Failing to Understand the Exponential, Again
101–110 of 266 posts
Re: Failing to Understand the Exponential, Again
#102Re: Failing to Understand the Exponential, Again
#103Earlier quoted context omitted.
Yes exponential is only an approximation of the first part of S curves. And this author claims that he understands the exponential better than others…
That is even true for covid for obvious reasons, because Covid runs out of people it can infect at some point.
Re: Failing to Understand the Exponential, Again
#104> People notice that while AI can now write programs, design websites, etc, it still often makes mistakes or goes in a wrong direction, and then they somehow jump to the conclusion that AI will never be able to do these tasks at human levels, or will only have a minor impact. When just a few years ago, having AI do these things was complete science fiction! Both things can be true, since they're orthogonal. Having AI…
Re: Failing to Understand the Exponential, Again
#105Earlier quoted context omitted.
Infectious diseases rarely see actual exponential growth for logistical reasons. It's a pretty unrealistic model that ignores that the disease actually needs to find additional hosts to spread, the local availability of which starts to go down from the first victim.
If you assume the availability of hosts is local to the perimeter of the infected hosts, then the relative growth is limited to 2/R where R is the distance from patient 0 in 2 dimensions. It's becuase an area of the circle defines how many hosts are already ill but the interaction can only happen on the perimeter of the circle. The disease is obviously also limited by the total amount of hosts, but I assume there's a…
Back on the subject of AI, I think the flat part of the curve has always been in sight. Transformers can achieve human performance in some, even many respects, but they're like children who have to spend a million years in grade school to learn their multiplication tables. We will have to figure out why that is the case and how to improve upon it drastically before this stuff really starts to pay off. I'm sure we will but we'll be on a completely different S-shaped curve at that point.
Re: Failing to Understand the Exponential, Again
#106> Given consistent trends of exponential performance improvements over many years and across many industries, it would be extremely surprising if these improvements suddenly stopped. I'm sure people were saying that about commercial airline speeds in the 1970's too. But a lot of technologies turn out to be S-shaped, not purely exponential, because there are limiting factors. With LLM's at the moment, the limiting fac…
> a lot of technologies turn out to be S-shaped, not purely exponential, because there are limiting factors. Yes of course it’s not going to increase exponentially forever. The point is, why predict that the growth rate is going to slow exactly now? What evidence are you going to look at? It’s possible to make informed predictions (eg “Moore’s law can’t get you further than 1nm with silicon due to fundamental physica…
It’s likely that it will slow down at some point, but the highest likelihood scenario for the near future is that scaling will continue.
Re: Failing to Understand the Exponential, Again
#107> Given consistent trends of exponential performance improvements over many years and across many industries, it would be extremely surprising if these improvements suddenly stopped. I'm sure people were saying that about commercial airline speeds in the 1970's too. But a lot of technologies turn out to be S-shaped, not purely exponential, because there are limiting factors. With LLM's at the moment, the limiting fac…
And, maybe I'm missing something, but to me it seems obvious that flat top part of the S curve is going to be somewhere below human ability... because, as you say, of the training data. How on earth could we train an LLM to be smarter than us, when 100% of the material we use to teach it how to think, is human-style thinking?
Maybe if we do a good job, only a little bit below human ability -- and what an accomplishment that would still be!
But still -- that's a far cry from the ideas espoused in articles like this, where AI is just one or two years away from overtaking us.
Re: Failing to Understand the Exponential, Again
#108> Given consistent trends of exponential performance improvements over many years and across many industries, it would be extremely surprising if these improvements suddenly stopped. I'm sure people were saying that about commercial airline speeds in the 1970's too. But a lot of technologies turn out to be S-shaped, not purely exponential, because there are limiting factors. With LLM's at the moment, the limiting fac…
> a lot of technologies turn out to be S-shaped, not purely exponential, because there are limiting factors. Yes of course it’s not going to increase exponentially forever. The point is, why predict that the growth rate is going to slow exactly now? What evidence are you going to look at? It’s possible to make informed predictions (eg “Moore’s law can’t get you further than 1nm with silicon due to fundamental physica…
Why predict that the (absolute) growth rate is going to keep accelerating past exactly now?
Exponential growth always assumes a constant relative growth rate, which works in the fiction of economics, but is otherwise far from an inevitability. People like to point to Moore's law ad nauseam, but other things like "the human population" or "single-core performance" keep accelerating until they start cooling off.
> And note, there are good reasons to predict a speedup, too; as models get more intelligent, they will be able to accelerate the R&D process.
And if heaven forbid, R&D ever turns out to start taking more work for the same marginal returns on "ability to accelerate the process", then you no longer have an exponential curve. Or for that matter, even if some parts can be accelerated to an amazing extent, other parts may get strung up on Amdahl's law.
It's fine to predict continued growth, and it's even fine to predict that a true inflection point won't come any time soon, but exponential growth is something else entirely.
Re: Failing to Understand the Exponential, Again
#109Earlier quoted context omitted.
The narrative quietly assumes that this exponential curve can in fact continue since it will be the harbinger of the technological singularity. Seems more than a bit eschatological, but who knows. If we suppose this tech rapture does happen, all bets are off; in that sense it's probably better to assume the curve is sigmoidal, since the alternative is literally beyond human comprehension.
Barring fully reversible processes as the basis for technology, you still quickly run into energy and cooling constraints. Even with that, you'd have time or energy density constraints. Unlimited exponentials are clearly unphysical.
At the stage of development we are today, no one cares how fast it takes for the exponent to go from eating our galaxy to eating the whole universe, or whether it'll break some energy density constraint before it and leave a gaping zero-point energy hole where our local cluster used to be.
It'll stop eventually. What we care about is whether it stops before it breaks everything for us, here on Earth. And that's not at all a given. Fundamental limits are irrelevant to us - it's like worrying that putting too many socks in a drawer will eventually make them collapse into a black hole. The limits that are relevant to us are much lower, set by technological, social and economic factors. It's much harder to say where those limits lay.
Re: Failing to Understand the Exponential, Again
#110I feel like there should be some take away from the fact that we have to come up with new and interesting metrics like “Length of a Task That Can Be Automated” in order to point out that exponential growth is still happening. Fwiw, it does seem like a good metric, but it also feels like you can often find some metric that’s improving exponentially even when the base function is leveling out.