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.
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