Comments on: Raining cats and dogs …

By: Mac Thomason

Mac Thomason — Wed, 27 Oct 2004 17:08:51 +0000

That’s pretty unattractive. However, implying that John Edwards is the moral equivalent of David Duke, as Landsberg did yesterday, is utterly loathsome.

By: Backword Dave

Backword Dave — Tue, 26 Oct 2004 10:50:55 +0000

I agree with dsquared (but then I’m guilty of the mobile phone parody, so that shouldn’t surprise anyone). As Walt summed up Steve’s contribution:

2) Steven is right that given the peculiar restrictions imposed by resorting to quantum entanglement, it’s interesting to study these sorts of games in their own right.

I’ll take issue with the subordinate clause. Why is it interesting? And what does study mean here? If we were doing physics, we’d be working toward an experimental hypothesis. I don’t see one at the end of this. All we have is a model which shows off how well informed a few egg-heads who read this site and Marginal Revolution are. Bringing in game theory may be a pedagogic tool for undergraduates, but it looks like a cul-de-sac to me. And BTW, you may all be wrong on the FTL side of things too. There’s an explanation here (scroll down to “physics professor”). The FTL part isn’t necessary for the original set-up, but Glenn seems to be taking it as read, and I don’t think that he should. Lurch only has to move at c, like, for example, a mobile phone signal.

By: dsquared

dsquared — Mon, 25 Oct 2004 23:54:54 +0000

It is easy to prove that no particles obeying the laws of classical physics could ever give you that combination of correlations. Just to keep this absolutely clear, this is not true without a bunch-load of other restrictions. Lurch is made entirely out of particles obeying the laws of classical physics and he could give you that combination of correlations if he wanted to. The objection, Steven, is to publishing these things as if they were new economics, rather than interesting curiosa using old economics to do new quantum theory.

By: Steven E. Landsburg

Steven E. Landsburg — Mon, 25 Oct 2004 23:29:06 +0000

zak: i dont understand your last comment. we are not given the answers. nobody disputes the (mild) interest of games like the dog/cat game as exercises in understanding, even though nobody actually ever plays them. i put forward a different game: the dog/cat game with access to entangled particles, and i pointed out that you get a different (and perhaps unexpected) set of optimal strategies. what’s the objection to doing that?

By: Zak Catem

Zak Catem — Mon, 25 Oct 2004 23:15:08 +0000

But it doesn’t, Steven. If we are given the answers along with the questions, the game is pointless. The only strategy is to answer as told. If by strategy you meant the way the particles are used, then that has nothing to do with game theory, and you’ve filed it under the wrong heading.

By: Steven E. Landsburg

Steven E. Landsburg — Mon, 25 Oct 2004 23:10:07 +0000

zak: if the particles start in the state 0>1> + 1>0> (or more precisely, the state represented by that vector), and if the first party holds his measuring apparatus either vertical or at angle pi/4, while the other holds his measuring apparatus at angle either pi/8 or -pi/8, then they win a) 85% of the cat/cat trials, b) 85% of the cat/dog trials, c) 85% of the dot/cat trials and d) 85% of the dog/dog trials. This is easy to verify if you’re comfortable with the yoga of quantum mechanics, and, of course, completely unverifiable if you’re not. It is easy to prove that no particles obeying the laws of classical physics could ever give you that combination of correlations.

By: Steven E. Landsburg

Steven E. Landsburg — Mon, 25 Oct 2004 23:03:21 +0000

Zak: The point is that there are (speculative for sure, but not outrageously so) reasons to think that in the not too distant future, we might be communicating via channels that would make it easy for players to coordinate their actions in this particular way, as opposed to some other way. So it might be interesting to think about how the game turns out in those circumstances. Let me point out that there is nothing intrinsically interesting about the dog/cat game itself. There is no plausible scenario, classical or quantum, in which anybody will play this game. But we still think it’s an interesting to work out optimal strategies in such games. The quantum version of the dog/cat game is no more likely to ever be played than the classical version. But it’s still interesting to work out the results, just as in the classical case, because it might give us some insight into strategic behavior in more complicated situations that might (or might not) be likelier to arise in the future than they are right now.

By: Zak Catem

Zak Catem — Mon, 25 Oct 2004 22:59:42 +0000

Also, what happens in your quantum method when one party gets cat and one gets dog? What is the result of comparing a filtered measurement with an unfiltered one?

By: Zak Catem

Zak Catem — Mon, 25 Oct 2004 22:52:49 +0000

Stephen: You’re quite correct, I apologise. It’s a side-point, though, as my main contention was that the results of particle observations do allow the participants to infer information about what the other party is doing, which I believe I’ve shown. I notice that you also haven’t addressed my final question, and I think it’s a good one. What’s the point of a game where you give the players all the information they need to win everytime? What can we possibly learn from this example?

By: dsquared

dsquared — Mon, 25 Oct 2004 19:58:57 +0000

note of course, that although no information is transferred, the state of one particle is a correlation (by which I mean a proper correlation; you would expect that almost surely, in an arbitrarily long series of measurements, the pairwise results would not be the same as they would for two independent particles) between the measurement performed on one qubit and the measurement performed on the other. If this were not the case, then we would never have been able to verify the phenomenon experimentally.

By: Steven E. Landsburg

Steven E. Landsburg — Mon, 25 Oct 2004 19:43:50 +0000

It is possible to have two quantum-coins in separate locations that have different properties depending on if only one coin is flipped or if both coins are flipped. Wrong. No property of either coin is changed by flipping the other. This coordination is achieved faster than light so it is not considered “communication” Wrong. The reason it is not considered communication is because no information is transmitted. The only relevance of the faster-than-light stuff is that it proves no information is transmitted. If the same coordination had been achieved by radio waves, it would be considered “communication”. Wrong. No information is transferred whether you use radio waves or not. Certainly not a whole new world. Well, of course not. I haven't seen anyone in this long thread try to insinuate otherwise.

By: Mark Duty

Mark Duty — Mon, 25 Oct 2004 19:35:35 +0000

My understanding of this dispute: It is possible to have two quantum-coins in separate locations that have different properties depending on if only one coin is flipped or if both coins are flipped. This coordination is achieved faster than light so it is not considered “communication” If the same coordination had been achieved by radio waves, it would be considered “communication”. So as long as the rules say no “communication” you can beat the game by using this faster-than-light coordination. If the rules say [no “communication” AND no faster-than-light coordination] then we are back to the original game, with these quantum-coins outlawed just like walkie-talkies. The entire impact of quantum-coins on game theory is that non-communication games have to outlaw quantum-coins as well as slower than light communication. It seems that D-squared is right as far as this is a pretty small impact. Certainly not a whole new world.

By: dsquared

dsquared — Mon, 25 Oct 2004 17:48:44 +0000

Just when I thought this had died down, it flares up again … When I left for work this morning, we had agreed that I would never learn anything about John’s answers, or about the questions he was asked (in either case), and that therefore no “information” in any important sense was passing from room to room. We had, however, also established that over time I would learn about the correlation between John’s answers and the questions he was asked. I could learn about this through my possession of a qubit which I and John were both measuring (because our measurements would be correlated in a known manner), or I could learn about it through the descriptions given by Lurch under the communication protocol I had described. Because I learn (and fail to learn) exactly the same things in both cases, I established that a quantum game could be analysed as a classical game with cheap, noisy talk. Or in other words the physical properties of qubits do not introduce new issues to the game considered as a mathematical entity which cannot already modelled. I established this using the argument detailed above; that in cases where classical probability and quantum probability can both be calculated, they agree, and that for games with a definite payoff matrix, classical probabilities can always be calculated. I don’t think anyone has argued against this, so it has not been established that I am “just wrong”. In fact, AFAICS, I’m not. For the physicists present, I’d note that one indicator that, in the game theoretic sense, the qubit channel is equivalent to cheap-talk communication is that it can be used to give me misinformation. For example, say that JQ takes against me and decides to cause trouble. Instead of making the measurements we agreed upon on his qubit, he measures a different observable. I am now certainly going to learn something worth knowing; as my losses build up, I will come to realise that John is no longer my friend. And I come to learn this without ever getting any information about what happened in the other room.

By: Glenn Bridgman

Glenn Bridgman — Mon, 25 Oct 2004 16:44:33 +0000

Reimer, I guess the question then is whether the game forbids the gain of information or communication. I maintain that those are not bijective concepts. Joshua said it better than I ever could. I really wish I had the physics/information theory toolkit to discuss this properly.

By: Joshua W. Burton

Joshua W. Burton — Mon, 25 Oct 2004 16:16:32 +0000

I do not believe this. I don’t believe any number of classically correlated bits will allow them to beat the game more than 75% of the time. In particular, your “pawns if it’s cats, knights if it’s dogs” strategy quite clearly doesn’t work. Ah, I see. You’ve set up the rules of the game cleverly, so that “winning” means a match in the dogs/dogs case only. I lost track of the original problem, in all the smoke. Yes, in this game the prior arrangement of a singlet qubit state can beat any classical prior arrangement, still without any communication. This comes about because of the way the two negative bits of correlation (“pawns” and “knights”, or x- and z-spin) are related by a continuous rotation in the quantum singlet case. D can look at “pnights” and “kawns” while J looks at chessmen, and (by the ingeniously contrived win/loss criterion of this game) that’s checkmate. Daniel is just wrong. Thanks for clarifying.