QuoteHis icon-volcano is the most beautiful picture of chaos and order. "Order" "Order" "Order" "Order", Blow Up, "Order" "Order" "Order" "Order" "Order" "Order", Blow Up....My Icon is an actual picture of Volcano Tungurahua in Ecuador 100 Km south of Quito,It's been in activity for 7+ years, Volcano TungurahuaTungurahua 2Tungurahua 3Life at its purest

QuoteOriginally posted by: robsan7QuoteHis icon-volcano is the most beautiful picture of chaos and order. "Order" "Order" "Order" "Order", Blow Up, "Order" "Order" "Order" "Order" "Order" "Order", Blow Up....My Icon is an actual picture of Volcano Tungurahua in Ecuador 100 Km south of Quito,It's been in activity for 7+ years, Volcano TungurahuaTungurahua 2Tungurahua 3Life at its purestMight Tunguraha be responsible for the catastrophic climate change in 6th century?

QuoteOriginally posted by: CollectorThere is much to learn by carefully watching the ticker tapeAnother type of tick data, sometimes with jumps.Daily Racing Form, 1973

QuoteOriginally posted by: CollectorThere is much to learn by carefully watching the ticker tape if you stare a random noise or brownian motion long enough, you'll eventually see a pattern.

NYT - Sept 28Order in the Apparent Chaos of currentsScientists have made strides in making images of the underlying mechanics of flowing air and water.

QuoteOriginally posted by: robsan7NYT - Sept 28Order in the Apparent Chaos of currentsScientists have made strides in making images of the underlying mechanics of flowing air and water. well, the key distinction is that NO order can be sustainable in capital markets. why? because order allows arbitrageurs to get rich, which will beget more arbitrageurs, who will get rich, which will beget more and more arbitrageurs ad infinitem. If this continues for long enough, pretty soon everyone is rich! But that's impossible because if everyone is independently wealthy -- who is going to do the work? And there just aint that much wealth to go around in the world...

A little article to reopen the topic Chaos in economics and financethe best would be to combine chaos dynamic and stochastic features, maybe with a nonlinear stochastic PDE for option pricing. A nonlinear dynamic process over a brownian motion could be good.

Chaos and imaginary are two words that should be banished from all mathematical discussions.It's a lot cheaper and easier to put a webcam on a lava lamp to get random data, the SIlicon Graphics patent on said is about to expire.

QuoteOriginally posted by: outrunQuoteOriginally posted by: frenchXthe best would be to combine chaos dynamic and stochastic features*but* you can trade without modeling dynamics, (have good event driven behavior)I agree with you Outrun. What I think is if you consider behavioural aspect :-learning: a good trader (or a lucky one) who makes money make more and more with time (cause he applies and optimizes his skills)-the sheep rule: if a value becomes fashionable all the speculators will be on it-the crash panic: when a value fell down under a certain amount in a very short time, everybody would sell-limited liquidity when a bubble is rising-bid and ask spread noise for HF traders etc... a lot of features in fact I think that if you incorporate those features (and others) in portofolio theory you should have a nonlinear theory which could gives chaos, bubbles and crashes. You can consider the asset as classical lognormal random walk with drift but for example when the value increases I think that the drift should reduces (due to liquidity probably and also a behavioural aspect, people prefers to have a lot of small amount contracts for diversification rather than a few of big valued contracts), that would be like a population dynamic in a limited environment so I expect the drift m to be replace by a term (1-S)*m' . Moroeover chaos occurs very rarely in continous model but very often in discrete ones so a discrete process should be used to model that.It was my 2 cents (I'm really not a specialist of finance), but I think it is an interesting topic.

72,96,3,2,32,72,71,3,2,32,72,75,3,2,32,102,99,3,2,42,102,91,3,2,42,102,200,3,2,42,102,115,3,2,42,102,143,3,2,42,3,8,12,57,52,3,2,22,57,39,3,2,22,57,56,3,2,22,57,56,3,2,22,57,60,3,2,22,57,56,3,2,22....some numbers from my lamp, random, chaos, perfect order? Dose God play dice?It partly also depends on the observer (as I am sure you already know), what is order for one observer, can naturally be equivalent to random for observers with less information, but it is actually more complex than this.I shake a coin inside my hands, but I take a look at the coin without showing the coin to you, but you know I looked at it. I know what side is up and down, you don't. For me it is order/non random (actually the degree of order for me will be strongly dependent also on a interdependent factor, according to a scientist only 3 people understand this factor, and for sure he did not include me among these 3). For you, your best guess on what side will show up, is equivalent to random, but it is not random (and also the randomness is actually somewhat different than you think, you only have a rough approximation probability theory, that often is very useful, other times it fails dramatically). But you know it not is random, or at least not much random for me (but this is actually also just partly the truth). It is partly your lack of information that makes your best guess on what will show up equivalent to random for you. Because I looked at the coin I naturally have a big advantage, but again this advantage is dependent also on something else, that we can scratch at the surface, or understand at much deeper level.okay what I try to explain, I explain in a somewhat diffuse way (what I say is not in perfect order, neither is it perfect chaos). What I talk about must seems like nonsense or close to nonsense to most of you. But what for some seems like nonsense can mean order in understanding for others, again it partly depends on the observer.What seems like random nonsense to most can seems like order to a mad man But some times it is not the mad man that is mad, but simply the people thinking the man is mad because they not can see the hidden order in the chaos.I have actually not looked at the coin this time, but I have tried to understand the interdependent factor. Well I will try to write this in plain NorEglish another time...The key to the doors of chaos and order is well hidden! I don't have the key, but I am like many of you searching for the key!

Collector's post reminded me of a story about some artificial intelligence software that could play the paper-rock-scissors game. Against human competitors this software would win very consistently after a short run of roughly random wins/losses because the software built up a state transition matrix of the human player's behavior. That is, for example, the software would learn that its human opponent tended to pick "rock" after picking "paper" or tended to choose "scissors" after a win. Thus, the software would learn the order in the human player's strategy.Now imagine some combination of randomness and this software controlling the physics behind the coin in the hand. The outside observer (the one who must try to predict the outcome of the unseen coin) would judge the degree of order or disorder from the patterns of success in predicting the hidden coin's face. If the outside observer can predict the coin's face 100% of the time, then they would say that the system is ordered (and controlled by whatever rule the observer used to forecast the outcome). If the outside observer predicts the coin's face only 50% of the time (and the coin shows each face 50% of the time), then the observer might say the coin system was disordered. But what if the observer predicts the coin's face exactly 0% of the time so that no matter what the observer predicts, the coin shows the opposite face? Isn't that a kind of negative order? (Some would say that the financial markets are a bit like this.)What does this have to do with chaos? The Lyapunov exponent is a measure of the divergence between the forecast future state of the system and the true future state of the system given some small discrepancy between the measured current state and the true current state. If the coin is perfectly ordered, then one can predict the coin's outcome on a second flip before even seeing the outcome of the first flip by assuming the prediction of the first flip is correct. In the fully ordered case, one can accurately predict flip 1, 2, 3, ...., INF. If the coin is chaotic, then the accuracy of the Nth prediction would grow exponentially worse in N according to the Lyapunov exponent. But chaotic systems are not stochastic systems and the phase effects mean that the forecast can be worse than randomly decoupled from the true system -- we can easily find ourselves being 100% wrong.P.S.: I'm sure I'm not among the 3 people who understand the "interdependent factor" but I'll venture a few wild guesses: 1) we're assuming that the looker has perfect eyesight so that there is zero chance of the coin actually being 'tails' given that the looker thought they saw 'heads'; 2) the looker only sees the visible face and must assume there is only one invisible alternative (i.e, the coin only has two faces, not three or more, which affects calculations of order/disorder); 3) the looker must assume the coin remains in a fixed state after they look but before they reveal the coin to the outside observer. I look forward to more of Collector's NorEglish!

Deterministic chaos is just a measure of the uncertainties of the value on the initial conditions. The more the Lyapunov coefficient is high, the more it will be sensitive of course. The more the fractal dimension is high, the more the pattern will look chaotic but guys it's deterministic chaos, let's have some fun about quantum chaos because it is well know that in quantum probability there are no hidden info underlying (Bell violation) So Collector what about a schrödinger coin ?