1. Evolutionary Dynamics by Martin Nowak

Wherever information replicates, wherever there is life or culture, whether in the fields of stocks, language, viruses, cancers, HIV, infections, rumors, games, there is evolution. Evolutionary Dyamics is a masterful book, the kind that you will wish to read 5 or 10 times that gives you a foundation for studying the processes involved, and then applies it to all the fields. I can't recommend the book too highly.

It starts with a discussion of how simple models can lead to extraordinarily complex behavior. The discussion of finite difference equations and how the basic equation   X(t+1 ) = X(t)(1-X(t) * A can lead to all the paths that you have ever seen or imagined with time series in your life.

A discussion of the basic mathematics of how an error in replication, a mutation, can change the dynamics and lead to all sorts of ultimate outcomes from coexistence, to complete exclusion to survival of the first is also a point of departure for all topics covered.

Each chapter applies the basics to a new field. The fields covered include cancer, language, epidemics, viruses, HIV. The chapter starts with a discussion of a basic dynamic equation, how it relates to the foundation laid in previous relative to growth rates, carrying capacities, feedback effects, and equilibrias. Diagrams illustrate the main points. And summaries at the end of each chapter contain a nice review of all the main points.

 The book uses differential equations as the basic building block for illuminating all the applied fields covered. A knowledge of the basic solutions is helpful. However, the layman without that training can get the gist, and with a pencil and paper, and review of each chapter can find himself marveling about how much fuzzy thinking in the field is clarified by precise counting and tracing.

If there is one suggestion I have for the book, it would have been to use difference equations more than just once or twice to illustrate the topics covered rather than using the closed form mathematical solution. It also would have been nice to see how the computer friendly reader or researcher might have simulated the conclusions and principles reached. Applications to economics would also have been appreciated.

I can't recommend the book too highly. It's set in easy to read type. And it has a great discussion of the history and development of each field in it. I intend to read it over and over as a lynchpin for understanding modern biology, disease, and meme transmission. Darwin and Galton would both have expressed keen appreciation and amazement at the clarity which this superb book brings to the many areas that they studied.

2. The search for isomorphisms, propositions of the same structure valid in two or more disciplines, was part of systems analysis as developed by Kenneth Boulding as a way of unifying the sciences, natural and social.

-Nathan Keyfitz, in a biography of Kenneth Boulding.

What isomorphisms are useful for augmenting our knowledge and profits in markets?

Peter Grieve writes: 

 I think that unification is the highest scientific endeavor. For me, taking two things that look completely different on the surface and demonstrating an underlying unity is as good as it gets.

The highest example of this (for me) has to be when Einstein did it with space and time. He unified them into the concept of "interval" ( although they are not quite isomorphic since time has that minus sign). He also unified electric and magnetic fields to the same degree, and they appear very different on the surface.

Gary Rogan writes:

Until we answer how the physical laws "know" to work in every part of the Universe or at least a lot of it, we won't know anything but the symptoms of the cause. There is something very strange and basic about the structure of the Universe that keeps some aspects invariant.



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