Anthropology and a fundamental problem of computer science ( P vs NP problem )

I had found that some unsolved fundamental problems of mathematics and computer science can have anthropological or field solution.P vs NP problem is usually considered as abstract problem of the most formal mathematical science. Nevertheless, such sort of problem can really exist in " trivial " reality of human economics, correspondingly, the field anthropologist may find a new understanding of that problem in the terms of some "Anthro-Platonism" in general.I called my attempt as "computational anthropology" or "complexity anthropology " ( please, see my arguments in arXive's article ),and I suppose that there exists "invisible" beautiful garden of NP problems , associated with computational limits of human mind and anthropological strategies to overcome it.

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Whoa, man. Hold up a second. Where is your evidence that any of your readers here have the faintest clue what a P vs NP problem is? Please explain P and NP in terms that give us non-mathematicians a clue about what you are talking about.
Thank You for asking.Definition of NP problem was introduced by Moscow mathematician Levin in 1973 ( Kolmogorov, Yablonskii in 1960s as well ) and St Cook (USA ) in order to define a class of step -by-step problems having hard computer solutions in a given time and for memory space ( so-called "Perebor" standard problems ). It is well-known,huge literature and fantastic variety of solutions are developed now (Wiki ) It is not easy to define NP -problems in general if you believe that P=NP always, but in some cases, NP - problem can be reduced to SAT( logical simplification) problem. In my arXiv article ( computer science arXiv 0904.3074 v1- please see text ) I used namely such reduction. Market as whole is computational complexity, produced some unsolved difficulties like financial crisis etc.etc.In non-mathematical terms,by "perebor" ( by computer, or its logical analogy- Turing machine ) you simply cannot find winning combination for real market in real time,because astronomical number of combinations are existing in reality.Some people believe that some traders can solve such problems and there is Universal Solution for all unsolved problems of the class of NP ("perebor"-like ). Mathematically, P = NP can produce dramatic collapse of all bank system and traditional Western mathematical culture (please, see, Notes 1 and Notes 2 of the article ).I suppose it is real problem of anthropology of cognitive limits of human mind.
Hi Michael,

I've read your article, which I supplemented with Wikipedia entries on P = NP, polynomial time and Non-deterministic Turing machines. I'm working my way through the mathematical aspects, but I'm still wondering what you've discovered and/or how it relates to cognitive anthropology, including existing applications of game theory in anthropology (or anthropology to game theory/quantum game theory). What anthropological perspectives did you apply to your study and why did you feel that this made a qualitative difference to your quantitative method?
The gist of this, as I undestand it, has to do with problems that are easier to solve than to give a mathematical expression. This is certainly a good area for anthropology. There is a very interesting anthropological application of catastrophe theory in a book by Michael Thompson called 'Rubbish Theory'; this has always been a favourite of mine. In it Thompson looks at why certain objects are highly valued as antiques while others 'catastrophically' lose their value and become 'rubbish'. The answers require various kinds of models plus ethnographic description of people knocking through walls in their houses to make them more fashionable. Worth a look perhaps.
Francine Barone, Thank You for exactness,
1.Some games are older than human consciousness and classical game theory developed by Neumann and Morgenstern have some limits. Quantum game theory ( Meyer, Eisert et al) had found new and more exact approximation to game reality.Experimentalists and our "native" are playing some unconscious games against Nature and Society in which the observer tries to maximaze the information obtained from the system under considretaion. It is more complex world than classical formalisms by Neumann. Analogies of quantum pseudo-telepathy games introduce some sort of new cooperativity between players ( similar with famous "participation ") and change Nash -equilibrium. Generally speaking, quantum - like games are competetive games where the player /players compete against themselvs, teams and "nature" ( in some cases of real games in ecology,economics and cosmology ). I suppose that in future it is natural to await real cooperation between anthropologists, game mathematicians, computer scientists and physical LABORATORIES to define exact meaning of our taking games seriously. I made some attempts in this direction - it is not impossible ( paper "Anderson's quantum game " for Newton's Math Inst,Cambridge,Dec 2008 was surprisingly accepted ).
2. In history of our anthropology, mathematical taste is not something new. Structuralist anthropologists attempted to use some elements of abstract group theory in semantic games of mythology. Unfortunately, it was very modest applications of such sort of perfectly developed mathematics ( applied now from nuclear physics to cosmology ). Shirokogoroff in his Tungus ethnography developed very futuristic mathematics of self-organization of ethnic groups( based on psycho-mental complex). Unfortunately, soviet anthropologists ( Yulian Bromley in USSR Ac Sciences ) forgot about this mathmatics, and, new developed ethnicity theory became less effective and elegant.
Huon, I agree, Thome's Catastrophe theory (CT) can provide not only pure qualitative insight, but also some kind of geometric imagination and intuitive description, expressed by Thompson. Today,CT is a part of more general KAM ( Kolmogorov-Arnold-Moser) theory of chaos, however, Thom's initial biologism and intuitive geometry cannot be forgotten. Even G.Soros in his attempt to use chaos theory to predict "superbubbles" in global economics cannot avoid Thom's-like intuitions, probably, because Soros's "intuitive reflexivity" is NP-incomplete problem...

Huon Wardle said:
The gist of this, as I undestand it, has to do with problems that are easier to solve than to give a mathematical expression. This is certainly a good area for anthropology. There is a very interesting anthropological application of catastrophe theory in a book by Michael Thompson called 'Rubbish Theory'; this has always been a favourite of mine. In it Thompson looks at why certain objects are highly valued as antiques while others 'catastrophically' lose their value and become 'rubbish'. The answers require various kinds of models plus ethnographic description of people knocking through walls in their houses to make them more fashionable. Worth a look perhaps.
Michael, I am glad this is of some relevance - there is certainly a big gap between the imagination of anthropology and the mathematical elegance you are also seeking - personally I find Levi-Strauss earlier conjectures on kinship relatively convincing but his later myth work wildly tendentious. I have to admit also I am drawn to the geometric when it comes to this kind of thing - as are economists when they don't know what they are talking about; hence they draw big teleologically framed loops showing when a depressive 'cycle' is predicted to end (see the discussion on 'consumer confidence' in the economic anthropology group). What concerned me about your paper was that it consisted of two hypothetical actors whose wider beliefs remain unexplored as does anything to do with the wider conditions of their choices. How resilient are your models to the kinds of 'complex' (in a true sense of the word) phenomena empirically minded anthropologists might be interested in? I hope that the meeting between mathematics and anthropology is possible, but it would involve a very thoughtful examination of the language we use and our notions of what counts as relevant.

Michael Alexeevich Popov said:
Huon, I agree, Thome's Catastrophe theory (CT) can provide not only pure qualitative insight, but also some kind of geometric imagination and intuitive description, expressed by Thompson. Today,CT is a part of more general KAM ( Kolmogorov-Arnold-Moser) theory of chaos, however, Thom's initial biologism and intuitive geometry cannot be forgotten. Even G.Soros in his attempt to use chaos theory to predict "superbubbles" in global economics cannot avoid Thom's-like intuitions, probably, because Soros's "intuitive reflexivity" is NP-incomplete problem...
Huon Wardle said:
The gist of this, as I undestand it, has to do with problems that are easier to solve than to give a mathematical expression. This is certainly a good area for anthropology. There is a very interesting anthropological application of catastrophe theory in a book by Michael Thompson called 'Rubbish Theory'; this has always been a favourite of mine. In it Thompson looks at why certain objects are highly valued as antiques while others 'catastrophically' lose their value and become 'rubbish'. The answers require various kinds of models plus ethnographic description of people knocking through walls in their houses to make them more fashionable. Worth a look perhaps.
Huon, thank you. My main idea is not theoretical, but experimental anthropological ( non-lab ) attempt to solve a serious mathematical problem.After 2 years of adaptation, I had found that quantum-like game (Oxford PvNP game ) is most suitable for field experiment. As is well-known, the best strategy that exists ( in classical games,including used by american anthropologists games ) cannot be succeed with probability 1 - Ln2 = 0.31...( no matter how many players are involved ).In my experiment (2004-2008) quantum -lile player " Alice " ( it is traditional name in quantum games ) can succeed with probability 1 !. It is fact. Thus, I had found mathematics in the field, but not in theory. And my experiment suggests,at least, that the best way to find contact with math - to do field anthropology. Mathematics is more than language ( it is only analytical tradition in Anglo-Americal philisophy of mathematics ). I am sure that this sort of style is reproducible. Moreover, I hope soon to find way to perform experimental attempt to solve mathematical problem publicly on the internet !

Huon Wardle said:
Michael, I am glad this is of some relevance - there is certainly a big gap between the imagination of anthropology and the mathematical elegance you are also seeking - personally I find Levi-Strauss earlier conjectures on kinship relatively convincing but his later myth work wildly tendentious. I have to admit also I am drawn to the geometric when it comes to this kind of thing - as are economists when they don't know what they are talking about; hence they draw big teleologically framed loops showing when a depressive 'cycle' is predicted to end (see the discussion on 'consumer confidence' in the economic anthropology group). What concerned me about your paper was that it consisted of two hypothetical actors whose wider beliefs remain unexplored as does anything to do with the wider conditions of their choices. How resilient are your models to the kinds of 'complex' (in a true sense of the word) phenomena empirically minded anthropologists might be interested in? I hope that the meeting between mathematics and anthropology is possible, but it would involve a very thoughtful examination of the language we use and our notions of what counts as relevant.

Michael Alexeevich Popov said:
Huon, I agree, Thome's Catastrophe theory (CT) can provide not only pure qualitative insight, but also some kind of geometric imagination and intuitive description, expressed by Thompson. Today,CT is a part of more general KAM ( Kolmogorov-Arnold-Moser) theory of chaos, however, Thom's initial biologism and intuitive geometry cannot be forgotten. Even G.Soros in his attempt to use chaos theory to predict "superbubbles" in global economics cannot avoid Thom's-like intuitions, probably, because Soros's "intuitive reflexivity" is NP-incomplete problem...
Huon Wardle said:
The gist of this, as I undestand it, has to do with problems that are easier to solve than to give a mathematical expression. This is certainly a good area for anthropology. There is a very interesting anthropological application of catastrophe theory in a book by Michael Thompson called 'Rubbish Theory'; this has always been a favourite of mine. In it Thompson looks at why certain objects are highly valued as antiques while others 'catastrophically' lose their value and become 'rubbish'. The answers require various kinds of models plus ethnographic description of people knocking through walls in their houses to make them more fashionable. Worth a look perhaps.
Michael, I will enjoy hearing more about your game demonstration. I suppose my question was in part motivated by considering whether the field you have taken on (market behaviour in a capitalist society) has, on the one hand, a strong affinity with the mathematical approach you are exploring and may, hence, be context specific rather than universalisable. I sense that, for you mathematics is a kind of Platonic form, independent of individual intuition, from which individual intuition nonetheless feeds. So, my question was not really so much about whether your model remains analytic rather than empirically synthetic, but rather to do with my worry that Alice, Rob and the real Michael are too capitalistic: would the model have any applications for thinking about the ecisions peoples who do not use multiplex counting systems or make controlled market decisions?
Huon, following merely my own empirical observations ( but not the rules of some kind of open game with uncertain Nash equilibrium between "communists" and "capitalists " ), I'd like to remark that it is possible to imagine just Three Kinds of Society based on fundamental PvsNP assumption:

Society, based on P=NP,
where people believe in an existence
of Universal Solution for all problems ( 1 )
( "scientific socialism", "Government
as universal algorithm", or, even
"superAdministration in the form of Quantum
Computer" etc ).
Society, based on P is not NP, where
people believe in chaos, power of self- ( 2 )
organization or anarchy, market without
equilibria,etc.
Society, based on NP=M, associated with
creative development and culture of counter-
intuitive decision (M-desicions), which pro-
duce semi-ordered effective economy and
well-ballanced structure. ( 3 )

Correspondingly, Three styles of Art Thinking, expressed in the terms of Architecture Style:

Dogmatic Style ( based on P=NP ) with elements of constructivism and attempts of creation of the Units of Simplicity.
Nigilistic Style ( based on P is not NP) with elements of deconstruction; and
Creative Style ( based on third solution - P is not NP, but NP=M ) based on some kind of " pseudo-telepathy" and quantum play-forms. Today, I try to understand this kind of style and its consequences ( please, see my attachment ) may be in the terms of "anthropology of creativity"...
Well I have to admit a personal preference for your type 3. Are you trying to demonstrate that these 'societies' have ever existed/might exist or are they a new set of Platonic forms that, say, I might draw on in one of my thought processes in order to discard in the next?
Huon, thank you. This is just an attempt of theorem ( conjecture ) on cognitive limits. It is possible to imagine ( Like Plato's solids ).Limits are real.
I suppose there must exist freedom of will and the taste.You can make any rational choice. There are more interesting questions : why P=NP is impossible? If mathematics is just language , then P=?NP is a problem of language? Or it is just Western tradition? Hence, can field anthropologists find any non-Western counter-example ? How we can represent NP=M style in the terms of modern architecture ? etc.

Huon Wardle said:
Well I have to admit a personal preference for your type 3. Are you trying to demonstrate that these 'societies' have ever existed/might exist or are they a new set of Platonic forms that, say, I might draw on in one of my thought processes in order to discard in the next?

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