complexity theory – An Autonomous Agent

Scale – Geoffrey West

anautonomousagent — Sun, 12 Aug 2018 03:54:09 +0000

Scale, by Geoffrey West, is a thought provoking book about coarse grained quantitative network theories which concern the entire human species and its interaction with the environment. Although verbose — as I think the intended audience is upper high school and entry-level college — it is clear in its depictions and explanations. This book is an important summary of really profound work and research performed at the Santa Fe Institute. And it is a great introduction to understanding power laws and scaling in biology and network topologies.

Order Out of Chaos – Ilya Prigogine and Isabelle Stengers

anautonomousagent — Sat, 13 Jan 2018 18:03:08 +0000

A little bit of quantum physics, chemistry, biology and philosophy all rolled up into one important book. Order Out of Chaos (La Nouvelle Alliance as originally published in French) by Ilya Prigogine and Isabelle Stengers is a paradigm changing book. The first parts of the book are an excellent overview on the historical development of science – the evolution of dynamics and the discovery of thermodynamics and their relationship is particularly fascinating.

Once the reader gets to the later parts, it becomes somewhat abstract and the reader may not be able to get through it without a background in chemistry and physics. Chapter Nine, when the phrase “Order Out of Chaos” is developed, is difficult. Despite this, it is much more accessible than a scientific paper on the subject. It may take two or three reads to fully absorb the ideas presented. Overall it is one of my favorite reads.

Some important conclusions from the book:

The arrow of time objectively exists and it arises from non-equilibrium and irreversibility at the microscopic level.
The 2nd Law of Thermodynamics can be understood as a selection principal. It operates as a negative on allowable initial conditions, in other words it restricts systems with certain initial conditions from existing.
Time travel to the past is not allowed by thermodynamics because time reversal requires infinite information concerning the initial conditions of the system, an impossibility to an observer in the universe. This implies that information is closely connected to irreversibility and time.
Thermodynamics can be expressed from dynamics through the idea of correlations and internal-time operators. Thus, dynamics has been extended once again (general relativity, quantum mechanics, and chaos theory).
The universe as a whole is in a non-equilibrium state and it is an irreversible process with pockets of reversible dynamics.
In general, one of the goals of the authors is to make dynamics and thermodynamics consistent with each other.

Hidden Forces – Interview Series

anautonomousagent — Thu, 28 Dec 2017 22:13:13 +0000

Hidden Forces, hosted by Demetri Kofinas is an nice set of interviews with various people on topics including: finance, complexity, mathematics, and cryptocurrencies. I struggled listening to some of the interviewees because I did not agree with their ideas or conclusions; but I guess it is good to have conflicting opinions in order to encourage debate in the comments and to help review one’s own opinions and understandings. Regardless, Kofinas provides a highly accessible medium through which advanced ideas can be grasped.

I first ran across Hidden Forces while listening to the interview with Ray Monk about philosophical mathematics. Monk’s narration on the work of Frege, Russell, Whitehead, Wittgenstein, and Gödel is excellent – by far one of the clearest and easiest to grasp. It was learning about these paradigms and paradoxes of mathematics via Hofstadter’s famous book which led me to start this website.

New Theories on the Origin of Life with Dr. Eric Smith

anautonomousagent — Mon, 24 Apr 2017 15:09:31 +0000

Dr. Eric Smith’s lecture on the origin of life really challenged everything I thought I understood regarding how life functions and possibly originated on Earth. Make sure to watch the question and answer at the end for some good points regarding panspermia and Miller’s experiments.

Ecology of Mind – Nora Bateson Documentary

anautonomousagent — Thu, 18 Feb 2016 17:30:20 +0000

Nora Bateson, daughter of Gregory Bateson, created an insightful documentary about her father’s ideas. You can purchase the DVD here. I also found it on YouTube:

On the Distribution of Kingdom/Dynasty/Government Lengths

anautonomousagent — Thu, 29 May 2014 16:41:00 +0000

Do there exist studies on the distribution of the lengths of kingdoms and dynasties — distinct political entities — since the 3rd millennium B.C.E.? It seems likely that someone has already studied this topic, but I can not find any papers online. To explain, I have included a file, here, containing the beginning and end dates of about 700 distinct social groups since the dawn of recorded history. It was complied from various Wikipedia pages. I do not doubt that the data is not very reliable, however, graphing the histogram of these lengths, see Figure 1, would provide at least a rough idea of their distribution.

Figure 1

It does seem that a nice distribution curve exists which models the data. The distribution seems to take the shape of a power law at first glance. Doing some work in R, I found that a power law with one set of parameters fits the tail nicely but fails to fit the first half; and vice versa, a power law with a different set of parameters fits the majority but not the tail. My hypothesis is that a power law with alpha equal to 3 may be the best fit. This is a prediction based on the lectures of Geoffrey West, in which he explains that most biological systems exhibit power law distributions with alpha in the 2.5-3.0 range. However, as seen in Figure 2, this does not seem to be the correct range for alpha if a power law is the best fit for this preliminary data.

Figure 2

The tail of the distribution does not fit well with the parameters shown in Figure 2.

I would venture to guess that the data may not be reliable in the displayed tail region. This would suggest that the data may need improvement in the portion where kingdoms and dynasties exist for longer than 200 years. The data I compiled, may of course be missing many kingdoms and dynasties. I believe that my sample is biased, due to these missing kingdoms and dynasties.

To improve this rough sketch of the distribution of kingdoms and dynasties, a highly systematic method must be devised to correctly measure the length of time of existence for any dynasty and kingdom. Also, this method must consistently be able to distinguish when a kingdom or dynasty begins and ends. The general idea is to measure the length of existence of a distinct political entity in a geographical region.

A sample must be obtained which is not biased. A dataset containing the population of all existing kingdoms and dynasties existing since the 3rd millinium B.C.E. would work best. Even so, this would be biased because it would ignore all the dynasties and kingdoms existing before that time.

1177 B.C.: The Year Civilization Collapsed – Eric Cline

anautonomousagent — Tue, 13 May 2014 12:24:00 +0000

Eric Cline’s book, 1177 B.C.: The Year Civilization Collapsed, provides a scholarly summary on the rise and decline of the bronze age in the Mediterranean region. Citing a number of different reasons for collapse, I find the most interesting to be a complex systemic failure arising from a continuous wave of natural disasters combined with external attacks by “sea peoples” which the “global” system could not withstand. These shocks were applied to the ancient system at its peak, in terms of power and interconnectedness, which indicates that collapses seem to occur near peaks, not troughs, in societal wealth and prosperity. And several civilizations tend to disappear at the same time; much as species extinction tends to occur in clusters. Chinese dynasties, Mesopotamian cities, Persian kings, the Mongols, the Romans and countless other examples show the same pattern.

I am interested in seeing a frequency plot showing the number of states, governments, societies which last a given length of time (similar to here except with plots; the average tells us nothing about the shape of the distribution). And if no such plot exists I will try to create one. Collapse occurs time and time again in the history of humans and biological evolution. To me, this seems to indicate a natural law of growth which applies to all biological growth phenomena. And such a law has been mentioned by Robert Prechter and provides a basis for mathematical analysis.

“THE CHAOTIC UNIVERSE” – Ilya Prigogine, John Cage, Huston Smith

anautonomousagent — Fri, 07 Mar 2014 04:59:00 +0000

Art Meets Science & Spirituality in a Changing Economy – “THE CHAOTIC UNIVERSE” – Ilya Prigogine, John Cage, Huston Smith

Old, but good!

Price Simulation of Trader Matrix Video

anautonomousagent — Sun, 01 Dec 2013 02:02:00 +0000

The following video is the time evolution of a network of 10,000 traders and their effect on the price movement of a stock.

For more information, please read the following paper:

Non-normal Model of Stock Prices

An Interesting Model of Asset Price Behavior using a Tri-Valued Matrix of States

anautonomousagent — Thu, 28 Nov 2013 18:39:00 +0000

Stock prices, as seen by many appear to be purely random processes with no patterns and thus no predictability. And more often than not, people unfamiliar with stochastic processes will equate the work of financial engineers as “hocus-pocus,” “rocket science,” or just plan gambling. Are these people correct? Are asset managers playing roulette with the public’s money? If so, then it would seem that the life work of people such as Ito, Merton, Black, Scholes, Hull, Cox, White, Detemple, Sornette, and others amount to no more than speculation or the ramblings of an inmate in an insane asylum. Assuming otherwise, and that there is method to the madness of these academics, prices are predictable. And stochastic calculus provides a framework with which to build predictions. But how well and how reliable are the calculations? How can we use this predictability to properly manage risk?

There are at least two important responsibilities for risk managers:

1. Risk managers must make rational decisions. An empirical and purely quantitative forecast of future returns should be made with a clear understand of model assumptions.

2. With the foresight provided by the model, a suitable strategy must be taken. If the observations are indicating current market bubble conditions, then managers should be selling, or at the very least not buying.

These responsibilities are general and do not depend on the model being implemented to forecast returns. The accuracy of the forecast depends greatly on the assumptions used to create the model. The majority of models assume:

1. That returns are independent in time.

2. That volatility is constant.

3. That markets are efficient.

4. That prices follow the Geometric Brownian Motion

In other words, most models assume that human emotions, psychology, and behavior are not factors in determining the price movements of assets. How can such critical factors be ignored by financial engineers? The number of papers dealing with the effects of behavior on stochastic equations are few. Instead, the academic community has and continues to brush off these factors with the wrongly conceptualized idea that the sum total of all human interactions will create Brownian Motion. The billions of collisions on a grain of pollen in H₂O are what stirred the creation of this type of stochastic process. So, the question is: Can we equate the process which creates Browian Motion as observed by Brown himself, to the structure of asset price movement? One is created through thermal random thermal interactions; the other through human emotion, psychology, and behaviour.

Risk managers should realize these assumptions and they should be cautious.

If risk managers believe in the predicatablity of prices, then we must, by force of principle assume that there is an underlying structure. In other words, consider the prediction of Earthquakes. The fact that we even consider the ability to predict their occurrence suggests that we have some degree of knowledge regarding their underlying structure. By believing in the predictability of price trajectories, we naturally assume some underlying structure. But what is this structure? How do we monitor the processes at work?

Are returns predictable? According to much research, the answer to this question is a firm, yes. But arbitrage theory says that such predicatablity can not exist. So, what does the risk manager believe? Does he believe that prices are Brownian Motions; that markets are efficient machines, not affected by the emotions, psychology, and behavior of humans; or does he disregard these assumptions in search for a better stochastic model? The answer to this question lies in controversy and may not be resolved for a long time. However, the risk manager has 100 billion of assets which he must manage today. Where is he to look for alternative models which disregard the assumptions of his collegues and predecessors? This paper provides the beginning of one such alternative.

This paper presents a stochastic model of the form: change(price) = function(volume). The volume depends on a matrix with a fixed number of agents. The intuition behind this model comes from the concept that a stock price’s movement should reflect not a normal distribution, which has roots in the idea of Brownian motion and particles in heat transfer, but rather a bi-directional “tug-of-war” between agents who are buying and selling with human emotions, psychology, and behavior. Just as in the youthful tug-of-war game, there are times when it appears that the right side has the upper hand, when, all of the sudden the left side makes a determined effort and brings down the right side. These drastic and rapid phase transitions are unheard of in a Brownian idea of price movements. The Brownian application to asset price movements provide a decent first approximation. However, stochastic processes with Brownian Motion will never evolve in a manner to explain the stylized facts observed from the actual distribution of asset returns. Thus, to truly model price behavior, practitioners should study the fundamental structure of the market.

Consider this thought experiment:

Take a snapshot of all market participants in a security XYZ. This is period zero (t = 0). Suppose there are a fixed number, N, total people in the financial system who can own and trade XYZ. In other words, the price movement of this asset should depend only on the actions of these N traders. Now count the number of traders who currently hold a short position in XYZ and a long position in XYZ. Let S₀and L₀ represent the number of traders who are currently short and long, respectively, the asset XYZ. Let S₀ + L₀< N, thus there are a number of traders, H₀, who hold neither a short nor a long position. Thus, H₀ = N – S₀– L₀. The current price of XYZ is P₀. Assume that all transactions only involve 1 share of XYZ. Further posts will seek to address the important consideration of number of shares.

Now consider the next possible moves for all traders in the market (t = 1). There are assumed to be four possibilities:

An XYZ owner with a long position sells. (L₁ = L₀ – 1 and H₁ = H₀+ 1)
A trader short XYZ covers his/her position. (S₁ = S₀ – 1 and H₁ = H₀+ 1)
A neutral trader initiates a long position. (L₁ = L₀ + 1 and H₁ = H₀– 1)
A neutral trader initiates a short position. (S₁ = S₀ + 1 and H₁ = H₀– 1)

Thus, numbers 1 and 2 increase the number of neutral traders, while 3 and 4 decrease that number. Assume that both 2 and 3 cause the price of XYZ to increase by some factor and 1 and 4 decrease the price of XYZ by the same factor. Thus the movement of the price of XYZ should be a bi-directional “tug-of-war” battle: traders going long and shorts covering versus traders shorting and longs selling.

To represent this computationally, a matrix can be created which holds the current state of all traders. To create the initial state matrix, called StateMatrix₀, form an √N x √N square matrix (for simplification, it would be best to choose N as a perfect square). Then fill the matrix randomly with the value -1 for the correct number of traders short XYZ, S₀. Do likewise with L₀and H₀, represented by 1 and 0, respectively. Thus, the initial StateMatrix₀ will be randomly filled with {-1,0,1}, representing the traders who are short, neutral, and long.

Now, proceed one period to t = 1. To calculate the next StateMatix₁, do the following:

Assume that each trader is influenced by U of his peers and that this influence is proportional to a factor representing the general market “mood.” Call the mood factor for the current period, M_t. To find what the trader will do in the transition from t = 0 to t =1, sum the values of his U neighbors, find their average, multiply by the current M_t and round. In addition, include a possibility for trader_[i,j] to form his own independent value {-1,0,1} and ignore his U neighbors with probability, IDIO (an idiosyncratic change of asset position).

For example, suppose that at t = 0, trader_[i,j] of the matrix was short, i.e. the value was -1 and that his 4 neighbors at i = 0 had values {1,0,1,-1}. Suppose the M₁ at this time is 1.2 and IDIO = 0.20. If this trader_[i,j] does not choose an idiosyncratic position, then he mimics his neighbors. The sum of his four neighbors is thus SumTrader_[i,j] = 1 + 0 + 1 – 1 = 1 and the average is ¼. Thus ¼*1.2 = 0.3. Rounding give a value of 0. Thus, the trader_[i,j] should change his value to 0, in other words the trader_[i,j] will cover his position.

Performing this calculation for every trader on the grid will create the StateMatrix₁. And doing this for T periods will create a StateMatrix_{t=[0,T]} sequence of trader states. To calculate the actual price movement based on this model do the following:

Sum over all values of trader_[i,j]of StateMatrix_t
Sum over all values of trader_[i,j]of StateMatrix_t+1
Calculate the difference, StateMatrix_t+1 – StateMatrix_tand divide by N. Multiply by P_t. This value = C, the change in the price from the previous price
Price_t+1 = Price_t+ C

This will form the evolution of the price through the states of the StateMatrix_{t=[0,T]} sequence.

Note: In order to make the M_tfactor suitable, its values must fall between [0,1.5). If not, then values of the traders_[i,j] may be other than {-1,0,1}. The M_t factor can be calculated at each period with the following calculation:

M_t = #L_t-1/#S_t-1

In other words, the Mood factor M_tfor the next period is the ratio of the number of current traders who are long to the number of current traders who are short. There may be other ways to define this factor.

Look at the previous post, here, to see an example. In that post I used:

N = 1,000,000

T = 700

U = 4

S₀ = 0.4*N

L₀ = 0.4*N

IDIO = 0.19