The infinite monkey theorem states that a monkey, given a typewriter and infinite time, will be able to produce any text, such as the full script of Shakespeare’s Hamlet. The monkey would be typing randomly at the keys, and thus would be able to somehow get to the small probability of writing out all words in consecutive order (definitely with infinite time).
In 2002, some bizarre art students decided to try this out as their university project. Unsurprisingly, the monkeys were not only unable to type out Hamlet, but their pages mostly consisted of the letter “S.” Then, they promptly destroyed the keypad with stones and feces.
Which brings me to the question: instead of a keyboard, what would be the chance that a monkey would be able to scribble out, physically, a word? Of course, given random pixel-moving directions and spaces, it would be quite similar to the infinite monkey theorem in ideal conditions—with lots of flexibility in what counts as the correct letter (machine learning, anyone?).
However, real monkeys, as seen with the 2002 experiment, are very different from these abstract concepts. For example, they would be much more likely to put down a straight line vertically by thrusting their hand downwards than draw a complex scribble. Now, let’s go back to the English alphabet:
N O P Q R S T U V W X Y Z
If we don’t consider the lowercase alphabet (full of curves, which are less likely to produce and harder to distinguish if written in bad handwriting), the uppercase alphabet can be seen as quite optimal for a monkey situation: vertical and diagonal lines, with minimal curves—which could even be substituted with these types of letters used by ancient Romans:
With the exception of the letters O and Q, the Romans were good about one thing—keeping lines straight. This was probably because they wrote in stone, so we could give our monkeys a stone tablet.
Next, since we now know that the monkeys would be capable of badly handwriting capital English letters, we examine the biggest problem in random scribbles: spacing. Not only would it be difficult to set standards for what counts as a full word (diagonally written? upside down?), real monkeys are more than likely to overwrite what they have already written. However, for this particular thought experiment, overlaps are actually beneficial, because it would mean that the monkeys would fit more letters into a confined space—giving a higher probability of a distinguishable word appearing in an area. Since I am considering “words” instead of the full Hamlet, it is also easier to disregard any spacing between letters—so if a phrase spells out akfowbananaowlkd, “banana” would count as an acceptable word. It also would not be too much of a stretch to accept words written in whichever direction, as long as all the letters are somewhat in proximity to each other and are in uniform direction.
Thus, given a monkey a soft stone tablet (marble, perhaps) and a stylus, I hypothesize that it would be able to produce a readable English word within a few days—which, compared to the 5 pages of “S”s produced from the typewriter, is much more efficient.
Furthermore, I also hypothesize that giving monkeys stone tablets would give rise to a chance of monkeys developing their own writing system. Who knows?