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.
the actual analog isn’t a million monkeys. you only need one monkey. but it’s for an infinite amount of time. the probability isn’t practically zero, it’s one. that’s how infinity works. not only will it happen, but it will happen again, infinitely many times.
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.
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.
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.
if you exclude the possibility of something happening it won’t happen
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.
so the results will include every possible string of characters ever.
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.
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.
Infinite monkeys and infinite time is equally stupid, because obviously you can’t have either, for the simple reason that the universe is finite.
And apart from that, it’s stupid because if you use an infinite random, EVERYTHING is contained in it!
I’m sorry it just annoys the hell out of me, because it’s a thought experiment, and it’s stupid to use this as an analogy or example to describe anything in the real world.
You wouldn’t need infinite time if you had infinite monkeys.
An infinite number of them would produce it on the very first try!
You wouldn’t need infinite time if you had infinite monkeys.
Obviously, but as I wrote BOTH are impossible, so it’s irrelevant. I just didn’t think I’d have to explain WHY infinite monkeys is impossible, while some might think the universe is infinite also in time, which it is not.
I also already wrote that if you have an infinite string everything is contained in it.
But even with infinite moneys it’s not instant, because technically each monkey needs to finish a page.
But I understand what you mean, and that’s exactly why the theorem is so stupid IMO. You could also have 1 monkey infinite time.
But both are still impossible.
When I say it’s stupid, I don’t mean as a thought experiment which is the purpose of it. The stupid part is when people think they can use it as an analogy or example to describe something
