Timeline for Given an infinite number of monkeys and an infinite amount of time, would one of them write Hamlet?
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| Sep 17, 2022 at 10:47 | history | edited | Cheese Cake | CC BY-SA 4.0 |
improved formatting
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| Mar 4, 2018 at 2:33 | comment | added | Matt | The probability of flipping 50 consecutive heads, $1/2^{50}$, has just 15 zeros after the decimal point. Describing this number by falsely saying it is as small as a number with $3\times 10^{23}$ zeros after the decimal point is, to put it politely, an inaccurate comparison. The chance of dying from a random lack of oxygen is approximately the same as the chance of flipping $10^{24}$ consecutive heads. Not $50$ consecutive heads. Not even close. | |
| Mar 4, 2018 at 2:32 | comment | added | Matt | Let's do a rough calculation. To die from random absence of oxygen, say you need around 5 minutes of no oxygen. During these 300 seconds, you might take 200 panicked breaths, each around 0.5 liters, so we are talking roughly 100 liters, or 130 grams, of air being oxygen-free. This is roughly 5 moles of gas, and each gas molecule has about a 4/5 chance of being something other than oxygen, so the chance of 5 moles $(30\times 10^{23} molecules)$ being oxygen-free is around $(4/5)^{30\times 10^{23}}=10^{-3\times 10^{23}}$. That's about $3 \times 10^{23}$ zeros after the decimal point! | |
| Mar 4, 2018 at 2:32 | comment | added | Matt | But this quote from the professor is very wrong. The chance of 50 heads, $1/2^{50} \approx 10^{-15}$, one in a quadrillion, is indeed low: There are roughly one quadrillion hairs on people's heads on Earth, so it's the chance of winning a lottery where you have to pick the right strand of hair on the right person's head. But the chance of dying from lack of oxygen is far, far lower. If the chance of randomly not having any oxygen for 5 minutes were as big as $1/10^{15}$, then someone would die from "random lack of oxygen" every year. | |
| May 10, 2017 at 14:34 | comment | added | electronpusher | +1 for professor's quote, great metaphor for visualizing how unlikely such a small probability truly is. | |
| Nov 21, 2011 at 6:59 | comment | added | Mateen Ulhaq | Also, I doubt the monkeys will specifically twist their hands for each letter. The QWERTY keyboard was designed to make it slower/harder to type, after all, so I doubt the mindless monkeys will go to all that trouble to contort their 'inferior' hands. | |
| Jan 14, 2011 at 6:10 | comment | added | Mateen Ulhaq | @ShreevatsaR Talk about practical thinking. | |
| Jan 12, 2011 at 22:58 | history | edited | Jonas Meyer | CC BY-SA 2.5 |
cleaned up a little
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| Jan 12, 2011 at 20:33 | comment | added | Armstrongest | And there would need to be an infinite amount of space to contain the monkeys... not to mention infinite typewriters... better ramp up typewriter production in China. | |
| Jan 12, 2011 at 14:42 | comment | added | ShreevatsaR | From a [ultra]finitistic perspective, I don't think you can say "NO"; you can only say that the question is meaningless as there's no such thing as infinite time or infinite monkeys. | |
| Jan 12, 2011 at 8:41 | comment | added | Asaf Karagila♦ | Ultrafinitism takes out all the fun from mathematics. Especially from the parts dealing with infinite processes. | |
| Jan 12, 2011 at 8:07 | history | answered | epeleg | CC BY-SA 2.5 |