Posted by Tomte 10 hours ago
>My understanding is that this represents 3-4 “generations” of different technology (propellers, turbojets, etc). Each technology went through normal iterative improvement, then, when it reached its fundamental limits, got replaced by a better technology. The last technology, ramjets, reached its limit at about 3500 km/h, and there wasn’t the economic/regulatory will to develop anything better, so the record stands.
You don't have one sigmoid, you have multiple each stacked on top of each other. Airplanes aren't just one technology they are multiple technologies that happen to do the same thing.
Each one is following a sigmoid perfectly. It only looks exponential(ish) because of unpredictable discoveries that let you switch to another sigmoid that has a higher maximum potential.
The same is true in AI. If you used the same architecture as GPT2 today you're in for a bad time training a new frontier model. It's only because we have dozens of breakthroughs that the capabilities of models have improved as much as they have.
That said exponential and sigmoids are the wrong model to use for growth. Growth is a differential equation. It has independent inputs, it has outputs and some of those outputs are dependent inputs again. What happens depends entirely on what the specific DE that governs the given technology is. We can easily have a chaotic system with completely random booms and busts which have no deep fundamental rhyme or reason. We currently call that the economy.
That said... if the exponential is made of stacked sigmoids, it's still an exponential on the whole! The fact that it's made of stacked sigmoids is relevant to the engineers making it, but not so relevant to the users or those otherwise affected by it.
Edit: in particular I don’t agree with
But if someone claims that the trend toward increasing AI capabilities will never reach some particular scary level...
The important thing we can show it in hindsight only. We don't know which other tasks we are currently mistaken about requiring intelligence. Maybe none of them are?
We don't know. We don't know what intelligence is. If we look at decades and even centuries of attempts to define intelligence, it is all looks like a goalposts moving. When a definition of intelligence starts to include people or things we don't like to think as of intelligent ones, we change the definition.
I don't think you can use lindy on trends as if trends are static objects, but that's another conversation.
I mean, that's called "having an opinion".
Yes, that's called "having an opinion". Typically people writing argumentative pieces are doing so because they have a belief about the matter. I'm not sure what exactly you expect here.
> if he's wrong I would hope he owns up to it
I think Scott Alexander is pretty good about that.
If we don't understand the fundamental limits to any particular kind of trend, our default assumption should be that it will continue for about as long as it has gone on already.
We can, in fact, easily put a confidence interval on this. With 90% odds we're not in the first 5% of the trend, or the last 5% of the trend. Therefore it will probably go on between 1/19th longer, and 19 times longer. With a median of as long as it has gone on so far.
This is deeply counterintuitive. When we expect something to last a finite time, every year it goes on, brings us a year closer to when it stops. But every year that it goes on properly brings the expectation that it will go on for a year longer still.
We're looking at a trend. We believe that it will be finite. Our intuition for that is that every year spent, is a year closer to the end. But our expectation becomes that every year spent, means that it will last yet another year more!
How can we apply that? A simple way is stocks. How long should we expect a rapidly growing company, to continue growing rapidly?
For example, take something like a fad or trend; they don't have a hard end date like human lifespan, so it should follow Lindy's law.
However, the likelihood, on average across the population, that you observe a trend is going to be higher at the end of a trend lifecycle than at the beginning. This is baked into the definition - more and more people hear about a trend over time, so the largest quantity of observers will be at the end of the lifecycle, when the popularity reaches its peak.
In other words, if you are a random person, finding out about a trend likely means it is near the end rather than the middle.
The law only applies for certain types of processes, and is completely wrong for other types (e.g. a human who has lived 50 years may live 50 more, but one who has lived 100 years will certainly not live 100 more). So the question becomes: what type of process are you looking at? And that turns out to be exactly the question you started with: is there a fundamental limit to this growth curve, or not.
Did you even read the post? It’s an estimate in the context where you have zero information on which to base an accurate estimate. The author’s point is that if you’re making a different estimate you need to actually say what information is informing that.
Human lifespan is obviously not a case where we have zero information, so what is your point in bringing that up?
"The Lindy effect applies to non-perishable items, like books, those that do not have an "unavoidable expiration date"."
And later in the article you can see the mathematical formulation which says the law holds for things with a Pareto distribution [2]. I'd want to see some sort of good analysis that "the life span of exponential growth curves" is drawn from some Pareto distribution. I don't think it's completely out of the question. But I'm also nowhere near confident enough that it is a true statement to casually apply Lindy's Law to it.
The argument given is the same as the one that I first ran across, not by that name, in https://www.nature.com/articles/363315a0. https://en.wikipedia.org/wiki/Doomsday_argument claims that it was a rediscovery of something that was hypothesized a decade article.
I hadn't tried to give it a name, or thought to apply it outside of that context.
As for the mathematical qualms, I'm a big believer in not letting formal mathematical technicalities get in the way of adopting an effective heuristic. And the heuristic reasoning here is compelling enough that I would like to adopt it.
But that's the entire idea of Bayesian reasoning. Which has proven to be surprisingly effective in a wide range of domains.
I'm all for quantifying my ignorance, and using it as an outside view to help guide my expectations. Read the book Superforecasting to understand how effective forecasters use an outside view to adjust their inside view, to allow them to forecast things more precisely.
So for example, the longer a time bomb ticks, the less likely it is to go off any time soon. (Assuming the timer isn't visible.) :)
We expect fresh processes to terminate quickly and long running processes to last for a while longer.
The naive expectation is that AI will slow down b/c Moore's law is coming to an end, but if you really think about the models and how they are currently implemented in silicon, they are still inefficient as hell.
At some point someone will build a tensor processing chip that replaces all the digital matmuls with analogue logamp matmuls, or some breakthrough in memristors will start breaking down the barrier between memory and compute.
With the right level of research funding in hardware, the ceiling for AI can be very high.
All the easily verifiable domains such as mathematics, coding, and things that can be run inside a reasonable simulation are falling very very fast.
By next year if not sooner, mathematicians will be wildly outpaced by LLMs for reasoning.
So it's not impossible to have things that seem orthogonal, like generation speed or context length, have an impact on quality of result.
I'm pretty sure there's a 3 year design goal starting this year that'll do that to any of the qwen, deepseek, etc models. There's a lot you could do with sped up models of these quality.
It might even be bad enough that the real bubble is how much we don't need giant data centers when 80-90% of use cases could just be a silicon chip with a model rather than as you say, bloated SOTA
If there's a breakthrough in memristors, you could end up with another 20x reduction in circuit elements (get rid of memory bottlnecks, start doing multiplication ops as log transform voltage addition)
The ceiling is ultra high for how far AI can go.
All exponential eventually becomes a sigmoid because exponential growth always expose limiting factors that weren't limiting at the beginning. Silicon manufacturing had lots of room for high-margin customers like Nvidia even a year ago (by the mere virtue of outbidding lower-margin customers), but now it is mostly gone, and no amount of money will make fabs build themselves overnight.
[1]: https://stockanalysis.com/stocks/nvda/metrics/revenue-by-seg...
I don't know if they can get their numbers right this way, but this seems a way more useful metric, than theoretic capabilities.
It is purely a test of capabilities (can it do a thing that takes a human $X hours), not efficiency (how fast will it do it).
At least I want AI to solve my problems, not score high on a academic leaderboard.
At first the models turned a 5 minute task into a 5 second task (by 5 seconds I mean a very short amount of time, not precisely 5 seconds). Then they turned a 15 minute task into a 5 second task.
Opus 4.6 completes 8 hour tasks all the time but (at least in my experience) it isn't spitting the answer out in 5 seconds anymore. It's using chain of thought and tools and the time to completion is measured in minutes or maybe hours.
In my experiments with local LLMs, a substantial part of the gap between frontier and local (for everyday use) is in tooling and infrastructure.
That is why I am sympathetic to the idea we are leveling off. But to bring in the air speed example from the article, I don't think we've reached the equivalent of the ramjet yet. I suspect in the coming years there will be new architectures, new hardware, and new ways to get even more capable models.
I trained an LLM to write the whole Harry Potter series, and that took JK Rowling like 17 years.
For my next point on the graph, I'll train the LLM to write the Bible, something that took humans >1500 years.
The tasks are obviously all of the form "Go do this, and if you get the following output you passed". Setting up a web server apparently takes 15 minutes for a human, which is news to me since I'm able to search for https://gist.github.com/willurd/5720255, find the python one-liner, and copy it within about ten seconds.
Anyway, this is cool but it does not mean Claude can perform any human tasks that take less than 8 hours and are within its physical capabilities.
I'm curious what people really mean when they say this. Intelligence is famously hard to define, let alone measure; it certainly doesn't scale linearly; it only loosely correlates to real-world qualities that are easy to measure; etc. Are you referring to coding ability or...?
emoji face with eyes rolling upward
Scott makes a Lindy effect argument which is plausible, but don't let that fool you, we still don't know what's going to happen.
All exponentials eventually become sigmoids? Don’t think this can be true without qualifiers.
The issue is that the exponential-looking part of the sigmoid might contain all of human history, sure, but most folks who espouse this theory probably agree that over time everything reaches a steady-enough state to be considered non-exponential, or become oscillatory.