I had to laugh at this report from the BBC.
Two Australian mathematicians have called into question an old adage, that if given an infinite amount of time, a monkey pressing keys on a typewriter would eventually write the complete works of William Shakespeare.
Known as the "infinite monkey theorem", the thought-experiment has long been used to explain the principles of probability and randomness.
However, a new peer-reviewed study led by Sydney-based researchers Stephen Woodcock and Jay Falletta has found that the time it would take for a typing monkey to replicate Shakespeare's plays, sonnets and poems would be longer than the lifespan of our universe.
Which means that while mathematically true, the theorem is "misleading", they say.
As well as looking at the abilities of a single monkey, the study also did a series of calculations based on the current global population of chimpanzees, which is roughly 200,000.
The results indicated that even if every chimp in the world was enlisted and able to type at a pace of one key per second until the end of the universe, they wouldn't even come close to typing out the Bard's works.
There would be a 5% chance that a single chimp would successfully type the word "bananas" in its own lifetime. And the probability of one chimp constructing a random sentence - such as "I chimp, therefore I am" - comes in at one in 10 million billion billion, the research indicates.
There's more at the link.
I wonder how many man-hours of research went into that particular study - and at what cost per hour? What's more, the report says it was "peer-reviewed". Precisely what "peers" are we discussing? Gorillas? Orangutans? Perhaps the gibbon or the colobus were asked to opine? (Although, since Australia has no native species of monkey or ape, the platypus or the Tasmanian devil might have to stand in for them.)
On the other hand, with odds like that, perhaps we could turn loose a troop of monkeys among the slot machines in a top Las Vegas casino, along with an infinite supply of quarters to feed them. Who knows what they might not win?
Peter
14 comments:
We're the monkeys, and we've already produced the complete works of William Shakespeare, et. al.
On the surface it seems like a trivial topic to research, but during the history of science there were some other cases of apparently frivolous topics of study which provided practical results later on. A case fairly recent is that of Andre Geim's experiment in levitating a frog by magnetism (got the Ig-Nobel prize for that) which gave him some insights in studying the behavior carbon allotropes (particularly graphene) in a magnetic field (for which he got the Nobel).
Either they missed the point of "infinity", or are trying to explain just how infinite it is.
The headline at NPR is "Infinite Monkey Theorem is impossible within our universe's lifetime, study shows". Right! That's infinity.
Someone's line (which I can't find to properly credit) was, "If you put an infinite number of monkeys in a room with an infinite number of typewriters, the smell would be terrible."
And of course, there's this take :
https://youtu.be/Ngmf8G5xKas?feature=shared
Genesis 1:1!!!
R.A. Lafferty anticipated the mathematicians' result over fifty years ago: https://gwern.net/doc/fiction/humor/1970-lafferty.pdf
The Aussies screwed up as chimps are considered apes, not monkeys. Baboons are well known typing and keyboard skills. The New World monkeys have the advantage of using their prehensile tails. I'm sure the world population of monkeys could produce one Stephen King novel a week give modern word processors.
How many angles can dance on the point of a pin? Two infinities; do they match in size. Real math expressed in culturally appropriate terms. So the monkeys typing (inifinite) forever (infinite) to produce a given product. A simple restatement in presently culturally appropriate terms.
So, the math on this isn't actually that difficult. If we ignore punctuation (since I don't know the extent of the punctuation Shakespeare used), the possible combination math is 27 (26 letters and spacebar) for every single keystroke, multiplied by the number of keys. So, "egg" is 27x27x27=19,683. Divide by number of letters per minute(60 per monkey) and you get 328 minutes for a monkey typing at 60 characters per minute to write the word egg. The math problem is simple:
Given:
41 keys per typewriter (letters, spacebar, numbers, period, semicolon, comma, question mark, but ignoring capitalization completely)
Given monkey hitting 1 key per second
S=number of characters in all of Shakespeare's works
M=number of monkeys in the world, each typing 24/7)
Time to Shakespeare =41^S/(M*86400(keys/day)
Lifetime data and populations could be added to the calculation if you really wanted to, but those wouldn't be hard to find. The only real issue is finding the computing power to solve that 41 to the power of the number of letters in the complete list of Shakespeare's works(Google says 884,421 words. For a ballpark, if we average them to 4 letters each{its likely more, but...} we get 3.54million letters, add in 1 space per word, we get 41^4422105). [Every calculator I tried errored out at 41^4422, so this should give you an idea of the computation problem . 41^442=3.7×10^193, and we need to go up exponentially a few thousand times that number. ]
~Squire
I suppose, given the logic, if enough tornados blow through enough Home Depots over enough time, eventually a house would be built. No intelligent design required.
Theoretically, one could do it during its lifetime.
If I were given a study like that and paid to read it, I would go to the beach and have it pier reviewed.
An infinite number of monkeys with an infinite number of typewriters and given an infinite amount of time MIGHT produce the works of Shakespeare but I bet one monkey with one typewriter and half an hour could produce the lyrics for a rap song.
Cost of bananas not included.
Phil B
i vaguely recall an article a few years back wherein researchers put 20 monkeys in a rom with typewriters for several hours to see what would happen, and proved that even the math is bunkum, becuz the math presumes random keypresses, but the monkeys gravitated to certain letters in an apparent liking of the shapes. The lower-case r was particularly over-represented in their output, with many strings of repeated r's in lenghts of 20 or more keystrokes.
All in all, the researchers concluded it'd take even longer than the math suggests as a result.
I don't think these "researchers" actually understand the word infinite....
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