QuoteOriginally posted by: CuchulainnQuoteT4A, Collector, I regret that I contribute to the chaos of the discussion on chaosJoin the club. Is your chaos a kind of meta-chaos?No, it is the type of chaos on top of which you develop and run your fantastic C++ programs (a chaos, which guaranties you that your cleverly programmed patterns are not stuck in unexpected underlying patterns)

QuoteOriginally posted by: exneratunriskT4A, Collector, I regret that I contribute to the chaos of the discussion on chaos. It is not to destroy everything by neglecting definitions ... I, for one, enjoy the chaotic order and ordered chaos you bring.QuoteOriginally posted by: exneratunriskHowever, there are other views on the emergence of non-deterministic behaviour from the application of simple rules?Indeed, so! The technical definition of chaos and chaotic systems usually refers to a system with a simple set of fixed dynamical rules in discrete time or continuous time and in a regular tessellated space or smooth continuous space. A different category of systems (complex adaptive systems) includes mechanisms by which the dynamical rules of the system may change over time. The ultimate example of a complex adaptive system is found in the evolution of life in which the length of DNA (and the resulting complexity of the organism) is also a dynamical parameter in the context of populations of individuals of populations of species interacting over a geographically-distributed heterogeneous environment.QuoteOriginally posted by: exneratunriskWith that in mind I see "a computer" as a perfect "chaotic" system (derived fron simple construction rules), universal, because it allows all type constructs which do not run into loops, are not caught by minima, ..That's very true and long as the computer doesn't use single precision floats. QuoteOriginally posted by: exneratunriskAnd I ask myself, whether a free market shall be chaotic (universal) in that sense. Allowing for "financial" programming (constructing and trading its instruments, interpreting results, finding patterns, ... ) ? Provocatively speaking, only the "true-chaos" can run programs derived from chaos-theory. Technically, markets are worse than chaotic because the market participants attempt to adapt the dynamical rules over time. Rather than have a fixed nonlinearity, markets contain nonlinear, time-varying nonlinearities. That is, markets are complex adaptive systems. Moreover, markets are multiply-nested complex adaptive systems in that a market is composed of companies, each of which is a complex adaptive system, and a company is composed of individuals, each of which is a complex adaptive system (both the brain and mammalian immune system are considered complex adaptive system in their own right). Needless to say, the behavior of such systems can be highly nonlinear.QuoteOriginally posted by: exneratunriskAnd I am with Fermion, we NEVER had a situation where markets were free (IMO, because we always mix economic with ideological and final social aspects)?I, too, agree with this -- markets are never entirely free if the constituent agents are bounded rational (i.e., lack perfect information), gain seeking (i.e., want to maximize personal utility), or control seeking (i.e., want to constrain the actions of others). All of the suppliers, companies, customers, and governments of this world exhibit all three properties and all act in ways that prevent true free markets. And yet, most markets in most developed countries are relatively free with only a moderate discrepancy between the observed state and the idealized free-market state.

One key issue, with respect to complex adaptive systems is that a large population of agents will ALWAYS outsmart a small population of agents. No subset of the system can predict what the entire system will do because the capacity for complexity of the system will, by definition, exceed the capacity for complexity of any subset of that system. This issue of complexity is why a distributed system (e.g., a capitalist semifree market) will outperform a centralized system (e.g., one with government-controlled means of production). The distributed system will explore the space of potential optima faster than will the centralized system and the distributed system will have fewer single-point-of-failure modes (although not zero modes as we've seen recently) than will the centralized system.Using Exner's computer analogy, a small cluster of computers (even supercomputers) cannot predict the real-time behavior of an entire computer network composed of that small cluster plus 6.7 billion other computers. The smartest guys in the room will always be outsmarted by the billions of people outside the room.

T4A, I only can say thank you for this detailed reply.(single precision? a Turing machine --> )

QuoteOriginally posted by: exneratunriskQuoteOriginally posted by: CuchulainnQuoteT4A, Collector, I regret that I contribute to the chaos of the discussion on chaosJoin the club. Is your chaos a kind of meta-chaos?No, it is the type of chaos on top of which you develop and run your fantastic C++ programs (a chaos, which guaranties you that your cleverly programmed patterns are not stuck in unexpected underlying patterns) When developing software for any problem, we can safely say that it has all been done before; it's just the context is different. Problem is Aha Erlebnis needs 3 iterations.History repeats itself, no chaos.aka Mr Finn is vined again

That's all very interesting, but a little besides the point. Physicists use (rather) precise measures and terminology. They are able to look at microstates and compare them with macrostates and the interaction. In economics there are no precise measures and no precise terminlogy. The idea that finance will be resolved by some super-maths is quite misguided. The problem starts with maths in the first place. For example many problems of physics can be solved by a geometric language, rather than by an arithmetic language. If one tries to find a mathematical theory of accounting one is destined to fail. Most problems of finance are not reducable to time-series, so IMO rather a problem of logic than arithmetic. If one has a daily quote for a public traded company, there is no more information in the timeseries than in a, say yearly quote timeseries of a privately held company.

Macrotrade,I largely agree with you. The weak link between a mathematic theory and a given real-world system is in the validity of the axioms. Aside from nasty Godelian situations, math tells us P({Theorem_j}|{Axiom_i}) = {1,0} with perfect certainty. But what is P(Axiom_i) for a real world system? For economics, the axioms are often provably wrong (even if they make for theoretical elegance) so it's not too surprising that the resulting theorems don't work that well. Worse, the truth state of the axiom can vary in time in economic systems both due to natural influences and due to the actions of the component agents (i.e., central bankers believed that bankers were rational and bankers knew that central bankers thought this). Many aspects of economic systems violate the prerequisites for the scientific and mathematical methods used in hard sciences.My one minor quibble is that the daily time series of a company's equity prices does contain significantly more information than does the yearly time series. Given the daily price data, one can pinpoint the industry, country, and commodity-dependencies of the company with some high degree of certainty. With yearly data, such estimates would be significantly less certain. Of course, converting either price series into a prediction of absolute future returns is another matter (and maybe that was your point) .....

I would think"Chaos is the seed of Order, Order is the seed of Chaos"also is contradicting the second law of thermodynamics in some way??if so I think there are good reasons to believe it is right, no not the second law of thermodynamics (except under some assumptions that do not hold completely across large areas of spacetime), yes I am nuts!Please how is perfect chaos and perfect randomness related to the second law of thermodynamics?

"Chaos is the seed of Order (given the correct far from equilibrium conditions), Order is the seed of Chaos (given correct near equilibrium conditions )": )

2nd law:"That the entropy of an isolated system which is not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium."So when will the whole universe according to main frame science reach equilibrium? Is the big amount of order (+ chaos) explained by that we not yet had enough time to reach equilibrium because too little time has gone by since the (assumed) Big Bang?so concerning the 2nd-law, the reason we not yet have reached equilibrium in whole universe yet must according to main frame science be based on:1) The Universe started with a Big Bang2) Not enough time has gone by since big bang to reach equilibrium yet.3) Or there is a force working like anti-entropy that we not fully understand yet? like gravity or so???? not my speciality please tell me you enlightened people with background in physics, chaos theory and cosmology...

QuoteOriginally posted by: CollectorI would think"Chaos is the seed of Order, Order is the seed of Chaos"also is contradicting the second law of thermodynamics in some way??if so I think there are good reasons to believe it is right, no not the second law of thermodynamics (except under some assumptions that do not hold completely across large areas of spacetime), yes I am nuts!Please how is perfect chaos and perfect randomness related to the second law of thermodynamics?What is Order?Many thousands of pine needles are falling in my yard now. I can rake them into piles, or arrange them in smooth rows, or....But nature let them drift to the ground in a haphazard manner and yet they had their own order that way as well.

exactly, for a non isolated system, pushed far from equilibrium, such as one would imagine the financial can be (due to foolish central bankers, economic gurus and politicians), entropy can be decreased, its called spontanious self organisation.

QuoteOriginally posted by: hungryquant entropy can be decreased, its called spontanious self organisation.What is the main frame scientific force behind this? any references would be helpfullOh I was not thinking about finance, but about cosmos (well finance is a very very small part of it)

Partly it comes back to Law concerning the Conservation of Energy.It is not important for the pine needles to be lined in to perfect rows, so they may fall straight down, or be carried by the wind - no excess force is exerted on the system to put it into "Order"..However, DNA follows fairly strict rules on pairing and expression - so that is an example of a more rigorous ordering.Looking at "normality" and "viability", "mistakes" are still made - sometimes we see freaks or monsters - kittens with two faces or (recently) a puppy with five legs. (A woman adopted this puppy and had the fifth leg removed - he now conforms to normative puppy standards.)But nature tends to clean up after herself also. Serious errors in the expression of genetic code do not tend to survive for long.