1. Life’s longing for itself Speculations on propagation, prediction, purpose and progress Amsterdam, October 2004 (Updated version of Ulam Lectures given Sept. 2002) J. Doyne Farmer Santa Fe Institute

2. Kahlil Gibran, The Prophet Your children are not your children. They are the sons and daughters of Life’s longing for itself. They come through you but not from you, And though they are with you yet they belong not to you. … For life goes not backward nor tarries with yesterday.

3. Lecture 1: Propagation What are complex systems? The history of the mechanistic view Entropy and information What is a machine? Organisms and artifacts evolve How might the first copy machine have been built? The symbiosis of human population and technology

4. Main points of lecture 1 Why is the world populated with functional structures? –Propagation implies prevalence. Not reducing universe to “just mechanics” –Through self-organization, machines are capable of far more than previously thought. Biological life, human artifacts, and human societies all evolve. –Relationship becoming increasingly intimate.

5. Lecture 2: Prediction Prediction, action and survival Methods of prediction Limits to prediction and their loopholes Personal history: –Roulette –financial markets A mechanistic model of a market. How prediction makes reality more subjective –Markets manias, and other social schizophrenias.

6. Lecture 3: Purpose and progress The progress debate The purposeful arrow of time What is progress? Happiness vs. purpose A few speculations about the future

7. Prediction, action, and survival Prediction is a prerequisite for purposeful behavior. Purposeful behavior consists of three parts –Sensation –Prediction –Action Purposeful behavior (and therefore prediction) exists because it is useful for propagation.

8. Prediction, action and survival

9. Lecture 2: Prediction Prediction, action and survival Methods of prediction Limits to prediction and their loopholes Personal history: –Roulette –financial markets A mechanistic model of a market. How prediction makes reality more subjective –Markets manias, and other social schizophrenias.

10. Methods of prediction How is the model constructed? –First principles vs. empirical What does the model predict? –Dynamical vs. contemporaneous predictions Modeling paradigm –Deterministic vs. random processes

11. Astrological prediction of stock prices

12. Fibonnaci predicts social trends !

13. How is the model constucted? First principles. Based on an understanding of the world. –Requires high degree of sophistication Empirical. Build a model automatically by fitting historical data. –Simple organisms: Hard-wired models, tuned by evolution –Complex organisms: Further tuning by experience

14. What does the model predict? Dynamical systems: –Predict the future based on the past Contemporaneous models: –Relate one property of the world to another property of the world at the same time. –Useful in simplifying description of the world.

15. Modeling paradigm Deterministic –World is described by a single point in state space. Completely determines future. Rule that does this is called a dynamical system. Random –Evolution of future states is not determined by present states.

16. Dynamical prediction Key idea is state space. A state is a list of numbers that gives the information needed to determine the future. If you have N such numbers, it is useful to think of them as defining an N-dimensional space. E.g. from Newton’s laws, knowing forces, position and velocity are sufficient to determine future motion. Position and velocity are the state.

17. How do bacteria do it? Don’t know in detail. –Must predict concentration –Involves measuring the concentration at different points in time and comparing. –If concentration is increasing, keep swimming –Otherwise tumble and/or eat State space: –One number: Rate of change of concentration –(concentration now – concentration earlier)

18. Lecture 2: Prediction Prediction, action and survival Methods of prediction Limits to prediction and their loopholes Personal history: –Roulette –financial markets A mechanistic model of a market. How prediction makes reality more subjective –Markets manias, and other social schizophrenias.

19. Limits to prediction Limits to prediction come from complicated geometry of state space, which causes nearby states to diverge rapidly. Produce behavior that looks random, even in purely deterministic setting. Small uncertainties in initial measurements are amplified, limiting predictability even when model is known.

20. On Hurricane Charlie You can’t plan for the unforeseen. God doesn’t follow the linear directions of computer models. And these are powerful storms that don’t behave in any kind of way that you can say with certainty where they are going. Jeb Bush

21. Poincare’ on Fortuitous phenomena A very small cause which escapes our notice determines a considerable effect that we cannot fail to see, and then we say that the effect is due to chance. If we knew exactly the laws of nature and the situation of the universe at the initial moment, we could predict exactly the situation of that same universe at a succeeding moment. But even if it were the case that the natural laws had no longer any secret for us, we could still only know the initial situation approximately. If that enabled us to predict the succeeding situation with the same approximation, that is all we require, and we should say that the phenomenon had been predicted, that it is governed by laws. But it is not always so; it may happen that small differences in initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon.

22. Chaos is a double-edged sword On one hand, long-term behavior is effectively random (though dynamics are deterministic) On the other hand, short-term behavior is predictable if model is known. –Systems otherwise believed random become predictable in the short term. –Simple mechanical oscillators, transition fluid flows, sunspots, timing of ice ages, … (joint work with John “Sid” Sidorowich).

23. Rolling ball on a circular track with counter-spinning inside track

24. Classical physics problem Newton could have solved. –Measuring position and velocity at a given time determines future motion. Wind resistance is main force –complication due to tilt Prediction is difficult because of: – circularity of wheel (like taking remainder in division) –imperfections in track and ball creates “turbulence” –Chaotic bouncing on cups Roulette

25. Shoe computer

26. Shoe + computer

27. Histogram + battery boat

29. Copy machines

32. Illustration of two methods of prediction Roulette provided a good illustration of two methods of prediction: –Version (1) based on first principles –Version (2) based on empirical method –(1) was more accurate but less robust

33. Making predictions can alter the future After the book The Eudeamonic Pie was published in 1984 –Nevada passed a law against using computers to predict the outcome of “a game”. –Huxley roulette wheel company designed a new roulette wheel with lower cups and more elastic balls. –Winning players who place bets at the last minute are immediately asked to take their business elsewhere. –Altered the rest of my life

34. Limits to short term prediction Limits to short-term prediction come from Data needed to build a good model increases exponentially with dimension of the state space Even worse : High dimensionality, chaos, ability to measure only some variables, means that some systems are fundamentally random, even for very short term prediction – Casdagi, Eubank, Farmer, Gibson (1991) Weather, the economy, … –high dimensional + chaotic The curse of dimensionality

35. What about free will? The brain as a dynamical system

36. Prediction can make the world less predictable Market efficiency: most economists believe that future price movements are fundamentally unpredictable. –If there are patterns in prices, profit-seeking behavior of participants will eliminate them. –E.g. if people think the price is going to rise, more people will buy, which drives the price up, so the price rise happens before it is possible to take advantage of it. –The future becomes the present Effect of predictions complicates dynamics. Result: unpredictable prices -- “market efficiency” To first approximation a good model

37. Prediction Company (cofounded in 1991 with Norman Packard) (Empirical, dynamical prediction, random process) Manages money under exclusive relationship with United Bank of Switzerland (Warburg Dillon Reed) “Cerebellar” approach to market forecasting –empirically searches for patterns in historical data –keys are feature extraction, law of large numbers –little understanding of origin of patterns –relies on abundant past data, stationary conditions. Trading is fully automated (no human decisions).

38. Harvard Business Review, 1992

39. Prediction Co. performance

40. Nonetheless Profits are limited –Market has friction -- trading changes prices –Particularly felt with frequent trading –Market is “pretty efficient” - like any business

41. Lecture 2: Prediction Prediction, action and survival Methods of prediction Limits to prediction and their loopholes Personal history: –Roulette –financial markets A mechanistic model of a market. How prediction makes reality more subjective –Markets manias, and other social schizophrenias.

42. Mechanistic properties of markets Market institutions shape our behavior Neoclassical economic models assume perfect rationality of agents We explore alternative: Random behavior –Make a physics style model –Agents make random orders at random times

43. Order driven market Two fundamental types of orders –Market order: buy or sell given number shares at best available price –Limit order: buy or sell given number shares at a specified price. Does not guarantee execution! Patient traders use limit orders; impatient traders use market orders

44. price ( $ ) BID ASK VOLUME Patient trading Patient traders place non-marketable limit orders that do not lead to an immediate transaction Non-marketable limit orders accumulate Limit order book is a storage device NEW ASK Limit Order BUY / SELL # OF SHARES LIMIT PRICE

45. price ( $ ) Impatient trading Market order: An order to buy or sell up to a given volume No limit price is defined Executed immediately Often causes unfavorable price impact Market Order BUY / SELL # OF SHARES BID ASK BID NEW ASK VOLUME

46. Order cancellation price ( $ ) Limit order cancellations: Limit orders can be cancelled by the owner Market defined expiration price ( $ ) VOLUME

47. The Basic Model u Limit order arrival: unit size, in time & price;   Market order arrival: unit size, random in time;   Cancellation: Random in time (like radioactive decay);   Assume prices are continuous. Depth of the book n  p,t  tells how many shares are in the book at price p at a given time t. BID SELL LIMIT ORDERS  ASK BUY LIMIT ORDERS  SELL MARKET ORDERS  BUY MARKET ORDERS  0

48. Parameters of model Three fundamental dimensional quantities: shares, price, time Five parameters: Results in simple formulas predicting volatility, liquidity, spread,..

49. London Stock Exchange data set London screen

51. Continuous double auction Execution priority of limit orders: Price priority: lower sell / higher buy limit prices Time priority: applicable only for limit orders with same price price ( $ ) SPREAD PRIORITY (BEST) BID (BEST) ASK VOLUME SELL BUY VOLUME LIMIT ORDERS

53. Predicted price diffusion rate

54. Top 10 Russian jokes, Oct. 23, 2003 с сайта "Немецкая волна" http://www.dw-world.de/russian/0,3367,2212_A_985770_1_A,00.html Ученые-экономисты давно стараются понять закономерности, которым подчиняются биржевые курсы, и используют для этого математические модели. На протяжении многих десятилетий такие модели исходили из представлений о брокерах как об аналитиках с выдающимися умственными способностями, обладающих исчерпывающей информацией о рынке и действующих исключительно рационально. Однако удовлетворительно описать реальные изменения биржевых курсов эти модели оказались не в состоянии. Значительно успешнее справляется с этой задачей новая модель, предложенная Дойном Фармером (J. Doyne Farmer), сотрудником Института Санта-Фе в штате Нью-Мексико. Она базируется на предположении, что брокеры Ц полные Ђидиотыї, действующие совершенно случайно и к тому же лишенные какой бы то ни было информации. Сравнив данные, рассчитанные на основе этой модели, с реальными курсами лондонской фондовой биржи за период с 1998-го по 2000-й годы, ученые выявили очень высокую степень совпадения

55. Lecture 2: Prediction Prediction, action and survival Methods of prediction Limits to prediction and their loopholes Personal history: –Roulette –financial markets A mechanistic model of a market. How prediction makes reality more subjective –Markets manias, and other social schizophrenias.

56. The 2 nd millenium technology bubble (NASDAQ)

57. Second millenium tech bubble (CISCO)

58. from: Hidden Collective Factors in Speculative Trading, by Bertrand M. Roehner (2001) Wheat price in Munich (1815-1820)

59. Monthly wheat price in Paris (1691-1694) from: Hidden Collective Factors in Speculative Trading, by Bertrand M. Roehner (2001)

60. from: Hidden Collective Factors in Speculative Trading, by Bertrand M. Roehner (2001) Price of Bananas

61. Fortune teller problem Predicting the future influences the future

62. Feedback between prediction and reality … if a dream can tell the future it can also thwart that future. For God will not permit that we shall know what is to come. He is bound to no one that the world shall unfold just so upon its course and those who by some sorcery or by some dream might come to pierce the veil that lies so darkly over all that is before them may serve by just that vision to cause that God should wrench the world from its heading and set it upon another course altogether and then where stands the sorcerer? Where the dreamer and his dream? Cormac McCarthy, The Crossing

63. Seth Lloyd Seth and Dmitriy Dmitriy Cherkashin

64. A simple game with feedback between perception and reality Assume N agents bet on event at time t. –e.g. a horse race. Odds based on net wager on each outcome. Allow outcome to be influenced by odds. –financial markets provide a good example. –supply and demand are inherently subjective. Simplest case is coin flip –only two outcomes –coin can be biased -- bias can depend on odds

65. Examples where perception can influence reality Gambling Economics Politics Global climate change Personal achievement

66. Agent strategies Assume N+ 1 players bet (0, 1/N, 2/N, …, 1) of their money on heads Give them all equal wealth to start with.

67. Purely objective reality

68. Self-defeating prophesy

69. Bias of coin vs. time

70. Weak self-fulfilling prophesy Bias of coin vs. bias of predictions

71. Weak self-fulfilling prophesy Bias of coin vs. time

72. Perfectly self-fulfilling

73. Perfectly self-fulfilling prophesy Bias of coin vs. time

74. Over self-fulfilling

75. Bias of coin vs. time

76. Perfectly self-fulfilling prophesy Bias of coin vs. time

77. Feedback and reality If you are able to create reality, reality can become unstable due to feedback. You must make yourself part of the prediction; must also model others. Danger of schizophrenia

79. Creating reality Guys like you are ‘in what we called the reality-based community’, defined as people who ‘believe that solutions emerge from your judicious study of discernable reality. That’s not the way the world really works anymore. We’re an empire now, and when we act we create our own reality.’ A senior advisor to G.W. Bush, to Ron Susskind

80. Summary Prediction is a key element of purposeful behavior coming out of propagation. Predictions come in many shapes and sizes As the sophistication of predictions increases, their affect on the environment can make prediction more difficult, and make dynamics unstable.

81. Thanks Else Neeft