Sojourner553

The following is from Michael Shermer (President of Skeptics.com's newsletter):


In the latest issue of Scientific American, the Editor-in-Chief John Rennie
wrote a brilliant article entitled "15 Answers to Creationist Nonsense,"
debunking creationist arguments

<a href="http://www.sciam.com/article.cfm?articleID=000D4FEC-7D5B-1D07-8E49809EC588EEDF&pageNumber=1&catID=2" target="_blank">http://www.sciam.com/article.cfm?articleID=000D4FEC-7D5B-1D07-8E49809EC588EEDF&pageNumber=1&catID=2</a>

Per Shermer:

In the article is a reference to Richard Hardison study,

"on how long it would take a monkey to randomly type 'To be or not to be.' It would take 26 to the power of 13 trials for success, which is 16 times as great as the total number of seconds that have elapsed in the 4.5 billion years of our solar system. But Hardison designed a computer program that acts like natural selection: it preserved the gains and eradicated the mistakes. In other words, the computer "selected" for or against letters as they were randomly produced (if "T" preserve, if "Z" skip), and took an average of only 335.2 trials to produce the sequence TOBEORNOTTOBE. It took only 90 seconds.
Hardison calculated that the entire Hamlet play could be done in 4.5 days.

...

IN "UPON THE SHOULDERS OF GIANTS" BY RICHARD HARDISON, 1985, University Press
of America, pp. 123-124:

"Taking exception to the view that orderliness could be chance-determined, the anti-evolutionists point out that while the monkeys might type Hamlet in theory, they could not do so in the real world, for the time required would
be much too great.

Let us imagine an intrepid monkey punching away at a typewriter keyboard. For the monkey to stumble onto just the few words, "To Be Or Not To Be" would require a prohibitive improbability. Mathematical expectancy would lead us to
anticipate some 26 to the 13th power number of trials before the litttle rascal prints out the desired sequence and sends his typewriter off for a much-needed ribbon replacement. This number of trials is so large that it is roughly 16 times as great as the total number of seconds that have elapsed in the four and one half billion years of the solar system's existence.

These enormous numbers apply for just the first 13 letters of Hamlet's siloloquy, and for every additional letter, the odds against continued
success grow by leaps and bounds. More significant still is the fact that
producing Hamlet is child's play when compared with constructing the human eye or inventing the process of reproduction. Rather discouraging.

However, this just isn't the way evolution works. To the contrary, nature keeps the successes and discards the failures. The gains are perpetuated, so to continue the typewriter analogy, when our simian friend happens upon a T, that letter is kept and he goes on randomly typing until he strikes an O, which in turn is retained. And so on.

What then are the chances of arriving at the opening line of Hamlet's question with this scheme of modified randomness? At first glance, this may seem the kind of problem that is not suited to calculation (since one end of
the distribution curve is infinite) but it is possible, using a simple formula that is proved by calculus and infinite geometric series, to arrive at the theoretical number of trials that would be expected (338), and it is also possible to program a computer to test the calculations empirically. Let us have the computer randomize alphabet selection until a T is drawn. Then it
will be programmed to do the same for the O and continue accordingly for the desired 13 letters. Interested readers should consult APPENDIX E for a print out of the "Basic" program that will perform this test of empirical probability ten successive times.

When running the program through a home computer 1000 times, it developed that an average of 335.2 trials were required in order to produce the
sequence of letters "TOBEORNOTTOBE." Small computers do not have perfect random number generators, but the outcome gives reasonable support to the theoretical expectancy of 338. Clearly 338 is a number of vastly different
magnitude than the number of seconds that have elapsed in the history of the solar system."


Sojourner

beausoleil

My mistake - it's getting late, and I guess I was laughing too much.

[ June 23, 2002: Message edited by: beausoleil ]</p>

beausoleil

Blimey, how complicated!

Each time the monkey strikes the keyboard at random it has 1 chance in 26 of hitting the currently desired letter. If something happens on average once every 26 instances, and you need 13 successes, you need on average 26x13 = 338 instances. The same as for any specific sequence of 13 letters. If that weren't true, at the end of the experiment you'd end up with a probability per letter different from 1/26.

Look - no program, calculus or infinite geometric series!

[ June 23, 2002: Message edited by: beausoleil ]</p>

beausoleil

Boy - I'm having a bad day today! - that's 2 inadvertent postings in close succession. Maybe I should have a monkey use this keyboard.

[ June 23, 2002: Message edited by: beausoleil ]

[ June 23, 2002: Message edited by: beausoleil ]</p>