An exponential function is a precise mathematical concept, like a circle or an even number. I’m not sure what you mean by “asymptote” here - an exponential function of the form y = k^x asymptotically approaches zero as x goes to negative infinity, but that doesn’t sound like what you’re referring to.
People often have bad intuition about how exponential functions behave. They look like they grow slowly at first but that doesn’t mean that they’re not growing exponentially. Consider the story about the grains of rice on a chessboard.
How about this, this is a real easy one.
What type of function is this:
There is a theorem that “all smooth functions are locally linear”. In other words, most “normal” functions are indistinguishable from a straight line on the graph if you zoom in far enough.
So that’s not just not an easy one, it is an impossible one.
They’re not saying that slow growth is definitely evidence it’s exponential. They’re saying that slow growth doesn’t prove that it isn’t exponential, which seemed to be what you were saying.
It’s always hard to identify exponential growth in its early stages.
Or you can just admit you dont have any data to quantify your assertion that AI advancement is exponential growth.
Ah, that’s a fair argument. LLMs growing exponentially is just an assertion being made and we’re supposed to believe that then the steep growth must be just around the corner.
But all over this post you’ve got heavily downvoted comments that sound like you are misunderstanding exponential functions rather than doubting that they’re the right model for this.
We might be on the steep part of an S function right now.
The exponential function has a single horizontal asymptote at y=0. Asymptotes at x=1 and x=-4 would be vertical. Exponential functions have no vertical asymptotes.
An exponential function is a precise mathematical concept, like a circle or an even number. I’m not sure what you mean by “asymptote” here - an exponential function of the form
y = k^xasymptotically approaches zero asxgoes to negative infinity, but that doesn’t sound like what you’re referring to.People often have bad intuition about how exponential functions behave. They look like they grow slowly at first but that doesn’t mean that they’re not growing exponentially. Consider the story about the grains of rice on a chessboard.
Its a horizontal asymtote. From x=1, as demonstrated in the graph, to around x=-4, where the asymtote is easily estimated by Y, it is 5 units.
Man just say you don’t understand functions and that’s it, you don’t have to push it
Tell me how im wrong. Or why did you even bother?
Or you can just admit you dont have any data to quantify your assertion that AI advancement is exponential growth. So youre just going off vibes.
Would you even admit that linear growth can grow faster than exponential growth?
Edit:
How about this, this is a real easy one.
What type of function is this:
There is a theorem that “all smooth functions are locally linear”. In other words, most “normal” functions are indistinguishable from a straight line on the graph if you zoom in far enough.
So that’s not just not an easy one, it is an impossible one.
And yet you want me to believe that because “exponential functions can have a slow build up” it is definitely exponental.
They’re not saying that slow growth is definitely evidence it’s exponential. They’re saying that slow growth doesn’t prove that it isn’t exponential, which seemed to be what you were saying.
It’s always hard to identify exponential growth in its early stages.
Do you accept that if we put together a metric to measure the advancement of AI that it would indicate it is growing over time?
I do not.
See my other response to your pre-edit comment.
Then what are we arguing about?
What exponential growth fundamentally is.
Ah, that’s a fair argument. LLMs growing exponentially is just an assertion being made and we’re supposed to believe that then the steep growth must be just around the corner.
But all over this post you’ve got heavily downvoted comments that sound like you are misunderstanding exponential functions rather than doubting that they’re the right model for this.
We might be on the steep part of an S function right now.
You can read. Read my comments.
The exponential function has a single horizontal asymptote at y=0. Asymptotes at x=1 and x=-4 would be vertical. Exponential functions have no vertical asymptotes.
I didnt say there are asymtotes at 1 and -4. I said at x=-4, the asymtote can be estimated by Y.