No they won't.
If you give an infinite number of monkeys their typewriters, there's a small chance that one of them will type out Shakespeare's entire collection. There's a greater chance that some number of them will type out bits of Shakespeare. These can be combined, along with the one or two who type out entire plays, into the desired Riverside Collection. But you'll have to wait until they've finished... Which is when? Never, actually - the time they have is infinite.
There's an infinitesimal chance that all of the oxygen molecules in the room will gather in one corner. If you consider infinity as your time line, there's going to be a chance that this will happen for a miniscule moment, and also for an infinite amount of time. Either way, you're not feeling too well.
Because that miniscule chance never occurs.
The basic problem being that an infinite amount of time cannot equal a moment. A moment can seem like an infinity, but it's not - there is a beginning, a middle (it's irrelevant how brief that bit is) and an end. It's finite. Infinite, as the religious often tell us, has no beginning and no end. Does it have a middle? That's a theological question I'll leave for another day. :-)
So how are the oxygen molecules similar to the monkeys? It's reusing the argument that "over an infinite period of time, what can theoretically occur, will occur". So, if you give one monkey a typewriter and an infinite amount of time, it should also produce the entire Shakespearean opus. In fact, the monkey should produce endless variations on them.
Similarly, if we consider one oxygen molecule, it could potentially spend its entire "life" in the corner of a room. Erm... Let's assume that a plant in the room produced that oxygen molecule. it took in a molecule of carbon dioxide, did its magic and one molecule of oxygen was produced. That molecule was quickly (instantly?) shunted to the top right corner as perceived from the door of the room. Well, it would have to be instantly - otherwise we couldn't say it had spent its entire "life" in that corner.
Let's be lax. We'll saw that the time spent getting to the corner has the same precision we use to define "corner". So it could be a moment, or a moment or two. But over an infinite long time, the oxygen molecule can be seen in the top right corner as you walk into the room.
So one oxygen molecule can prove that over infinite time, it can be said to be spatially restricted relative to other relative points in space. Oops. We can't say that, can we? Because that assumes that all dimensions are fixed. It also assumes that the molecules making up that corner are static. But they're not - in summer, the materials expand a little. In winter, they contract a bit. They change dimensions. Relative to each other. And to the oxygen molecule.
So let's try something. If we define "the corner" as an absolute measurement, with a high degree of flexibility for exact placement we, erm, just destroyed our own argument. But it's the only way we can make the argument lose enough to work. In other words, we don't have an argument and need to construct special cases to prove it might.
Why stick with a thousand monkeys, anyway? Why not specify a million? Or ten? It's the same loose definition, the same special case. A thousand monkeys typing over an infinite number of years is the same as an infinite number of monkeys typing over an infinite number of years. And why restrict our monkeys to writing plays and sonnets? Why not give a thousand monkeys paint brushes and paints? One of them will eventually produce the Mona Lisa. One might even replicate a Jackson Pollock.
Let's say we give the monkeys typewriters that produce different notes when the keys are hit. That monkey has a typewriter that produces a C, that one a C#, yet another a middle F, and so on. While we have them laboring away producing Shakespeare, is there any reason to assume that they can't also manage the tune to "Surfin' USA"? How about a nice rendition of Eine Kleine Nachtmusik?
We can assume that within an infinite batch of monkeys, there's going to be one that will do nothing but type out Shakespeare. And one that will produce all of Shakespeare's works, but always one typewriter key off. So where Old Bill wrote "e", this monkey typed "r". Another one would type "w". And another would be arbitrary but always one key off. (And that's ignoring the rows of keys above and below the "e"!)
How about that being the same monkeys who are typing Shakespeare? Over an infinite period, there's no reason to assume that any number of arbitrary events could happen, simultaneously. There's absolutely no reason to assume that these events couldn't happen for an infinite period of time, either.
Oops.
If we're measuring over an infinite period of time, and the event or events occur over an infinite period of time, are we willing to wait an infinite period of time before the event(s) occur? That's the equivalent of "it won't happen, but it might".
The simple fact is that what could happen won't if the odds are against it happening.
What about the sentiment behind the quote? It's stupid. It basically says that Shakespeare didn't think about his craft. If we accept that, but say "well, it's going to be a copy because Shakespeare wrote it first!" all we're saying is that we've got a copy machine that can't produce copies within a period of time. But what of the classics that future authors will produce? Will the monkeys produce one of those? Yes. There's no reason to assume one won't. Does that mean that the person who writes it, or the group that constructs it, have nothing to contribute. Basically - yes. Therefore, Shakespeare had nothing to contribute. Not even Mozart or Michelangelo.
We can also assume that the wit who came up with the little bit of nonsense about "x monkeys over infinity" also contributed nothing. But they did manage to help nonsense become accepted for logic. So they did make a contribution, just not an especially meaningful one. Which means - they proved their own point wrong.
Just like the case where all the oxygen molecules congregate in a corner, leaving you a little unwell (assuming they don't spend an infinite amount of time in that corner, which they might - because over an infinite period of time, all things are apparently possible...). If it's possible, it must happen at some point... Right?
Nope.
The oxygen molecules can't simultaneously hold a union meeting for a moment, and for an infinite amount of time. An infinite number of monkeys can't produce Shakespeare, but they might be able to produce a workable copy. Assuming we can recognize it from the dross they otherwise produce.
It's a stupid saying. I basically wrote this while waiting for the Mrs to take a shower. (She's now waiting for me...) I didn't actually think about the saying; I just decided to write a refutation of it. Because, to me, it's the same lazy logic that leads to religion. It's the same laziness that leads people to denying equal rights to gays, and to denying the obviousness of evolution. And to the transgender community insisting on things that are patently idiotic. ("Cis", for instance.)
Carolyn Ann
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