Almost all growth is exponential growth

post by lemonhope (lcmgcd) · 2025-01-21T07:16:24.686Z · LW · GW · 7 comments

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7 comments

Why is almost everything either overwhelming or nonexistent? I can't step outside without stepping on a pigeon, but I haven't seen a cardinal in years. Topics are discussed either constantly or never. You bike 200 miles per week or never. You are probably cancer free or dead from cancer. Your old stocks and coins are either worthless or worth a fortune. Stuff from my old popular science magazines is either in the palm of my hand or nonexistent.

The answer is what you would expect. Memes and bike clubs and cancer and companies and technology and pigeons all tend to grow/improve/multiply at a rate proportional to their current size/capabilities/population. If you've forgotten precalc, that's the definition of exponential growth.

There is some resistance force against all things, but even an exponential resistance (eg by the immune system) rounds to zero eventually if it grows even slightly slower than its target. 1% growth per second is 10,000x more per day than 0.99% growth per second.

Of course earth can only nourish so many pigeons, but after the strong exponential is over, growth basically completely stops. There's not really a long linear phase or anything. Growth is just zero until it is exponential until it is zero again. This approximation is accurate enough to call it reality.

If someone offers you exponential returns on your investment then it's probably a scam, but banks do that and they just call it "compounding growth". That is a much more descriptive name.

It's a bit crazy to think AI capabilities will improve exponentially. I am a very reasonable person, so I just think they'll improve some amount proportional to their current level.

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comment by Adam Zerner (adamzerner) · 2025-01-22T21:36:24.521Z · LW(p) · GW(p)

The central claim that "almost all growth is exponential growth" is an interesting one. However, I am not really seeing that this post makes an argument for it. It feels more like it is just stating it as a claim.

I would expect an argument to be something like "here is some deep principle that says that growth is almost always in proportion to the thing's current size". And then to give a bunch of examples of this being the case in various domains. (I found the examples in the opening paragraph to be odd. Bike 200 miles a week or never? Huh?) I also think it'd be helpful to point out counterexamples and spend some time commenting on them.

Replies from: lcmgcd
↑ comment by lemonhope (lcmgcd) · 2025-01-23T20:27:00.756Z · LW(p) · GW(p)

OK I'll bite. Memes and genes are obvious enough, but why is the rate of technological improvement proportional to the current technological level (or basically zero)? Don't ideas get harder to find?

Well Big Ideas do get harder to find, but if you make a 1% improvement to the US's steel production, then you get an extra 800,000 tons of steel. That doesn't help you think up new improvements but it does mean that the next 1% improvement will yield 808,000 tons.

Basically, any cost reduction or speedup or quality improvement is on top of what you have. How would you save a silicon foundry $500,000 flat, without saving them more money as they expand? Maybe you could get a one-time government grant or a one-time supplier discount. You have to do a lot of one-time things like this for it to add up to anything significant.

Consider a technological improvement that seems to be constant or linear. Say you come up with a voltage regulator that uses 1 microwatt less than its predecessor. There's two reasons this isn't actually so linear. First, the total power consumption reduction is proportional to the number of times that circuit is used across all chips/devices. Second, if someone later finds a 1% power save across all transistors, then your little circuit will probably get that improvement too. It ends up being like a deposit into a savings account with interest.

If your savings account doesn't have interest, then you probably will never be a millionaire from small deposits. If some branch of technology hasn't found a few sequential compounding improvements then it probably won't go anywhere.

Replies from: adamzerner
↑ comment by Adam Zerner (adamzerner) · 2025-01-24T01:04:30.960Z · LW(p) · GW(p)

For the sake of argument, I'll accept your points about memes, genes, and technology being domains where growth is usually exponential. But even if those points are true, I think we still need an argument that growth is almost always exponential across all/most domains.

comment by Gunnar_Zarncke · 2025-01-21T21:14:57.839Z · LW(p) · GW(p)

Except where it is not or rather where it has saturated at a low level. Almost all growth is logistic growth and it is difficult to extrapolate logistic functions.

comment by CstineSublime · 2025-01-24T01:54:13.653Z · LW(p) · GW(p)

This seems more to be about the threshold of perception than population distributions, clustering illusions and such. After all the relative difference between an extreme and the average is always a matter of the sample you take. I don't think people in my circle constantly discuss David Bowie, but they do discuss him with a certain regularity. Same with the filmmaker Andrei Tarkovksy. David Lynch recent passing made him a extreme mainstay on social media, but I reckon once a month someone would tell me how much they loved his work. That's not constant, that's not an extreme.

Maybe I'm just projecting: when I find I am self-pitting and say sweeping generalization "why can I never do X" or "why is it every time I X I get bad-result-Y" it's very hard to list three examples that all fall into the same taxonomy. I may find three related examples, but not three events which neatly fit in the same box.

I don't think it's all-or-nothing at all. I think it's just you only notice the absence or the abundance. It's just how perception is trained.

comment by pandamonium · 2025-01-22T12:28:52.117Z · LW(p) · GW(p)

I agree with the fact that there are many examples of exponential growth in real life, but this post seems to overstate their importance. 

Here, I feel that approximating a little quantity to zero led to a false conclusion. A lot of cool (and I guess bad) things in life are present in small quantity and it's enough for them to be valuable and have a strong impact. There is one ethical breeder of the breed of dogs you love in France (example taken from a friend ;) ) : that's all you need ! If you were limited to the main topics in conversations, it would get boring very fast. Thankfully, there are plenty of small new topics of conversations that appear when you talk to new people ! And, taking an example closer to LessWrong, you only need one powerful AI with weak safeguards to get the world into trouble.

comment by Daniel V · 2025-01-21T17:14:56.659Z · LW(p) · GW(p)

I really like this succinct post.

I intuitively want to endorse the two growth rates (if it "looks" linear right now, it might just be early exponential), but surely this is not that simple, right? My top question is "What are examples of linear growth in nature and what do they tell us about this perception that all growth is around zero or exponential?"

A separate thing that sticks out is that having two growth rates does not necessarily imply generally two subjective levels.