Patience and work, or about real madness
Patience and work will grind everything down, says the famous proverb. In contrast, Vaas Montenegro has repeatedly said that madness comes down to a series of repeated attempts that follow one after another. Well, if we take an infinite resource and an infinite time, and stubbornly try the probabilities, will anything useful come out of it?
An army of monkeys and endless typewriters
According to the infinite monkey theorem, if we had an army of monkeys typing forever, they would eventually create all of Shakespeare's works, but they would do so by pure chance. This is a mathematical exercise about probabilities when infinity is involved. In fact, if there is a non-zero probability of an event happening, it will almost certainly happen if we have infinite time.
This is theoretically true, but it is obvious that in our finite universe it is impossible to have an infinite number of monkeys or an infinite time. Mathematicians in Australia asked the question of counting and came up with interesting results.
Approach to calculations
We decided to estimate the probability that a given string of characters would be typed by a finite number of monkeys within a finite period of time, corresponding to estimates of the lifespan of our Universe.
Stephen Woodcock, one of the lead authors of the study.
For their calculations, the team assumed that the monkeys were using a keyboard containing 30 keys—the 26 letters of the English alphabet, plus the most common punctuation marks. Each chimpanzee is assumed to press one random key every second. Will it be cryptoanarchismwhat if we use similar simulations for encryption?
They then calculated the probability that certain texts would be typed by one chimpanzee in its lifetime, and also calculated the workload for a population of 200,000 individuals—a rough estimate of the number of living chimpanzees in the world. In the experiment, monkeys must work until the thermal death of the universe. It is believed that this will happen approximately 1 googol years from now, which is 1 followed by 100 zeros. They have time.
Relationship between letters and time
Of course, the simpler the phrase, the more likely the monkeys are to write it among their random keystrokes. We have a 5% chance that one chimpanzee will correctly type the word “bananas” during its 30-year lifespan, and a 100% chance that the word “bananas” will be found among the ramblings of 200,000 such chimpanzees before the universe ends.
The slightly more complex phrase “I am a chimpanzee, therefore I exist” will be written with a probability of 0.00000000000000000000000001%, by one chimpanzee in 1 of his life. However, again, the probability of writing this phrase is close to 100%, provided that we work “until the death of the Universe.” Loyal enough conditions for self-development.
But as the length of texts increases, the chances of writing them rapidly decrease. The children's monkey story “Curious George” is 1,800 words long. To this end, if 200,000 monkeys work until the universe dies, then the probability of a successful outcome is 15,000 zeros after the decimal point.
For the original Planet of the Apes novel, which is approximately 83,000 words long, the probability is closer to 700,000 decimal places. And for the complete works of the Bard, which is approximately 885,000 words, there are 7.5 million zeros.
Returning to the Hypothetical Monkey Experiment
In other words, it would take 200,000 apes four universes before they arrived at Curious George, six universes before Planet of the Apes, and seven universes before Shakespeare's works. I wonder what things would be like if we added the factor of use to the equation nootropic drugs?
This discovery puts the theorem on par with other probabilistic puzzles and paradoxes, such as the St. Petersburg paradox, Zeno's quantum paradox, and the Ross-Littlewood paradox, where using the idea of infinite resources produces results that are not the same as what we get when we consider limitations of our Universe.
Stephen Woodcock, one of the lead authors of the study.
Of course, one could argue that the point of the original thought experiment is not to take it as a literal method for creating great works, but simply as one method for illustrating the concept of infinity. After all, having 200,000 immortal or self-replicating apes working in sequence until the end of the universe is as unrealistic as having infinite time. Still, sometimes it helps to mark things up a little.
Thus, the article concludes, we must conclude that Shakespeare himself inadvertently provided an answer to the question of whether ape labor can be a meaningful substitute for human labor as a source of science or creativity.
To quote Hamlet, Act 3, Scene 3, Line 87: “No.”
