mathematics – An Autonomous Agent

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.

The Misbehavior of Markets: A Fractal View of Financial Turbulence – Benoit Mandelbrot

anautonomousagent — Wed, 27 Aug 2014 23:45:00 +0000

I’ve been wanting to read The Misbehavior of Markets: A Fractal View of Financial Turbulence by Benoit Mandelbrot for a number of years. Mandelbrot helped to change the way people view financial market dynamics. This book is definitely a must read for people working in the financial industry. However, Mandelbrot was not the first. It is a little surprising that Mandelbrot did not talk in detail about the work of R.N. Elliott or Robert Prechter, among others, which I think complement Mandelbrot’s work on financial fractals. Patrick Harris wrote a short paper discussing whether Mandelbrot should have cited Elliott (link to paper).

To me, the idea of infinite memory processes is one of the most important concepts touched on by Mandelbrot in this book. It suggests that economists and traders should be developing models and theories which value the importance of price series and data going back decades. And it makes sense to me that people and prices do not change their fundamental behavior over extended periods of technological evolution. However, I suspect that organisms do change their fundamental behavior if the time horizon is thousands or millions of years. I am very curious to read more about Hurst’s studies of the Nile.

Dangerous Knowledge – David Malone BBC

anautonomousagent — Wed, 16 Jul 2014 03:04:00 +0000

Dangerous Knowledge, by David Malone, summarizes the work and life of some of the greatest thinkers in late 19th and 20th centuries. Includes the work and life of Cantor, Boltzmann, Godel, and Turing.

Watch it here: Dangerous Knowledge

Kondratieff Waves, Warfare and World Security: Volume 5 NATO Security through Science Series: Human and Societal Dynamics – T.C. Devezas

anautonomousagent — Sun, 13 Jul 2014 17:53:00 +0000

Kondratieff Waves, Warfare and World Security: Volume 5 NATO Security through Science Series: Human and Societal Dynamics by T.C. Devezas is what I am currently reading.

Fascinating to say the least.

Also, see: A Spectral Analysis of World GDP Dynamics: Kondratieff Waves, Kuznets Swings, Juglar and Kitchin Cycles in Global Economic Development, and the 2008–2009 Economic Crisis Korotayev, Andrey V and Tsirel, Sergey V.

All Watched Over by Machines of Loving Grace – Adam Curtis

anautonomousagent — Sun, 13 Jul 2014 13:02:00 +0000

All Watched Over by Machines of Loving Grace, by Adam Curtis, provides a grand overview of many of the people and ideas which have shaped the development of computers, systems, social theory, and politics over the past century. It is one of the better documentaries I have every seen and definitely worth watching; however, I agree with the reviewer John Preston who said it had an “…infuriating glibness too as the web of connectedness became ever more stretched. No one could dispute that Curtis has got a very big bite indeed. But what about the chewing, you ask. There wasn’t any – or nothing like enough of it to prevent a bad case of mental indigestion.”

Watch it:

Shush.se
All Watched Over by Machines of Loving Grace

Vimeo
All Watched Over by Machines of Loving Grace

The Tao Is Silent – Raymond Smullyan

anautonomousagent — Mon, 07 Jul 2014 11:40:00 +0000

The Tao Is Silent, by Raymond Smullyan, has been a wonderful read. Insightful and witty to say the least. It’s a series of discourses on life, religion, culture, logic, and philosophy; I would recommend the book to anyone interested in these subjects. Once again I am surprised how long it took me to discover a wonderful author. I look forward to reading several of his other works.

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.

Black Holes and Time Warps: Einstein’s Outrageous Legacy – Kip S. Thorne

anautonomousagent — Tue, 28 Jan 2014 17:31:00 +0000

It has been a long time since I read a book on astrophysics and I am now interested in Black Holes and Time Warps: Einstein’s Outrageous Legacy, by Kip S. Thorne. I hope this book will be thought provoking and fun to read.

The Evolution of Physics – Albert Einstein and Leopold Infeld

anautonomousagent — Tue, 28 Jan 2014 17:24:00 +0000

One of the next books I will be reading is The Evolution of Physics by Albert Einstein and Leopold Infeld. Even though the book was published in the 1960’s, most people seem to be in agreement that the book is still a must read for anyone interested in physics and the mind of Einstein.

Our Mathematical Universe – Max Tegmark

anautonomousagent — Tue, 28 Jan 2014 17:12:00 +0000

Max Tegmark’s book, Our Mathematical Universe, takes a deep look at the physical world and shows readers the importance of math throughout the universe. An interesting book regardless of your own personal beliefs.