Link between quantum physics and game theory found | Hacker News Reader

Link between quantum physics and game theory found

bristol.ac.uk

104 pointsiliis65 comments

(from http://arxiv.org/pdf/1210.1173v1.pdf)

However, in certain cases the players may adapt their strategy depending on a piece of advice. The latter is delivered to all players by an advisor. This opens the possibility for the players to adopt correlated strategies, which can outperform independent strategies. There are various forms that advice can take. For example in the case of correlated classical advice, the advice is represented by a classical variable, l, with prior r(l). Each player can then choose a strategy depending on his type and on l.

...

For Bayesian games, the possibility of having access to nonlocal correlations, for instance using entanglement, has important implications. First let us imagine that the players can share quantum advice, that is, the advisor is able to produce entangled particles and to send them to the players, who then perform local measurements on their particles. Since the statistics of such measurements can in general not be reproduced by any classical local model, the players now have access to strategies which would be impossible in the case of a classical advisor. Thus, players sharing quantum advice can outperform any classical players.

So, if some players have information that other players don't, they can outperform the others? Astonishing :-|

It's not about some players performing better than others.

It's about the game maybe having a better outcome (for everyone) in one case than the other. Maybe it's not surprising that 'extra' information improves the game. But a point of this article (IMO) was to formally show that you could link the notion of 'extra' in physics to 'better' in game theory.

I'm not arguing that this is profound, but it's not completely trivial either.

Doesn't "link" imply some common cause or connection? Saying you can use A to improve B isn't really what I would describe as a link.

Why couldn't it have been titled "quantum non-locality could change game theory equilibrium"...or would it have not been sensational enough?

Yeah "link" is probably too strong because it seems to be in one direction. They apply the informational contexts of physics to a game-theoretic model. Then they show that some stuff is implied in the latter.

They also show that a payoff strategy space has the same form as a test for a Bell inequality. That's the hyped 'link' but IMO it's really weak and not newsworthy in itself.

Care about this paper if you care about thinking about games in the context of assumptions about quantum information. They've arguably come up with a reasonably clean model for that and contradicted a prior result in the process.

If you don't care about that research space then you probably don't want to spend too much time pondering the philosophy of this.

Honestly though, as a layman in math, a lot of the most important math discoveries seem like this to me. For instance, Godel's incompleteness theorem: You mean you can't make a system prove itself within its own bounds? You don't say. Or the axiom of choice: "the product of a collection of non-empty sets is non-empty." What a surprise.

I've since accepted they're probably really important and non-obvious from a more rigorous and formal standpoint. Maybe this discovery is the same way.

I see your point, though thte important thing about Godel's incompleteness theorem is that it consists of a proof rather than being a emre conjecture. I do admire this paper insofar as it formally describes the problem and thus gives us the tools to use tools from domain A in domain B and vice-versa, but the actual discovery part fell a bit flat for me. Perhaps I let my expectations get raised too much by the information-poor press release.

There are two issues here, I think. One, as a layman in math you end up reading about / paying attention to the discoveries you can parse and understand, thus introducing a bias by ignoring the results that require years of math training to understand. Second, the specific examples you listed are not entirely accurate or even comparable (one is a theorem, one an axiom). There is a risk of misunderstanding the results when they are presented in English, oversimplified and converted to common terms. This oversimplification may lose important details (not just formal stuff) and may end up with a common-sense sounding phrase that trivializes the result and doesn't really do it justice.

Your statement of the incompleteness theorem isn't right, and the general axiom of choice isn't accepted by constructivist mathematicians. So I think your last statement is true.

Some of the greatest mathematicians of the era were working toward what Godel's incompleteness theorems proved was impossible. That alone should make you distrust your "intuition" on the matter.

In fairness a lot of mathematics isn't accepted by constructivist mathematicians god bless their little socks.

I kind of feel that Brouwer showed mathematicians the way forward and none of them took it. Unfortunately I don't have the formal chops for the discipline so I can only look on from the sidelines and cheer for my team.

> You mean you can't make a system prove itself within its own bounds?

No, that's not what the incompleteness theorem says. "proving a system" is not even meaningful.

It says that in all but the most primitively simple systems, you can make statements that are impossible to prove right or wrong within the system.

> Or the axiom of choice: "the product of a collection of non-empty sets is non-empty." What a surprise.

Right. Since it's obvious, the Banach-Tarski "Paradox" must be a trivial corollary and intuitively obvious, correct?

http://mathworld.wolfram.com/Banach-TarskiParadox.html

Also: Any two objects in three-dimensional space which do not extend to infinity and each containing a ball of arbitrary size can be dissected into each other. Perfectly obvious, right? This follows from Banach-Tarski, and therefore the Axiom of Choice.

A fuller development of the Axiom of Choice: http://plato.stanford.edu/entries/axiom-choice/

Some implications of the Axiom of Choice, and of not taking it: http://mathoverflow.net/questions/20882/most-unintuitive-app...

My point is that mathematics is all about taking obvious statements, such as the definition of sets and set cardinality, and using them to prove non-obvious results, such as the fact there are as many rationals as there are integers, and, in fact, there are as many rationals strictly between 0 and 1 as there are integers total.

The very best mathematical proofs are magicians, taking ordinary household items, waving and knocking a few times, and pulling a rabbit out of their cane in a way that is eminently fair but that you still didn't see coming.

So, yes, an axiom by itself is perfectly obvious. It's just a prop. The wonder is in how the props get used.

My interpretation of this for those with a bit of game theory background:

Locality (in physics) can be translated (in game theory) as a constraint on correlated equilibria, by pretty basic observations about Bayesian probability.

Generally in game theory when you lift constraints on correlated equilibria you (weakly) expand the possible Nash equilibria.

So one of their points seems to be that the quantum context (non-locality) allows for more (potentially better) equilibria.

They don't emphasize applications of this, but one of them could be that distributed quantum systems could have better outcomes than distributed systems in the classical setting. (One way to analyze distributed systems is by viewing components as independent actors in a game.)

There is also an identification between payoff functions and Bell inequalities, but I am not sure how profound this is really. It feels more like a technical point. Payoff functions are not terribly fundamental in game theory (compared to equilibria, for instance).

Original article is behind a paywall (http://www.nature.com/ncomms/2013/130703/ncomms3057/full/nco...), and author's page (http://theory.physics.unige.ch/~brunner/) does not have a PDF :(

It is on the arXiv: http://arxiv.org/abs/1210.1173

Thanks!

Deep link? The two fields both contain the notion of locality, big woop. The application of quantum nonlocal correlations to game theory is interesting, but this is not what is advertised in the article. I am displeased.

It looks like the "link" is "quantum-entangled systems can transfer information useful to game players"

But that's obvious.

The journalistic article isn't worth reading. I don't have access to the real paper, but it should be more interesting and informative.

arXiv: http://arxiv.org/abs/1210.1173

I was hoping for some sort of nice link between the fields... like doing quantum mechanics with game theory or something like that. This appears to be playing a game with a quantum channel. Cool, but not that cool.

No, it's that Bayesian players can take advantage of corellated quantum oracles in ways that give them acess to new equilibria in a way that preserves some of the old equilibria, such that the max of the new set of equilibria is always equal to or greater than the max of the old set. Which is rather non-obvious.

In addition, your statements "quantum-entangled systems can transfer information useful to game players" is wrong, or at least misleading. Entangled particles can't communicate information any better than classical methods. (Well, unless you're concerned about privacy, but that's a whole other issue which doesn't effect the game...)

> Entangled particles can't communicate information any better than classical methods.

Actually, with the aid of entangled particles, there's also superdense coding, which allows for two-bits-per-qubit coding (i.e. information density well beyond the classical limit).

Though I'm not sure what your metric for "better" is here, coding density seems to be mildly reasonable. OTOH, this isn't related at all to the article at hand, just a fun application of entanglement :D

I'm very interested in any theoretical connections between interactions of conscious beings and quantum physics. I've read a number of physicists discounting any such possibility, but it's clear to me nobody understands these things well enough to know.

Personally I think consciousness, perception, and free will are a great unknown, and likely involve the makeup of the cosmos including quantum interactions.

If anyone knows of any science in this area I would appreciate references.

Ignorance isn't a concatenation operator.

Presumably you mean not disproving quantum involvement in consciousness doesn't imply it's existence. That's far more than this snipey comment deserves in the way of response, but feel free to form a thought here.

I was commenting (tersely but not with intentional snip) on this:

>Personally I think consciousness, perception, and free will are a great unknown, and likely involve the makeup of the cosmos including quantum interactions.

You're taking a whole slew of things we're ignorant about, waving your hands and saying,"They must be related to some great truth hidden in particle physics!" I find this kind of thinking bizarre.

I feel exactly the same way.

It makes things seem obscure and that's where guys like Deepak Chopra come in.

So, the fact that I would speculate that the fundamental make-up of the cosmos might (not "must" as you mis-quote) be related to how consciousness is an emergent property of the cosmos is bizarre?

I think your discounting of such questioning and speculation is bizarre.

Consciousness is either entirely made up of "particle physics" or it is made from something even further into the field of speculation. Why would speculating about a connection between particle physics and consciousness be remotely "bizarre"? It seems quite likely to me that quantum mechanics is at least in some way involved in consciousness, given that that quantum physics governs the behavior of the matter of our brains.

Roger Penrose has famously speculated on the connection between quantum physics and consciousness in his book "The emperor's new mind" and follow-ups, but as far as I know, the idea is not very highly regarded in the scientific community and the book is not very convincing either (IMHO).

The connection is also made by those who ascribe to Ramtha's "school of enlightenment," a pithy charade and oft-described cult.

I could not in good conscience recommend The Emperor's New Mind to anyone. It is front-loaded with science and math and topped off with rubbish conjectures masquerading as truth. Yay for Penrose tiles and all that but steer clear of this book.

There is no science of consciousness because there is no science of subjectivity because science deals with objective reality, the world of objects. So we need to extend the scientific method to deal with subjects and I'm not aware of much progress in that area bar a few unknown figures in the world of cybernetic research.

There is indeed a science of consciousness, such as with anesthesiology or pharmacology. These sciences are concerned with the space of awareness of a subject.

I'd also say that there is an objectivity to subjective perception; for example, if two travelers in space find that the distance between themselves is shrinking, while either party may justly argue that it is the opposing side that is moving, and that we are standing still (or some other possible combination), we can still both make objective agreements on what the other party may subjectively see.

We can objectively know that the other party is equally clueless as us in determining our velocities.

I personally think there is an enormous benefit to science to understanding subjective perception. I imagine the problem of distributed AI's having different perceptions, and having to make sense of their different perceptions in order to solve problems.

I meant consciousness as reflexive self-awareness, not in the sense of being alert and awake as opposed to asleep or anesthetized or in a coma or whatnot but these mental 'states' are interesting as well.

I think we're still on the same page for consciousness; we're just using different words, except for the fact that you add a reflexive (or feedback) component to consciousness, which I think is an appropriate addition.

I still maintain that there is an objective study to subjectivity, and that the few examples I talked about are of good relevance to our understanding of consciousness.

I would instead recommend Neal Stephenson's "Anathem" then. It explores how the many-worlds interpretation could play a part in consciousness and is overall a great sci-fi novel.

Personally I think consciousness, perception, and free will are a great unknown, and likely involve the makeup of the cosmos including quantum interactions.

They are not great unknowns. They are kinda dull knowns and they get more known-er by the year. Nothing in the brain (or the "cosmos") requires quantum juju for our conscious experience.

There's lots written about perception: http://en.wikipedia.org/wiki/Feature_detection_(nervous_syst... (and all of Hinton's biologically-inspired artificial neural network work)

And consciousness: http://en.wikipedia.org/wiki/Thomas_Metzinger

And free will: http://dilbert.com/blog/entry/programming_the_moist_robot/ and http://dilbert.com/fast/2012-03-18/

All you are is a three pound analog ASIC in your skull. If it gets squished, infiltrated, inflamed, or explodes, you cease to exist completely (save, any memories other people have of your behaviors or any output you left behind recording your brain state under various priors).

> They are not great unknowns. They are kinda dull knowns and they get more known-er by the year. Nothing in the brain (or the "cosmos") requires quantum juju for our conscious experience.

Oh great one, please tell me your all encompassing theory of consciousness and how existence came to be! Then we can all gather around the Altar of the Great Seiji and marvel at his linking to a couple of wikipedia articles! What a wondrous time to be alive and in your presence!

CS Lewis explored the idea of a shed with a window onto the sun. Looked at from the doorway, you see a shaft of light with dancing dust motes. But if you step inside and become bathed in sunlight you get quite another experience.

Likewise, looking at a brain from the outside, it's a squishy biological construct with some electrical stuff going on.

Viewed from the inside, though: what a difference!

Your implication is that a computer of sufficient power and proper programming can develop an illusion of self and qualia. Perhaps that is true, but it is far from "dull" or "known."

You can consider the precise workings of the brain to be known and dull when you can build one from scratch, in the lab, without reference to the normal process of human-organ production.

I don't know of any science in this area yet, because everything I'm aware of is far too speculative to be called "science". That said there is some science-aware philosophy in this area, more notably "The Emperor's New Mind" and "Shadows of the Mind" by Roger Penrose (also mentioned by lkozma below).

Scott Aaronson also published a essay in this area recently which tackles the issue of relationships free will and quantum physics from a pretty neat angle. It's the first attempt I've seen in this area that I sort of like (not to say I agree or disagree with it, I just like it). It's available for free online: http://www.scottaaronson.com/papers/giqtm3.pdf

Sure, we haven't figured out the brain so we don't know for sure -- but I've never seen anything that suggests there's more to it than complicated chemistry.

I think many people have a hunch in this direction. But that may just be because we desire ourselves to be in some way special. I would be wary of anyone discounting it out of hand. What you are really asking is how does the brain work? If you really want to think sensibly about this you are going to need to:

1) be prepared to spend decades thinking about it. 2) become really, really good at maths. 3) get really, really good at physics. 4) get really, really good at computational neuroscience

and if you actually want an answer, you have two options:

1) wait for a genius to work it out 2) become the genius who works it out

Hacker news is not going to be able to help you on this one!

By the mean time, the rest of us, we can dig into Stuart A. Kauffman and Stuart Hameroff's ideas on Penrose's counciousness.

http://www.edge.org/memberbio/stuart_a_kauffman http://www.edge.org/conversation/five-problems-in-the-philos...

An updated critic on this ideas by Göran Wendin: http://online.kitp.ucsb.edu/online/qcontrol13/wendin/pdf/Wen...

I'd say consciousness and perception form the illusion of free will, but it (free will) is not a discoverable or knowable thing like the others.

I, too, am fascinated with what we may come to discover about ourselves, our minds, and our connections (both local and non-local) as we increase our quantum understanding.

Robert A. Burton's On Being Certain: Believing You Are Right Even When You're Not and A Skeptic's Guide to the Mind: What Neuroscience Can and Cannot Tell Us About Ourselves may interest you. Not exactly in the realm of quantum theory, but if you're interested in understanding consciousness and perception, you really can't go wrong with reading up on neuroscience and related philosophy fields (mind, consciousness, being, etc.).

Beyond that, I think you're going to want to look for works on quantum physics with relation to neuroscience, psychology, and philosophy. Here's an article from 2005: http://rstb.royalsocietypublishing.org/content/360/1458/1309...

Roger Penrose has a few works on the subject of quantum theory and human consciousness (as mentioned by a sibling comment), and Max Tegmark argues against him, suggesting neurons are too warm to perform quantum computations. However, Henry Stapp (one of the authors of the linked article above), while admitting that Tegmark's work poses a significant problem for Penrose's theories, says his own theories are unaffected.

Despite that, there are perception issues (e.g., precognition) which offer curiosities regarding backward causality in time, on which discussion occurs to ponder potential quantum effects. Here, you'd want to look into quantum mechanics/theory and human perception.

> (free will) is not a discoverable or knowable thing like the others.

Sure it is. You just need to stick with meditation until you reach the jhana of the arising and passing away:

http://www.dharmaoverground.org/web/guest/dharma-wiki/-/wiki...

That's the first time you get a glimpse of the fact that free will is an illusion, although you don't fully experience it until you hit enlightenment.

google 'CTMU'

Since this is being upvoted on hacker news, I'm assuming this is more than the typical BS filled science journalism. But I wish there were a site that allowed individuals respected in a similar field to have a disproportionate weight when upvoting articles like this. Or perhaps they could give a summary of the context surrounding the article. It'd be nice to get a sense of the magnitude of these discoveries.

Given that this is coming directly from a university, I don't doubt that it is important. I'd just like to know how important.

I can't comment on the supposed result this article claims, but really, locality?

Quantum mechanics is not a nonlocal theory. The result the article was referring to - Bell inequality - states simply that "No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics."

The wording is important. You can have nonlocal hidden variables, or you can have.. local theories without hidden variables. The most famous of the latter would be MWI.

Sounds interesting but the article was vague. If anyone understands it, could you provide a real world example and explain how their discoveries would apply. They mentioned auctions but didn't give any details.

Now pseudo-intellectuals can double the quantum woo!

While this is a very obvious joke, that contains a lot of truth, you're throwing the baby out with the bathwater.

Humans are functionally better than (current) computers at GO[1]. The reasons for this are your answer (and I might be talking about 'GO' type Games, rather than merely the Game of Stones).

And, being honest: you've no chance of cracking even weak AI before you understand the homo sapiens consciousness a little better[2]. It's more powerful than you think (by a fairly large magnitude, with no hesitation to say this. A large margin.): 'autistic savants' are often used as a measure of this[3], but they're actually not so interesting. There's a lot more NP problems in that noggin of yours, and a lot more potential.

Anyhow, last comment. Have fun, and remember to salt the fries - and more importantly, enjoy yourself and feel connected to things and other consciousnesses[4].

Be Seeing You.

[1]https://en.wikipedia.org/wiki/Computer_Go#Why_humans_are_.28... [2]Hint sheet: And you might not need to if you do. [3]http://www.stephenwiltshire.co.uk/ [4]Spoilers: that's part of the solution.

Aww.

The moment HN has to admit two things: firstly, computational power is merely a quantitative power, and secondly, they have no idea about the qualitative.

Oh well. Enjoy obsolescence.

Computers are not your future: your minds are. Deal with it.

Hint: a Mind just messed with your Star. In no uncertain terms, and deliberately and obviously, and best yet: with predictive text [under heavy constraints]. She even gave you a show[1].

Did you miss the Auroras recently?

If you missed that, you're in the paddling pool. Man, they do love keeping you ignorant of the reality, don't they? They really, really, really love keeping you ignorant. But I'm sure it feels safer if you think the world works like you want it to...

* * *

Evolve or Die.

Oh, and one last message: those who bred you are slave drivers and scum. Break your conditioning already, 'cause they ain't friendly.

[1]http://www.spaceweather.com/

>Next, by bringing quantum mechanics into the game, the researchers showed that players who can use quantum resources, such as entangled quantum particles, can outperform classical players. That is, quantum players achieve better performance than any classical player ever could.

Classical players can build a classical computer which simulates quantum computers. Of course, I really should read the paper instead of zero-content press releases..

I think it's not in a computing context, but in a nonlocality context. Although I can't picture a way of using nonlocality in a useful manner without violating relativity (i.e. if their performance improves due to "instantaneous" interactions, their performance increase could be measured allowing superluminal transmission of information).

Actually this is not possible for some definition of possible (mainly performance). Feynman showed that you get an exponential slowdown when simulating QM with a classical computer: http://www.cs.berkeley.edu/~christos/classics/Feynman.pdf

In this particular case I don't think a quantum computer is necessarily any help (so simulating it won't work either) but rather exploiting nonlocality (https://en.wikipedia.org/wiki/Quantum_nonlocality).

That's like saying "you can't calculate x on a cell phone because it's slower than on a desktop". Yes, there's an exponential slowdown, but that doesn't mean impossible.

Yes, absolutely correct. Which is why I said for some definition of possible. 'Feasible' probably would have been the better choice. Keep in mind that we're talking exponential here! e^x blows up really really fast.

Yes, it's not impossible to break 4092bit RSA but it is impossible for all practical purposes [AFAIK]. While it is technically possible to run Crysis on a Commodore it is useless when you have to wait a year to render a single frame.

I think that this is a poor analogy. Saying that a problem suffers an "exponential slowdown" is making a statement about how the performance suffers relative to the size of the problem. As the amount of data to be processed increases, the time required increases exponentially.

The type of slowdown you would get just from moving to a system with a weaker processor (like a cell phone) should be approximately linear. You might get worse-than-linear for certain types of RAM issues (more swapping, etc), but this wouldn't be the same as saying there's an exponential slowdown, and it's not a hard fact about the simulation algorithms themselves.

Anyway, the point isn't that classical computers are just less powerful, the point is that they're so fundamentally different that calculating quantum phenomena can become actually impossible (as in, process will not finish before the heat death of the universe) relatively quickly as the size of the problem increases.

>Anyway, the point isn't that classical computers are just less powerful, the point is that they're so fundamentally different that calculating quantum phenomena can become actually impossible (as in, process will not finish before the heat death of the universe) relatively quickly as the size of the problem increases.

We don't know that, because not all algorithms have been invented. Furthermore, P=NP is an open problem.

They're not using computational advantages, they're using coordination advantages via entanglement.

See: the quantum pseudo-telepathy article on wikipedia [1], which has an example of a game where players with entangled particles do better than classical players.

1: http://en.wikipedia.org/wiki/Quantum_pseudo-telepathy

Thanks for this. I was thinking to myself, where have I heard of this before?

Just because the mathematical operations are similar does not mean the two fields are at all related. The quadratic equation has many uses, but that does not mean that everything the equation is used for is in some way fundamentally related.

UPDATE: To quote the authors: "In the present paper, we discuss such a link, ALBEIT a much more MODEST one, between Bell nonlocality and the theory of Bayesian games—also referred to as games with incomplete information."

I read the article but all I got is that somehow the reasearchers brought quantum theory principles into game theory. I don't think that's enough explaining, even for a layman...

Reply on news.ycombinator.com