Comment on If AI was going to advance exponentially I'd of expected it to take off by now.
agamemnonymous@sh.itjust.works 4 days agoThey grow proportionately to ax^n . Correspondingly, for values of x < 1, they look very similar to a simple library slope. For values of x > 1, they grow very rapidly. Both portions are part of the function, it doesn’t suddenly “become” exponential at the rapid increase, it’s exponential the whole time.
Clinicallydepressedpoochie@lemmy.world 4 days ago
Well there it is
agamemnonymous@sh.itjust.works 4 days ago
What metric are you using? Data can’t really be fit to a curve without data to plot.
The entire contention is you misunderstanding how exponential functions work., i.e. “if it’s exponential, shouldn’t we be rapidly accelerating by now?” Betrays a fundamental misunderstanding.
People don’t expect AI to be exponential because of existing data. It’s because once AI starts significantly improving itself, the advancement of AI, x, starts to apply to itself x^2 .
We won’t know if it is, in fact, exponential until after the “knee” of the curve. But a slow advancement now does not preclude rapid acceleration in the near future. You’ve repeatedly demonstrated throughout the thread that you don’t understand this.
Clinicallydepressedpoochie@lemmy.world 4 days ago
Without the “knee” of the curve there is no exponential growth.
agamemnonymous@sh.itjust.works 4 days ago
Again, buddy, no. That’s not how math works. Math does not fit things to curves, math generates the curves. The object of math is the function, the ones that take data sets and fit them to curves are data analysts, for the purpose of predicting future behavior.
Zooming in on a particular section of a curve and observing that it looks roughly linear at that scale does not make the underlying function, which generates that curve, linear. Exponential growth is exponential growth, and it starts before the “knee”. It’s there the whole time, even when it looks linear.
Every continuous function looks linear when you zoom in enough, that’s how derivatives work in calculus. The exponential function looks linear right up until it starts to not look linear anymore. The point of mapping real world systems to functions is to predict their future behavior, not just describe their present status.
The prediction that AI will go exponential is based on the premise of AI generating future AIs. Obviously, as AI gets better, the AIs that it generates will get better. As AI increases, the AIs thus generated increase by a factor of AI^2 . Once AI generated AIs are equivalent to those developed by a human, i.e. AI = 1, the rate of increase will accelerate, since every new model can make an even better model, which can make even better ones, ad infinitum.
No one knows for sure exactly what is going to enable AI to generate powerful AIs, but once it happens that’s the knee. That’s why it’s hypothesized to be exponential. And that has big consequences, which is why people are eager not to miss the signs that it’s ramping up.