In connection with the fine tuning problem, the
argument of the typist monkey is often used as an illustration that even very
unlikely events can occur spontaneously. Depending on the author of the quote, the
text supposedly written by the monkey can be the complete works of Shakespeare,
Don Quixote, or even a shorter and less specific work. For instance, John Leslie, in his book

*Universes**(Chapter One), writes:*

*Our universe can indeed look as if designed. In reality, though, it may be merely the sort of thing to be expected sooner or later. Given sufficient many years with a typewriter, even a monkey would produce a sonnet.*

Let us simplify the problem. We are going to ask the monkey
to type, by pounding randomly the keys of the typewriter, something much
shorter than a work by Shakespeare, or even a sonnet. We will just ask for the
first sentence in Don Quixote:

**En un lugar de la Mancha, de cuyo nombre no quiero acordarme, no ha mucho tiempo que vivía un hidalgo de los de lanza en astillero, adarga antigua, rocín flaco y galgo corredor.**

We assume further that the typewriter has only the
minimum number of keys: 27 letters, comma, period and blank space. To simplify
even more, we accept a text written in lower case. Can we estimate how long it
would take the monkey to write this text, by pounding the keys at random?

Drawing by Gustavo Doré |

Let's see. The probability that a certain text of 177
characters is generated by banging randomly on 30 keys (we assume that the
probability of the monkey pressing any key is the same) is 30

^{-177}»3.5´10^{-262}.
Assume that the monkey is able to type 177 characters
per minute. In that case, what he produces every minute can be considered an
attempt to reproduce the first sentence of Don Quixote. Assuming (a big assumption)
that no text is repeated, that all the attempts are different, how long would be
needed to produce all the possible variations of the characters in the
indicated text, one of which is this piece of Don Quixote? It is easy to see that
it would take 2.8´10

^{261}minutes (the inverse of the number of variations), equivalent to about 5.3´10^{255}years, i.e., 3.8´10^{245}times the age of the universe (a 3 and an 8 followed by 244 zeros).
The conclusion is obvious: however many years we left
the monkey with the typewriter, it is not reasonable to think that it would be able to type that small piece
of Don Quixote, as it would die much earlier. In fact, if we force the poor monkey
to pound all the time on the typewriter, with no time to eat or sleep, its life
expectancy will be dramatically reduced.

Yes, I know, the monkey is metaphorical, and the
objective of the problem is to show that, given enough time, however
long, even extremely improbable events may happen (those with a very small
probability, greater than zero). But look at the question from the opposite
side. If we find the text quoted above, which of the following two hypotheses
should be considered more rational?

•
That the text was written by a person with a certain
intention.

•
Or that the text arose by chance, as though it had been
produced by a monkey pounding on a typewriter.

**The same post in Spanish**

**Thematic thread on Multiverse and Fine Tuning: Preceding Next**

**Thematic Thread on Statistics: Previous Next**

**Manuel Alfonseca**

**(For Fonch)**

Excellent post!! Elena from the USA

ReplyDeleteThank you so much for the interesting article on a suggestion I've always found unsound.

ReplyDeleteThanks. I have a couple of things to add to the post:

ReplyDelete1. An event may have a very low probability, but its occurrence may be certain. So, if you buy a single ticket for a lottery with 100.000 different numbers, your probability of winning is 10^-5, but if all the numbers are sold, someone will win the first prize anyway, even with such a low probability. This happens because there are many people playing, and if a number is sold, nobody else can buy it.

Does this happen in the monkey case? Not at all. Let us assume that the probability of a text being written were 10^-500, and that there are 10^500 monkeys pounding on typewriters in parallel. Would the text in question be sure to written in this situation? No, because we couldn't assume (as I did in the post) that two monkeys will always write different texts. In fact, the number of repetitions could be very large, without any limitation. Therefore it would not be certain that the text in don Quixote would ever be written.

2. The multiverse hypothesis has been introduced to solve the fine tuning problem, but it doesn't. String theory, for instance, postulates the existence of 10^500 possible different universes. But even if there were 10^500 universes in existence, we wouldn't be able to assure that there were no repetitions, therefore we would be in the same situation as the 10^500 monkeys pounding on typewriters. Therefore those multiverses do not solve the fine tuning problem. To do that, the only way is postulating the existence of an infinite number of universes (as Tegmark does). But this introduces other problems, as I have pointed in previous posts in this blog.