Wanna bet?
A commenter on my previous post writes:
What all these scientists who are crying about the teaching of evolution should do is propose bets to creationists based on the outcomes of experiments … You think that these D-wave guys won’t be able to do something they’re claiming to be able to do? It might be a good exercise to make that statement precise … If someone has a conjecture of the form “There should exist a theory that explains X”, people roll their eyes, essentially because there’s no way of deciding the implicit bet.
Alright, imagine the following conversation:
Layperson: I just heard on the radio about this new Yood d’Shnood Theory of the Universe. What do you think the odds are that it’ll turn out to be true?
Scientist: Well, so far I haven’t seen any good evidence that…
Layperson: Sure, but what’s your prediction?
Scientist: As I said, the evidence seems to be explained a lot more easily by…
Layperson: But what if you had to bet?
Scientist: Well, there are two ways to think about this. What the Yood d’Shnood proponents argue is that…
Layperson: No, don’t give me a dissertation, just give me a number!
Here’s the thing: when my PhD diploma arrived in the mail, it didn’t imbue me with some sort of supernatural power to predict the outcomes of future quantum computing experiments, unmediated by the evidence and arguments of the temporal world. (This despite the fact that my diploma was signed by a time-travelling cyborg, in his official capacity as Governor of California and Regent of the UC system.)
Of course, the reason scientists worry about evidence is that ultimately, we want our theories to cohere with reality and our predictions to come out right. The experience of the last four centuries suggests this hope is far from futile. The trouble is that, once you’ve decided to adopt the evidence-centric strategy that’s worked so well in the past, you have to forget temporarily about betting odds. For the mindset of the scientist toying with rival explanations, and that of the Bayesian handicapping horses in a race, are (at least in my experience) simply too incompatible to inhabit the same brain at the same time.
If you’ll forgive the metaphor, asking for gambling odds on every scientific question is like asking a woman to sleep with you on the first date. Of course it’s in the back of your mind (and possibly not only yours), but it tends to be counterproductive even to bring it up. If you’re ever going to reach the summit, then you have to act like all that really matters to you is the climb, and the only reliable way to act like it is to remake yourself into the sort of person for whom it’s true. Such is the paradox of science and of life.
So, did D-Wave succeed in using the quantum adiabatic algorithm to solve Sudoku puzzles in fewer steps than those same puzzles would be solved with classical simulated annealing? I don’t know. To repeat, I don’t know. What I know is that I haven’t seen the evidence, and that the burden of providing such evidence rests with the people making the claim.
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Comment #1 June 3rd, 2007 at 7:22 pm
Oh my God! I can’t believe you got your diploma signed by Arnie!!! 🙂
Comment #2 June 3rd, 2007 at 7:37 pm
For the mindset of the scientist toying with rival explanations, and that of the Bayesian handicapping horses in a race, are (at least in my experience) simply too incompatible to cohabit the same brain at the same time.
Excellent point Scott. And since to sustain life one cannot completely wait for the ultimate outcome of scientists/theorists I guess we have engineers/practitionists.
Comment #3 June 3rd, 2007 at 8:19 pm
Trying to arrange a bet with Creationists might help reveal that there are no experiments that can make them change their minds.
Comment #4 June 3rd, 2007 at 9:18 pm
the paragraph with the metaphor is excellent (though it might just be my brain interpretting everything as profound for the moment). in either case it inspires the same fear of weakminded-ness in me as Feynman, Russell and Hicks, almost (but not quite) to the point where i suspect i might be better off not reading your writing as to develop my own opinions.
Comment #5 June 3rd, 2007 at 10:01 pm
If you’ll forgive the metaphor, asking for gambling odds on every scientific question is like asking a woman to sleep with you on the first date. Of course it’s in the back of your mind (and possibly not only yours), but it tends to be counterproductive even to bring it up.
This conjecture was proven false by Feynman.
Comment #6 June 3rd, 2007 at 10:07 pm
Well, he certainly claimed to disprove it, but we all know how trustworthy physicist-proofs are.
Comment #7 June 3rd, 2007 at 10:24 pm
Both Feynman and his Art mentor Jiryar Zorthian told me, in 1968, the same story.
Feynman noticed that whenever he visted the Zorthian ranch, in the foothills of the San Gabriel Mountains above Pasadena, that there were beautiful naked women posing as models for Zorthian’s paintings.
“How do you get all those women to take their clothes off?” asked Feynman.
“Have you ever thought of asking them?” answered Zorthian.
Feynman was soon learning, from Zorthian, how to draw and paint. He learned quite well, as some of the examples in the memorial issue of Physics Today illustrate.
This is, as I observed, both a Physicist proof and a painter/sculptor proof.
Ricard Feynman and Jiryar Zorthian are both buried in Mountain View Cemetery, Altadena, California. The view, from underground, is sadly theoretical. But the site is peaceful and scenic. At Zorthian’s private funeral, I threw earth into the grave, onto the casket, and thought to say something that Feynman might have said. I said, seriously, but with a Feynmanesque smile:
“Atoms to atoms, quarks to quarks.”
Comment #8 June 3rd, 2007 at 10:30 pm
I think finding one counterexample is not that hard (especially if you are Feynman and those are the 60’s).
Moreover, I think that that’s what makes people so mad (or sceptical) when they read those Feynman quotes, is exactly the “climbing for the climbing’s sake” attitude all scientists are supposed to have.
When you hear a scientist claiming to be proud of just reaching the top of the tree in some non science field (sex, money, golf), it’s like hearing a Rabbi boasting about his ability to get a good bargin on a Honda.
In our minds, real Rabbi’s won’t bargin…
Comment #9 June 3rd, 2007 at 10:57 pm
I do not think that Feynman was boasting. My family knew him for two generations. He was a very honest man, for all his apparent gamesmanship. He was himself very skeptical of anyone putting on airs, or claiming exclusive privileges. He disdained organizations which, to him, existed for people who sat around complementing themselves on how smart they were, and planning whom to exclude from membership.
Feynman insisted that there are no ultimate experts. That if you really love a subject, and work hard enough, you can learn as much as anyone, and be your own expert. There are no bargains there, except with yourself. Nature does not bargain. You cannot, as he said in his Minority Report to the Challenger Commission, fool Nature.
But she does sometimes give up her secrets to those who, with creativity, honesty, initiative, persistence, and luck seek for truth and beauty.
Comment #10 June 4th, 2007 at 12:50 am
Sudoku’s all very well, but I want to see D-Wave solve arbitrary Rubik’s cube configurations in less than twenty moves.
Comment #11 June 4th, 2007 at 2:29 am
Ah, but he disproved it with a counter example! There is no arguing with that.
Comment #12 June 4th, 2007 at 3:22 am
All the problems here originate with the silly idea that scientists should be making predictions. But that’s not their job – their job is to create knowledge.
Predictions, unbased theories and personal beliefs are nice, and somewhat more credible when they originate from a person who is both intelligent and well endowed in the relevant field (such as scientists) – but the laymen get these confused with the truths that scientists work on which are well based.
Comment #13 June 4th, 2007 at 4:58 am
> This despite the fact that my diploma was signed by a time-travelling cyborg, in his official capacity as Governor of California and Regent of the UC system
I suggest that i) you sell your diploma on eBay to cash in on Arnie’s signature and ii) you use the proceeds to come up with some sort of bet with D-wave.
Comment #14 June 4th, 2007 at 5:21 am
Oh shit, you wrote a whole post about this? I’ll read it in the morning, but I’m sure it’s very good (and of course funny).
Comment #15 June 4th, 2007 at 7:11 am
Well, he certainly claimed to disprove it, but we all know how trustworthy physicist-proofs are.
This was exactly what I meant when I asked you in the last post about using “complexity” based theorems and “quantum” based theorems for limitation theorems. But I understand you rely on physicists’ assumptions not physicists’ proofs.
Comment #16 June 4th, 2007 at 7:31 am
Nagesh, I really hope you mean physicists inferences from experimental data, not their assumptions!
Comment #17 June 4th, 2007 at 7:41 am
Perhaps the following information will help in deciding how
to place your bets on the D-wave issue.
D-wave implements a Hamiltonian on 16 qubits on a 4 x 4 lattice. The Hamiltonian couples nearest neighbor qubits on the lattice. At the end of the quantum adiabatic computation the Hamiltonian is that of 16 classical spins on a 4 x 4 lattice and the goal is to have those spins sit in the ground-state of this classical Hamiltonian. The reason that this is interesting is that finding the ground-state and the ground-state energy for such a problem on a 2D lattice is known to be NP-complete.
OK, so since we believe that quantum nor classical computers can solve NP-complete problems exactly, the quantum algorithm that D-wave implements must solve this ground-state problem approximately.
Now there are 2 types of approximation algorithms;
ones in which we have a guarantee on how good our approximation is (how far from the optimum) and
all other approaches which we call heuristics. Right now D-wave’s approach fits in the heuristic category since they have no knowledge on how good their approximation is.
But it is clear that an efficient approximation algorithm with guarantees is much more desirable than any heuristic approach.
So here is the deal: there is in fact an approximation algorithm (a so-called PTAS) for the problem of finding the ground-state energy of spins on a 2D lattice. The approximation algorithm is linear in n, the number of spins and scales like 2^{c/epsilon} for relative error epsilon and some constant c, which is pretty good for a PTAS. This algorithm and the D-wave connection is described in our recent posting http://arxiv.org/abs/0705.1115
So we asked how can a quantum computer improve on this purely classical approximation algorithm? Can we even get a sqrt-speedup on the best classical approach? Our conclusion in our paper is that (unfortunately) it is even hard to get a quantum sqrt-speedup on the best classical approximation algorithm for this problem.
Comment #18 June 4th, 2007 at 8:07 am
Joe, I really hope physicists’ assumptions are based on the inferences from their thorough experimental evidence.
Comment #19 June 4th, 2007 at 9:08 am
Thanks for the pointer, Barbara!
Comment #20 June 4th, 2007 at 9:13 am
Ah, but he disproved it with a counter example! There is no arguing with that.
Joe, since when is a statement that begins “it tends to be” disproved by a single counterexample?
(All the time and effort I put in to phrase things carefully so commenters won’t be able to jump on them, and then they just ignore my careful phrasing and jump on them anyway…)
Comment #21 June 4th, 2007 at 10:28 am
I think a counterexample would be someone for whom it doesn’t “tend to be” that way with a sufficiently large pecentage of all women.
Or perhaps a very big group of women who find this kind of aproach appealing so as to question the “tendency”.
It seems Feynman provided the first, but perhaps it’s not such an impressive result.
Everybody knows a Nobel prize in physics is the true key to the ladies hearts.
Comment #22 June 4th, 2007 at 10:55 am
Hi Barbara!
Thank you very much for the pre-print reference!
At the end of the quantum adiabatic computation the Hamiltonian is that of 16 classical spins
I’ve got two naive questions about quantum adiabatic computation:
* What if H_{final} has non-diagonal entries and the ground-state is a superposition?
* What if H_{final} is diagonal but the energy minimum is degenerated? Does the quantum adiabatic protocol drive the initial ground state into a quantum state which is a superposition of two corresponding basis states?
Comment #23 June 4th, 2007 at 10:57 am
Ok, Scott, you got me. I commented without carefully reading the claim. I know that its an unforgivable offense.
Comment #24 June 4th, 2007 at 10:58 am
In my defense I was slightly riled up by your anti-physicist stance.
Comment #25 June 4th, 2007 at 11:12 am
Nextquant:
If the final Hamiltonian is not classical, the final state will indeed typically be a superposition of classical states and we can measure the qubits to project them on one of these classical states.
If the final Hamiltonian is classical but has a degenerate ground-space and one starts the adiabatic computation (without noise) in a pure state than the final state will be some pure state in this ground-space.
Barbara
Comment #26 June 4th, 2007 at 12:58 pm
How does a layperson distinguish between Scott’s betting on theory X $500 while betting $2000 on theory Y anyway? In order to make sense of his bet we need to lay the original problem aside and study Scott instead. I guess this is where we assume a spherical Scott with uniform density…
Comment #27 June 4th, 2007 at 3:19 pm
Ah, but Scott knows that physicists doesn’t mint proofs, they show the way or discuss the tao.
Which gets us back to the problems with using a spherical Scott in the proof factory. And Feynman perhaps showing that nothing is impossible for a physicist.
Comment #28 June 4th, 2007 at 3:31 pm
I guess this is where we assume a spherical Scott
Koray, that assumption is quickly becoming truer than you think. (Now excuse me while I go for some more Ben & Jerry’s…)
Comment #29 June 4th, 2007 at 3:35 pm
Excellent joke:) I love your sense of humor:))
Comment #30 June 4th, 2007 at 3:39 pm
I suppose an animosity towards physicists is natural, since I suspect to get an analytic result, we’d need to consider a spherical Scott in a vacuum, and that can’t be too comfortable.
Comment #31 June 4th, 2007 at 3:40 pm
In our minds, real Rabbi’s won’t bargin…
Anonymus: Actually, I think it’s one of the graduation requirements at rabbinical school…
(To preempt the obvious joke)
Comment #32 June 4th, 2007 at 3:42 pm
And that’s not even mentioning all the demands for experimental verification.
Comment #33 June 4th, 2007 at 3:44 pm
Thanks, Nagesh! But could you try laying off the unqualified praise for a few months? My ego might burst.
Comment #34 June 4th, 2007 at 3:55 pm
:)) Sure I will and if you need to me lay it off further you can check out my health posts!
Comment #35 June 4th, 2007 at 3:55 pm
err:need me to
Comment #36 June 4th, 2007 at 8:11 pm
OTOH the ideal Scott would be observed without gravity, which in comparison seems easy to fulfill.
Comment #37 June 4th, 2007 at 10:56 pm
OK, Scott, I wouldn’t disagree with anything in your post (except that I would never ask you to bet on something as imprecise as a theory). Of course science moves slow etc. I was just hoping I could prod you into making your skepticism into something more precise. Maybe something like Feynman’s challenge to build a motor smaller than some particular size. You probably said before what you said above about really having no idea about precise statements that could be made about D-wave’s work, but I just didn’t believe you really meant it in such an extreme form.
Actually, one quibble is that you put yourself in the debate with D-wave (I think — if they called you out, please correct me), yet in your imaginary dialog above, the poor scientist was minding his own business when he got cornered in the frozen-food section by the aggressive layman. Maybe your setting should have been a listener calling in to a radio show on which the scientist has been expressing skepticism about theory X, and the listener says, “You’ve been expressing lots of skepticism about X. How skeptical are you? 2-to-1? 100-to-1? 10000-to-1?”
Wow. I sound really critical. Actually, if paired against an equally ignorant mathematician, I would most likely bet on you over D-wave. If we could think of a precise wager.
Comment #38 June 4th, 2007 at 11:32 pm
James, regarding the question of “who started it”: I still remember hoping the story would blow over if I just ignored it for a week! Then journalists started calling me for quotes, and people starting asking about it in unrelated comment threads, and the ability of quantum computers to solve NP-complete problems by trying every solution in parallel started being an international news item. In such a context, wouldn’t silence itself be a statement?
Comment #39 June 5th, 2007 at 12:12 am
Hi Barbara!
Thanks for the reply! 🙂
Comment #40 June 5th, 2007 at 5:56 am
Consider an n-spherical Scott in a false vacuum, for n approaching infinity. In the game of QC-hyper versus Scott, each has a strategy that can be described as a simplex. What is the complexity of finding a Nash equilibrium; and how many Nash equilibria are there, asymptotically in n? What is the density of the set of strategies which are dynamically chaotic? Will Scott be able to win a greater fraction of games if he has an actual QC and QC-hyper does not? If both Scott and GC-hyper have genuine QCs and are entangled, what new Nash equilibria are there, and what fraction are quaternionic? And will the mainstream Press be able to identify the winner of the game with probability 1/2 + epsilon?
Comment #41 June 5th, 2007 at 6:37 am
Ah, well there is empirical evidence for this. Observations show that more often than not the mainstream press get the answer wrong. Obviously this could be adapted into a winning strategy by simply negating whichever answer is most prevalent in the press.
Comment #42 June 5th, 2007 at 12:05 pm
I’d say it is fine to not have an opinion on a subject, in which case it would be fine to have no odds to offer. What would be harder to defend would be to express opinions on a subject, opinions that can be reasonably interpreted by observers as offering a judgment that goes beyond summarizing the available evidence, and then not being willing to bet on it. You have clearly expressed some judgments on D-wave that go beyond summarizing the evidence, and so on those topics you should be more willing to offer or accept bets.
Comment #43 June 6th, 2007 at 2:13 pm
The comment I’m about to make isn’t terribly relevant, and I maybe should be making it in the thread where this post originally appeared… but:
This is one thing that gets me about these evolution debates. Most of the arguing I hear is about what ideological spin to put on the same evidence. What all these scientists who are crying about the teaching of evolution should do is propose bets to creationists based on the outcomes of experiments, or since probably no creationist would accept such a bet, make it known that they would enjoy accepting bets from them. If there is such an experiment (I’m no expert) and the creationists accept the bet, then you win.
I think it’s worth taking the time to note that if you follow the creationism wars closely for awhile, it will become immediately obvious that this could never work. The reason why is that it actually turns out that Creationists love bets. Creationists actually already propose bets all the time. And they never, ever, ever follow through on them.
In the most obvious case, this covers big flashy publicity-stunt bets that by design could never be collected on. For example take Kent Hovind’s $25,000 challenge, a monumental bounty that was claimed upfront to be a challenge to anyone who could prove “evolution”, but in the fine print required that any applicant satisfy a laundry list of arbitrary and maybe impossible conditions, incidentally including requiring any applicant to empirically prove that God does not exist and the Big Bang occurred without any extrauniversal causative agent (worded in a way that I think would present real problems for advocates of colliding brane models).
I assume James wouldn’t include Hovind’s challenge as an example of the kind of thing he was talking about, though, since he seems to be more talking about predicting the outcome of a simple factual matter or experiment where the bet and the result can be readily agreed upon by both sides. Alas, we see these kinds of bets being embraced by the creationists too. And it never really works out.
The serial offender here is a Mr. William Dembski (research theologian at the Southern Baptist Theological Seminary in Louisville, Kentucky), who I’ve seen over the last few years propose enough simple bets on his blog, then quietly delete or just forget about those bets later on when they don’t go the way he’d planned, that I’ve lost count. The most recent example of this happened just a couple days ago; the most famous is probably the one he issued a few years before the Dover, Pennslyvania “Intelligent Design” trial was first filed, in which he said
To my knowledge no such bottle of scotch has ever been produced.
When it comes down to it none of this should be surprising. The idea of making a bet implicitly depends on the idea of the betters being able to agree after the fact that the bet occurred and such and such an outcome was reached, or otherwise on the existence of some kind of impartial judge existing who can decide who won the bet. The entire thing that distinguishes creationists from the rest of us, meanwhile, is that they reject the authority of the thing that normally we’d expect to be the impartial judge in a scientific experiment– the scientific method and its conclusions. So why, having made a bet, would any creationist ever admit to having lost it? Since they’ve already made the decision to make their own reality in the case of the entire scope of how we interpret Biology, it’s not much of a big step to decide to make their own reality over the outcome of a small agreed-upon bet…
Comment #44 June 6th, 2007 at 9:56 pm
Coin, a usual procedure for bets between polite but not entirely trusting parties is to deposit bets with a third party who is charged with judging who wins.
Comment #45 June 7th, 2007 at 11:30 am
Robin, that could work, but here’s the thing. What conceivable third party exists which could be simultaneously trusted by both creationists and science advocates?