They grow proportionately to ax^n . Correspondingly, for values of x < 1, they look very similar to a simple linear 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.
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.
Without the “knee” of the curve there is no exponential growth.
What best describes this curve
Edit: Maybe I have it wrong. From now on I will only model data as exponential functions because they are potentially exponential and the data set is just incomplete.
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.
Real world data does not behave according to a precieved underlying function. The functions we use are only useful as models. Models are approximations.
Dude, your question is dumb and useless. I “avoided” your question by explaining why it was dumb and useless. Re-read, then re-read again, then watch some YouTube videos about exponential functions, then watch some videos about the AI singularity, then do whatever you want after that because I’m done trying to teach the unteachable.
In algebra? The basic properties of exponential functions, for one.
Let’s start there then. What are the basic properties of exponential functions?
They grow proportionately to ax^n . Correspondingly, for values of x < 1, they look very similar to a simple linear 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.
Well there it is
What type of growth would you use to describe the advancement of AI?
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.
Without the “knee” of the curve there is no exponential growth.
What best describes this curve
Edit: Maybe I have it wrong. From now on I will only model data as exponential functions because they are potentially exponential and the data set is just incomplete.
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.
Way to avoid my question for the umpteenth time
What best describes this curve.
Real world data does not behave according to a precieved underlying function. The functions we use are only useful as models. Models are approximations.
Dude, your question is dumb and useless. I “avoided” your question by explaining why it was dumb and useless. Re-read, then re-read again, then watch some YouTube videos about exponential functions, then watch some videos about the AI singularity, then do whatever you want after that because I’m done trying to teach the unteachable.