>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 through causal chains of arbitrary complexity. 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.

I don't know when (or if) AI will implode or succeed with any degree of provable certainty, because that's not my area of expertise. Rather, I can point out and discuss flaws in the common booster and doomer arguments, and identify problems neither side seems willing to discuss. That brings me cold comfort, but it's not enough to stake my money on one direction or another with any degree of certainty - thus I limit my exposure to specific companies, and target indices or funds that will see uplift if things go well, or minimize losses if things go pear-shaped.

I also think relying on such mathematics to justify a position in the first place is kind of silly, especially for technical people. Mathematical models work until they don't, at which point entirely new models must be designed to capture our new knowledge. On the other hand, logical arguments are more readily adapted to new data, and represent critical, rather than mathematical, thinking and reasoning.

Saying AI is going boom/bust because of sigmoids or Lindy's Law or whathaveyou is not an argument, it's an excuse. The real argument is why those things may or may not emerge, and how do we address their consequences within areas inside and outside of AI through regulation, innovation, or policy.

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?

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... 

I don't think you can use lindy on trends as if trends are static objects, but that's another conversation.

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...

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.

2. What's even worse than predicting that some growth curve flattens before X happens is predicting it will flatten before X happens but after Y happens, which is what we see when it comes to AI in software development. Too many people predict that AI will be able to effectively write most software, replacing software engineers, yet not be able to replace the people who originate the ideas for the software or the people who use them. I see no reason why AI capability growth should stop after the point it's able to write air-traffic control or medical diagnosis software yet before the point where it's able to replace air traffic controllers and doctors.

3. While we don't know much about AI (or, indeed, intelligence in general), we do know something about computational complexity. Some predictions about "scary things" happening (the ones I'm guessing Alexander is alluding to, though I can't be certain) do hit known computational complexity limits. Most systems affecting people are nonlinear (from weather to the economy). Predicting them requires not intelligence but computational resources. Controlling them, similarly, requires not intelligence but either computational resources or other resources. It's possible that people choose to give control over resources to computers (although probably not enough to answer many tough, important questions), although given how some countries choose to give control to people with below-average intelligence (looking at you, America), I don't see why super-human intelligence (if such a thing even exists) would be, in itself, exceptionally risky.

In this model, the exponential growth that everybody is freaking out about is only the realization of the modular software dream ("we'll only have to write an ORM once for all of human history!") and the sheer amount of knowledge in libraries.

It's at least falsifiable.

My mental model has been 3D computer graphics: doubling the polygon count had huge returns early on but delivered diminishing returns over time.

Ultimately, you can't make something look more realistic than real.

I don't know what the future holds, but the answer to the question "can LLMs be more realistic than real" will determine much about whether or not you think the curve will level off soon.

All positive growth eventually flattens out and becomes sigmoid, but a lot of phenomena experience negative growth and nose dive. No gentle curve, but a hard kink and perfect flat line at zero. Forever. I think it would be a stretch to categorize that pattern as sigmoid. Predicting a sigmoid pattern for negative growth implies some sort of a soft landing (depending on your definition of soft).

We can think of many populations that are no longer with us. So just a caution about over applying this reasoning in the negative case.

https://news.ycombinator.com/item?id=46199723

This is the crux of the article. To a large extent continued progress depends on a stable increase in compute, an increase in training data, and an increase in good ideas to squeeze more out of both of them.

One calculation you could do is a survival function: for each of the above, how long before it is disrupted? For example, China could crack down on AI or invade Taiwan. Or data centers become politically unpopular in the US. Or, we could run out of great ideas. Very hard to predict.

All exponentials eventually become sigmoids? Don’t think this can be true without qualifiers.

For example, When a car starts, it's speed and acceleration become more than zero. But what about rate of change in higher degrees? It suddenly doesn't change from zero acceleration to non-zero. That means the car has a non-zero derivative at all degrees. In other words, the movement is exponential. The same thing happens in reverse when the car reaches a constant speed.

While we're at it, the "exponentials are actually sigmoïds" meme is not necessarily true. While exponentials are never exponentials, sigmoids are not guaranteed. Overshoot-and-collapse examples also happen in tech, e.g. the dotcom bubble, or the successive AI winters.

Good example of this is number of submissions to neurips/icml/iclr. In 2017 that curve was exponential.

I could probably make increasingly larger fires for years if I was willing to burn the entire world.

Except innovation. When one sigmoid tapers off we keep finding new ones to keep the climb going.

Lindy's Law is not actually a law and many exact minds will be provoked by the very name; it also fails spectacularly in certain contexts (e.g. lifetime of a single organism, though not necessarily existence of entire species).

But at the same time, I am willing to take its invocation in the context of AI somewhat seriously. There is an international arms race with China, which has less compute, but more engineers and scientists. This sort of intellectual arms race does not exhaust itself easily.

A similar space race in the 1950s and 1960s progressed from first unmanned spaceflight to a moonwalk in mere 12 years, which is probably less than what it takes to approve a bicycle lane in Chicago now.

This doesn't say much, and the author fights their own points a couple times, suggesting that they maybe didn't think through what they wanted to write until they were in the middle of writing it and started realizing their assumptions didn't match what they expected the data to say.

I really don't get the point of what I just read.

Attention is all you need took us by surprise and we don't know how big the wave is let alone if there are other waves behind it.