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- cross-posted to:
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If this is the way to superintelligence, it remains a bizarre one. “This is back to a million monkeys typing for a million years generating the works of Shakespeare,” Emily Bender told me. But OpenAI’s technology effectively crunches those years down to seconds. A company blog boasts that an o1 model scored better than most humans on a recent coding test that allowed participants to submit 50 possible solutions to each problem—but only when o1 was allowed 10,000 submissions instead. No human could come up with that many possibilities in a reasonable length of time, which is exactly the point. To OpenAI, unlimited time and resources are an advantage that its hardware-grounded models have over biology. Not even two weeks after the launch of the o1 preview, the start-up presented plans to build data centers that would each require the power generated by approximately five large nuclear reactors, enough for almost 3 million homes.
That’s not true. Something can be infinite and still not contain every possibility. This is a common misconceptoin.
For instance, consider an infinite series of numbers created by adding an additional “1” to the end of the previous number.
So we can start with 1. The next term is 11, followed by 111, then 1111, etc. The series is infinite since we can keep the pattern going forever.
However at no point will you ever see a “2” in the sequence. The infinite series does not contain every possible digit.
why do you keep changing the parameters? yeah, if you exclude the possibility of something happening it won’t happen. duh?
that’s not what’s happening in the infinite monkey theorem. it’s random key presses. that means every character has an equal chance of being pressed.
no one said the monkey would eventually start painting. or even type arabic words. it has a typewriter, presumably an English one. so the results will include every possible string of characters ever.
it’s not a common misconception, you just don’t know what the theorem says at all.
That’s exactly my point. Infinity can be constrained. It can be infinite yet also limited. If we can exclude something from infinity then we have shown that an infinite set does NOT necessarily include everything.
this has nothing to do with the matter
That’s just not true. One monkey could spend eternity pressing “a”. It does’t matter that he does it infinitely. He will never type a sentence.
If the keystrokes are random that is just as likely as any other output.
Being infinite does not guarantee every possible outcome.
Any possibility, no matter how small, becomes a certainty when dealing with infinity. You seem to fundamentally misunderstand this.
no. you don’t understand infinity, and you don’t understand probability.
if every keystroke is just as likely as any other keystroke, then each of them will be pressed an infinite number of times. that’s what just as likely means. that’s how random works.
if the monkey could press a for an eternity, then by definition it’s not as likely as any other keystroke. you’re again changing the parameters to a monkey whose probability of pressing a is 1 and every other key is 0. that’s what you’re saying means.
for a monkey that presses the keys randomly, which means the probability of each key is equal, every string of characters will be typed. you can find the letter a typed a million times consecutively, and a billion times and a quadrillion times. not only will you find any number of consecutive keystrokes of every letter, but you will find it repeated an infinite number of times throughout.
being infinite does guarantee every possible outcome. what you’re ruling out from infinity is literally impossible by definition.
Anything with a nonzero probability will happen infinitely many times. The complete works of Shakespeare consist of 5,132,954 characters, 78 distinct ones. 1/(78^5132954 ) is an incomprehensibly tiny number, millions of zeroes after the decimal, but it is not zero. So the probability of it happening after infinitely many trials is 1. lim(1-(1-P)^n ) as n approaches infinity is 1 for any nonzero P.
An outcome that you’d never see would be a character that isn’t on the keyboard.
This is actually a way dumber argument than you think you’ve made.
The original statement was that if something is infinite it must contain all possibilities. I showed one of many examples that do not, therefore the statement is not true. It’s a common misconception.
Please use your big boy words to reply instead of calling something “dumb” for not understanding.