Someone on twitter/X asked the following question:
A mathematician emerges from a cave, hands you the photo below, and asks "Will a chimp type the complete works of William Shakespeare if the chimp hits keys at random on a typewriter for an infinite amount of time?" What is your answer?
I have no idea why this is so controversial with people arguing with each other. Someone banging on about infinite number of infinite sets and all sorts of baloney. And then answering no! Eh?? The answer is obviously yes.
People seem to think the chimp could avoid certain letters forever. That it would be possible for the chimp to, say, type out an infinite number of "A"s. It isn't. Nor any other specific infinite series. Any such specific infinite series (e.g. an infinite number of A's), would have a probability of 1/infinity of occurring. Which is 0.
All finite strings will not only eventually occur, each and every one of them also occurs an infinite number of times!
Incidentally, I haven't read anything up about this. It's just me thinking about it for 5 mins.
7 comments:
I have to disagree about this. There is a vast difference between order and disorder. It is perfectly conceivable to have infinite degrees and variations on a disordered outcome, or even a randomly ordered outcome such as aaaaaaa . . .. However it is 'infinitely' more difficult to arrive at a very specifically ordered sequence. An ordered sequence, furthermore, is imbued with and severely limited in its extent by 'meaning', which is highly ordered. I find it difficult to see how randomness can ever simulate a sequence inspired in every word, by 'meaning', when random disorder is so much easier to perpetuate into infinity. Perhaps I am limiting my understanding of infinity here, but I don't think so. Chaos theory also must have some part to play in this debate, as small initial differences surely lead inevitably to more and more randomness.
"I have to disagree about this".
{Shrugs} I imagine I won't convince you otherwise, so I'll leave it at that.
Or maybe think about it again? Or shall we both just imagine that we can't convince each other otherwise? :-)
I don't need to think about it again.
You will find an interesting discussion of this very topic in 'The Paranormal' by Stan Gooch - Fontana, 1979 pp 179-184. If you can't access a copy let me know and I will scan the relevant pages for you
There's nothing to discuss. It's all straightforward and obvious.
Actually, it's not straightforward and obvious, and unless you investigate potential alternatives fully, you can never be sure that your contention is true. I propose that you have probably not investigated fully. The alternative that I am putting forward involves five pages of text - rather a lot to post here, but if you don't mind that I will do a scan and post it.
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