Archive for the ‘Metaphysical Spouting’ Category

Alright, so here are my comments…

Sunday, June 12th, 2022

… on Blake Lemoine, the Google engineer who became convinced that a machine learning model had become sentient, contacted federal government agencies about it, and was then fired placed on administrative leave for violating Google’s confidentiality policies.

(1) I don’t think Lemoine is right that LaMDA is at all sentient, but the transcript is so mind-bogglingly impressive that I did have to stop and think for a second! Certainly, if you sent the transcript back in time to 1990 or whenever, even an expert reading it might say, yeah, it looks like by 2022 AGI has more likely been achieved than not (“but can I run my own tests?”). Read it for yourself, if you haven’t yet.

(2) Reading Lemoine’s blog and Twitter this morning, he holds many views that I disagree with, not just about the sentience of LaMDA. Yet I’m touched and impressed by how principled he is, and I expect I’d hit it off with him if I met him. I wish that a solution could be found where Google wouldn’t fire him.

My first-ever attempt to create a meme!

Wednesday, April 27th, 2022

Why Quantum Mechanics?

Tuesday, January 25th, 2022

In the past few months, I’ve twice injured the same ankle while playing with my kids. This, perhaps combined with covid, led me to several indisputable realizations:

  1. I am mortal.
  2. Despite my self-conception as a nerdy little kid awaiting the serious people’s approval, I am now firmly middle-aged. By my age, Einstein had completed general relativity, Turing had founded CS, won WWII, and proposed the Turing Test, and Galois, Ramanujan, and Ramsey had been dead for years.
  3. Thus, whatever I wanted to accomplish in my intellectual life, I should probably get started on it now.

Hence today’s post. I’m feeling a strong compulsion to write an essay, or possibly even a book, surveying and critically evaluating a century of ideas about the following question:

Q: Why should the universe have been quantum-mechanical?

If you want, you can divide Q into two subquestions:

Q1: Why didn’t God just make the universe classical and be done with it? What would’ve been wrong with that choice?

Q2: Assuming classical physics wasn’t good enough for whatever reason, why this specific alternative? Why the complex-valued amplitudes? Why unitary transformations? Why the Born rule? Why the tensor product?

Despite its greater specificity, Q2 is ironically the question that I feel we have a better handle on. I could spend half a semester teaching theorems that admittedly don’t answer Q2, as satisfyingly as Einstein answered the question “why the Lorentz transformations?,” but that at least render this particular set of mathematical choices (the 2-norm, the Born Rule, complex numbers, etc.) orders-of-magnitude less surprising than one might’ve thought they were a priori. Q1 therefore stands, to me at least, as the more mysterious of the two questions.

So, I want to write something about the space of credible answers to Q, and especially Q1, that humans can currently conceive. I want to do this for my own sake as much as for others’. I want to do it because I regard Q as one of the biggest questions ever asked, for which it seems plausible to me that there’s simply an answer that most experts would accept as valid once they saw it, but for which no such answer is known. And also because, besides having spent 25 years working in quantum information, I have the following qualifications for the job:

  • I don’t dismiss either Q1 or Q2 as silly; and
  • crucially, I don’t think I already know the answers, and merely need better arguments to justify them. I’m genuinely uncertain and confused.

The purpose of this post is to invite you to share your own answers to Q in the comments section. Before I embark on my survey project, I’d better know if there are promising ideas that I’ve missed, and this blog seems like as good a place as any to crowdsource the job.

Any answer is welcome, no matter how wild or speculative, so long as it honestly grapples with the actual nature of QM. To illustrate, nothing along the lines of “the universe is quantum because it needs to be holistic, interconnected, full of surprises, etc. etc.” will cut it, since such answers leave utterly unexplained why the world wasn’t simply endowed with those properties directly, rather than specifically via generalizing the rules of probability to allow interference and noncommuting observables.

Relatedly, whatever “design goal” you propose for the laws of physics, if the goal is satisfied by QM, but satisfied even better by theories that provide even more power than QM does—for instance, superluminal signalling, or violations of Tsirelson’s bound, or the efficient solution of NP-complete problems—then your explanation is out. This is a remarkably strong constraint.

Oh, needless to say, don’t try my patience with anything about the uncertainty principle being due to floating-point errors or rendering bugs, or anything else that relies on a travesty of QM lifted from a popular article or meme! 🙂

OK, maybe four more comments to enable a more productive discussion, before I shut up and turn things over to you:

  1. I’m aware, of course, of the radical uncertainty about what form an answer to Q should even take. Am I asking you to psychoanalyze the will of God in creating the universe? Or, what perhaps amounts to the same thing, am I asking for the design objectives of the giant computer simulation that we’re living in? (As in, “I’m 100% fine with living inside a Matrix … I just want to understand why it’s a unitary matrix!”) Am I instead asking for an anthropic explanation, showing why of course QM would be needed if you wanted life or consciousness like ours? Am I “merely” asking for simpler or more intuitive physical principles from which QM is to be derived as a consequence? Am I asking why QM is the “most elegant choice” in some space of mathematical options … even to the point where, with hindsight, a 19th-century mathematician or physicist could’ve been convinced that of course this must be part of Nature’s plan? Am I asking for something else entirely? You get to decide! Should you take up my challenge, this is both your privilege and your terrifying burden.
  2. I’m aware, of course, of the dizzying array of central physical phenomena that rely on QM for their ultimate explanation. These phenomena range from the stability of matter itself, which depends on the Pauli exclusion principle; to the nuclear fusion that powers the sun, which depends on a quantum tunneling effect; to the discrete energy levels of electrons (and hence, the combinatorial nature of chemistry), which relies on electrons being waves of probability amplitude that can only circle nuclei an integer number of times if their crests are to meet their troughs. Important as they are, though, I don’t regard any of these phenomena as satisfying answers to Q in themselves. The reason is simply that, in each case, it would seem like child’s-play to contrive some classical mechanism to produce the same effect, were that the goal. QM just seems far too grand to have been the answer to these questions! An exponentially larger state space for all of reality, plus the end of Newtonian determinism, just to overcome the technical problem that accelerating charges radiate energy in classical electrodynamics, thereby rendering atoms unstable? It reminds me of the Simpsons episode where Homer uses a teleportation machine to get a beer from the fridge without needing to get up off the couch.
  3. I’m aware of Gleason’s theorem, and of the specialness of the 1-norm and 2-norm in linear algebra, and of the arguments for complex amplitudes as opposed to reals or quaternions, and of the beautiful work of Lucien Hardy and of Chiribella et al. and others on axiomatic derivations of quantum theory. As some of you might remember, I even discussed much of this material in Quantum Computing Since Democritus! There’s a huge amount to say about these fascinating justifications for the rules of QM, and I hope to say some of it in my planned survey! For now, I’ll simply remark that every axiomatic reconstruction of QM that I’ve seen, impressive though it was, has relied on one or more axioms that struck me as weird, in the sense that I’d have little trouble dismissing the axioms as totally implausible and unmotivated if I hadn’t already known (from QM, of course) that they were true. The axiomatic reconstructions do help me somewhat with Q2, but little if at all with Q1.
  4. To keep the discussion focused, in this post I’d like to exclude answers along the lines of “but what if QM is merely an approximation to something else?,” to say nothing of “a century of evidence for QM was all just a massive illusion! LOCAL HIDDEN VARIABLES FOR THE WIN!!!” We can have those debates another day—God knows that, here on Shtetl-Optimized, we have and we will. Here I’m asking instead: imagine that, as fantastical as it sounds, QM were not only exactly true, but (along with relativity, thermodynamics, evolution, and the tastiness of chocolate) one of the profoundest truths our sorry species had ever discovered. Why should I have expected that truth all along? What possible reasons to expect it have I missed?

An Orthodox rabbi and Steven Weinberg walk into an email exchange…

Friday, October 22nd, 2021

Ever since I posted my obituary for the great Steven Weinberg three months ago, I’ve gotten a steady trickle of emails—all of which I’ve appreciated enormously—from people who knew Steve, or were influenced by him, and who wanted to share their own thoughts and memories. Last week, I was contacted by one Moshe Katz, an Orthodox rabbi, who wanted to share a long email exchange that he’d had with Steve, about Steve’s reasons for rejecting his birth-religion of Judaism (along with every other religion). Even though Rabbi Katz, rather than Steve, does most of the talking in this exchange, and even though Steve mostly expresses the same views he’d expressed in many of his public writings, I knew immediately on seeing this exchange that it could be of broader interest—so I secured permission to share it here on Shtetl-Optimized, both from Rabbi Katz and from Steve’s widow Louise.

While longtime readers can probably guess what I think about most of the topics discussed, I’ll refrain from any editorial commentary in this post—but of course, feel free to share your own thoughts in the comments, and maybe I’ll join in. Mostly, reading this exchange reminded me that someone at some point should write a proper book-length biography of Steve, and someone should also curate and publish a selection of his correspondence, much like Perfectly Reasonable Deviations from the Beaten Track did for Richard Feynman. There must be a lot more gems to be mined.

Anyway, without further ado, here’s the exchange (10 pages, PDF).

Update (Nov. 2, 2021): By request, see here for some of my own thoughts.

The Zen Anti-Interpretation of Quantum Mechanics

Thursday, March 4th, 2021

As I lay bedridden this week, knocked out by my second dose of the Moderna vaccine, I decided I should blog some more half-baked ideas because what the hell? It feels therapeutic, I have tenure, and anyone who doesn’t like it can close their broswer tab.

So: although I’ve written tens of thousands of words, on this blog and elsewhere, about interpretations of quantum mechanics, again and again I’ve dodged the question of which interpretation (if any) I really believe myself. Today, at last, I’ll emerge from the shadows and tell you precisely where I stand.

I hold that all interpretations of QM are just crutches that are better or worse at helping you along to the Zen realization that QM is what it is and doesn’t need an interpretation.  As Sidney Coleman famously argued, what needs reinterpretation is not QM itself, but all our pre-quantum philosophical baggage—the baggage that leads us to demand, for example, that a wavefunction |ψ⟩ either be “real” like a stubbed toe or else “unreal” like a dream. Crucially, because this philosophical baggage differs somewhat from person to person, the “best” interpretation—meaning, the one that leads most quickly to the desired Zen state—can also differ from person to person. Meanwhile, though, thousands of physicists (and chemists, mathematicians, quantum computer scientists, etc.) have approached the Zen state merely by spending decades working with QM, never worrying much about interpretations at all. This is probably the truest path; it’s just that most people lack the inclination, ability, or time.

Greg Kuperberg, one of the smartest people I know, once told me that the problem with the Many-Worlds Interpretation is not that it says anything wrong, but only that it’s “melodramatic” and “overwritten.” Greg is far along the Zen path, probably further than me.

You shouldn’t confuse the Zen Anti-Interpretation with “Shut Up And Calculate.” The latter phrase, mistakenly attributed to Feynman but really due to David Mermin, is something one might say at the beginning of the path, when one is as a baby. I’m talking here only about the endpoint of the path, which one can approach but never reach—the endpoint where you intuitively understand exactly what a Many-Worlder, Copenhagenist, or Bohmian would say about any given issue, and also how they’d respond to each other, and how they’d respond to the responses, etc. but after years of study and effort you’ve returned to the situation of the baby, who just sees the thing for what it is.

I don’t mean to say that the interpretations are all interchangeable, or equally good or bad. If you had to, you could call even me a “Many-Worlder,” but only in the following limited sense: that in fifteen years of teaching quantum information, my experience has consistently been that for most students, Everett’s crutch is the best one currently on the market. At any rate, it’s the one that’s the most like a straightforward picture of the equations, and the least like a wobbly tower of words that might collapse if you utter any wrong ones.  Unlike Bohr, Everett will never make you feel stupid for asking the questions an inquisitive child would ask; he’ll simply give you answers that are as clear, logical, and internally consistent as they are metaphysically extravagant. That’s a start.

The Copenhagen Interpretation retains a place of honor as the first crutch, for decades the only crutch, and the one closest to the spirit of positivism. Unfortunately, wielding the Copenhagen crutch requires mad philosophical skillz—which parts of the universe should you temporarily regard as “classical”? which questions should be answered, and which deflected?—to the point where, if you’re capable of all that verbal footwork, then why do you even need a crutch in the first place? In the hands of amateurs—meaning, alas, nearly everyone—Copenhagen often leads away from rather than toward the Zen state, as one sees with the generations of New-Age bastardizations about “observations creating reality.”

As for deBroglie-Bohm—well, that’s a weird, interesting, baroque crutch, one whose actual details (the preferred basis and the guiding equation) are historically contingent and tied to specific physical systems. It’s probably the right crutch for someone—it gets eternal credit for having led Bell to discover the Bell inequality—but its quirks definitely need to be discarded along the way.

Note that, among those who approach the Zen state, many might still call themselves Many-Worlders or Copenhagenists or Bohmians or whatever—just as those far along in spiritual enlightenment might still call themselves Buddhists or Catholics or Muslims or Jews (or atheists or agnostics)—even though, by that point, they might have more in common with each other than they do with their supposed coreligionists or co-irreligionists.

Alright, but isn’t all this Zen stuff just a way to dodge the actual, substantive questions about QM, by cheaply claiming to have transcended them? If that’s your charge, then please help yourself to the following FAQ about the details of the Zen Anti-Interpretation.

  1. What is a quantum state? It’s a unit vector of complex numbers (or if we’re talking about mixed states, then a trace-1, Hermitian, positive semidefinite matrix), which encodes everything there is to know about a physical system.
  2. OK, but are the quantum states “ontic” (really out in the world), or “epistemic” (only in our heads)? Dude. Do “basketball games” really exist, or is that just a phrase we use to summarize our knowledge about certain large agglomerations of interacting quarks and leptons? Do even the “quarks” and “leptons” exist, or are those just words for excitations of the more fundamental fields? Does “jealousy” exist? Pretty much all our concepts are complicated grab bags of “ontic” and “epistemic,” so it shouldn’t surprise us if quantum states are too. Bad dichotomy.
  3. Why are there probabilities in QM? Because QM is a (the?) generalization of probability theory to involve complex numbers, whose squared absolute values are probabilities. It includes probability as a special case.
  4. But why do the probabilities obey the Born rule? Because, once the unitary part of QM has picked out the 2-norm as being special, for the probabilities also to be governed by the 2-norm is pretty much the only possibility that makes mathematical sense; there are many nice theorems formalizing that intuition under reasonable assumptions.
  5. What is an “observer”? It’s exactly what modern decoherence theory says it is: a particular kind of quantum system that interacts with other quantum systems, becomes entangled with them, and thereby records information about them—reversibly in principle but irreversibly in practice.
  6. Can observers be manipulated in coherent superposition, as in the Wigner’s Friend scenario? If so, they’d be radically unlike any physical system we’ve ever had direct experience with. So, are you asking whether such “observers” would be conscious, or if so what they’d be conscious of? Who the hell knows?
  7. Do “other” branches of the wavefunction—ones, for example, where my life took a different course—exist in the same sense this one does? If you start with a quantum state for the early universe and then time-evolve it forward, then yes, you’ll get not only “our” branch but also a proliferation of other branches, in the overwhelming majority of which Donald Trump was never president and civilization didn’t grind to a halt because of a bat near Wuhan.  But how could we possibly know whether anything “breathes fire” into the other branches and makes them real, when we have no idea what breathes fire into this branch and makes it real? This is not a dodge—it’s just that a simple “yes” or “no” would fail to do justice to the enormity of such a question, which is above the pay grade of physics as it currently exists. 
  8. Is this it? Have you brought me to the end of the path of understanding QM? No, I’ve just pointed the way toward the beginning of the path. The most fundamental tenet of the Zen Anti-Interpretation is that there’s no shortcut to actually working through the Bell inequality, quantum teleportation, Shor’s algorithm, the Kochen-Specker and PBR theorems, possibly even a … photon or a hydrogen atom, so you can see quantum probability in action and be enlightened. I’m further along the path than I was twenty years ago, but not as far along as some of my colleagues. Even the greatest quantum Zen masters will be able to get further when new quantum phenomena and protocols are discovered in the future. All the same, though—and this is another major teaching of the Zen Anti-Interpretation—there’s more to life than achieving greater and greater clarity about the foundations of QM. And on that note…

To those who asked me about Claus Peter Schnorr’s claim to have discovered a fast classical factoring algorithm, thereby “destroying” (in his words) the RSA cryptosystem, see (e.g.) this Twitter thread by Keegan Ryan, which explains what certainly looks like a fatal error in Schnorr’s paper.

Once we can see them, it’s too late

Saturday, January 30th, 2021

[updates: here’s the paper, and here’s Robin’s brief response to some of the comments here]

This month Robin Hanson, the famous and controversy-prone George Mason University economics professor who I’ve known since 2004, was visiting economists here in Austin for a few weeks. So, while my fear of covid considerably exceeds Robin’s, I met with him a few times in the mild Texas winter in an outdoor, socially-distanced way. It took only a few minutes for me to remember why I enjoy talking to Robin so much.

See, while I’d been moping around depressed about covid, the vaccine rollout, the insurrection, my inability to focus on work, and a dozen other things, Robin was bubbling with excitement about a brand-new mathematical model he was working on to understand the growth of civilizations across the universe—a model that, Robin said, explained lots of cosmic mysteries in one fell swoop and also made striking predictions. My cloth facemask was, I confess, unable to protect me from Robin’s infectious enthusiasm.

As I listened, I went through the classic stages of reaction to a new Hansonian proposal: first, bemusement over the sheer weirdness of what I was being asked to entertain, as well as Robin’s failure to acknowledge that weirdness in any way whatsoever; then, confusion about the unstated steps in his radically-condensed logic; next, the raising by me of numerous objections (each of which, it turned out, Robin had already thought through at length); finally, the feeling that I must have seen it this way all along, because isn’t it kind of obvious?

Robin has been explaining his model in a sequence of Overcoming Bias posts, and will apparently have a paper out about the model soon the paper is here! In this post, I’d like to offer my own take on what Robin taught me. Blame for anything I mangle lies with me alone.

To cut to the chase, Robin is trying to explain the famous Fermi Paradox: why, after 60+ years of looking, and despite the periodic excitement around Tabby’s star and ‘Oumuamua and the like, have we not seen a single undisputed sign of an extraterrestrial civilization? Why all this nothing, even though the observable universe is vast, even though (as we now know) organic molecules and planets in Goldilocks zones are everywhere, and even though there have been billions of years for aliens someplace to get a technological head start on us, expanding across a galaxy to the point where they’re easily seen?

Traditional answers to this mystery include: maybe the extraterrestrials quickly annihilate themselves in nuclear wars or environmental cataclysms, just like we soon will; maybe the extraterrestrials don’t want to be found (whether out of self-defense or a cosmic Prime Directive); maybe they spend all their time playing video games. Crucially, though, all answers of that sort founder against the realization that, given a million alien civilizations, each perhaps more different from the others than kangaroos are from squid, it would only take one, spreading across a billion light-years and transforming everything to its liking, for us to have noticed it.

Robin’s answer to the puzzle is as simple as it is terrifying. Such civilizations might well exist, he says, but if so, by the time we noticed one, it would already be nearly too late. Robin proposes, plausibly I think, that if you give a technological civilization 10 million or so years—i.e., an eyeblink on cosmological timescales—then either

  1. the civilization wipes itself out, or else
  2. it reaches some relatively quiet steady state, or else
  3. if it’s serious about spreading widely, then it “maxes out” the technology with which to do so, approaching the limits set by physical law.

In cases 1 or 2, the civilization will of course be hard for us to detect, unless it happens to be close by. But what about case 3? There, Robin says, the “civilization” should look from the outside like a sphere expanding at nearly the speed of light, transforming everything in its path.

Now think about it: when could we, on earth, detect such a sphere with our telescopes? Only when the sphere’s thin outer shell had reached the earth—perhaps carrying radio signals from the extraterrestrials’ early history, before their rapid expansion started. By that point, though, the expanding sphere itself would be nearly upon us!

What would happen to us once we were inside the sphere? Who knows? The expanding civilization might obliterate us, it might preserve us as zoo animals, it might merge us into its hive-mind, it might do something else that we can’t imagine, but in any case, detecting the civilization would presumably no longer be the relevant concern!

(Of course, one could also wonder what happens when two of these spheres collide: do they fight it out? do they reach some agreement? do they merge? Whatever the answer, though, it doesn’t matter for Robin’s argument.)

On the view described, there’s only a tiny cosmic window in which a SETI program could be expected to succeed: namely, when the thin surface of the first of these expanding bubbles has just hit us, and when that surface hasn’t yet passed us by. So, given our “selection bias”—meaning, the fact that we apparently haven’t yet been swallowed up by one of the bubbles—it’s no surprise if we don’t right now happen to find ourselves in the tiny detection window!

This basic proposal, it turns out, is not original to Robin. Indeed, an Overcoming Bias reader named Daniel X. Varga pointed out to Robin that he (Daniel) shared the same idea right here—in a Shtetl-Optimized comment thread—back in 2008! I must have read Daniel Varga’s comment then, but (embarrassingly) it didn’t make enough of an impression for me to have remembered it. I probably thought the same as you probably thought while reading this post:

“Sure, whatever. This is an amusing speculation that could make for a fun science-fiction story. Alas, like with virtually every story about extraterrestrials, there’s no good reason to favor this over a hundred other stories that a fertile imagination could just as easily spin. Who the hell knows?”

This is where Robin claims to take things further. Robin would say that he takes them further by developing a mathematical model, and fitting the parameters of the model to the known facts of cosmic history. Read Overcoming Bias, or Robin’s forthcoming paper, if you want to know the details of his model. Personally, I confess I’m less interested in those details than I am in the qualitative points, which (unless I’m mistaken) are easy enough to explain in words.

The key realization is this: when we contemplate the Fermi Paradox, we know more than the mere fact that we look and look and we don’t see any aliens. There are other relevant data points to fit, having to do with the one sample of a technological civilization that we do have.

For starters, there’s the fact that life on earth has been evolving for at least ~3.5 billion years—for most of the time the earth has existed—but life has a mere billion more years to go, until the expanding sun boils away the oceans and makes the earth barely habitable. In other words, at least on this planet, we’re already relatively close to the end. Why should that be?

It’s an excellent fit, Robin says, to a model wherein there are a few incredibly difficult, improbable steps along the way to a technological civilization like ours—steps that might include the origin of life, of multicellular life, of consciousness, of language, of something else—and wherein, having achieved some step, evolution basically just does a random search until it either stumbles onto the next step or else runs out of time.

Of course, given that we’re here to talk about it, we necessarily find ourselves on a planet where all the steps necessary for blog-capable life happen to have succeeded. There might be vastly more planets where evolution got stuck on some earlier step.

But here’s the interesting part: conditioned on all the steps having succeeded, we should find ourselves near the end of the useful lifetime of our planet’s star—simply because the more time is available on a given planet, the better the odds there. I.e., look around the universe and you should find that, on most of the planets where evolution achieves all the steps, it nearly runs out the planet’s clock in doing so. Also, as we look back, we should find the hard steps roughly evenly spaced out, with each one having taken a good fraction of the whole available time. All this is an excellent match for what we see.

OK, but it leads to a second puzzle. Life on earth is at least ~3.5 billion years old, while the observable universe is ~13.7 billion years old. Forget for a moment about the oft-stressed enormity of these two timescales and concentrate on their ratio, which is merely ~4. Life on earth stretches a full quarter of the way back in time to the Big Bang. Even as an adolescent, I remember finding that striking, and not at all what I would’ve guessed a priori. It seemed like obviously a clue to something, if I could only figure out what.

The puzzle is compounded once you realize that, even though the sun will boil the oceans in a billion years (and then die in a few billion more), other stars, primarily dwarf stars, will continue shining brightly for trillions more years. Granted, the dwarf stars don’t seem quite as hospitable to life as sun-like stars, but they do seem somewhat hospitable, and there will be lots of them—indeed, more than of sun-like stars. And they’ll last orders of magnitude longer.

To sum up, our temporal position relative to the lifetime of the sun makes it look as though life on earth was just a lucky draw from a gigantic cosmic Poisson process. By contrast, our position relative to the lifetime of all the stars makes it look as though we arrived crazily, freakishly early—not at all what you’d expect under a random model. So what gives?

Robin contends that all of these facts are explained under his bubble scenario. If we’re to have an experience remotely like the human one, he says, then we have to be relatively close to the beginning of time—since hundreds of billions of years from now, the universe will likely be dominated by near-light-speed expanding spheres of intelligence, and a little upstart civilization like ours would no longer stand a chance. I.e., even though our existence is down to some lucky accidents, and even though those same accidents probably recur throughout the cosmos, we shouldn’t yet see any of the other accidents, since if we did see them, it would already be nearly too late for us.

Robin admits that his account leaves a huge question open: namely, why should our experience have been a “merely human,” “pre-bubble” experience at all? If you buy that these expanding bubbles are coming, it seems likely that there will be trillions of times more sentient experiences inside them than outside. So experiences like ours would be rare and anomalous—like finding yourself at the dawn of human history, with Hammurabi et al., and realizing that almost every interesting thing that will ever happen is still to the future. So Robin simply takes as a brute fact that our experience is “earth-like” or “human-like”; he then tries to explain the other observations from that starting point.

Notice that, in Robin’s scenario, the present epoch of the universe is extremely special: it’s when civilizations are just forming, when perhaps a few of them will achieve technological liftoff, but before one or more of the civilizations has remade the whole of creation for its own purposes. Now is the time when the early intelligent beings like us can still look out and see quadrillions of stars shining to no apparent purpose, just wasting all that nuclear fuel in a near-empty cosmos, waiting for someone to come along and put the energy to good use. In that respect, we’re sort of like the Maoris having just landed in New Zealand, or Bill Gates surveying the microcomputer software industry in 1975. We’re ridiculously lucky. The situation is way out of equilibrium. The golden opportunity in front of us can’t possibly last forever.

If we accept the above, then a major question I had was the role of cosmology. In 1998, astronomers discovered that the present cosmological epoch is special for a completely different reason than the one Robin talks about. Namely, right now is when matter and dark energy contribute roughly similarly to the universe’s energy budget, with ~30% the former and ~70% the latter. Billions of years hence, the universe will become more and more dominated by dark energy. Our observable region will get sparser and sparser, as the dark energy pushes the galaxies further and further away from each other and from us, with more and more galaxies receding past the horizon where we could receive signals from them at the speed of light. (Which means, in particular, that if you want to visit a galaxy a few billion light-years from here, you’d better start out while you still can!)

So here’s my question: is it just a coincidence that the time—right now—when the universe is “there for the taking,” potentially poised between competing spacefaring civilizations, is also the time when it’s poised between matter and dark energy? Note that, in 2007, Bousso et al. tried to give a sophisticated anthropic argument for the value of the cosmological constant Λ, which measures the density of dark energy, and hence the eventual size of the observable universe. See here for my blog post on what they did (“The array size of the universe”). Long story short, for reasons that I explain in the post, it turns out to be essential to their anthropic explanation for Λ that civilizations flourish only (or mainly) in the present epoch, rather than trillions of years in the future. If we had to count civilizations that far into the future, then the calculations would favor values of Λ much smaller than what we actually observe. This, of course, seems to dovetail nicely with Robin’s account.

Let me end with some “practical” consequences of Robin’s scenario, supposing as usual that we take it seriously. The most immediate consequence is that the prospects for SETI are dimmer than you might’ve thought before you’d internalized all this. (Even after having interalized it, I’d still like at least an order of magnitude more resources devoted to SETI than what our civilization currently spares. Robin’s assumptions might be wrong!)

But a second consequence is that, if we want human-originated sentience to spread across the universe, then the sooner we get started the better! Just like Bill Gates in 1975, we should expect that there will soon be competitors out there. Indeed, there are likely competitors out there “already” (where “already” means, let’s say, in the rest frame of the cosmic microwave background)—it’s just that the light from them hasn’t yet reached us. So if we want to determine our own cosmic destiny, rather than having post-singularity extraterrestrials determine it for us, then it’s way past time to get our act together as a species. We might have only a few hundred million more years to do so.

Update: For more discussion of this post, see the SSC Reddit thread. I especially liked a beautiful comment by “Njordsier,” which fills in some important context for the arguments in this post:

Suppose you’re an alien anthropologist that sent a probe to Earth a million years ago, and that probe can send back one high-resolution image of the Earth every hundred years. You’d barely notice humans at first, though they’re there. Then, circa 10,000 years ago (99% of the way into the stream) you begin to see plots of land turned into farms. Houses, then cities, first in a few isolated places in river valleys, then exploding across five or six continents. Walls, roads, aqueducts, castles, fortresses. Four frames before the end of the stream, the collapse of the population on two of the continents as invaders from another continent bring disease. At T-minus three frames, a sudden appearance of farmland and cities on the coasts those continents. At T-minus two frames, half the continent. At the second to last frame, a roaring interconnected network of roads, cities, farms, including skyscrapers in the cities that were just trying villas three frames ago. And in the last frame, nearly 80 percent of all wilderness converted to some kind of artifice, and the sky is streaked with the trails of flying machines all over the world.

Civilizations rose and fell, cultures evolved and clashed, and great and terrible men and women performed awesome deeds. But what the alien anthropologist sees is a consistent, rapid, exponential explosion of a species bulldozing everything in its path.

That’s what we’re doing when we talk about the far future, or about hypothetical expansionist aliens, on long time scales. We’re zooming out past the level where you can reason about individuals or cultures, but see the strokes of much longer patterns that emerge from that messy, beautiful chaos that is civilization.

Update (Jan. 31): Reading the reactions here, on Hacker News, and elsewhere underscored for me that a lot of people get off Robin’s train well before it’s even left the station. Such people think of extraterrestrial civilizations as things that you either find or, if you haven’t found one, you just speculate or invent stories about. They’re not even in the category of things that you have any serious hope to reason about. For myself, I’d simply observe that trying to reason about matters far beyond current human experience, based on the microscopic shreds of fact available to us (e.g., about the earth’s spatial and temporal position within the universe), has led to some of our species’ embarrassing failures but also to some of its greatest triumphs. Since even the failures tend to be relatively cheap, I feel like we ought to be “venture capitalists” about such efforts to reason beyond our station, encouraging them collegially and mocking them only gently.

The Complete Idiot’s Guide to the Independence of the Continuum Hypothesis: Part 1 of <=Aleph_0

Saturday, October 31st, 2020

A global pandemic, apocalyptic fires, and the possible descent of the US into violent anarchy three days from now can do strange things to the soul.

Bertrand Russell—and if he’d done nothing else in his long life, I’d love him forever for it—once wrote that “in adolescence, I hated life and was continually on the verge of suicide, from which, however, I was restrained by the desire to know more mathematics.” This summer, unable to bear the bleakness of 2020, I obsessively read up on the celebrated proof of the unsolvability of the Continuum Hypothesis (CH) from the standard foundation of mathematics, the Zermelo-Fraenkel axioms of set theory. (In this post, I’ll typically refer to “ZFC,” which means Zermelo-Fraenkel plus the famous Axiom of Choice.)

For those tuning in from home, the Continuum Hypothesis was formulated by Georg Cantor, shortly after his epochal discovery that there are different orders of infinity: so for example, the infinity of real numbers (denoted C for continuum, or \( 2^{\aleph_0} \)) is strictly greater than the infinity of integers (denoted ℵ0, or “Aleph-zero”). CH is simply the statement that there’s no infinity intermediate between ℵ0 and C: that anything greater than the first is at least the second. Cantor tried in vain for decades to prove or disprove CH; the quest is believed to have contributed to his mental breakdown. When David Hilbert presented his famous list of 23 unsolved math problems in 1900, CH was at the very top.

Halfway between Hilbert’s speech and today, the question of CH was finally “answered,” with the solution earning the only Fields Medal that’s ever been awarded for work in set theory and logic. But unlike with any previous yes-or-no question in the history of mathematics, the answer was that there provably is no answer from the accepted axioms of set theory! You can either have intermediate infinities or not; neither possibility can create a contradiction. And if you do have intermediate infinities, it’s up to you how many: 1, 5, 17, ∞, etc.

The easier half, the consistency of CH with set theory, was proved by incompleteness dude Kurt Gödel in 1940; the harder half, the consistency of not(CH), by Paul Cohen in 1963. Cohen’s work introduced the method of forcing, which was so fruitful in proving set-theoretic questions unsolvable that it quickly took over the whole subject of set theory. Learning Gödel and Cohen’s proofs had been a dream of mine since teenagerhood, but one I constantly put off.

This time around I started with Cohen’s retrospective essay, as well as Timothy Chow’s Forcing for Dummies and A Beginner’s Guide to Forcing. I worked through Cohen’s own Set Theory and the Continuum Hypothesis, and Ken Kunen’s Set Theory: An Introduction to Independence Proofs, and Dana Scott’s 1967 paper reformulating Cohen’s proof. I emailed questions to Timothy Chow, who was ridiculously generous with his time. When Tim and I couldn’t answer something, we tried Bob Solovay (one of the world’s great set theorists, who later worked in computational complexity and quantum computing), or Andreas Blass or Asaf Karagila. At some point mathematician and friend-of-the-blog Greg Kuperberg joined my quest for understanding. I thank all of them, but needless to say take sole responsibility for all the errors that surely remain in these posts.

On the one hand, the proof of the independence of CH would seem to stand with general relativity, the wheel, and the chocolate bar as a triumph of the human intellect. It represents a culmination of Cantor’s quest to know the basic rules of infinity—all the more amazing if the answer turns out to be that, in some sense, we can’t know them.

On the other hand, perhaps no other scientific discovery of equally broad interest remains so sparsely popularized, not even (say) quantum field theory or the proof of Fermat’s Last Theorem. I found barely any attempts to explain how forcing works to non-set-theorists, let alone to non-mathematicians. One notable exception was Timothy Chow’s Beginner’s Guide to Forcing, mentioned earlier—but Chow himself, near the beginning of his essay, calls forcing an “open exposition problem,” and admits that he hasn’t solved it. My modest goal, in this post and the following ones, is to make a further advance on the exposition problem.

OK, but why a doofus computer scientist like me? Why not, y’know, an actual expert? I won’t put forward my ignorance as a qualification, although I have often found that the better I learn a topic, the more completely I forget what initially confused me, and so the less able I become to explain things to beginners.

Still, there is one thing I know well that turns out to be intimately related to Cohen’s forcing method, and that made me feel like I had a small “in” for this subject. This is the construction of oracles in computational complexity theory. In CS, we like to construct hypothetical universes where P=NP or P≠NP, or P≠BQP, or the polynomial hierarchy is infinite, etc. To do so, we, by fiat, insert a new function—an oracle—into the universe of computational problems, carefully chosen to make the desired statement hold. Often the oracle needs to satisfy an infinite list of conditions, so we handle them one by one, taking care that when we satisfy a new condition we don’t invalidate the previous conditions.

All this, I kept reading, is profoundly analogous to what the set theorists do when they create a mathematical universe where the Axiom of Choice is true but CH is false, or vice versa, or any of a thousand more exotic possibilities. They insert new sets into their models of set theory, sets that are carefully constructed to “force” infinite lists of conditions to hold. In fact, some of the exact same people—such as Solovay—who helped pioneer forcing in the 1960s, later went on to pioneer oracles in computational complexity. We’ll say more about this connection in a future post.

How Could It Be?

How do you study a well-defined math problem, and return the answer that, as far as the accepted axioms of math can say, there is no answer? I mean: even supposing it’s true that there’s no answer, how do you prove such a thing?

Arguably, not even Gödel’s Incompleteness Theorem achieved such a feat. Recall, the Incompleteness Theorem says loosely that, for every formal system F that could possibly serve as a useful foundation for mathematics, there exist statements even of elementary arithmetic that are true but unprovable in F—and Con(F), a statement that encodes F’s own consistency, is an example of one. But the very statement that Con(F) is unprovable is equivalent to Con(F)’s being true (since an inconsistent system could prove anything, including Con(F)). In other words, if the Incompleteness Theorem as applied to F holds any interest, then that’s only because F is, in fact, consistent; it’s just that resources beyond F are needed to prove this.

Yes, there’s a “self-hating theory,” F+Not(Con(F)), which believes in its own inconsistency. And yes, by Gödel, this self-hating theory is consistent if F itself is. This means that it has a model—involving “nonstandard integers,” formal artifacts that effectively promise a proof of F’s inconsistency without ever actually delivering it. We’ll have much, much more to say about models later on, but for now, they’re just collections of objects, along with relationships between the objects, that satisfy all the axioms of a theory (thus, a model of the axioms of group theory is simply … any group!).

In any case, though, the self-hating theory F+Not(Con(F)) can’t be arithmetically sound: I mean, just look at it! It’s either unsound because F is consistent, or else it’s unsound because F is inconsistent. In general, this is one of the most fundamental points in logic: consistency does not imply soundness. If I believe that the moon is made of cheese, that might be consistent with all my other beliefs about the moon (for example, that Neil Armstrong ate delicious chunks of it), but that doesn’t mean my belief is true. Like the classic conspiracy theorist, who thinks that any apparent evidence against their hypothesis was planted by George Soros or the CIA, I might simply believe a self-consistent collection of absurdities. Consistency is purely a syntactic condition—it just means that I can never prove both a statement and its opposite—but soundness goes further, asserting that whatever I can prove is actually the case, a relationship between what’s inside my head and what’s outside it.

So again, assuming we had any business using F in the first place, the Incompleteness Theorem gives us two consistent ways to extend F (by adding Con(F) or by adding Not(Con(F))), but only one sound way (by adding Con(F)). But the independence of CH from the ZFC axioms of set theory is of a fundamentally different kind. It will give us models of ZFC+CH, and models of ZFC+Not(CH), that are both at least somewhat plausible as “sketches of mathematical reality”—and that both even have defenders. The question of which is right, or whether it’s possible to decide at all, will be punted to the future: to the discovery (or not) of some intuitively compelling foundation for mathematics that, as Gödel hoped, answers the question by going beyond ZFC.

Four Levels to Unpack

While experts might consider this too obvious to spell out, Gödel’s and Cohen’s analyses of CH aren’t so much about infinity, as they are about our ability to reason about infinity using finite sequences of symbols. The game is about building self-contained mathematical universes to order—universes where all the accepted axioms about infinite sets hold true, and yet that, in some cases, seem to mock what those axioms were supposed to mean, by containing vastly fewer objects than the mathematical universe was “meant” to have.

In understanding these proofs, the central hurdle, I think, is that there are at least four different “levels of description” that need to be kept in mind simultaneously.

At the first level, Gödel’s and Cohen’s proofs, like all mathematical proofs, are finite sequences of symbols. Not only that, they’re proofs that can be formalized in elementary arithmetic (!). In other words, even though they’re about the axioms of set theory, they don’t themselves require those axioms. Again, this is possible because, at the end of the day, Gödel’s and Cohen’s proofs won’t be talking about infinite sets, but “only” about finite sequences of symbols that make statements about infinite sets.

At the second level, the proofs are making an “unbounded” but perfectly clear claim. They’re claiming that, if someone showed you a proof of either CH or Not(CH), from the ZFC axioms of set theory, then no matter how long the proof or what its details, you could convert it into a proof that ZFC itself was inconsistent. In symbols, they’re proving the “relative consistency statements”

Con(ZFC) ⇒ Con(ZFC+CH),
Con(ZFC) ⇒ Con(ZFC+Not(CH)),

and they’re proving these as theorems of elementary arithmetic. (Note that there’s no hope of proving Con(ZF+CH) or Con(ZFC+Not(CH)) outright within ZFC, since by Gödel, ZFC can’t even prove its own consistency.)

This translation is completely explicit; the independence proofs even yield algorithms to convert proofs of inconsistencies in ZFC+CH or ZFC+Not(CH), supposing that they existed, into proofs of inconsistencies in ZFC itself.

Having said that, as Cohen himself often pointed out, thinking about the independence proofs in terms of algorithms to manipulate sequences of symbols is hopeless: to have any chance of understanding these proofs, let alone coming up with them, at some point you need to think about what the symbols refer to.

This brings us to the third level: the symbols refer to models of set theory, which could also be called “mathematical universes.” Crucially, we always can and often will take these models to be only countably infinite: that is, to contain an infinity of sets, but “merely” ℵ0 of them, the infinity of integers or of finite strings, and no more.

The fourth level of description is from within the models themselves: each model imagines itself to have an uncountable infinity of sets. As far as the model’s concerned, it comprises the entire mathematical universe, even though “looking in from outside,” we can see that that’s not true. In particular, each model of ZFC thinks it has uncountably many sets, many themselves of uncountable cardinality, even if “from the outside” the model is countable.

Say what? The models are mistaken about something as basic as their own size, about how many sets they have? Yes. The models will be like The Matrix (the movie, not the mathematical object), or The Truman Show. They’re self-contained little universes whose inhabitants can never discover that they’re living a lie—that they’re missing sets that we, from the outside, know to exist. The poor denizens of the Matrix will never even be able to learn that their universe—what they mistakenly think of as the universe—is secretly countable! And no Morpheus will ever arrive to enlighten them, although—and this is crucial to Cohen’s proof in particular—the inhabitants will be able to reason more-or-less intelligibly about what would happen if a Morpheus did arrive.

The Löwenheim-Skolem Theorem, from the early 1920s, says that any countable list of first-order axioms that has any model at all (i.e., that’s consistent), must have a model with at most countably many elements. And ZFC is a countable list of first-order axioms, so Löwenheim-Skolem applies to it—even though ZFC implies the existence of an uncountable infinity of sets! Before taking the plunge, we’ll need to not merely grudgingly accept but love and internalize this “paradox,” because pretty much the entire proof of the independence of CH is built on top of it.

Incidentally, once we realize that it’s possible to build self-consistent yet “fake” mathematical universes, we can ask the question that, incredibly, the Matrix movies never ask. Namely, how do we know that our own, larger universe isn’t similarly a lie? The answer is that we don’t! As an example—I hope you’re sitting down for this—even though Cantor proved that there are uncountably many real numbers, that only means there are uncountably many reals for us. We can’t rule out the possibly that God, looking down on our universe, would see countably many reals.

Cantor’s Proof Revisited

To back up: the whole story of CH starts, of course, with Cantor’s epochal discovery of the different orders of infinity, that for example, there are more subsets of positive integers (or equivalently real numbers, or equivalently infinite binary sequences) than there are positive integers. The devout Cantor thought his discovery illuminated the nature of God; it’s never been entirely obvious to me that he was wrong.

Recall how Cantor’s proof works: we suppose by contradiction that we have an enumeration of all infinite binary sequences: for example,

s(0) = 00000000…
s(1) = 01010101…
s(2) = 11001010….
s(3) = 10000000….

We then produce a new infinite binary sequence that’s not on the list, by going down the diagonal and flipping each bit, which in the example above would produce 1011…

But look more carefully. What Cantor really shows is only that, within our mathematical universe, there can’t be an enumeration of all the reals of our universe. For if there were, we could use it to define a new real that was in the universe but not in the enumeration. The proof doesn’t rule out the possibility that God could enumerate the reals of our universe! It only shows that, if so, there would need to be additional, heavenly reals that were missing from even God’s enumeration (for example, the one produced by diagonalizing against that enumeration).

Which reals could possibly be “missing” from our universe? Every real you can name—42, π, √e, even uncomputable reals like Chaitin’s Ω—has to be there, right? Yes, and there’s the rub: every real you can name. Each name is a finite string of symbols, so whatever your naming system, you can only ever name countably many reals, leaving 100% of the reals nameless.

Or did you think of only the rationals or algebraic numbers as forming a countable dust of discrete points, with numbers like π and e filling in the solid “continuum” between them? If so, then I hope you’re sitting down for this: every real number you’ve ever heard of belongs to the countable dust! The entire concept of “the continuum” is only needed for reals that don’t have names and never will.

From ℵ0 Feet

Gödel and Cohen’s achievement was to show that, without creating any contradictions in set theory, we can adjust size of this elusive “continuum,” put more reals into it or fewer. How does one even start to begin to prove such a statement?

From a distance of ℵ0 feet, Gödel proves the consistency of CH by building minimalist mathematical universes: one where “the only sets that exist, are the ones required to exist by the ZFC axioms.” (These universes can, however, differ from each other in how “tall” they are: that is, in how many ordinals they have, and hence how many sets overall. More about that in a future post!) Gödel proves that, if the axioms of set theory are consistent—that is, if they describe any universes at all—then they also describe these minimalist universes. He then proves that, in any of these minimalist universes, from the standpoint of someone within that universe, there are exactly ℵ1 real numbers, and hence CH holds.

At an equally stratospheric level, Cohen proves the consistency of not(CH) by building … well, non-minimalist mathematical universes! A simple way is to start with Gödel’s minimalist universe—or rather, an even more minimalist universe than his, one that’s been cut down to have only countably many sets—and then to stick in a bunch of new real numbers that weren’t in that universe before. We choose the new real numbers to ensure two things: first, we still have a model of ZFC, and second, that we make CH false. The details of how to do that will, of course, concern us later.

My Biggest Confusion

In subsequent posts, I’ll say more about the character of the ZFC axioms and how one builds models of them to order. Just as a teaser, though, to conclude this post I’d like to clear up a fundamental misconception I had about this subject, from roughly the age of 16 until a couple months ago.

I thought: the way Gödel proves the consistency of CH, must be by examining all the sets in his minimalist universe, and checking that each one has either at most ℵ0 elements or else at least C of them. Likewise, the way Cohen proves the consistency of not(CH), must be by “forcing in” some extra sets, which have more than ℵ0 elements but fewer than C elements.

Except, it turns out that’s not how it works. Firstly, to prove CH in his universe, Gödel is not going to check each set to make sure it doesn’t have intermediate cardinality; instead, he’s simply going to count all the reals to make sure that there are only ℵ1 of them—where 1 is the next infinite cardinality after ℵ0. This will imply that C=ℵ1, which is another way to state CH.

More importantly, to build a universe where CH is false, Cohen is going to start with a universe where C=ℵ1, like Gödel’s universe, and then add in more reals: say, ℵ2 of them. The ℵ1 “original” reals will then supply our set of intermediate cardinality between the ℵ0 integers and the ℵ2 “new” reals.

Looking back, the core of my confusion was this. I had thought: I can visualize what ℵ0 means; that’s just the infinity of integers. I can also visualize what \( C=2^{\aleph_0} \) means; that’s the infinity of points on a line. Those, therefore, are the two bedrocks of clarity in this discussion. By contrast, I can’t visualize a set of intermediate cardinality between ℵ0 and C. The intermediate infinity, being weird and ghostlike, is the one that shouldn’t exist unless we deliberately “force” it to.

Turns out I had things backwards. For starters, I can’t visualize the uncountable infinity of real numbers. I might think I’m visualizing the real line—it’s solid, it’s black, it’s got little points everywhere—but how can I be sure that I’m not merely visualizing the ℵ0 rationals, or (say) the computable or definable reals, which include all the ones that arise in ordinary math?

The continuum C is not at all the bedrock of clarity that I’d thought it was. Unlike its junior partner ℵ0, the continuum is adjustable, changeable—and we will change it when we build different models of ZFC. What’s (relatively) more “fixed” in this game is something that I, like many non-experts, had always given short shrift to: Cantor’s sequence of Alephs ℵ0, ℵ1, ℵ2, etc.

Cantor, who was a very great man, didn’t merely discover that C>ℵ0; he also discovered that the infinite cardinalities form a well-ordered sequence, with no infinite descending chains. Thus, after ℵ0, there’s a next greater infinity that we call ℵ1; after ℵ1 comes ℵ2; after the entire infinite sequence ℵ0,ℵ1,ℵ2,ℵ3,… comes ℵω; after ℵω comes ℵω+1; and so on. These infinities will always be there in any universe of set theory, and always in the same order.

Our job, as engineers of the mathematical universe, will include pegging the continuum C to one of the Alephs. If we stick in a bare minimum of reals, we’ll get C=ℵ1, if we stick in more we can get C=ℵ2 or C=ℵ3, etc. We can’t make C equal to ℵ0—that’s Cantor’s Theorem—and we also can’t make C equal to ℵω, by an important theorem of König that we’ll discuss later (yes, this is an umlaut-heavy field). But it will turn out that we can make C equal to just about any other Aleph: in particular, to any infinity other than ℵ0 that’s not the supremum of a countable list of smaller infinities.

In some sense, this is the whole journey that we need to undertake in this subject: from seeing the cardinality of the continuum as a metaphysical mystery, which we might contemplate by staring really hard at a black line on white paper, to seeing the cardinality of the continuum as an engineering problem.

Stay tuned! Next installment coming after the civilizational Singularity in three days, assuming there’s still power and Internet and food and so forth.

Oh, and happy Halloween. Ghostly sets of intermediate cardinality … spoooooky!

My second podcast with Lex Fridman

Monday, October 12th, 2020

Here it is—enjoy! (I strongly recommend listening at 2x speed.)

We recorded it a month ago—outdoors (for obvious covid reasons), on a covered balcony in Austin, as it drizzled all around us. Topics included:

  • Whether the universe is a simulation
  • Eugene Goostman, GPT-3, the Turing Test, and consciousness
  • Why I disagree with Integrated Information Theory
  • Why I disagree with Penrose’s ideas about physics and the mind
  • Intro to complexity theory, including P, NP, PSPACE, BQP, and SZK
  • The US’s catastrophic failure on covid
  • The importance of the election
  • My objections to cancel culture
  • The role of love in my life (!)

Thanks so much to Lex for his characteristically probing questions, apologies as always for my verbal tics, and here’s our first podcast for those who missed that one.

My video interview with Lex Fridman at MIT about philosophy and quantum computing

Monday, February 17th, 2020

Here it is (about 90 minutes; I recommend the 1.5x speed)

I had buried this as an addendum to my previous post on the quantum supremacy lecture tour, but then decided that a steely-eyed assessment of what’s likely to have more or less interest for this blog’s readers probably militated in favor of a separate post.

Thanks so much to Lex for arranging the interview and for his questions!

“Quantum Computing and the Meaning of Life”

Wednesday, March 13th, 2019

Manolis Kellis is a computational biologist at MIT, known as one of the leaders in applying big data to genomics and gene regulatory networks. Throughout my 9 years at MIT, Manolis was one of my best friends there, even though our research styles and interests might seem distant. He and I were in the same PECASE class; see if you can spot us both in this photo (in the rows behind America’s last sentient president). My and Manolis’s families also became close after we both got married and had kids. We still keep in touch.

Today Manolis will be celebrating his 42nd birthday, with a symposium on the meaning of life (!). He asked his friends and colleagues to contribute talks and videos reflecting on that weighty topic.

Here’s a 15-minute video interview that Manolis and I recorded last night, where he asks me to pontificate about the implications of quantum mechanics for consciousness and free will and whether the universe is a computer simulation—and also about, uh, how to balance blogging with work and family.

Also, here’s a 2-minute birthday video that I made for Manolis before I really understood what he wanted. Unlike the first video, this one has no academic content, but it does involve me wearing a cowboy hat and swinging a makeshift “lasso.”

Happy birthday Manolis!