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.
This is guaranteed with infinite monkeys. In fact, they will begin typing every single document to have ever existed, along with every document that will exist, right from the start. Infinity is very, very large.
Excellent. Now I just need to figure out which one of them is doing my taxes.
no, it is not. the chance of it happening will be really close to 100%, not 100% though. there is still small chance that all of the apes will start writing collected philosophical work of donald trump 😂
It’s not close to 100%, it is by formal definition 100%. It’s a calculus thing, when there’s a y value that depends on an x value. And y approaches 1 when x approaches infinity, then y = 1 when x = infinite.
it is not
you weren’t paying attention in your calculus.
y is never 1, because x is never infinite. if you could reach the infinity, it wouldn’t be infinity.
for any n within the function’s domain: abs(value of y in n minus limit of y) is number bigger than zero. that is the definition of the limit. brush up on your definitions 😆
Except, that’s in the real world of physics. In this mathematical/philosophical hypothetical metaphysical scenario, x is infinite. Thus the probability is 1. It doesn’t just approach infinite, it is infinite.
oh boy, no. if anything, it would be the other way around. in real world calculations, you can sometime approximate and still get reasonably precise result, or boundary, depending on your needs. not so in math.
hence the jokes like “for mathematician, pi as a pi. for physicist, pi is roughly 3,14, for civil engineer, pi is roughly 3.”
it is not.
x is not infinite. x is a variable, that is to be substituted by specific number. infinity is not a number, it is a concept that express the fact that you explore how the function behaves when you are substituting bigger and bigger numbers. but none of these numbers are “infinity”. it is always specific number and the result never reaches the limit of the function. in this case, it is never 1, no matter how big number you substitute.
https://en.wikipedia.org/wiki/Limit_of_a_function
There’s 100% chance that all of Shakespeare’s and all of Trump’s writings will be started immediately with infinite monkeys. All of every writing past, present, and future will be immediately started (also, in every language assuming they have access to infinite keyboards of other spelling systems). There are infinite monkeys, if one gets it wrong there infinite chances to get it right. One monkey will even write your entire biography, including events that have yet to happen, with perfect accuracy. Another will have written a full transcript of your internal monologue. Literally every single possible combination of letters/words will be written by infinite monkeys.
No, not how it works
Care to elaborate?
sure. 100% means something will happen every single time in the observed set. if something does not happen every single time, then it is not 100%.
this will not happen every single time. among all possible results, there will be results where none of the monkeys start any kind of shakespeare. there will be instances where every single work they start will be just the paper full of letter “a”. or something else than shakespeare. as you add monkeys (approach the infinity) the smaller such chancegets, until it gets extremely unlikely, but it is not going to be zero.
imagine you are throwing a 6 sided dice hundred times and i ask you - is it possible there will be no 6 among those one hundred throws?
anyone who passed some basic math understand it is indeed unlikely, but it is not impossible. if you keep throwing long enough, there will be cases with zero 6s in it.
probability of that happening is (5/6)^100, which is 1,2 x 10^-8, eg it will happen roughly 1,2 times in ten million cases. not likely, but not impossible.
in 1000 dice throws, the chance drops to (5/6)^1000, roughly 6,6 x 10^(-80), or 6,6 in 100 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 cases.
fun fact: the above number (1 with 80 zeros) is called One Hundred Quinvigintillion (had to google that indeed).
if you further increase the number of throws in the series, the chance of not having single 6 will be getting even smaller, but never zero.
or in other word, if you raise 5/6 to any positive number, the resulting number is always positive number.
https://www.wolframalpha.com/input?i=%285%2F6%29%5En
for further study, the relevant concept here is limit of the function
we say that limit of the above function is zero, which means it will approach the zero really close (infinitely close), but will never reach it.
Thanks for elaborating. I knew limits were going to show up.
You make a good point, although I would like to point out that one hundred quinvigintillion is basically right next to the number 1 on the number line that goes to infinity. The chance of the monkeys not writing Shakespeare is infinitesimally small. You winning every possible lottery every day for the rest of your life is infinitely more probable than the monkeys not writing Shakespeare.