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Why most things fail: Evolution, Extinction & Economics

已有 4642 次阅读 2009-9-4 20:10 |系统分类:科研笔记|关键词:Evolution, Extinction, Economics

Fornew readers and those who request to be “好友 good friends”please read my 公告first.
Why most things fail: Evolution, Extinction & Economics - A book by Paul Ormerod , John Wiley 2005
This is a fascinating and entertaining read. The author, a professional economists and popular lecturer, cuts a wide swath using data mostly from the 19th and 20th century and examples from biology, Darwinism, economics, mathematical game theory, and public social policy to illustrate the title of the book which he claims. It is nevertheless, in this writer’s opinion, speculative, persuasive, but not totally convincing.
The author’s main thesis is that large scale problems such as:
·        Species evolution and extinction in biology
·        Commercial firm failures in a market economy
·        Ineffectiveness of Public social policy
are basically extremely complex problems involving interactions among large number of agents and causes. Because of such complexity, it is impossible to predict and account for the future computationally or theoretically using simple models. As a result, we have “ . . . the best laid plan of mice and men . . .” – a essentially random outcome.
 
While I basically agree with the conclusion of the book title, it occurs to me that there is a better explanation of the ”How and WHY“ in terms of a scientific paper I wrote a couple of year before the publication of the book, "The No Free Lunch Theorem, Complexity and Computer Security" (with Q.C. Zhao and D. Pepyne), IEEE Trans. On AC, v. 48, #5 pp783-793, May 2003. (this paper while technical should be accessible to most scientists or technology workers at least the first half of it) Let me give here a simple intuitive explanation of the thesis.
 
  1. If you believe in “causality” , i.e., everything happens due to a cause, then mathematically you can express this (a causality relation ) as an input-output function y=f(x) where x is the input cause and y the resultant outcome. 

  2. Assuming a finite world, i.e., in the real world there can be enormously large numbers ,e.g., the total number of possible values of x above, but no infinity, then for any finite set of x the number of possible outcomes y=f(x)  are y raised to the x power. This is an exponentially large number of possible outcomes. Exponential growth is one thing science and mathematics has not learned to conquer. 

  3. Computationally, human beings at any time can only deals with or plan for polynomially large numbers of possible outcomes but not exponentially large number of possibilities. Otherwise the famous P=?=NP question will not be an outstanding mathematics problem .

  4. Thus, in the real world, there will always be exponentially large number of outcomes we cannot predict, account, or plan for (exponential number – polynomial number is still exponentially large). 

  5. When these unaccounted for outcome occurs, and they will, good or bad outcome are equally likely. Thus, since you have no reason to assume otherwise, to a first approximation, failure is 50-50 and unavoidable.If you say you have some knowledge over the probability of some of the possible outcomes, then these outcomes belong in the polynomially accounted for case. What are left which are still exponentially large again can be assumed to be totally random.

  6. However, this does not mean we should simply give up. More planning will always be desirable. If you plan and do more, on the average you will succeed longer and the others fail. As the old saying “when a grizzly bear is chasing you and your companion, you do not need to run faster than the bear but only your companion“. Thus, men proposes and God disposes. One should always be striving and optimistic. 



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