“my wife’s family and my family do”), why you are against Trump (“literally EVERYBODY in my social circle agrees with me”), etc. etc. That’s your go-to argument these days: “my position is popular, everyone I know agrees with me, your position is fringe.” That’s your go-to insult: “fringe.” You’re “fringe.” You’re a “conspiracy theorist.” You’re “extreme.” But those aren’t actually real arguments, are they?
Tell me this: What is a single position on anything, that you’ve ever expressed on this blog, that was genuinely unpopular or controversial or original?
Comment #177 October 17th, 2024 at 7:55 am
Isle of the Manx #176: HAHAHAHAHAHAHAHA. So basically, this blog is the restaurant that no one ever goes to anymore because it’s too crowded. I’m condemned because I never say anything that would earn condemnation.
Except I’m not sure if that works? Were you here a decade ago for the great debate about nerds, feminism, and dating—when Salon, RawStory, and other major magazines did condemn me, when I woke up each morning to 10,000 new tweets by the Popular Kids of High School about how I’m totally gross, when—though engaging sympathetically with hundreds of people who came here in good faith—I stood by my original convictions and did not apologize for them, even when it looked for a few weeks like my career and public life might be over? Have you ever done similarly?
More recently, have you seen just how unpopular my stances in defense of Israel have been, among fellow academics and blog commenters? Though they’re apparently still more popular than my Platonism about elementary arithmetic…. 😀
And then, while I didn’t mention it in this post, there’s my view that the No-Cloning Theorem might be relevant to personal identity and free will (the “freebit picture”), which is so absurdly unpopular that, in more than a decade of talking about it, I’ve encountered (I think) two other people who said it seemed plausible to them.
At most you could say that each of my stances is popular among those with whom it’s popular (a different set of people for each stance), and that I preferentially associate with people who have similar values to me and who therefore tend to agree with me more than the average person. Shocker.
Comment #178 October 17th, 2024 at 8:13 am
So then why, whenever a Trump supporter or a Putin supporter or an antisemite or an Andrew Tate fan or an anti-vaxxer or a climate change denier comes to this blog, do you respond to them with some variation of
“Holy crap, do you realize how fringe you are and how unpopular your beliefs are? In my entire social circle I know zero people who agree with you. I can’t believe that fringe people are so overrepresented in my comment section. You are a conspiracy theorist and an extremist and no sensible person in academia who I could possibly care about agrees with you…”
etc etc.
Do you realize that this is an empty argument? Do you realize that telling someone that their beliefs are outside the Overton window is NOT a cogent argument against their position, ever? So can we agree that this style of argument that is ever more common on your blog is fallacious and empty?
Yes, I am well aware of your cancellation episode over the nerds and feminists thing. I’m imagining that this might be the pscyhological origin of your mainstream beliefs (on Russia, just to pick one example)—you oppose Putin on this blog because you don’t want to be shamed and ostracized again like you were over the nerds and feminists thing.
Comment #179 October 17th, 2024 at 8:45 am
Scott #171
A pair of lines crossed by a third line that is perpendicular to them might both intersect (model curvature > 0) or not intersect (model curvature <=0). There could be one calculation in the true quantum field theory where choice should be taken and another where its negation must be.
We could (?) make the consistency of ZFC part of the definition of Turing machines. Then the discovery of a halting path for the Yedidia-Aaronson machine would be defended with, "you must have been using a nonstandard model – real Turing machines work with real sets, which are something else." In that case the rejoinder might be "I'm doing real mathematics with this model, and every other definition is generalized over models."
If Euclid and ¬Euclid both lead to real mathematics, along with Choice and ¬Choice, maybe Halt(T) and ¬Halt(T) will be found one day that also lead to two equally interesting outcomes; not by finding an example that contradicts itself but by exploiting an under-specification in PA to find two equally interesting models. Inconsistency search is not necessarily what I have in mind: maybe something else is both independent of PA and equivalent to a halting problem.
Or maybe not. I don't know if there's something special about PA and Turing machines that makes model-dependencies necessarily trivial. I would love to know…
Comment #180 October 17th, 2024 at 8:47 am
Hans Heum #175
Rovelli, like Heisenberg, is apparently aligned with Buddhist philosophy. You probably know that already. Schrodinger also discovered non-dualistic eastern philosophy, via Schopenhauer.
Comment #181 October 17th, 2024 at 8:54 am
Isle of the Manx #178: The entire reason I’m not on Twitter—the entire reason I’m one of the last holdouts who still writes a WordPress blog like in 2006—is that Twitter reminds me too much of a high school lunchroom, with too many popularity-based arguments. “I can’t even.” “Look at my outgroup, having a normal one.” In a comment section like this one, by contrast, people are strongly encouraged to spell out their arguments and try to change each other’s minds. If someone thinks Vladimir Putin is actually a hero of liberalism and Enlightenment—or that the truth or falsehood of the Goldbach Conjecture depends on how you feel about it—let them come here and make their case. It won’t be perfect, but we try.
Having said that, I think I’m now going to leave your further comments from you in moderation, not because you’re a weird conspiracy theorist outside my Overton Window (though you might be), but just because this meta-conversation is boring me. Thanks for participating! 🙂
Comment #182 October 17th, 2024 at 9:22 am
To expand on #181, one of the best pieces of advice I ever received was, don’t even try to be original.
Just try to be correct, both factually and morally. Try to answer the questions that need answering, invent the things that need inventing, help the people who need helping. Try to build things that are as good, as useful, or as beautiful as you can manage. If you do well enough at all this, originality (and even some contrarianism) will come as free byproducts.
Comment #183 October 17th, 2024 at 9:37 am
Thanks for the reply Scott. I agree with your hopeful solutions to some of the climate problems. I’m also optimistic about carbon capturing too – I think we’ll be able to do lots with it in the future.
Comment #184 October 17th, 2024 at 9:48 am
Concerned #179:
We could (?) make the consistency of ZFC part of the definition of Turing machines …
If Euclid and ¬Euclid both lead to real mathematics, along with Choice and ¬Choice, maybe Halt(T) and ¬Halt(T) will be found one day that also lead to two equally interesting outcomes
Those are precisely the statements that I deny, spelled out with unusual clarity. The definition of a Turing machine, just like the definition of a positive integer, doesn’t require knowing anything about the consistency of ZFC (as indeed, most people who learn arithmetic or programming don’t know anything about ZFC).
And arithmetic fundamentally differs from geometry or set theory in that we know a-priori which model of the positive integers we’re “trying” to capture—namely, the one whose elements are {1, 2, 3, 4, …}.
Kant, of course, thought that the geometry relevant to our universe was knowable a-priori, but he was mistaken. So how do I know I’m not similarly mistaken? Well, I claim that if we didn’t already know what we meant by “positive integer” prior to doing logic, then we couldn’t have even started doing logic itself—which requires writing down strings of symbols in one-to-one correspondence with the integers, counting to see if the parentheses balance, etc. Our position would be self-undermining.
Comment #185 October 17th, 2024 at 10:13 am
Scott #184
I’ve been thinking about what you are saying, and I’m starting to understand both your position, and logic (itself) a lot better.
Incompleteness means that no individual axiomatization captures arithmetic, but you say you’ve got prior knowledge of the model you mean by “integers.” That means you’re able to tell me which new equivalence class it lies in whenever I split the models of a formal system by adding either an independent axiom, or its negation. This must continue through the infinite regress incompleteness guarantees. In the end, we’re arguing about Choice. 🙂
Comment #186 October 17th, 2024 at 10:35 am
Scott #135
You say you aren’t in favor of war in abstract, but you seem to support every particular war. To tie things back to CS, this strikes me as ω-inconsistent. The only thing you’ve proposed here is more weapons and more escalation, no matter what. You’ve even come out and said that the US should never have withdrawn from Afghanistan and that if you had it your way, the American occupation would continue indefinitely. That really is a nutty extremist belief, and it’s especially hard to fathom given the full benefit of hindsight in knowing what a staggering failure the whole endeavor was.
(It’s funny how “Professor admits to suffering from pyschosexual problems” is the headline that caused a big uproar, while “Professor voices support for indefinite military occupation” gets crickets. In a more just world, those reactions would be reversed.)
As far as WWII, there are obviously all sorts of alternative history scenarios. I guess Britain and France could have declared war earlier? I have no idea what effects that would have had. They could also have unwound their immoral colonial empires earlier. Would that have helped? Who knows. I don’t think that the one and only lesson to be learned is that every country is Nazi Germany. Maybe I would be more convinced if the treat-all-invasions-like-Czechoslovakia rule were applied with any consistency. But for example, France went on to “help itself” to Vietnam right on the heels of WWII. Why wasn’t that treated like Czechoslovakia? If it had been, America would have avoided involvement in Vietnam, a war that turned out to be a staggering failure.
Now, the purpose of this post is to highlight how reasonable your beliefs are. And every point except one is phrased as “I believe X; however, I also believe certain aspects of not-X”. Point 9 says: I support such and such American foreign policy, but I also support immigration. These two things are unrelated; it’s “I believe X; however, I also believe Y”. I invite you to consider a more nuanced statement of your foreign policy ideas, such that it would actually take the X/not-X form. (Or I guess you could embrace the neocon hawk position and say: there is no “but” to this one.)
Comment #187 October 17th, 2024 at 11:27 am
Hi Scott,
I have nothing profound to contribute on the mind-body problem or P/NP or the hard problem of consciousness or whatever. But I’m a long-time reader (10+ years) and I just wanted to say I think your opinions are mostly non-crazy, interesting, and well thought out, and I hope you keep publishing them.
Remember: most people aren’t Very Online sneer-club weirdos, they just shout a lot, and loudly.
Comment #188 October 17th, 2024 at 1:25 pm
Nick Drozd #186: I favor the kind of peace that prevailed in Western Europe, Japan, and America after WWII—a peace that came not from appeasing genocidal maniacs but from defeating them. More generally, I favor the historic decline of violence that Steven Pinker and others have documented, which has come with the spread of liberal ideals and the defeat of despotic ones all over the world.
I asked you very concrete questions: should Putin be appeased in his conquest of Ukraine, or resisted? If China invades Taiwan, should it be appeased, or resisted? You declined to answer those questions, instead just talking in general about how I’m a warmonger. Should I take that to mean that you do favor appeasement in both cases?
Comment #189 October 17th, 2024 at 1:27 pm
Wow! I agree with just about everything on your list.
I am withholding judgement on #7 because I don’t know what’s going on there, and I have a caveat for #11, where I am more optimistic that Earth can sustain first-world living standards for over 9 billion people.
Comment #190 October 17th, 2024 at 1:40 pm
Hans Heum #175
I read “Zen and the Art of Motorcycle Maintenance” quite a long time ago, and remember being deeply affected by the author’s depiction of his own mental breakdown (basically losing his mind over his academic research on whether ‘quality’ is some sort of absolute)… I could be wrong, but I don’t recall getting that much about actual Eastern philosophy and their study of mind practices from it… it’s also the case that Zen Buddhism isn’t the most approachable Buddhist practice because the Western mind tends to try and find meaning in its ‘puzzles’ when the practice is really all about breaking conceptual thinking by embracing nonsense sentences (I would recommend Tibetan Dzogshen instead). For me, it was basically a trip into someone else’s neurosis, like the recent video game “Hellblade – Senua’s Sacrifice”.
I remember enjoying much more Pirsig’s next book, “Lila: An Inquiry into Morals”, which I read twice. I think I’m gonna re-read it right now, hehe.
Comment #191 October 17th, 2024 at 2:41 pm
Scott #171
“By contrast, saying for example that a given Turing machine either halts or doesn’t halt, even if none of our current formal systems prove which, seems to me like a minimum commitment for talking sensibly about math at all.”
First off, I’m probably restating things which you already know about, I’ll expand a little on the comment #133. I can imagine a Turing machine halting or not halting being “true platonically”, however in rejecting the Excluded middle as a “true thing” I’m more talking about reasoning by cases in cases where we do not know a priori which is which. So proving theorem T by reasoning as “if Turing machine H halts, then (argument here), and so T; also if Turing machine H does not halt then (different argument here), and so T”, feels to me like slightly suspect reasoning. Platonically speaking, when we do not know yet what case H falls into, this is usually due to our own inadequacy, although theorems in mathematical logic show that there are some exceptions where this failure is more structural, but this reasoning still feels like asking for trouble. More troublesome from the point of my personal intuition however is when we start quantifying over halting/non-halting machines, saying “for all non-halting machines H there exists a halting machine H’ with some property P(H,H’)” (and so on) might introduce some subtly wrong/non-sensical concepts, and doing a case by case analysis within a quantifier starts looking ever more troublesome. This is somewhat analogous to proper classes in ZFC set theory, where considering this or that proper class is fine, as a shorthand for a first order formula, but quantifying over proper classes is asking for trouble. Then again, as long as these concepts are not contradictory (of which the evidence we have is empirical), and they allow an extension of intuition in a useful direction (useful meaning, for those areas of mathematics which are “actually real”), then I consider these concepts “useful fictions” which are worth investigating.
For instance, considering elliptic curves over the complex numbers and trascendental uniformization functions over them, is very useful to discover properties of elliptic curves, which remain true when we consider the more “legitimate” objects that are the elliptic curves over (say) the rational number, and which was ultimately one of the ingredients in the proof of Fermat’s last theorem. So analysis is useful in this sense, and so is integration which is a part of that, and so is the axiom of choice which appears many times when setting up measure theory.
For an example of an axiom I am fine with that most mathematicians aren’t I’d consider the existence of inaccessible cardinals. This has applications when setting up Grothendieck topologies in algebraic geometry. It is not logically needed for this application, as one can remove this assumption in this application by introducing some bookkeeping, but this is nevertheless completely unrelated to the mathematical ideas in the theory, and so it is something of a distraction from a didactical point of view, so in this case, I’m fine with inaccessible cardinals. And of course algebraic geometry is basically talking about solutions of polynomials, with some modern language decoration around it, so this is an entirely “legitimate” field of study.
In a similar vein, I could be convinced to accept compact or measurable cardinals or what have you, but I am not aware of a similar application to “legitimate” mathematics.
Comment #192 October 17th, 2024 at 6:57 pm
The Law of the Excluded Middle is nothing more than saying that indirect proof is good enough for you. I know I have failed in the past to explain anything of interest to you Scott that comes from not *assuming* LEM, but equally there is nothing requiring me to accept indirect proof as sufficient to label actual knowledge. There is a category difference between a proof that is finite and you can actually construct directly and one that relies upon an indirect step assuming knowledge that cannot be finitely and directly constructed.
Forget platonism… it is about what you accept as proof.
I simply don’t accept that proof by contradiction deserves to be regarded as equivalent in esteem to a direct proof by construction. You think otherwise.
Comment #193 October 17th, 2024 at 7:18 pm
Scott #188
> […] should Putin be appeased in his conquest of Ukraine, or resisted? If China invades Taiwan, should it be appeased, or resisted?
I’ll add a bit: should fundamentalist militant groups be supported or resisted? The answer is resounding “resisted!”. I totally agree: autocracy/”partocracy”/theocracy vs democracy, it’s not much of a choice. Enter Gaddafy, Chun Doo-hwan, Mujahideen.
Benevolent strategy can coexist with deontologically questionable tactical decisions. But you don’t want people to mull on that much, so you reframe goals for those tactical decisions as virtuous. Politics 101.
I might be obsessed with the Great Game, but the real questions that were discussed might have been “Is it acceptable to sacrifice Ukraine (by trickling down weapons) to weaken Russia that for some reason keeps producing autocratic governments?”, “Is it acceptable for communist China to lay its hands on the world’s largest semiconductor industry?”
Comment #194 October 17th, 2024 at 9:47 pm
With the recent victories by Israel, I sometimes wonder right-wing leaders do get results, no matter how others despise them or their methods. Staying in the middle does not get one anywhere, just a deadlocked situation. Remember if Bush had not invaded Iraq, they would perennially be threatening its neighbors, with that part of the region being always volatile
Comment #195 October 17th, 2024 at 11:00 pm
Adam Treat #192:
LEM proofs certainly make things easier. Is there a constructive proof that n^2 even –> n even?
On the other hand, many things proven using AC are interesting but not essential for any applications.
For example (as I recall) Landau, Titchmarsh, etc., numbered many theorems in calculus and analysis such that each theorem only relied on earlier theorems. The first time AC is ever needed is proving the existance of a non lebesgue measurable subset of R. OK, that is interesting, but so what?
Comment #196 October 18th, 2024 at 8:37 am
Prasanna #104
that’s the exact same argument authocrats have been making against democracies, e.g. China/Russia get shit done while Western democracies seem impotent and unable to agree and coordinate on anything…
Bibi and his fascist government are adopting the same playbook, letting nothing get in their way, especially not international rule of law. Sure, you get “things done” this way, but at what cost?
The truth is that democracy is the hardest form of government, but democracies eventually get things done, it just takes longer, by design: Putin didn’t expect the pushback and mobilization behind Ukraine and China thought the could divide and conquer the West, but now most European governments seem them exactly for what they are, with their “iron hand in velvet glove” bully tactics.
Comment #197 October 18th, 2024 at 9:50 am
Scott #177:
“And then, while I didn’t mention it in this post, there’s my view that the No-Cloning Theorem might be relevant to personal identity and free will (the “freebit picture”), which is so absurdly unpopular that, in more than a decade of talking about it, I’ve encountered (I think) two other people who said it seemed plausible to them.”
Let’s make it three!
Comment #198 October 18th, 2024 at 10:19 am
Raoul,
“LEM proofs certainly make things easier.”
Sure! … if you consider a proof by contradiction to be a proof. But that’s my point. LEM is saying that proof by contradiction and direct constructive proof are equal in terms of what a proof is. I don’t think this is the case and I think I have good reason to doubt it.
LEM allows ¬¬A→A which is saying that ¬¬A and A are logically equivalent. If you think in terms of proofs this would seem to imply that there is a bijection between proofs of A and proofs of ¬¬A, but this is not the case.
Take the seemingly obvious statement, “every infinite binary sequence contains a 1 or it does not” which is a lesser form of LEM. We know that this cannot be proven either classically (where it’s just a trivial implication of *assuming* LEM) nor constructively. It can only be *assumed* or taken on faith. This faith will never be paid off. The fact that we *know* this faith will never be paid off makes me doubt the efficacy of such a faith.
Comment #199 October 18th, 2024 at 10:32 am
Vanessa Kosoy #148: Thanks for this Vanessa!
I really like that there is indeed a sense in which Pi2 sentences are testable. After all, it is nice for me to know that problems like P != NP or the twin prime conjecture have a Platonic truth value. And that accepting this does not force me to also accept the same for Pi3 sentences.
I highly doubt that this is a reformulation of an argument by Scott. He would have “tried its intuition on me” otherwise, out of pure curiousity whether it would change my mind about Pi2 sentences.
Comment #200 October 18th, 2024 at 11:10 am
Raoul Ohio 195, Adam Treat 192:
“For example (as I recall) Landau, Titchmarsh, etc., numbered many theorems in calculus and analysis such that each theorem only relied on earlier theorems. The first time AC is ever needed is proving the existance of a non lebesgue measurable subset of R. OK, that is interesting, but so what?”
For the interested reader, Simpson’s “Subsystems of Second Order Arithmetic” offers rather comprehensive version of this exercise, for axiomatic systems of varying strength.
Comment #201 October 18th, 2024 at 12:57 pm
fred #190 I was about to say, sounds to me like you might enjoy Lila! Just read it this summer, really interesting book. Indeed, its main topic is the breakdown of subject-object duality, which is where Pirsig and Rovelli both seem to agree with Buddhist philosophy. Pirsig does also cover this in Zen, but if I recall, the deeper connection to Buddhist philosophy is mentioned only briefly, as that insight (“Quality is Zen” or similar) was the point where insanity hit. My own (admittedly circular-sounding) one-sentence summary of both authors’ conclusions, as far as I understand them, is: “Objective reality is a myth; instead, the only thing that can be said to be capital-R Real are relations among subjects.”
(Which is how you can have Everettian mechanics without many worlds—simply stop insisting that our world must have a singular objective existence independent of its subjects!)
RB #175 That’s really interesting, thank you! I’ll have a read.
Comment #202 October 18th, 2024 at 1:58 pm
Raoul Ohio #195
“On the other hand, many things proven using AC are interesting but not essential for any applications. ”
I was under the impression that at least some sort of countable choice was necessary for most applications of measure theory. But if you want to see something really dramatic, Terrence Tao has some notes on Hilbert’s fifth problem where he proves things about “K-approximate groups” and groups of polynomial growth (which are fairly concrete/finitary objects), using ultraproducts (needing existence of ultrafilters, at least) to obtain locally compact (local) groups where he can then apply structure theorems.
Comment #203 October 18th, 2024 at 2:54 pm
Vanessa Kosoy #148, #199: I guess what you meant by
was that the argument for Pi1 which Scott tried to apply to Pi2 by invoking his omniscient wizard could be formulated for Pi2 without wizards, thereby making it more acceptable for people like me.
Comment #204 October 18th, 2024 at 3:23 pm
Hans Heum #201
and, in the end, all descriptions of how the mind works can only be hints, by definition insights into how our subjective experience works can’t be translated into concepts (otherwise there would be no hard problem of consciousness), they can only be experienced through introspective practice.
It’s really like trying to explain the color red to a blind man, you can get lost in giving him countless facts about light, the anatomy of the eye, the visual cortex, etc… when no such fact can convey the actual direct immediate experience of red, that’s right there at the surface. And the Western academia is so centered on conceptual deconstruction that they totally dismiss all practices of mind introspection as mumbo jumbo voodoo… although I think newer generations of scientists are more open to this.
Comment #205 October 18th, 2024 at 7:55 pm
Vanessa Kosoy #148, gentzen #199
Any kind of prior over theorems that we could update during counterexample search must have t=BB(n) as a parameter because it sets the scale on the falloff in our hope that an n-state Turing machine halts at time t_n. BB(n) is uncomputable, but a few low values of n are known. It’s kind of interesting how well this aligns with the way we expect counterexample searches to succeed sufficiently often that we do them, but also don’t think much of it once they’ve shown that if a counterexample does exist it has to be large.
I would offer that keeping track of the changes in our belief in a conjecture as we look for counterexamples is useful on an island of smallness where we can have good priors on an undiscovered (kolmogorov?) basis, but that the framework of reference falls off as that f(n) goes to infinity.
Comment #206 October 18th, 2024 at 10:31 pm
Scott #123 + the discussion about Pi-sentences
> A Pi2-sentence is just a statement that a certain Turing machine with an oracle for Pi1-sentences runs forever.
I have an intuition that we are talking about the halting oracle hierarchy. I have followed it as far as Pi2 to get what follows. (Is it a well-known result? Am I wrong? I don’t know. Nobody who isn’t more equipped than I am to check this should believe my result! I just thought it would be better to write down than forget.)
Turing machines with access to a halting oracle half-answer questions in Pi2:
Let Q(x,y) be a computable function. We wish to know P(Q) = there exists an x such that for all y, Q. Let T1(x,Q) be a Turing machine that tries every y and halts if it finds one such that not Q(x,y). Let T2(Q) be a Turing machine that asks a halting oracle whether T1(x,Q) will halt, for every x; halting if it finds an x such that T1 does not halt. P(Q) = T2(Q) halts, QE½D.
Pi2 answers questions about Turing machines with access to a halting oracle:
Let T2 be a Turing machine with access to a halting oracle. Let f(i,T2) be an oracle candidate that purports to equal the time at which the machine specified in T2’s ith query to its oracle will halt, or -1 if it does not halt. Let F(T2,f) be a Turing machine that runs T2 with f standing in for the halting oracle (call it T2^f), along with all of the machines T2 makes queries about, accomplishing this through diagonalization. Let F halt if T2^f halts, or if a machine that T2^f makes a query about halts after the time predicted by f. The purpose of F is to run T2 given f while checking f for accuracy. Let P(T2) be the proposition that T2 runs forever.
P(T2 does not halt) = there exists an f such that for all times, F(T2,f) is still running, a proposition in Pi2.
Therefore Pi2 contains the second level of the uncomputability hierarchy. Next to the association between Turing machines and Pi1, we might conjecture this goes on for all Pi_n.
Comment #207 October 18th, 2024 at 10:58 pm
Concerned #206
Correction: F must also halt if step f(i,T2) in the simulation of machine i is reached without halting.
Comment #208 October 18th, 2024 at 11:48 pm
Raoul Ohio #195
> Is there a constructive proof that n^2 even –> n even?
Compute $n = 2q + r$, with $r < 2$. Then $n^2 = 4q^2 + 4qr + r^2$, so if $n^2$ is even $r^2 = n^2 – 4q^2 – 4qr$ is even, but $r < 2$, so $r = 0$ and $n = 2q$.
Comment #209 October 19th, 2024 at 1:47 am
Raoul Ohio #195: Yes, here’s a constructive proof that n² even implies n even.
“n even” is decidable: given n, we have either n even or n odd, and this can be proved constructively.
Given that, the conclusion follows: either n is even or n is odd, and if n² is even then n can’t be odd, so n must be even, QED.
Now, why is “n even” decidable?
Well, in general, anything you can determine with a finite computation is decidable!
The key is that for any natural number m, either m = 0 or m > 0. That’s true by induction.
Then to work out the “n is even” example in explicit detail: constructively there is a map f: N -> N that takes each number to its residue modulo 2, defined recursively by f(0) = 0 and f(n+1) = 1 – f(n). Now for all n, either f(n) = 0 or f(n) > 0, and n is even just if f(n) = 0, so either n is even or n is odd, QED.
Comment #210 October 19th, 2024 at 2:01 am
Gentzen #199,
Yeaaa, maybe “reformulation” was an overstatement. I was thinking about the “multiple wizards” problem from my previous comment and I realized that for Pi2 there’s an easy way to aggregate evidence from different wizards (that doesn’t easily generalize to Pi3). Namely, if a wizard showed you that for a specific x, there exists y s.t. P(x,y), then now you know this fact about x and it doesn’t matter from which wizard it came. So you just need to keep track of the set of x values like that.
Comment #211 October 19th, 2024 at 7:43 am
fred #204: This really hits the nail on the head. Yes, it’s metaphysics, but that doesn’t mean it’s not worth pondering.
Comment #212 October 19th, 2024 at 10:28 am
Scott #188
The Pinker reference is a strange non sequitur. Or you are claiming that American military actions since WWII are primarily responsible for the increase in general human wellbeing? That is farcical in light of the enormous suffering and destruction caused by the wars in Vietnam, Afghanistan, etc. Those wars were absolutely net negatives in terms of general human wellbeing. Maybe they were just the eggs that had to be cracked to make the omelet?
You are also throwing around “genocidal maniacs” in an awfully cavalier fashion. American foreign policy since WWII has had little to do with genocide. Again, the wars in Vietnam and Afghanistan, which were miserable failures, had nothing to do with genocide even in terms of their own propaganda campaigns. (The instability caused by the Vietnam war did facilitate the rise of the genocidal maniac Pol Pot — just one more legacy of that failure.)
Overall, the foreign policy approach you have been laying out just sounds to me like shrill and immoderate jingoism, sharply contrasting with the rest of the measured X-but-also-not-X points.
As far as these current conflicts, I have ambivalent feelings about them individually. What I don’t like is the aggregate — we have to keep sending weapons to Israel AND Taiwan AND Ukraine, and we have to keep doing all of this indefinitely to stand up to the evil despotic scourges of radical Islam AND communism AND, uh, nihilistic gangster capitalism. (Notice that on paper, Iran and China and Russia should be ideologically antipathetical to each other. It is quite a blunder that we have managed to unite them.)
This is just to say that I don’t have particular policy recommendations other than that full-steam-ahead with more-of-the-same is a bad idea.
Comment #213 October 19th, 2024 at 10:28 am
Raoul, Greg,
The field of reverse constructive mathematics is rich and growing. It is popularly overplayed how important LEM is in many areas of interest in mathematics and logic. I think one point that is often lost is that the constructive logician doesn’t *deny* LEM, but rather refuses to use it. It is simply an assumption grounded in faith that can never be proven. Not harboring this faith does not have catastrophic consequences as Hilbert seemed to think:
“Taking the principle of excluded middle from the mathematician would be the same, say, as proscribing the telescope to the astronomer or to the boxer the use of his fists. To prohibit existence statements and the principle of excluded middle is tantamount to relinquishing the science of mathematics altogether.” — David Hilbert
We now know Hilbert was very very wrong. The Curry-Howard-Lambek correspondence is built on not harboring faith in LEM. The importance of LEM is overwrought and the confusion stemming from misguided faith in it is underwrought.
Comment #214 October 19th, 2024 at 11:10 am
Greg #209
Just a note for anybody else who had trouble following, it was the construction of f that excluded the middle for Even and Odd. What a beautiful idea, ¬¬P->P for decidable P, with no need for the axiom.
Comment #215 October 19th, 2024 at 1:37 pm
For those who missed this – Donald Trump called for a rally at the MSG in NYC on October 27th.
https://nypost.com/2024/10/08/us-news/trump-books-madison-square-garden-rally-to-kick-off-final-stretch-of-2024-campaign/
A coincidence?
Comment #216 October 19th, 2024 at 1:41 pm
Though my metaphysical assumptions differ greatly from yours (I’m Catholic), I find your points to be largely defensible and well thought-out, even where I disagree. The tremendous exception is abortion. I see the child-mother relationship as sacred, even from conception, and I don’t think one needs to be a Christian to see some of the consequences of damaging it. How do you think a child would feel upon learning about an aborted brother or sister?
Comment #217 October 19th, 2024 at 2:02 pm
Ben S. 63: There are many, many people whose parents had a miscarriage, and I don’t think any of them regard it as if they had a brother or sister who they knew and loved and who then died. Anyway, if that (and religion) are the two biggest disagreements we have, then our views don’t sound terribly far!
Comment #218 October 19th, 2024 at 2:07 pm
Nick Drozd #212: To me, admitting you don’t have a better path is virtually the same as conceding. This is not like the interpretation of QM, where you can just shrug that you have no idea. When monstrous tyrants invade democratic countries, torture and murder dissidents, etc., you can either fight them or try to appease them: there’s no third option that leaves you morally pure. And as Garry Kasparov recently remarked, anyone who doesn’t like the cost of standing up to Putin (for example) should consider the far greater cost of not standing up to him.
Comment #219 October 19th, 2024 at 2:46 pm
Scott #217:
When my mother had a miscarriage, I felt as though I had a sister who I loved who had died. I remember learning about it more clearly than I remember learning about 9/11, and it happened a year earlier in my life. The former was much more painful for me than the latter.
Comment #220 October 19th, 2024 at 3:10 pm
Ben S. #219: I’m sorry to hear that. I’d never heard such a story before. Could it have had anything to do with your parents talking to you about the unborn baby as if it was a conscious, already-existing brother or sister?
Comment #221 October 19th, 2024 at 3:51 pm
Scott #220: I am pretty sure my parents never used the word “conscious”. They did speak of the baby as though she was, in fact, a baby, and deserved to be loved and cherished. This was their living example, not just words.
Further, on one hand, there is no ontological distance between an unborn baby and a brother or a sister – the baby is male or female, its sex being fixed at conception. On the other hand, even if the baby were not conscious – and I believe consciousness is a continuum – it could be said to be asleep. Sleep is active preparation for consciousness, and from conception, the baby is actively preparing to be conscious.
Comment #222 October 20th, 2024 at 6:12 pm
Scott #218:
If you have limited weapons stores and weapons production capacity, then standing up to everything in the world is not an option on the table any longer. You have to pick and choose battles.
Personally I think Taiwan and Asia are 100x more important than Ukraine for both the national interest and for preventing a world dominated by the Chinese communist party (Russia is too small economically to dominate).
But what is clear to me is absent a highly unlikely surge in defense spending and weapons manufacturing (which I would support but is not even on the horizon right now), that choosing Ukraine now means giving up on Taiwan tomorrow.
Comment #223 October 20th, 2024 at 7:55 pm
Opt #222: I have no idea if that’s true. The US spends almost $1 trillion per year on its military anyway; what’s it all for if not precisely these kinds of threats? (Fine, I know the answer: a lot is for shoveling to defense contractors headquartered in the states of appropriations committee chairs, to build things that will never be needed by anyone. In a sane system, that could all be redirected to Ukraine and Taiwan, who do need it, with plenty left over.)
Anyway, there’s also the opposite effect, wherein hitting one bully hard can deter the other bullies. Apparently China was emboldened to be more aggressive toward Taiwan after it saw our weak defense of Ukraine.
Comment #224 October 21st, 2024 at 4:02 am
The only nutty belief of those is indeed 3% chance for P=NP 🙂
The only clearly incorrect belief is worrying about overpopulation. It is incorrect for several reasons, including getting either the facts or the ethics wrong (or both), not paying enough attention to Robin Hanson, and ignoring the AI.
Comment #225 October 21st, 2024 at 6:39 am
Partial spectator #224: Is 3% nutty for being too high or too low? What’s the correct probability?
Comment #226 October 21st, 2024 at 9:46 pm
Scott
After reading this article about the ground situation, not just now but over the last couple of decades, your #6 in fact looks like an extremist view, by Israeli standards. There is no two-state solution that Israel is OK with. The internal debate is between the center and the right about the role of institutions in the country. Nobody can win an election there advocating for a two-state solution. The most likely path forward for Palestinians is a combination of expulsion and apartheid policies.
https://carnegieendowment.org/research/2024/10/israel-palestine-peace-settlement-challenges?lang=en
Comment #227 October 22nd, 2024 at 12:37 am
RB #226:
There is no two-state solution that Israel is OK with.
That’s a weirdly ahistorical statement. There were two-state solutions that the majority of Israelis were OK with—namely, the ones that multiple Israeli governments offered. The Palestinian side rejected those offers, and doubled down on the path of intifada, suicide bombing, and “liberating all of Palestine” instead. As a direct consequence of that—of that thing that happened and that we don’t get to pretend didn’t happen—now there’s no two-state solution that a majority of Israelis consider serious or credible, leaving only the left-wing dreamers like (err) me. My hope and belief is that, if there were ever a credible Palestinian offer of coexistence and peace, an Israeli majority for those things would reemerge as well (since after all, it emerged in the past even without the Palestinian prerequisite).
Comment #228 October 22nd, 2024 at 8:44 am
I feel like every time I hear you mention the many worlds interpretation, you are one step closer to accepting it, although still not quite there. I can see that there are confusing questions about personal identity and consciousness related to the many worlds interpretation, like “are the people that just split from my branch really me, a copy of me, or someone else that is similar to me?”, but these questions are not really related to the physics, (we can all agree on the physical questions but disagree on the identity questions). The question “but is anyone home in the other branches?” is not really about personal identity (or even consciousness unless you have some kind of dualist position. Or are the people in the other branches real, but only zombies?), it is simply a question of physics. The question about if these branches are real, makes complete sense to me in the same way that a question about if galaxies outside our lightcone exists. In both cases we have lost physical contact, but we have no reason to say that they are not real, and if we could make choices now that will affect people in future branches or in galaxies that will in the future go out of contact with us, we should count them as real, when weighing the costs and benefits. So I’m asking you to just come out and accept or reject as likely that the other branches are as real as the distant galaxies outside our lightcone. If you accept this I will consider you a full Evrettian, even if you have questions about personal identity and such. Welcome!
Comment #229 October 22nd, 2024 at 10:30 am
Scott #227
You are correct that there was a peace process in the 1990s and the failure of those negotiations, which can be litigated, have resulted in the death of the process for a couple of decades, with an intervening proposal by Olmert that even Tzipi Livni and Barak asked Abbas not to entertain. As the authors write elsewhere
So, not just after 10/7, but the debate within Israel hasn’t been about the two-state solution for a very long time, even if we pretend that this is a result of the latest bout of violence.
Comment #230 October 22nd, 2024 at 11:13 am
Håvard Ihle #228: I constantly look for better words to explain what I think. But I feel like if you’d asked me even 20 years ago, I would’ve said the same: MWI is the scientifically most conservative option if you take our own existence and identity out of the picture. But it’s not clear how much is left, even of science itself, once you do.
(Democritus’ Senses replying to the Intellect: “would you deny us, while it’s from us that you take your evidence? Your victory is your defeat.”)
Comment #231 October 22nd, 2024 at 11:18 am
RB #229: It’s true that being surrounded by people who want to kill you, who’ve made it clear at every turn that they reject every path that doesn’t involve killing you … tends to leave you with only bad options. Nevertheless, there’s still a large center-left in Israel, which I’d define as those who want to get back to a place where a two-state solution is again on the horizon, even if (mostly because of Palestinian choices) it hasn’t been for 15 years or more—and who are disgusted by the settlement project or anything else that puts that goal further out of reach.
Comment #232 October 22nd, 2024 at 11:35 am
Scott #231,
Even despite all that Gazan or West Bank residents have gone through, Hamas military in Gaza is about 30,000 out of a population of 2 million. Worth keeping in mind that the vast majority are not adopting a life of violence bent upon killing Israelis. Your viewpoint that the failure of the peace process is largely the Palestinian fault is a very conventional Israeli view. It doesn’t mean that this is the truth, as there is plenty of evidence to the contrary.
Comment #233 October 22nd, 2024 at 12:39 pm
Since it’s only the Camp David negotiations that merit discussion as an attempt to broker peace, there has been much documentation about how the July 2000 negotiations were made in bad faith, notwithstanding the press campaign from Barak or Clinton.
The Taba negotiations included counter-offers by Palestinians and it was the Israelis who broke off negotiations .
https://fair.org/home/the-myth-of-the-generous-offer/
As Shlomo Ben-Ami, the Israeli negotiator, said
Comment #234 October 22nd, 2024 at 2:58 pm
I realized post 2016 that the standard issue scientifically grounded enlightenment liberal belief set which overlaps strongly with your own is indeed increasingly an outlier even as the world gets more and more complicated due to technological advancement.
Comment #235 October 22nd, 2024 at 7:15 pm
Dear Scott,
You said you were terrified of right-wing authoritarian populists and their threat to the Enlightenment, but you were also concerned about woke stuff. I have been voting for Democrats for a while, but in recent years I see so much wokism that it terrifies me more than right-wing. IMHO the strongest threat to Enlightenment is censorship of the mind, and the woke left is strongly advocating for just that, far more so than the right.
I don’t think that today’s left is the lesser evil anymore. Perhaps in Texas one would support Democrats to mediate the dominant right, but in California, in New York, in the states where wokism is smothering free thoughts and demands compliance with the most outrageously illogical and counterfactual views, in such states it’s logical to support Republicans to mediate the dominant left.
In particular, antisemitism, vicious slander of Israel, “from the river to the sea” — all that is coming from the left, not the right. Unless Democrats clearly denounce wokism I don’t see how one can support them.
Comment #236 October 22nd, 2024 at 10:02 pm
Michael P #235: As it happens, right before I saw your comment I was reading this NYT article about John Kelly, who was Trump’s chief of staff and knew him as President better than just about anyone. Kelly describes Trump as a fascist and confirms he has zero understanding of any constitutional limits on his power and wishes to rule as dictator, also that he has no empathy and did indeed constantly mock soldiers who lost their lives or limbs defending the US (“what’s in it for them?”).
I feel like offering this as my full and complete answer to you. How much woke mishegoss would it take, how many transgender surgeries on illegal immigrants or whatever, to be 1% as terrifying as this?
Comment #237 October 23rd, 2024 at 12:09 am
Scott #236: That Trump expressed admiration for fascists (and, more accurately, some features of fascism) is beyond doubt. But this expressed admiration (even in combination with “far-right” and “authoritarian” characterizations) does not necessarily make Trump a fascist — according to the definition used by Mr. Kelly in the NYT article.
Trump is a deeply flawed (aka appalling) human being, lacking any semblance of inhibitions, who happens to be an exceedingly effective demagogue/politician; he clearly exhibits authoritarian tendencies, and the concept of the “rule of law” (let alone appreciation of the US Constitution) appears to be far beyond his grasp.
But calling Trump a “fascist” strikes me personally as at least borderline inaccurate, and, on balance, counterproductive.
Comment #238 October 23rd, 2024 at 1:08 am
It is beyond doubt that Trump is on record expressing his admiration for Kim Jong Un (and Arnold Palmer). This does not necessarily imply that Trump is a communist (or a great golfer).
Comment #239 October 23rd, 2024 at 6:53 am
AG #237: The point is not merely that Trump has repeatedly expressed admiration for dictators (even including Hitler), but rather that he obviously wants to be one, judging from his own statements and those of countless people who worked for him.
Comment #240 October 23rd, 2024 at 8:17 am
Doesn’t MWI imply that the worst things imaginable happen to everyone including our friends, family, and loved ones, over and over countless times in other branches? Am I missing something?
Comment #241 October 23rd, 2024 at 11:34 am
Scott #239: I am inclined to agree with Paxton — “one of the foremost American experts on fascism” — in being sceptical about the usefulness of the “fascist” label:
https://www.nytimes.com/2024/10/23/magazine/robert-paxton-facism.html
At his home in the Hudson Valley, I read back to him one of his earlier definitions of fascism, which he described as a “mass, anti-liberal, anti-communist movement, radical in its willingness to employ force . . . distinct not only from enemies on the left but also from rivals on the right.” I asked him if he thought it described Trumpism. “It does,” he said. Nonetheless, he remains committed to his yes-no paradigm of accuracy and usefulness. “I’m not pushing the term because I don’t think it does the job very well now,” Paxton told me. “I think there are ways of being more explicit about the specific danger Trump represents.”
Comment #242 October 23rd, 2024 at 12:51 pm
Dear Scott,
Replying to Comment #236, I am not a Trump supporter. Even though in his previous term he didn’t do half of the things Democrats allege he would if he gets elected, of course he’s a horrible candidate. However, there is one thing that’s more terrifying than a deranged dictator objectively limited by the systems he doesn’t understand: an oligarchical dictatorship not limited at all by the system designed to uphold it.
I was born and raised in late USSR that officially was ruled not a President, but a collective Presidium, and was unofficially ruled by party officials, headed by a replaceable General Secretary. And it was a horrendously oppressive system, where even having unorthodox thought was criminal. And, having seen elsewhere how it operates, how political correctness turns into oppressive dictatorship by the few, I observe in horror how the process has begun here, in the United States. And rumor has it in UK too. One thing worse than a dictator with a limited lifespan is a collective dictator with an unlimited lifespan.
The horror is not in the transgender surgeries; it’s in the oppression of free speech and even free thoughts, and also in identity politics and equity policies. But the key thing, the irreversible terror, the fascist dictatorship in the making, is the oppression of free expression that has become acceptable in the formerly free World.
In recent news a man was arrested and criminally charged in UK for standing quietly on public property outside of an abortion clinic and silently praying. Not harassing or talking to anybody, just quietly praying. Again, I am not pro-Trump, and I find Texas abortion ban extreme. What terrifies me is not this or that policy, it’s the disappearing ability to think and express oneself.
Comment #243 October 23rd, 2024 at 6:45 pm
#241 PS. Today’s NYT article I referenced (and quoted from) continues as follows — and the more I think about it the more I am struck by the ominent pertinence of Paxton’s “suggested” characterisation of “Trump’s phenomenon” in its concluding paragraph:
When we met, Kamala Harris had just assumed the Democratic nomination. “I think it’s going to be very dicey,” he said. “If Trump wins, it’s going to be awful. If he loses, it’s going to be awful too.” He scoured his brain for an apt historical analogy but struggled to find one. Hitler was not elected, he noted, but legally appointed by the conservative president, Paul von Hindenburg. “One theory,” he said, “is that if Hindenburg hadn’t been talked into choosing Hitler, the bubble had already burst, and you would have come up with an ordinary conservative and not a fascist as the new chancellor of Germany. And I think that that’s a plausible counterfactual, Hitler was on the downward slope.” In Italy, Mussolini was also legitimately appointed. “The king chose him,” Paxton said, “Mussolini didn’t really have to march on Rome.”
Trump’s power, Paxton suggested, appears to be different. “The Trump phenomenon looks like it has a much more solid social base,” Paxton said. “Which neither Hitler nor Mussolini would have had.”
Comment #244 October 24th, 2024 at 10:49 am
AG #243,
The analogies may be imprecise, but you are pointing out another reason why the Democratic party is closer to fascism than the Republican one: the Democratic process of nomination is not democratic at all. We’ve seen that already with Hillary who got fewer popular votes than Sanders, but because of the appointed super-delegates she was nominated. I am glad that Sanders didn’t get the chance to ruin US economy though; I am talking about the lack of democracy within the Democratic party.
And, with the freedom of expression severely limited by wokeness and censorship, I fear that the administration of the Democratic party can become what the elite of the Communist party used to be in the USSR, an opaque undemocratic institution that has a de-facto control of the country while answering to nobody. Basically a collective dictator.
Comment #245 October 24th, 2024 at 8:50 pm
@Rider #240:
That’s basically right. Of course it would equally be true that the best things imaginable are happening to them.
Comment #246 October 25th, 2024 at 5:40 am
@Michael P #242 said:
In recent news a man was arrested and criminally charged in UK for standing quietly on public property outside of an abortion clinic and silently praying.
—-
True. Unlike the US, the UK has decided that letting people get to their medical appointments without protestors having access to them is valuable. Given the vulnerability of this population, I’m not opposed to this. The cops did talk to him for 100 minutes to get him to go away: it’s not like they rocked up and chucked him in the paddywagon. This was a deliberate attempt to get arrested to provoke headlines like above by appearing innocuous, and it worked.
There are much worse examples in UK antiprotest law that were brought in by the Tories than this one.
Comment #247 October 25th, 2024 at 5:43 am
@Michael P #244:
The assertion that Clinton got fewer popular votes than Sanders doesn’t appear to be true, nor that the superdelegates “overturned” the democratic process (she won more “pledged” delegates). RealClearPolitics has Clinton winning by about 3.5 million votes. Insofar as there’s complexity to the question of raw votes, remember that caucus and primary states both exist and distort the (raw) totals.
So: With what evidence do you assert the facts in your comment?
Comment #248 October 25th, 2024 at 7:05 am
Has anyone tried to prove that a consistent extension of the axioms of arithmetic under which the Goldbach conjecture is resolvable must exist?
More generally, can there exist decision problems in NP such that no consistent extension of the axioms of arithmetic under which it’s possible to tell whether or not integers with that property exist exists?
Comment #249 October 25th, 2024 at 7:23 am
Two quick questions:
What is your response to the inherent problem of point 11). Don’t you have to say that at some point enough is enough? I just want a clarification of what you mean by “generally”.
Regarding 6) I am sure you as a liberal do have some reservations about any ethnostate. Unfortunately, antisemitism exists. Would you reject any ethnostate, including Israel, if antisemitism or any other similar form of prejudice and persecution did not exist?
Comment #250 October 25th, 2024 at 8:05 am
Peter #249:
– Almost all first-world countries now have below-replacement fertility. In a stable or declining population, I have little trouble seeing the birth of a newborn as the uncomplicated joy it’s been seen as for virtually all of human history. I don’t know where the line is; that’s a hard question.
– It’s weird how no one ever complains about China, India, Japan, or Finland being “ethnostates,” even though each one is dominated by a particular ethnic group. For that matter, while some of Israel’s laws give a special role to religion, none of them to my knowledge are about ethnicity per se: for example, converts to Judaism can equally well invoke the Law of Return. (And you can indeed find many Black Jews and Jews of every other racial category among the citizens of Israel, as well as Arabs, Bedouin, Druze, Bahai, and other non-Jewish populations. Israel does much better on minority rights than almost any of the surrounding countries, though just like in the US there’s still room for improvement.) And yes, in a hypothetical future world with no antisemitism, I would completely agree with you that things like the Law of Return would no longer be needed.
Comment #251 October 25th, 2024 at 10:12 am
Jacob #248: I would say that Gerhard Gentzen’s consistency proof of Peano arithmetic does that. Kurt Gödel’s Dialectica interpretation is another consistency proof.
The difference for me to Scott’s attempt at such a proof is that I see (and understand) how Scott’s proof fails, but I don’t see how Gentzen’s or Gödel’s proof fails. Additionally, Gentzen’s proof that epsilon_0 is well ordered feels extremely convincing to me. But unlike the model existence theorem, I don’t see yet why he can prove this, or what were his “ontological commitments” that allowed him to prove it.
However, for Mac Lane set theory (i.e. bounded Zermelo, or simple type theory) no such explicit consistency proofs exist. It would certainly be attractive to “be able to” accept such “type of arguments” for consistency. Timothy Chow had a hard time trying to understand why people like Joel David Hamkins don’t accept them. My attempt to explain my own reasons didn’t help him either. Later I tried a different approach, making the point that ignoring the encoding of the length of a string smuggles in finiteness by the backdoor. I think that at least convinced him that I personally really have trouble to accept such arguments.
Comment #252 October 25th, 2024 at 11:22 am
gentzen #251: No, I never claimed to prove the consistency of PA — that’s just a total misunderstanding, and completely orthogonal to what interests me here. My interest is in a philosophical argument (not a proof) for the definiteness of arithmetical statements — namely that once you’re talking about things like models, axioms, and consistency, you’ve already implicitly committed yourself to arithmetic at the very least (or how else were you manipulating logical formulas?). I certainly don’t see that you’ve refuted this argument.
Comment #253 October 25th, 2024 at 12:10 pm
Devin #246,
My comment was not about the access to medical appointments; it’s about freedom of expression that has been curbed so far that even the thoughts that haven’t even been expressed can land you in jail.
True, this is not the worst example. In North Korea you can get executed by a flamethrower for not applauding eagerly enough. Even though many companies in US rush to virtue signal, fearing that if they don’t promote woke nonsense eagerly enough the customers would go elsewhere, we are far away from North Korea.
But doesn’t mean that we once again should accept something as terrible as censorship of speech and even thought just because there are much worse examples of that?
Is this a new normal: always eagerly vote for the lesser evil? Do we have to choose between a deranged person who wants to be a dictator and derange party that acts as a collective dictator?
Comment #254 October 25th, 2024 at 12:29 pm
Scott #252: But if you could me convince of the definiteness of arithmetical statements, wouldn’t you have a hard time to understand why you didn’t also convince me of the consistency of PA, at the same time? Like Timothy Chow?
But you are right in that the consistency of PA is not enough for what you want to prove, and also not enough for what Jacob asked. I realized this quickly after I posted my comment.
Exactly, this is the question of the “ontological commitments”. And this question is answered in my case by “computation in the limit”.
The point is that your argument does not convince me.
Before Vanessa’s comment #148 appeared, I had tried your argument on the twin prime conjecture, but it didn’t convince me. (The concrete twin prime instance that the wizard responds with doesn’t add anything substantial in this case beyond the mere information that the wizard claims that there is one.) Then I tried myself to convince me that the twin prime conjecture is either true of false. I attempted something “in a similar direction” as Vanessa, but failed to get it working. That is why Vanessa’s comment was so convincing to me later when I studied it, because she got it working.
Comment #255 October 25th, 2024 at 1:21 pm
@Scott, 250
Thanks for the answer. I agree that the singling out of Israel should make you suspicious. But I would like to point out that your examples of ethnostates have very little in common apart from having a clear demographic majority. Ethnic/racial pride in China and India is very different to that in Finland, a country which until very recently had a very liberal immigration policy.
I should have been more clear what I mean by “ethnostate”: Not a state whose citizenry is just of the same race/ancestry but a citizenry whose customs, language, religion, moral values but also to some degree ancestry are shared by a majority. As far as I know “ethnicity” encompasses all these things and is more than just race/ancestry.
I am still surprised that Israel extends its Law of Return to converts. However, that it does not apply to Jewish converts to another religion is also something that probably does not sit well with Western liberals.
One last question: Do you think that any society with decidedly Western liberal values has the right to curb its intake of immigrants or even asylum seekers if the newly arrived undermine the “homogeneity of shared (liberal) values”? I have in mind things like rejection of democracy, new interreligious/interracial/interethnic conflicts, certain attitudes towards women and their rights, etc.
I am sorry if my posts comes across as some interrogation or tribunal. That is not my intention. Feel free to delete them. And if you want to know where I stand on things, I am willing to answer as best as I can.
Comment #256 October 25th, 2024 at 1:53 pm
Peter #255: That the Law of Return extends to converts isn’t surprising at all if you know anything about Judaism. Jews have never regarded themselves as a “race” — we have the Nazis to thank for that innovation. The idea in Judaism was always to not proselytize, in fact make potential converts do serious work to learn all the traditions, but once someone is in, they’re in for good, as though they’d always been Jewish, and one isn’t even supposed to bring up the fact that they converted. Certainly their race never enters into it at all.
Yes, I absolutely think that liberal societies have a right to set their own immigration policies. I would generally advocate that they choose policies that welcome immigrants from all over the world who share liberal values and are ready to contribute to the economy. Some countries, of course, have or take on an additional mandate to provide safe havens for populations who’ve been persecuted elsewhere.
Comment #257 October 25th, 2024 at 2:57 pm
@Scott 256
In all fairness, the halakhic definition of “who is a Jew”, clearly one based on proven ancestry precedes the law of return which itself underwent a change from a halakhic definition to a more liberal one.
This all might be needlessly based on race or ancestry for you but here in Germany we have the phenomenon of various public figures who proclaim themselves to be Jewish, usually based on the alleged existence of a Jewish grandfather (none of them converted or practice any form of Judaism). In some cases this has turned out to be true, in others it did not. The point is that these public figures have positioned themselves as very strong critics of Israel under the guise that they as Jews are “allowed” to do so. Some German Jews, who all count as Jewish under very exclusive definitions, were annoyed by this abuse of claimed ancestry as moral license and openly attacked even those with proven Jewish grandfathers as “Kostümjuden” (roughly “people who wear their Jewish identity as a suit”). A very prominent German Jewish historian, Michael Wolffsohn, denied the Jewish identity of those with Jewish grandfathers (but affirms the Jewish identity of converts).
https://www.nzz.ch/feuilleton/wird-hier-judenpolizei-gespielt-nein-es-ist-ganz-einfach-du-sollst-nicht-luegen-ld.1644665
So I think it is wrong to take the Law of Return and its application to persecuted people, antisemites after all do not care whether only your father is Jewish, as having any real relevance to the question of who is Jewish. And that is actually something that weighs against criticism of Israel as an ethnostate.
Comment #258 October 25th, 2024 at 3:39 pm
Peter #257: The halakhic definition says that you’re Jewish if your mother was Jewish or you underwent the process of conversion to Judaism. That’s been the case for like 2000 years.
The “Jewish” anti-Israel groups, like “Jewish Voice for Peace,” are a different story entirely—apparently some of their members are halakhacally Jewish and others not, but either way, they’ve been widely mocked by the 90-95% of Jews who are pro-Israel for total ignorance about Judaism. (E.g., displaying Hebrew lettering that goes left-to-right rather than right-to-left, or setting up “Liberation Sukkahs” that violate the basic rules of Sukkot.) This isn’t so surprising when you consider that the Hebrew Bible is mostly about Jews’ connection to the Land of Israel. You can’t sever that connection without eviscerating Judaism itself.
Comment #259 October 26th, 2024 at 12:50 am
gentzen #254
The definiteness of statements is a separate issue from the consistency of axiom systems we invent for them, and the distinction especially clear when we’re talking about axiom systems for physical laws. If an inconsistency was discovered in the postulates of quantum mechanics, we wouldn’t question physical reality, we would try to fix the postulates. Seeing the same sort of behavior in the history of set theory and arithmetic is what I think motivates some people to say that integers are clearly being treated like a reality that we are designing postulates to capture and rather than an arbitrary model of PA. I step off the platform around this point, because while we can transcend our language’s ability to refer to physical reality by pointing with our fingers, the integers are not possible to identify fully in a finite amount of time, due to incompleteness and the multiplicity of models for arithmetic. There are multiple models that satisfy QM as well (these are called interpretations!) but crucially when I point my finger I refer to a distinct and specific object.
Comment #260 October 26th, 2024 at 1:12 am
It might help if we reduced the question to an example in zeroth-order. If X,Y,Z are boolean variables and X^Y is the only axiom, you could say that Z is definitely either true or false, or you could say that while T,T,T and T,T,F are both models of X^Y, so T,T. The correct path is the one that accounts for your future knowledge: if new axioms will be added you might learn Z eventually, but in the event that you have an external way of knowing that it never appears you should remove it. We know that the consistency of PA is never going to be resolved by an axiom system that doesn’t have an equally troubling consistency problem, and we know that the predictions of different interpretations of the Schrodinger equation cannot be separated. In both cases I submit that we are talking about variables that should be struck out from our model.
Comment #261 October 26th, 2024 at 9:24 am
Concerned #260: You will have a hard time to understand my position, if you are focusing too much on “integer” and “arithmetic”, and not enough on “finiteness”. A sentence or formula is true for a given theory, if it can be derived from the axioms in “finitely” many deduction steps. Every formula is a “finite” string of letters over some alphabet. And axiom schemes can also have a special relation to “finiteness”. This raises the question of my “ontological commitments”, when I am willing to talk about PA and its consistency.
That is the background when Scott says that you cannot even start to do math, if you don’t accept the definiteness of arithmetical statements. But he didn’t manage to convince me (yet?), because it seems to me that “computation in the limit” (i.e. the definiteness of Delta_2 statements) is enough. (But even without this, oracles and wizards don’t feel very trustworthy to me. Maybe my criticism of Scott’s arguments would just as well apply to Gerhard Gentzen’s proof of the well-orderedness of epsilon_0, but it somehow fails to trigger my distrust in a way that I could point out why it is not a convincing proof.)
From my POV, neither Scott nor you even tried to convince me that definiteness of arithmetical statements and consistency of PA are independent. Maybe you are right, who knows? Still, note that the problem of consisteny of PA is a major motivation to be sceptical about definiteness of arithmetical statements for me. The consistency of primitive recursive arithmetic on the other hand “feels obvious” to me, and very few people have historically been sceptical about it.
Comment #262 October 26th, 2024 at 10:06 am
Scott #252
> namely that once you’re talking about things like models, axioms, and consistency, you’ve already implicitly committed yourself to arithmetic at the very least (or how else were you manipulating logical formulas?)
I feel like nobody is digging in to this very good point, so I will try to answer it. Checking an individual proof is an individual computation, so the validity of a proof given an axiom system is a Pi0-sentence. As a Pi0-finitist, I admit the validity of any true proof as a fact on the same ground as the arithmetical calculation performed to check it.
The language of all checkable proofs is recursively enumerable. While a program that decides it is a finite string, the equivalency of two Turing machines that recognize a language is undecidable. While a Turing machine has some properties that we would expect for the “name” for a set, it lacks others. We get serious philosophical issues as soon as we arrive at Pi1 centered around semidecidability and the meaning we assign to quasihalting programs.
We have a philosophical category already for a statement that can only be falsified, but shouldn’t be rejected by a reasonable person on those grounds: a scientific theory. Scientific theories map perfectly onto quasihalting programs that ingest individual facts and halt if they find a counterexample. It is understood that while theories can be effectively true they are not themselves “facts,” and that this separation of the hierarchy functions to prevent the universe of facts from being enlarged with an infinite number of unfalsifiable theories. I think this works really well to settle the disquiet created by incompleteness at the expense of the countably infinite degree of Platonism.
Comment #263 October 26th, 2024 at 10:27 am
gentzen #261: Consistency of PA and definiteness of arithmetic are not just two different statements—they’re two entirely different kinds of statement. Con(PA) is a mathematical statement that can be formalized in the language of PA itself. But the definiteness of arithmetical statements is not—it’s just a philosophical precondition to talking about the truth or falsehood of those statements at all. If you tried to formalize it, you’d just end up with a bunch of instances of the Law of the Excluded Middle (“this Turing machine either halts or runs forever, and so does this one, and so does this one…”), which unlike Con(PA) are completely trivial to prove. But proof in this or that formal system was never the relevant question there anyway.
Comment #264 October 26th, 2024 at 11:41 am
gentzen #261
Maybe we mean something different by arithmetical statements. To me, an arithmetical statement is a zeroth-order proposition that corresponds to an individual computation; it is a witness to its own definiteness. But you could also use “arithmetical statement” to refer to high-order propositions that may even be independent, in which case definiteness becomes a real question.
Propositions don’t all have truth values, such as “colorless green ideas sleep furiously.” The question of definiteness is the issue of how to define what propositions have truth values and which ones could be meaningless. I could have a consistent propositional calculus of colorless green ideas and we wouldn’t conclude those statements had meaning because consistency and definiteness are separate issues.
Scott #263 says that all semidecidable questions have truth values. That’s the “standard model” of models and I’ve seen it presented that way every time incompleteness is phrased as the idea that there are true, unprovable ideas relative to every axiom system. The problem with this view is that the universe becomes filled with unknowable facts.
I say that all decidable questions have truth values, relegating semideciable questions to the rank of scientific theories. I can “begin to do math” just as easily as I can begin to do science – I’m sacrificing only my license to be Platonistic about it.
Comment #265 October 28th, 2024 at 2:00 am
@Concerned #264:
Yeah, “arithmetic sentence” generally means that a sentence using only quantifiers over N (and arithmetic language and classical logic). So it might not be decidable. A Delta-0 sentence would usually be called something like “bounded arithmetic sentence” or “computable sentence”.
Addressing the third paragraph now, you are arguing that scientific theories don’t have truth values? That seems a bit strange…
Re: #260:
So, am I right in thinking that in your view, the MWI doesn’t work as an interpretation?
Because when I point at something, other mes are pointing at different things.
Comment #266 October 28th, 2024 at 7:23 am
Scott #263: Thanks. I did not expect that you would try to convince me. Interesting enough, you seem to assume that I am a formalist, or at least have a hard time to distinguish between “philosophical precondition” and formally provable statements. This is surprising to me, since I guess that neither of us is a formalist.
If you could convince somebody that one can universally quantify over the natural numbers, and get a definite answer (for the “standard” natural numbers), then I don’t see how that person could still doubt that PA is consistent. All those formulas that PA can talk about then define definite sets of natural numbers, and the deduction rules and axiom schemes of PA just state facts which are true for such sets.
However, my general expectation is that the Scott of 2024 is simply no longer interested in such questions as the Scott of 2002. I guess the Scott of 2002 would have been delighted if Harvey Friedman or Joel David Hamkins would have wanted to discuss such questions with him. But the Scott of 2024 would mostly try to be polite to Harvey or Joel, but wouldn’t really try to deeply engage with those questions. And that it perfectly fine for me. It was Timothy Chow who wanted to engage with those questions while I was also interested in them, and who caused me to deeply engage with them.
A more interesting question for me is whether the Scott of 2024 still has similar philosophical interests as the Scott of 2013. In #177 he wrote:
In principle, that essays is quite interesting, and nicely argumented from a philosophical point of view. And the idea idea of the relevance of the “practical” unclonability is cool. But is it really worth it to try to deeply study those 85 pages today? Hasn’t Scott moved on, just like the Scott of 2002, and would no longer be interested in engaging with those questions he raised back then?
Comment #267 October 28th, 2024 at 7:51 am
gentzen #266: I barely understand what you’re talking about. Sure, some of my views have importantly changed since 2002 or 2013 — you should worry if they hadn’t! But on the subjects you’re talking about, my views are pretty much the same. In 2002, I was a Platonist about arithmetic and computation and a (non-dismissive) formalist about all the rest. In 2024 I’m the same, for the same reasons. In 2013 I wrote an 85-page essay about the No-Cloning Theorem and personal identity. In 2024 I stand by what I wrote, and am not writing it again simply because I already wrote it!
On the narrower question, I agree that someone who was a Platonist about the positive integers would almost certainly accept Con(PA), treating N as a model for PA (though even then there’s no strict logical implication: maybe someone thinks PA’s induction schema is too strong!). But at any rate I don’t see the other direction: if you tell me someone accepts Con(PA), that seems to give only very weak probabilistic evidence as to whether they’re a Platonist about positive integers.
Comment #268 October 28th, 2024 at 9:11 am
Scott #267: Thanks for your nice answer. My guess is not so much that your views have changed, but that your interests changed. I guess that the 17 years old Scott who wrote the essay “Who Can Name the Bigger Number?” would have been more interested than you are today in questions like how you can approximate a Pi2 statement like the twin prime conjecture by a Pi1 statement. For example, if the gaps between the twin primes are smaller than some primitive recursive function, then this strengthened statement would be Pi1. However, if the gaps are bigger than the Ackermann function, but still smaller than the Goldstein sequence, then even this strengthened statement would still be Pi2 (I guess).
Indeed, that is what I meant when I wrote in #254:
Comment #269 October 28th, 2024 at 12:50 pm
Ben #265
Scientific theories in the Popperian sense (I know that a lot of people have many different views on this) can’t be observed directly, only supported by (scientific) induction, which says that if there are no counterexamples n<N then N is probably not a counterexample either. 🙂
They also carry with them a degree of ambiguity that comes from the limited view of the people who discovered them. So, there are two issues separating scientific theories from absolute facts, the semidecidable nature of Popperian falsification, and our limited ability to specify exactly what the theory is talking about. If someone wants to believe in final theories that describe nature absolutely, I can't deny them that, but they're kind of like deities in that they are ineffable and deeply different from the things we can create.
I see both of these qualities (irremovable ambiguity over models and the existence of questions that can only be answered if in the negative) in the semidecidable world of quasihalting programs and quantifiers. Since every proof depends implicitly on consistency, and statements with quantifiers can only be verified logically, all sentences that have quantifiers inherit a deep semidecidability to match the superficial semidecidability of a Turing machine that checks them one example at a time.
Comment #270 October 28th, 2024 at 3:41 pm
Ben #265 re #260 MWI
The other “me”s might be referring to different things as well, if they are talking about a phenomenon that only exists in their branch. They might also be talking about the same thing, if the discussion is about the overall wavefunction or the laws of physics. In every case the thing they’re pointing to would still correspond to what they were referring to. It’s not their statement itself (which in your example is the same between all of them) but the direction of their fingers that transcends model ambiguity. Their statements in themselves retain traces of model ambiguity, a feature of language generally.
Comment #271 October 28th, 2024 at 6:47 pm
Scott #184 condensed the definiteness question for semideciable problems into its essence: the issue of whether or not there is an axiom A with good mathematics on both sides of its negation, and such that A↔Halt(T). The A.Choice and the parallel postulate are examples of the first half of the condition, but it wasn’t clear how to relate either one to T. I have done a little more reading this evening, and am curious what the more experienced people on this blog think of the example I have thought of:
The existence of the set ℕ is an axiom of ZFC that is considered independent of set theory as modeled in PA. Models of PA containing numbers that are greater than every natural number are considered nonstandard, which we can require by using the axiomatizaton PA+¬Infinity. ZFC says that at least one of them (ℕ) exists, so the axiom of infinity leads to good mathematics (ZFC) along with its negation (less-nonstandard models of PA).
Relating this to Halt(T) for some T is relatively straightforward. A Turing machine that writes every natural number to its tape will halt at time ℕ in ZFC and run forever in PA+¬Infininty.
Comment #272 October 29th, 2024 at 1:08 am
Concerned #270:
The thing is, branches of the wavefunction are themselves ambiguously selected models. The only way to identify a branch is though my own presence in it (of course this is presumably synonymous with everyone else’s “presence”). And of course, a finger does not point in a definite direction until a branch is identified.
Comment #273 October 29th, 2024 at 6:54 am
Concerned #264: Between “an individual computation” and “high-order propositions”, we have first-order statements with unbounded quantification, and especially first-order statements with unbounded quantification alternating “a few times” between forall and exists.
Unbounded quantification bring up the “old” debate of potential infinity vs actual infinity (or completed infinity). Cantor’s ordinal numbers complicate that debate, because they themselves can never be completed, but they show that taking limit ordinals (i.e. completing an infinite process in a certain sense) and continuing beyond them can make sense.
Concerned #271: An axiomatizaton PA+¬Infinity would feel strange to me. Of course there are infinitely many natural numbers, so denying it should simply be inconsistent, if it were expressible as a first order sentence (or formula or axiom scheme). Maybe you meant something else, namely the axiom scheme which expresses that there is a number bigger than any of the numerals 0, S(0), S(S(0)), …
For the comparison to the situation with the parallel postulate, I would rather focus on the fact that Gauss considered the “actual” existence of non-Euclidean geometry possible, took part in measuring actual distance measurements and triangulation for the cartography of the Duchy of Brunswick, became the first director of the Observatory in Göttingen, and selected a related topic for Bernhard Riemann’s habilitation lecture.
The point is that mathematicians believe in the actual existence of models of axiom systems. But this is more a generic existence compared to the “intended model” you might have had in mind, when you wrote down your axiom system. But in such a generic model, you cannot separate the natural numbers that “you want” from other objects “that may or may not be numbers”, but which you forced the model to decide one way or the other.
Comment #274 October 29th, 2024 at 8:31 am
I find almost 100% matching with you beliefs. Can I be your friend?
Comment #275 October 29th, 2024 at 9:57 am
Zvika #274: I generally prefer real-life friends over pseudonymous Internet friends. Shoot me an email if you’re ever in Austin.
Comment #276 October 29th, 2024 at 10:58 am
Ben #272
>*a finger does not point in a definite direction until a branch is identified*
I agree with you that language alone can’t identify anything.
gentzen #273
> An axiomatizaton PA+¬Infinity would feel strange to me. […] Maybe you meant something else, namely the axiom scheme which expresses that there is a number bigger than any of the numerals 0, S(0), S(S(0)), …
Thanks for pointing out actual vs. completed infinity. Completed infinity may or may not exist in models of PA, but does exist in ZF. Excluding numbers bigger than any natural numbers would require a new axiom for PA. I think this can be related to the Infinity axiom that is in ZF:
I guess that denying Infinity in PA+Something could mean saying that there is no Godel number that encodes the set of all numbers in von Neuman notation, which would as you say, have to be bigger than any of the numerals. I am picturing naively encoding sets into arithmetic and then controlling the cardinality of the model of set theory through arithmetical axioms. I know large cardinals are difficult, but I do think Godel numbers make sense in them. Any theorem that follows from PA is true for every object in a model of PA; so large cardinals have prime factors and everything else needed to construct Godel numbers.
I’ve tried to see if infinite strings of digits are an uncountable model of PA but checking if induction can lead to contradictions between their uncomputable propositions exceeds me for now. 🙂
> The point is that mathematicians believe in the actual existence of models of axiom systems. […] in such a generic model, you cannot separate the natural numbers that “you want” from other objects […]
If I understand that, the phrase “the natural numbers {1,2,3…}” does not uniquely identify the standard model of integers as it is sometimes presented. We’re platonistic about something that we can’t uniquely describe or refer to through the phenomenological binding that precedes language. I have trouble accepting that “there exists (platonistically) a model of the intuitive natural numbers,” is a belief that human beings can say they have when we cannot verify our acceptance of a given candidate, or even offer a candidate.
Comment #277 October 29th, 2024 at 9:08 pm
It turns out that not only do nonstandard models differ on the halting of Turing machines encoded in standard natural numbers, thanks to exciting facts like Con(PA+¬Con(PA)), there exists for any f: N->N a nonstandard model wherein a standard natural number encodes a program that computes f.
Joel David Hamkins beat us to this question 8 years ago: 🙂
His blog post: https://jdh.hamkins.org/every-function-can-be-computable/
Associated Reddit discussion: https://www.reddit.com/r/math/comments/4c5ikz/every_function_can_be_computable_if_you_run_this/
The extended naturals *N turn out to form the basis of nonstandard analysis as well (see chapter 3, Robinson). A nonstandard natural number contains as much information as a function from the rationals to the integers, unless my understanding of order types is wrong. Every theorem in PA is true for *N including that every n in *N is the product of a countable sequence of prime factors and exponents bounded in multiplicity by some k in *N.
Comment #278 October 29th, 2024 at 10:29 pm
Correction: The countable nonstandard numbers used in nonstandard analysis have the same order type as pairs (rational, integer) in lexicographic (left first) order. The integers I’d have expected from (avoiding) induction on S from 0 but the rational structure of what I guess you could call the limit ordinals is quite astounding and beautiful.
Comment #279 October 30th, 2024 at 4:36 am
Michael P #244: I am personally of the view that Harris is no communist (as in “Marx/Lenin/Stalin/Brezhnev”) nor is Trump a fascist (as in “Mussolini/Hitler/Salazar/Perón”); and, more consequentially, labelling their supporters as such is neither well-conceived nor well-advised, either epistemologically or viscerally.
Comment #280 October 30th, 2024 at 12:54 pm
Fiona Hill, who has observed Putin for 25 years, had some interesting things to say about whether Trump is a fascist. She feels it is not helpful to use words like fascist because people’s minds automatically shut down. She thinks of Trump’s style of governance as autocratic/strongman politics with the power being directed towards internal adversaries. Similar to Putin.
Comment #281 October 30th, 2024 at 4:04 pm
AG #279
Words come to mean what they’re used to refer to over time. In that sense “fascist” means someone who isn’t actually a fascist and neither candidate has fascist tendencies by definition. On the other hand, the word at the time meant someone with a collection of very popular traits and that was loved by many including many intellectuals. The inapplicability of the archaic sense of the word is a lot less clear!
Comment #282 October 30th, 2024 at 10:07 pm
Concerned #281: These words are being dicussed not in a rarefied world of halting problems, but in the real world of electoral politics. The labels will stick (whoever is declared the winner) — and voters reaction to the imminent prospect of living under “facsim” (as in “Hitler”) or “communism” (as in “Stalin”) may turn violent.
Comment #283 October 31st, 2024 at 1:22 pm
AG #282
I think you’re coming at it from the gestalt perspective where “so-and-so is a 20th century radical modernist” is true to the degree that they would be *successful* at changing the American system of government. Other people might approach it from the perspective of trying to guess whether or not they want to change our system of government. I think that the only workable method is to base what we call them on what they say, even if most promises are lies, contradictions or lack definite meaning.
My perspective is that the former is breaking from the way adjectives normally work in politics (we wouldn’t say a student activist is not an environmentalist because they failed to stop any construction) and the second is impossible for pretty much any candidate whose primary form of communication is campaigning. An extreme example of that would be the way historians are still not sure what Mussolini actually believed, if anything: his only writing was his oratory. I conclude that the only way to choose adjectives is to make a list of properties they imply and compare quotes and statements from someone’s entourage to it.
Here is a blog post from a popular historian that does it: https://acoup.blog/2024/10/25/new-acquisitions-1933-and-the-definition-of-fascism/. I can’t think of any objections and believe me, I can think of objections to almost anything. 🙂
Comment #284 October 31st, 2024 at 1:47 pm
Concerned #283
By the way, the electoral demand for wage and price controls is extremely high in time of financial strain. That’s why Nixon, a conservative personally advised by Milton Friedman, who had promised never to enact them, brought wage and price controls into effect in 1971. The electoral demand for a strongman character that will finally put the common people on top of the elites, reign in the excesses of the moral minorities, and bypass the annoying contests of paperwork that the political enemy occasionally uses to halt progress, is also extremely high. Hitler-Stalin would make a very strong candidate if it were not for middle school history teachers and common sense.
Comment #285 October 31st, 2024 at 8:36 pm
Concerned #277, 278: I hope you worked out the order type of the countable nonstandard numbers to your satisfaction now. The initial segment of standard numbers is normally also included in the order type, but of course it is the boring part.
Actually it always the same program, always encoded by the same standard natural number.
His post which influenced me is older, from 2012. It is the one where he raised the question: Are we correct in thinking we have an absolute concept of the finite?
While searching/googling for it, I found a comment by Brian M. Scott which is spot-on in many ways:
Zeilberger’s writings on ultrafinitism are silly, indeed. But the real issue (ignoring Zeilberger’s writings now) is always the meaning of exists (and forall).
Concerned #276>:
They are typically still countable models. Take the unary encoding first, to see how it works. The trick is that some infinite 1111… strings are really infinite in the model, but other infinite 1111… strings represent nonstandard numbers. Those infinite 1111… strings might look all the same to you, but the model sees differences between them.
Comment #286 November 2nd, 2024 at 5:46 pm
gentzen #285
One of the things I learned while reading about logic for the first time is that within math, “There exists a model for S iff S is consistent” is the most prominent reference point for existence. Now I see why you were identifying Con(PA) with the existence of numbers. I don’t have any basis for disagreement, I think that makes a lot of sense, I only a desire to point to another way in which something can exist.
Between a natural system and a consistent system, there are idealized natural systems. Idealized natural systems can involve large infinities but have a way of never noticing them. For example linear systems of ordinary differential equations take place in the setting of R^R, have a structure expressible in R^n, but exhibit a logical power that is even less than PA. A physical model of a sphere is impossible in an unimportant way but a model of a physical system that can test the consistency of ZFC in finite time is impossible in an important one. I recognize primitive recursive arithmetic as the basic language of truth in this sense, but since it is not powerful enough to reach every conclusion we believe, obviously higher theories must be allowed somehow.
I’m comfortable with the hierarchy of using systems vaguely close to the power of PRA to study nature, and using theories more powerful than that to study the systems with the power of PRA. Arranging systems that way can live alongside the “witness to consistency” sense of existence, as long as existence can have more than one sense. I am pretty sure the outlawing of quantifiers is the thing that describes the power of idealized natural systems. I can’t defend my association of idealized natural systems with metaphysical reality but it is not uncommon.
Comment #287 November 4th, 2024 at 12:50 pm
Concerned #286: Thanks for your answer. I wanted to react earlier, but was unsure what to say. With respect to existence and consistency, I wanted to bring up Cantor earlier, but forgot to do it. Let me quote something I wrote at a time, when I was not yet familiar “with the hierarchy of using systems vaguely close to the power of PRA to study nature”:
In that post, I also quoted from Joseph W. Dauben
and added
At that time, I certainly wanted to gain some sort of “license” to be allowed to say my philosophical thoughts. And I thought that studying good logic and set theory books, and understanding the debates which went on at that time (I guess triggered by Vladimir Voevodsky and univalent foundations) would do the trick. It actually worked for computer science, which certainly was a pleasent surprise for me, but not for philosophy. Noam Chomsky learned the same lesson long ago.
Don’t wait or hope for approval of your philosophical ideas by me or Scott. Your ideas are not bad, but other people have their own interests. Maybe one can go beyond consistency, but is agreement in that domain really possible, beyond that which gets enforced by established authorities (or established practice)? As long as there are still some finitistic elements or “compactness”, then maybe yes. But when it comes to questions of whether uncountable stuff or true randomness “really” exists, I am less optimistic. Generic elements and similar stuff yes, but purely Platonic stuff without any convincing applications? Maybe if they somehow simplify the required picture of the mathematical universe. But even then, many mathematicians (and logicians and philosophers) will remain unconvinced.
Comment #288 November 14th, 2024 at 2:35 am
I’m really curious where you feel about the “realness” of things right above arithmetic truth. Namely is BB_TH(N) (Busy beaver with oracle access to all true first order statements about N) a “real” sequence or one you feel somewhat formalist about. I ask because I can’t think of where to draw a line after that but it feels weird for TH(N) to platonically exist but BB_TH(N) to be not.
Comment #289 March 24th, 2025 at 7:30 am
I posit that platonists feel that way because once a mathematical truth is known, it can be reverified over many places and times, giving the impression that it always was and always will be. Now, imagine math as a quantum system. A very entangled state with many possible observations and collapses. A person or other macro system observes a math fact. Math collapses to that state. Now it can be reverified forever.
Observations are always consistent, as quantum entanglement insists. However, observations are not fixed until measured.