Shtetl-Optimized

Today—January 20, 2017—I have something cheerful, something that I’m celebrating.  It’s Lily’s fourth birthday. Happy birthday Lily!

As part of her birthday festivities, and despite her packed schedule, Lily has graciously agreed to field a few questions from readers of this blog.  You can ask about her parents, favorite toys, recent trip to Disney World, etc.  Just FYI: to the best of my knowledge, Lily doesn’t have any special insight about computational complexity, although she can write the letters ‘N’ and ‘P’ and find them on the keyboard.  Nor has she demonstrated much interest in politics, though she’s aware that many people are upset because a very bad man just became the president.  Anyway, if you ask questions that are appropriate for a real 4-year-old girl, rather than a blog humor construct, there’s a good chance I’ll let them through moderation and pass them on to her!

Meanwhile, here’s a photo I took of UT Austin students protesting Trump’s inauguration beneath the iconic UT tower.

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Tomorrow, I’ll have something big to announce here.  So, just to whet your appetites, and to get myself back into the habit of blogging, I figured I’d offer you an appetizer course: some more miscellaneous non-Trump-related news.

(1) My former student Leonid Grinberg points me to an astonishing art form, which I somehow hadn’t known about: namely, music videos generated by executable files that fit in only 4K of memory.  Some of these videos have to be seen to be believed.  (See also this one.)  Much like, let’s say, a small Turing machine whose behavior is independent of set theory, these videos represent exercises in applied (or, OK, recreational) Kolmogorov complexity: how far out do you need to go in the space of all computer programs before you find beauty and humor and adaptability and surprise?

Admittedly, Leonid explains to me that the rules allow these programs to call DirectX and Visual Studio libraries to handle things like the 3D rendering (with the libraries not counted toward the 4K program size).  This makes the programs’ existence merely extremely impressive, rather than a sign of alien superintelligence.

In some sense, all the programming enthusiasts over the decades who’ve burned their free time and processor cycles on Conway’s Game of Life and the Mandelbrot set and so forth were captivated by the same eerie beauty showcased by the videos: that of data compression, of the vast unfolding of a simple deterministic rule.  But I also feel like the videos add a bit extra: the 3D rendering, the music, the panning across natural or manmade-looking dreamscapes.  What we have here is a wonderful resource for either an acid trip or an undergrad computability and complexity course.

(2) A week ago Igor Oliveira, together with my longtime friend Rahul Santhanam, released a striking paper entitled Pseudodeterministic Constructions in Subexponential Time.  To understand what this paper does, let’s start with Terry Tao’s 2009 polymath challenge: namely, to find a fast, deterministic method that provably generates large prime numbers.  Tao’s challenge still stands today: one of the most basic, simplest-to-state unsolved problems in algorithms and number theory.

To be clear, we already have a fast deterministic method to decide whether a given number is prime: that was the 2002 breakthrough by Agrawal, Kayal, and Saxena.  We also have a fast probabilistic method to generate large primes: namely, just keep picking n-digit numbers at random, test each one, and stop when you find one that’s prime!  And those methods can be made deterministic assuming far-reaching conjectures in number theory, such as Cramer’s Conjecture (though note that even the Riemann Hypothesis wouldn’t lead to a polynomial-time algorithm, but “merely” a faster exponential-time one).

But, OK, what if you want a 5000-digit prime number, and you want it now: provably, deterministically, and fast?  That was Tao’s challenge.  The new paper by Oliveira and Santhanam doesn’t quite solve it, but it makes some exciting progress.  Specifically, it gives a deterministic algorithm to generate n-digit prime numbers, with merely the following four caveats:

• The algorithm isn’t polynomial time, but subexponential (2^{n^o(1)}) time.
• The algorithm isn’t deterministic, but pseudodeterministic (a concept introduced by Gat and Goldwasser).  That is, the algorithm uses randomness, but it almost always succeeds, and it outputs the same n-digit prime number in every case where it succeeds.
• The algorithm might not work for all input lengths n, but merely for infinitely many of them.
• Finally, the authors can’t quite say what the algorithm is—they merely prove that it exists!  If there’s a huge complexity collapse, such as ZPP=PSPACE, then the algorithm is one thing, while if not then the algorithm is something else.

Strikingly, Oliveira and Santhanam’s advance on the polymath problem is pure complexity theory: hitting sets and pseudorandom generators and win-win arguments and stuff like that.  Their paper uses absolutely nothing specific to the prime numbers, except the facts that (a) there are lots of them (the Prime Number Theorem), and (b) we can efficiently decide whether a given number is prime (the AKS algorithm).  It seems almost certain that one could do better by exploiting more about primes.

(3) I’m in Lyon, France right now, to give three quantum computing and complexity theory talks.  I arrived here today from London, where I gave another two lectures.  So far, the trip has been phenomenal, my hosts gracious, the audiences bristling with interesting questions.

But getting from London to Lyon also taught me an important life lesson that I wanted to share: never fly EasyJet.  Or at least, if you fly one of the European “discount” airlines, realize that you get what you pay for (I’m told that Ryanair is even worse).  These airlines have a fundamentally dishonest business model, based on selling impossibly cheap tickets, but then forcing passengers to check even tiny bags and charging exorbitant fees for it, counting on snagging enough travelers who just naïvely clicked “yes” to whatever would get them from point A to point B at a certain time, assuming that all airlines followed more-or-less similar rules.  Which might not be so bad—it’s only money—if the minuscule, overworked staff of these quasi-airlines didn’t also treat the passengers like beef cattle, barking orders and berating people for failing to obey rules that one could log hundreds of thousands of miles on normal airlines without ever once encountering.  Anyway, if the airlines won’t warn you, then Shtetl-Optimized will.

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(-3) Bonus Announcement of May 30: As a joint effort by Yuri Matiyasevich, Stefan O’Rear, and myself, and using the Not-Quite-Laconic language that Stefan adapted from Adam Yedidia’s Laconic, we now have a 744-state TM that halts iff there’s a counterexample to the Riemann Hypothesis.

(-2) Today’s Bonus Announcement: Stefan O’Rear says that his Turing machine to search for contradictions in ZFC is now down to 1919 states.  If verified, this is an important milestone: our upper bound on the number of Busy Beaver values that are knowable in standard mathematics is now less than the number of years since the birth of Christ (indeed, even since the generally-accepted dates for the writing of the Gospels).

Stefan also says that his Not-Quite-Laconic system has yielded a 1008-state Turing machine to search for counterexamples to the Riemann Hypothesis, improving on our 5372 states.

(-1) Another Bonus Announcement: Great news, everyone!  Using a modified version of Adam Yedidia’s Laconic language (which he calls NQL, for Not Quite Laconic), Stefan O’Rear has now constructed a 5349-state Turing machine that directly searches for contradictions in ZFC (or rather in Metamath, which is known to be equivalent to ZFC), and whose behavior is therefore unprovable in ZFC, assuming ZFC is consistent.  This, of course, improves on my and Adam’s state count by 2561 states—but it also fixes the technical issue with needing to assume a large cardinal axiom (SRP) in order to prove that the TM runs forever.  Stefan promises further state reductions in the near future.

In other news, Adam has now verified the 43-state Turing machine by Jared S that halts iff there’s a counterexample to Goldbach’s Conjecture.  The 27-state machine by code golf addict is still being verified.

(0) Bonus Announcement: I’ve had half a dozen “Ask Me Anything” sessions on this blog, but today I’m trying something different: a Q&A session on Quora.  The way it works is that you vote for your favorite questions; then on Tuesday, I’ll start with the top-voted questions and keep going down the list until I get tired.  Fire away!  (And thanks to Shreyes Seshasai at Quora for suggesting this.)

(1) When you announce a new result, the worst that can happen is that the result turns out to be wrong, trivial, or already known.  The best that can happen is that the result quickly becomes obsolete, as other people race to improve it.  With my and Adam Yedidia’s work on small Turing machines that elude set theory, we seem to be heading for that best case.  Stefan O’Rear wrote a not-quite-Laconic program that just searches directly for contradictions in a system equivalent to ZFC.  If we could get his program to compile, it would likely yield a Turing machine with somewhere around 6,000-7,000 states whose behavior was independent of ZFC, and would also fix the technical problem with my and Adam’s machine Z, where one needed to assume a large-cardinal axiom called SRP to prove that Z runs forever.  While it would require a redesign from the ground up, a 1,000-state machine whose behavior eludes ZFC also seems potentially within reach using Stefan’s ideas.  Meanwhile, our 4,888-state machine for Goldbach’s conjecture seems to have been completely blown out of the water: first, a commenter named Jared S says he’s directly built a 73-state machine for Goldbach (now down to 43 states); second, a commenter named “code golf addict” claims to have improved on that with a mere 31 states (now down to 27 states).  These machines are now publicly posted, but still await detailed verification.

(2) My good friend Jonah Sinick cofounded Signal Data Science, a data-science summer school that will be running for the second time this summer.  They operate on an extremely interesting model, which I’m guessing might spread more widely: tuition is free, but you pay 10% of your first year’s salary after finding a job in the tech sector.  He asked me to advertise them, so—here!

(3) I was sad to read the news that Uber and Lyft will be suspending all service in Austin, because the city passed an ordinance requiring their drivers to get fingerprint background checks, and imposing other regulations that Uber and Lyft argue are incompatible with their model of part-time drivers.  The companies, of course, are also trying to send a clear message to other cities about what will happen if they don’t get the regulatory environment they want.  To me, the truth of the matter is that Uber/Lyft are like the web, Google, or smartphones: clear, once-per-decade quality-of-life advances that you try once, and then no longer understand how you survived without.  So if Austin wants to maintain a reputation as a serious, modern city, it has no choice but to figure out some way to bring these companies back to the negotiating table.  On the other hand, I’d also say to Uber and Lyft that, even if they needed to raise fares to taxi levels to comply with the new regulations, I expect they’d still do a brisk business!

For me, the “value proposition” of Uber has almost nothing to do with the lower fares, even though they’re lower.  For me, it’s simply about being able to get from one place to another without needing to drive and park, and also without needing desperately to explain where you are, over and over, to a taxi dispatcher who sounds angry that you called and who doesn’t understand you because of a combination of language barriers and poor cellphone reception and your own inability to articulate your location.  And then wondering when and if your taxi will ever show up, because the dispatcher couldn’t promise a specific time, or hung up on you before you could ask them.  And then embarking on a second struggle, to explain to the driver where you’re going, or at least convince them to follow the Google Maps directions.  And then dealing with the fact that the driver has no change, you only have twenties and fifties, and their little machine that prints receipts is out of paper so you can’t submit your trip for reimbursement either.

So yes, I really hope Uber, Lyft, and the city of Austin manage to sort this out before Dana and I move there!  On the other hand, I should say that there’s another part of the new ordinance—namely, requiring Uber and Lyft cars to be labeled—that strikes me as an unalloyed good.  For if there’s one way in which Uber is less convenient than taxis, it’s that you can never figure out which car is your Uber, among all the cars stopping or slowing down near you that look vaguely like the one in the app.

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Update (4/19): Inspired by Trudeau’s performance (which they clocked at 35 seconds), Maclean’s magazine asked seven quantum computing researchers—me, Krysta Svore, Aephraim Steinberg, Barry Sanders, Davide Venturelli, Martin Laforest, and Murray Thom—to also explain quantum computing in 35 seconds or fewer.  You can see all the results here (here’s the audio from my entry).

The emails starting hitting me like … a hail of maple syrup from the icy north.  Had I seen the news?  Justin Trudeau, the dreamy young Prime Minister of Canada, visited the Perimeter Institute for Theoretical Physics in Waterloo, one of my favorite old haunts.  At a news conference at PI, as Trudeau stood in front of a math-filled blackboard, a reporter said to him: “I was going to ask you to explain quantum computing, but — when do you expect Canada’s ISIL mission to begin again, and are we not doing anything in the interim?”

Rather than answering immediately about ISIL, Trudeau took the opportunity to explain quantum computing:

“Okay, very simply, normal computers work, uh, by [laughter, applause] … no no no, don’t interrupt me.  When you walk out of here, you will know more … no, some of you will know far less about quantum computing, but most of you … normal computers work, either there’s power going through a wire, or not.  It’s 1, or a 0, they’re binary systems.  Uh, what quantum states allow for is much more complex information to be encoded into a single bit.  Regular computer bit is either a 1 or a 0, on or off.  A quantum state can be much more complex than that, because as we know [speeding up dramatically] things can be both particle and wave at the same times and the uncertainty around quantum states [laughter] allows us to encode more information into a much smaller computer.  So, that’s what exciting about quantum computing and that’s… [huge applause] don’t get me going on this or we’ll be here all day, trust me.”

What marks does Trudeau get for this?  On the one hand, the widespread praise for this reply surely says more about how low the usual standards for politicians are, and about Trudeau’s fine comic delivery, than about anything intrinsic to what he said.  Trudeau doesn’t really assert much here: basically, he just says that normal computers work using 1’s and 0’s, and that quantum computers are more complicated than that in some hard-to-explain way.  He gestures toward the uncertainty principle and wave/particle duality, but he doesn’t say anything about the aspects of QM most directly relevant to quantum computing—superposition or interference or the exponential size of Hilbert space—nor does he mention what quantum computers would or wouldn’t be used for.

On the other hand, I’d grade Trudeau’s explanation as substantially more accurate than what you’d get from a typical popular article.  For pay close attention to what the Prime Minister never says: he never says that a qubit would be “both 0 and 1 at the same time,” or any equivalent formulation.  (He does say that quantum states would let us “encode more information into a much smaller computer,” but while Holevo’s Theorem says that’s false for a common interpretation of “information,” it’s true for other reasonable interpretations.)  The humorous speeding up as he mentions particle/wave duality and the uncertainty principle clearly suggests that he knows it’s more subtle than just “0 and 1 at the same time,” and he also knows that he doesn’t really get it and that the journalists in the audience don’t either.  When I’m grading exams, I always give generous partial credit for honest admissions of ignorance.  B+.

Anyway, I’d be curious to know who at PI prepped Trudeau for this, and what they said.  Those with inside info, feel free to share in the comments (anonymously if you want!).

(One could also compare against Obama’s 2008 answer about bubblesort, which was just a mention of a keyword by comparison.)

Update: See also a Motherboard article where Romain Alléaume, Amr Helmy, Michele Mosca, and Aephraim Steinberg rate Trudeau’s answer, giving it 7/10, no score, 9/10, and 7/10 respectively.

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As everyone knows, this was a momentous week in the history of science.  And I don’t need to tell you why: the STOC and CCC accepted paper lists finally came out.

Haha, kidding!  I meant, we learned this week that gravitational waves were directly detected for the first time, a hundred years after Einstein first predicted them (he then reneged on the prediction, then reinstated it, then reneged again, then reinstated it a second time—see Daniel Kennefick’s article for some of the fascinating story).

By now, we all know some of the basic parameters here: a merger of two black holes, ~1.3 billion light-years away, weighing ~36 and ~29 solar masses respectively, which (when they merged) gave off 3 solar masses’ worth of energy in the form of gravitational waves—in those brief 0.2 seconds, radiating more watts of power than all the stars in the observable universe combined.  By the time the waves reached earth, they were only stretching and compressing space by 1 part in 4×10²¹—thus, changing the lengths of the 4-kilometer arms of LIGO by 10^-18 meters (1/1000 the diameter of a proton).  But this was detected, in possibly the highest-precision measurement ever made.

As I read the historic news, there’s one question that kept gnawing at me: how close would you need to have been to the merging black holes before you could, you know, feel the distortion of space?  I made a guess, assuming the strength of gravitational waves fell off with distance as 1/r².  Then I checked Wikipedia and learned that the strength falls off only as 1/r, which completely changes the situation, and implies that the answer to my question is: you’d need to be very close.  Even if you were only as far from the black-hole cataclysm as the earth is from the sun, I get that you’d be stretched and squished by a mere ~50 nanometers (this interview with Jennifer Ouellette and Amber Stuver says 165 nanometers, but as a theoretical computer scientist, I try not to sweat factors of 3).  Even if you were 3000 miles from the black holes—New-York/LA distance—I get that the gravitational waves would only stretch and squish you by around a millimeter.  Would you feel that?  Not sure.  At 300 miles, it would be maybe a centimeter—though presumably the linearized approximation is breaking down by that point.  (See also this Physics StackExchange answer, which reaches similar conclusions, though again off from mine by factors of 3 or 4.)  Now, the black holes themselves were orbiting about 200 miles from each other before they merged.  So, the distance at which you could safely feel their gravitational waves, isn’t too far from the distance at which they’d rip you to shreds and swallow you!

In summary, to stretch and squeeze spacetime by just a few hundred nanometers per meter, along the surface of a sphere whose radius equals our orbit around the sun, requires more watts of power than all the stars in the observable universe give off as starlight.  People often say that the message of general relativity is that matter bends spacetime “as if it were a mattress.”  But they should add that the reason it took so long for humans to notice this, is that it’s a really friggin’ firm mattress, one that you need to bounce up and down on unbelievably hard before it quivers, and would probably never want to sleep on.

As if I needed to say it, this post is an invitation for experts to correct whatever I got wrong.  Public humiliation, I’ve found, is a very fast and effective way to learn an unfamiliar field.

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In my previous post, I linked to seven Closer to Truth videos of me spouting about free will, Gödel’s Theorem, black holes, etc. etc.  I also mentioned that there was a segment of me talking about why the universe exists that for some reason they didn’t put up.  Commenter mjgeddes wrote, “Would have liked to hear your views on the existence of the universe question,” so I answered in another comment.

But then I thought about it some more, and it seemed inappropriate to me that my considered statement about why the universe exists should only be available as part of a comment thread on my blog.  At the very least, I thought, such a thing ought to be a top-level post.

So, without further ado:

My view is that, if we want to make mental peace with the “Why does the universe exist?” question, the key thing we need to do is forget about the universe for a while, and just focus on the meaning of the word “why.”  I.e., when we ask a why-question, what kind of answer are we looking for, what kind of answer would make us happy?

Notice, in particular, that there are hundreds of other why-questions, not nearly as prestigious as the universe one, yet that seem just as vertiginously unanswerable.  E.g., why is 5 a prime number?  Why does “cat” have 3 letters?

Now, the best account of “why”—and of explanation and causality—that I know about is the interventionist account, as developed for example in Judea Pearl’s work.  In that account, to ask “Why is X true?” is simply to ask: “What could we have changed in order to make X false?”  I.e., in the causal network of reality, what are the levers that turn X on or off?

This question can sometimes make sense even in pure math.  For example: “Why is this theorem true?” “It’s true only because we’re working over the complex numbers.  The analogous statement about real numbers is false.”  A perfectly good interventionist answer.

On the other hand, in the case of “Why is 5 prime?,” all the levers you could pull to make 5 composite involve significantly more advanced machinery than is needed to pose the question in the first place.  E.g., “5 is prime because we’re working over the ring of integers.  Over other rings, like Z[√5], it admits nontrivial factorizations.”  Not really an explanation that would satisfy a four-year-old (or me, for that matter).

And then we come to the question of why anything exists.  For an interventionist, this translates into: what causal lever could have been pulled in order to make nothing exist?  Well, whatever lever it was, presumably the lever itself was something—and so you see the problem right there.

Admittedly, suppose there were a giant red button, somewhere within the universe, that when pushed would cause the entire universe (including the button itself) to blink out of existence. In that case, we could say: the reason why the universe continues to exist is that no one has pushed the button yet. But even then, that still wouldn’t explain why the universe had existed.

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Non-Lily-Related Updates (Jan. 22)

Uri Bram posted a cute little article about whether he was justified, as a child, to tell his parents that he wouldn’t clean up his room because doing so would only increase the universe’s entropy and thereby hasten its demise. The article quotes me, Sean Carroll, and others about that important question.

On Wednesday I gave a TCS+ online seminar about “The Largest Possible Quantum Speedups.” If you’re interested, you can watch the YouTube video here.

(I promised a while ago that I’d upload some examples of Lily’s MOMA-worthy modern artworks.  So, here are two!)

A few quotable quotes:

Daddy, when you were little, you were a girl like me!

I’m feeling a bit juicy [thirsty for juice].

Saba and Safta live in Israel. They’re mommy’s friends! [Actually they’re mommy’s parents.]

Me: You’re getting bigger every day!
Lily: But I’m also getting smaller every day!

Me: Then Goldilocks tasted the third bowl, which was Baby Bear’s, and it was just right!  So she ate it all up.  Then Goldilocks went…
Lily: No, then Goldilocks ate some cherries in the kitchen before she went to the bedroom.  And blueberries.
Me: Fine, so she ate cherries and blueberries.  Then she went to the bedroom, and she saw that there were three beds…
Lily: No, four beds!
Me: Fine, four beds.  So she laid in the first bed, but she said, “this bed is too hard.”
Lily: No, it was too comfortable!
Me: Too comfortable?  Is she some kind of monk?

Me [pointing to a taxidermed black bear in a museum]: What’s that?
Lily: A bear!
Me: Is it Winnie the Pooh?
Lily: No, it’s a different kind of bear.
Me [pointing to a tan bear in the next case]: So what about that one? Is that Winnie?
Lily: Yes! That’s Winnie the Pooh!
[Looking at it more closely] No, it’s a different kind of Winnie.

Lily: Why is it dark outside?
Me: Because it’s night time.
Lily: Why is it night time?
Me: Because the sun went to the other side of the world.
Lily: It went to China!
Me: Yes! It did in fact go to China.
Lily: Why did the sun go to China?
Me: Well, more accurately, it only seemed to go there, because the world that we’re on is spinning.
Lily: Why is the world spinning?
Me: Because of the conservation of angular momentum.
Lily: Why is the … consibation of amomomo?
Me: I suppose because of Noether’s Theorem, and the fact that our laws of physics are symmetric under spatial rotations.
Lily: Why is…
Me: That’s enough for today Lily!

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Somewhat along the lines of my last post, the other day a reader sent me an amusing list of questions about privacy and fundamental physics.  The questions, and my answers, are below.

1. Does the universe provide us with a minimum level of information security?

I’m not sure what the question means. Yes, there are various types of information security that are rooted in the known laws of physics—some of them (like quantum key distribution) even relying on specific aspects of quantum physics—whose security one can argue for by appealing to the known properties of the physical world. Crucially, however, any information security protocol is only as good as the assumptions it rests on: for example, that the attacker can’t violate the attack model by, say, breaking into your house with an ax!

2. For example, is my information safe from entities outside the light-cone I project?

Yes, I think it’s safe to assume that your information is safe from any entities outside your future light-cone. Indeed, if information is not in your future light-cone, then almost by definition, you had no role in creating it, so in what sense should it be called “yours”?

3. Assume that there are distant alien cultures with infinite life spans – would they always be able to wait long enough for my light cone to spread to them, and then have a chance of detecting my “private” information?

First of all, the aliens would need to be in your future light-cone (see my answer to 2). In 1998, it was discovered that there’s a ‘dark energy’ pushing the galaxies apart at an exponentially-increasing rate. Assuming the dark energy remains there at its current density, galaxies that are far enough away from us (more than a few tens of billions of light-years) will always recede from us faster than the speed of light, meaning that they’ll remain outside our future light-cone, and signals from us can never reach them. So, at least you’re safe from those aliens!

For the aliens in your future light-cone, the question is subtler. Suppose you took the only piece of paper on which your secrets were written, and burned it to ash—nothing high-tech, just burned it. Then there’s no technology that we know today, or could even seriously envision, that would piece the secrets together. It would be like unscrambling an egg, or bringing back the dead from decomposing corpses, or undoing a quantum measurement. It would mean, effectively, reversing the Arrow of Time in the relevant part of the universe. This is formally allowed by the Second Law of Thermodynamics, since the decrease in entropy within that region could be balanced by an increase in entropy elsewhere, but it would require a staggering level of control over the region’s degrees of freedom.

On the other hand, it’s also true that the microscopic laws of physics are reversible: they never destroy information. And for that reason, as a matter of principle, we can’t rule out the possibility that some civilization of the very far future, whether human or alien, could piece together what was written on your paper even after you’d burned it to a crisp. Indeed, with such godlike knowledge and control, maybe they could even reconstruct the past states of your brain, and thereby piece together private thoughts that you’d never written anywhere!

4. Does living in a black hole provide privacy? Couldn’t they follow you into the hole?

No, I would not recommend jumping into a black hole as a way to ensure your privacy. For one thing, you won’t get to enjoy the privacy for long (a couple hours, maybe, for a supermassive black hole at the center of a galaxy?) before getting spaghettified on your way to the singularity. For another, as you correctly pointed out, other people could still snoop on you by jumping into the black hole themselves—although they’d have to want badly enough to learn your secrets that they wouldn’t mind dying themselves along with you, and also not being able to share whatever they learned with anyone outside the hole.

But a third problem is that even inside a black hole, your secrets might not be safe forever! Since the 1970s, it’s been thought that all information dropped into a black hole eventually comes out, in extremely-scrambled form, in the Hawking radiation that black holes produce as they slowly shrink and evaporate. What do I mean by “slowly”? Well, the evaporation would take about 10⁷⁰ years for a black hole the mass of the sun, or about 10¹⁰⁰ years for the black holes at the centers of galaxies. Furthermore, even after the black hole had evaporated, piecing together the infalling secrets from the Hawking radiation would probably make reconstructing what was on the burned paper from the smoke and ash seem trivial by comparison! But just like in the case of the burned paper, the information is still formally present (if current ideas about quantum gravity are correct), so one can’t rule out that it could be reconstructed by some civilization of the extremely remote future.

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As a diversion from the important topics of shaming, anti-shaming, and anti-anti-shaming, I thought I’d share a little email exchange (with my interlocutor’s kind permission), which gives a good example of what I find myself doing all day when I’m not blogging, changing diapers, or thinking about possibly doing some real work (but where did all the time go?).

Dear Professor Aaronson,

I would be very pleased to know your opinion about time.  In a letter of condolence to the Besso family, Albert Einstein wrote: “Now he has departed from this strange world a little ahead of me. That means nothing. People like us, who believe in physics, know that the distinction between past, present and future is only a stubbornly persistent illusion.” I’m a medical doctor and everyday I see time’s effect over human bodies. Is Einstein saying time is an illusion?  For who ‘believe in physics’ is death an illusion?  Don’t we lose our dears and will they continue to live in an ‘eternal world’?

Is time only human perceptive illusion (as some scientists say physics has proved)?

Dear [redacted],

I don’t read Einstein in that famous quote as saying that time itself is an illusion, but rather, that the sense of time flowing from past to present to future is an illusion. He meant, for example, that the differential equations of physics can just as easily be run backward (from future to past) as forward (from past to future), and that studying physics can strongly encourage a perspective—which philosophers call the “block universe” perspective—where you treat the entire history of spacetime as just a fixed, 4-dimensional manifold, with time simply another dimension in addition to the three spatial ones (admittedly, a dimension that the laws of physics treat somewhat differently than the other three). And yes, relativity encourages this perspective, by showing that different observers, moving at different speeds relative to each other, will divide up the 4-dimensional manifold into time slices in different ways, with two events judged to be simultaneous by one observer judged to be happening at different times by another.

But even after Einstein is read this way, I’d personally respond: well, that’s just one perspective you can take. A perfectly understandable one, if you’re Einstein, and especially if you’re Einstein trying to comfort the bereaved. But still: would you want to say, for example, that because physics treats the table in front of you as just a collection of elementary particles held together by forces, therefore the table, as such, doesn’t “exist”? That seems overwrought. Physics deepens your understanding of the table, of course—showing you what its microscopic constituents are and why they hold themselves together—but the table still “exists.”  In much the same way, physics enormously deepened our understanding of what we mean by the “flow of time”—showing how the “flow” emerges from the time-symmetric equations of physics, combined with the time-asymmetric phenomena of thermodynamics, which increase the universe’s entropy as we move away from the Big Bang, and thereby allow for the creation of memories, records, and other irreversible effects (a part of the story that I didn’t even get into here). But it feels overwrought to say that, because physics gives us a perspective from which we can see the “flow of time” as emerging from something deeper, therefore the “flow” doesn’t exist, or is just an illusion.

Hope that helps!

Best,
Scott

(followup question)

Dear Professor,

I’ve been thinking about the “block universe” and it seems to me that in it past, present and future all coexist.  So on the basis of Einstein’s theory, do all exist eternally, and why do we perceive only the present?

(reply)

But you don’t perceive only the present!  In the past, you perceived what’s now the past (and which you now remember), and in the future, you’ll perceive what’s now the future (and which you now look forward to), right?  And as for why the present is the present, and not some other point in time?  Well, that strikes me as one of those questions like why you’re you, out of all the possible people who you could have been instead, or why, assuming there are billions of habitable planets, you find yourself on earth and not on any of the other planets.  Maybe the best answer is that you had to be someone, living somewhere, at some particular point in time when you asked this question—and you could’ve wondered the same thing regardless of what the answer had turned out to be.

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Recently, longtime friend-of-the-blog Greg Kuperberg wrote a Facebook post that, with Greg’s kind permission, I’m sharing here.

A parable about pseudo-skepticism in response to climate science, and science in general.

Doctor: You ought to stop smoking, among other reasons because smoking causes lung cancer.
Patient: Are you sure? I like to smoke. It also creates jobs.
D: Yes, the science is settled.
P: All right, if the science is settled, can you tell me when I will get lung cancer if I continue to smoke?
D: No, of course not, it’s not that precise.
P: Okay, how many cigarettes can I safely smoke?
D: I can’t tell you that, although I wouldn’t recommend smoking at all.
P: Do you know that I will get lung cancer at all no matter how much I smoke?
D: No, it’s a statistical risk. But smoking also causes heart disease.
P: I certainly know smokers with heart disease, but I also know non-smokers with heart disease. Even if I do get heart disease, would you really know that it’s because I smoke?
D: No, not necessarily; it’s a statistical effect.
P: If it’s statistical, then you do know that correlation is not causation, right?
D: Yes, but you can also see the direct effect of smoking on lungs of smokers in autopsies.
P: Some of whom lived a long time, you already admitted.
D: Yes, but there is a lot of research to back this up.
P: Look, I’m not a research scientist, I’m interested in my case. You have an extended medical record for me with X-rays, CAT scans, blood tests, you name it. You can gather more data about me if you like. Yet you’re hedging everything you have to say.
D: Of course, there’s always more to learn about the human body. But it’s a settled recommendation that smoking is bad for you.
P: It sounds like the science is anything but settled. I’m not interested in hypothetical recommendations. Why don’t you get back to me when you actually know what you’re talking about. In the meantime, I will continue to smoke, because as I said, I enjoy it. And by the way, since you’re so concerned about my health, I believe in healthy skepticism.

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