# interesting problem

## stevan apter — 2002-04-16 13:02:01

    "Now the last topic I would like to turn to is an illustration of the forces of evolution, to give you

    some idea of how powerful this new paradigm can be in explaining change and innovation. It's a

    very simple example which has nothing to do with satisficing, but I think you'll see its relevance

    to our current discussion immediately. I'd like to ask you to think about an experiment in which

    we randomly select nine letters of the English alphabet. What do think the chances are that such

    a draw will produce the phrase "CAPMLIVES"? Well, the odds are one in

    26^9 =5,429,503,678,976, approximately one in five-and-a-half trillion; very unlikely indeed.

    But I'm going to propose a little evolution in this example. Let's start with the random draw

    "TJIXOMSFZ", and suppose that this particular draw has 10 "offspring". By this I mean that 10

    new draws are generated from "TJIXOMSFZ", and here are the rules by which each offspring is

    produced: with 99 percent probability, each letter of an offspring will be the same as its parent,

    and with 1 percent probability it will change or "mutate". Therefore, the children will look very

    much like their parent. If a letter does mutate, it will change to any of the other 25 letters with

    equal probability. So to summarize, there's a one out of 100 chance that a mutation will occur

    for each letter, and if it does occur, there is a 1 in 25 chance that the mutation will be "beneficial"

    (in other words, the mutation will create a match to the corresponding letter in "CAPMLIVES").

    And let's assume that these random draws are independently and identically distributed for each

    letter of an offspring, and for all offspring. Finally, impose the following selection process for

    "survival of the fittest": of the 10 offspring produced in each generation, the only one that

    survives to "reproduce" is the offspring with the largest number of letters matching

    "CAPMLIVES" (in case of ties, we'll simply randomize). Then the process begins again, with

    the surviving offspring producing 10 children of its own under the same mechanism and with the

    same probabilities."

    from andrew lo:

    http://www.alphasimplex.com/research.html

## Manfred von Thun — 2002-04-18 01:02:43

    Nice paper, Nick, well done. And thanks to all who contributed.

    I have planted a link to this page in the main Joy page.

    Here it is again:

      http://groups.yahoo.com/group/concatenative/mandel.html

    I have done something hideous to all my old mail messages received,

    so I could not make this a proper "On ..date.. Nick Forde wrote.." reply.

    Sorry.

     - Manfred