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

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.

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

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.

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.

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

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.

Prediction, action and survival

QuickTime™ and aSorenson Video 3 decompressorare needed to see this picture.

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.

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

Astrological prediction of stock prices

Fibonnaci predicts social trends!

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

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.

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.

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.

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)

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.

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.

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

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.

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).

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

• 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

2(velocity) constant velocity of change of rate ×=

Roulette

Shoe computer

Shoe + computer

Histogram + battery boat

Copy machines

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

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

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

What about free will?

The brain as a dynamical system

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

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).

Harvard Business Review, 1992

Prediction Co. performance

Nonetheless

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

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.

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

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

price ($)

BID

ASK

VO

LUM

E

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

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

VO

LUM

E

Order cancellation

price ($)

Limit order cancellations:

• Limit orders can be cancelled by the owner

• Market defined expiration

price ($)price ($)

VO

LUM

E

The Basic Model

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 np,t tells how many shares are in the book at

price p at a given time t.

BID

SELL LIMIT ORDERS

AS

K

BUY LIMIT ORDERS

SELL MARKETORDERS

BUY MARKET ORDERS

),( tpΩ

p0

),( tpn

Parameters of model

(price) sizetick

(shares) sizeorder typical

(1/time) rate,on cancellatiorder

me)(shares/ti rate,order market

time)iceshares/(pr rate,order limit

====

×=

dpσ

Three fundamental dimensional quantities:shares, price, time

Five parameters:

Results in simple formulas predicting volatility, liquidity, spread, ..

London Stock Exchange data set

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

PRIORITY

(BEST) BID

(BEST) ASK

VOLUME

SELL

BU

Y

VO

LUM

E

LIMIT ORDERS

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are needed to see this picture.

Predicted price diffusion rate

€

5 / 2δ1/ 2σ −1/ 2

α 2

Top 10 Russian jokes, Oct. 23, 2003с сайта "Немецкая волна"

http://www.dw-world.de/russian/0,3367,2212_A_985770_1_A,00.htmlУченые-экономисты давно стараются понять закономерности, которымподчиняются биржевые курсы, и используют для этого математическиемодели. На протяжении многих десятилетий такие модели исходили из

представлений о брокерах как об аналитиках с выдающимися умственнымиспособностями, обладающих исчерпывающей информацией о рынке и

действующих исключительно рационально. Однако удовлетворительно описатьреальные 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, чтоброкеры Ц полные Ђидиотыї, действующие совершенно случайно и к тому же

лишенные какой бы то ни было информации. Сравнив данные, рассчитанные наоснове этой модели, с реальными курсами лондонской фондовой биржи запериод с 1998-го по 2000-й годы, ученые выявили очень высокую степень

совпадения

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.

The 2nd millenium technology bubble (NASDAQ)

Second millenium tech bubble (CISCO)

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

Wheat price in Munich (1815-1820)

Monthly wheat price in Paris (1691-1694)

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

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

Price of Bananas

Fortune teller problem

Predicting the future influences the future

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

Seth Lloyd

Dmitriy Cherkashin

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

heads)y probabilit - (1 y tailsprobabilit =

Examples where perception can influence reality

• Gambling

• Economics

• Politics

• Global climate change

• Personal achievement

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.

Purely objective reality

Self-defeating prophesy

Self-defeating prophesy

Bias of coin vs. time

Weak self-fulfilling prophesy

Bias of coin vs. bias of predictions

Weak self-fulfilling prophesy

Bias of coin vs. time

Perfectly self-fulfilling

Perfectly self-fulfilling prophesy

Bias of coin vs. time

Over self-fulfilling

Over self-fulfilling

Bias of coin vs. time

Perfectly self-fulfilling prophesy

Bias of coin vs. time

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

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

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.

Thanks

Else Neeft