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Saturday, October 20, 2007
Now, God help thee, poor monkey!
Quoth the lady.
I forgot to mention that we met Golden Rule Jones at the ALSC conference. He reported that the poetry reading - which, alas, I could not attend due to dormative powers - was quite fine. And he has something up at the moment that will, again, allow me to satisfy John Emerson’s constant clamoring for this and that bit of information or confession of thermodynamic unrealism:
Sooner or later, Wershler-Henry observes, “anyone writing about typewriting has to deal with the monkeys”: the monkeys, that is, who will eventually produce the complete works of Shakespeare. They appear to derive from a 1909 book on probability by the French mathematician Emile Borel, who invented the image of the “datylographic monkey” to illustrate a mathematical proposition named Kolmogorov’s Zero-One Law. According to the zero-one law, Borel explained, a typewriting monkey would eventually reproduce every single book in the Bibliotheque nationale. Typing monkeys have had their niche in the mathematical imagination ever since. Sometimes they reproduce the Library of Congress, and in a 1940 short story by Russell Maloney, “Inflexible Logic,” the British Library. Overhearing a man explain that six chimpanzees would eventually write all the works in the British Museum, a Mr. Bainbridge sets out to experiment. The experiment works almost too well, with the monkeys producing John Donne’s prose, the memoirs of Queen Marie of Romania, and a monograph on marsh grasses. It remains for his sobering mathematical friend, Mallard, to bring him back to earth: “These chimpanzees will begin to compose gibberish quite soon,” he predicts. “It is bound to happen. Science tells us so.”
More soberingly still, a physics professor at Yale, William R. Bennett, has calculated that if a trillion monkeys typed ten random characters a second, it would still take a trillion times longer than the universe has been in existence just to produce the sentence, “To be or not to be, that is the question.” Moving from calculation to experiment, The Monkey Shakespeare Simulator, in existence since 2003 with a hundred monkeys typing at a vastly accelerated speed, has produced just nineteen letters from The Two Gentlemen of Verona after 42,162,500,000 billion monkey years: “Valentine. Cease to 1dor:eFLPoFRjWK78aXz …”
An enterprising experiment that involved real monkeys produced even more confounding results, not least because “they get bored and they shit on the keyboard rather than type …”
The quote is from the TLS. A review of Wershler-Henry’s book, The Iron Whim
Comments
My most recent statement, derived from my earlier statement (I happen to be working on Eddington, et al):
One of my goals for philosophy is that philosophers come to use far-fetched hypotheticals and monkey-piano possibilities only in fear and trembling, and not promiscuously like picking up some whore at a bar. One way of discouraging thermodynamically-impossible (but not formally impossible) speculation would be to stipulate that whenever someone wants to use to old “not impossible, but merely very unlikely” dodge, they should be required to repeat the word “very” a thousand times, so the reader has some intuition of how bogglingly unlikely it is. Perhaps boggling improbability could be even quantified in terms of monkey-typewriter-Shakespeare units, so people would know whether a given event were merely MTS impossible, or (for example) MTS-squared impossible. (In this context, too, one chance in a million million million can be called “relatively likely on the MTS scale").
It might be noted that, once the monkeys had succeeded in banging out the plays of Shakespeare or some variant edition of them (along with whole galaxies of incoherent, non-Shakespearean or pre-Shakespearean typescript) finding Shakespeare in that mess would be more or less as time-consuming as producing the Shakespeare had been in the first place. You might just as well say that Shakespeare is all right there on the keyboard, which in some sense is true.
Note also that the supposedly improbably events of evolutions are not at all MTS impossible. The vaunted impossibilities anti-evolutionists talk about do not apporach the MTS level. On the MTS scale, they’re relatively likely.
Well, just as long as you don’t think I’M guilty, I don’t mind this stringent new policy.
I don’t think that your last sentence is really strong enough, John E. Given the formation of some kind of replication-with-errors process within a system with limited resources, evolution is not just likely: given a few hundred generations, it’s certain. It’s the same problem as with the failure to distinguish Einstein’s 1 g elevator thought experiment from the Wordworth on the beach one; the reason that Einstein’s was acceptible according to the principle that you’ve described was not that he was a Nobelist, but because what he described was not only not unlikely, it would always happen, every time, in that situation.
I suppose that you could say that specific evolutionary adaptations are more or less unlikely. But if there wasn’t the one that you were pointing to, there would be sure to be some other one, which might well look equally unlikely.
Well, it isn’t technically true that what Einstein said would happen every time, in that situation. Because sometimes the elevator would break down.
If the point of a given thought-experiment is not to establish the likelihood of some barely conceivable state of affairs, then pointing out the unlikelihood of the state of affairs is not - without the addition of further premises - clearly an objection.
Example: John has 5 dollars. He gives Mary 3 dollars. How many dollars does John have now?
Whatever one makes of this thought-experiment, I trust it does not turn on independent evaluation of the likelihood of there being someone named John who has exactly 5 dollars to his name. Not that this is so cosmically unlikely, mind you. But it isn’t clearly relevant.
Well, I was really pointing out that if you added the premise “thought experiments should not involve thermodynamic miracles or other equally unlikely events”, that made the Einstein elevator or evolutionary thought-experiments beside the point.
Someone named John having 5$ and only $5 is MTS-certain.
I sense an irresistible trend. First Puchalsky, then the world!
Rich 12:44: Agreed. I was just “making a case”.
42,162,500,000 billion monkey years is quite a long time.
Thinking it over philosophically, I have concluded that anything whatsoever which is even remotely possible should be described as MTS-certain. It’s true that we’ll have mutually exclusive events described as certain, but, you know, math. Very large numbers. They laughed at Cantor too.
Now all we need to do is hire a mathematician to slap in some proofs and shit, and we’re up and running.
Well, MTS-certain bears certain difficulties too. It starts to get close to the old “I can think of a unicorn. Given a large enough expanse of time and space, [naturally evolved] unicorns must exist. The universe has a large expanse of time and space. Therefore, unicorns exist.”
I like just adding the premise that I tried out above. It’s reasonable, because if we’re talking about something so unlikely that it’s probably not going to happen within the life of the universe, we can’t expect our ordinary language to really say much about it anyway. When we talk about the Wordsworth poem on the beach, it’s not really a Wordsworth poem, or even lines that look like a Wordsworth poem, but some kind of strange-physics thing, and our attempts to describe it are like trying to use classical mechanics in a quantum-mechanical situation. You can debate whether it’s metaphorically a particle or a wave, but the answer is that you’re using the wrong words, or something.
Rich semi-anticipated my next gambit:
Rich, consider three thought experiments.
A magic elf has five dollars but gives three to John. How much money does the elf have now?
Bob has five dollars but gives three to John. How much money does Bob have now?
Swampman, a creature generated by thermodynamic miracle, has five dollars but gives three to John. How much money does Swampman have now?
It seems to me the answer, in each case, is 2 dollars. John Emerson, on the other hand, seems compelled to say that really there are 3 different answers, due to very distinct MTS values in the three cases. Do you accept this consequence, John? (If so, will you also be lobbying the story-problem writers as well as the philosophers, in a reformist spirit?)
Rich has the right answer in the swampman case: namely, there is no reason to take as a premise ‘in case of miracles, keep using language in exactly the same way’. But this point isn’t going to help John E off the hook.
John: Why not just re-classify all such philosophy as (generally rather bad) SF and have it treated as such? At this point these guys are running on fumes and are just spinning tales to keep the tradition alive. I say, just reshelve it to the fiction section of the library and be done with it.
BTW, I’m currently reading a book on Baboon Metaphysics. I don’t see anything in the index about typewriters, but there is a chapter on Theory of Mind.
X having $5 and giving $3 to John is a routine, unproblematic proposition. Whatever you plug in for X doesn’t change the proposition, even if you add the fifth wheel “X is a thermodynamically impossible entity” (or, “X is the present king of France"). But some propositions are thermodynamically impossible without the fifth wheel.
“MTS-certain” is pretty much a joke. I’d say that “certainty” here has the same status as the “possibility” of a monkey-typewriter-Shakespeare.
What got me started on all this just now was the collection “The Philosophy of Time”, ed. MacBeath and Poidevin, Oxford, 1993, which is keyed on McTaggart and seems to me to zero in on sophisticated counterintuitive ideas (which it usually refutes) while vigorously avoiding any statement boring commensensical ideas (which happen to be true). This is a longstanding interest of mine, however.
In the Shakespeare on the beach example, I think that they hypothetical doesn’t work, because the only reasonable interpretation of intelligible text longer than a few letters is that it was produced by an intelligent being
We do have the possibility now of machine-generation by an algorithm. So at some point maybe we will have to do Turing tests on poetry.
I actually tried to produce a Trakl-generator awhile back, because Trakl has a very monotonous, repetitious vocabulary and uses a limited number of simple sentence-types. You could easily do it with surrealism, and I think budding linguists often toy with this specific poetic style as soon as they have sentence-generating algorithms.
At that point the game would be to figure out the algorithm and decide whether the algorithm produces good poetry. There’s still be a programmer and his algorithm behind the poem, though. Producing a meta-algorithm which produces poetry-algorithms might be possible too, I suppose.
But all that is quite different than Shakespeare on the beach.
Actually, if there’s someone out there who reads German and does that kind of linguistics, I’d love to talk to him about my Trakl generator.
The question involving the magic elf is actually pretty easy. Magic elves have a literary/cultural history as imaginary beings, and their range of behaviors in imaginary monetary transactions are well-understood (e.g. the elf might have two dollars left, or might have given John things that look like money but are actually acorns under an illusion, etc.) Only the second two questions really matter for these purposes, because only they purport to say something about the physical/metaphysical world rather than the cultural world. And I do think that the suggested premise is reasonable, if you’re going to be talking about physically-possible explanations. I think that Bill Benzon has it slightly wrong; Swampman isn’t SF, he’s fantasy—sort of a magical elf.
I’m predisposed to agree with John Emerson on this, of course, because of my own biases, which involve reduction of philosophical problems to physics.
Remember that, at Kant said, “A hundred real reals do not contain a centavo more than a hundred imaginary reals.”
Events are all MTS-certain or MTS-impossible (that’s Kolmogorov’s Zero-One Law). There are basically no other possibilities.
You’re right, Rich. Actually, this stuff is sui generis. So I say we just shift all the analytic philosophy from the philosophy section and move it to the genre fiction section and simply let it be analytic philosophy. So you have SF, fantasy, mystery, romance, westerns, horror, and analytic philosophy.
Given time, I suppose the monkeys could evolve to understand English. Has that possibility been factored in? It would tend to reduce their production of random characters. Perhaps the chance of monkeys eventually producing the works of Shakespeare are less than MTS.
What are the chances that any human being would ever write the works of Shakespeare? What the chances that the long chain of evolution would ever have produced the chap we call Shakespeare? We’re all highly unlikely; we all blow the doors off the MTS standard.
What are these monkeys supposed to demonstrate, anyway? That given infinite time (and an infinite supply of monkeys and monkey chow), any possible but highly unlikely event would occur? I don’t find that objectionable. But that doesn’t mean it’ll ever happen in our universe.
I acknowledge an analogy, but I think that Kolmogorov’s Zero-One Law classes thermodynamically impossible events as inevitable. So this is Emerson’s Zero-One Law, which share’s Kolmogorov’s Zero-One Law’s delightfully fanatic binarism, but skews in the opposite direction.