Many, if not most when taken to pedantic conclusions, seemingly-superlinear phenomena are logistic “s-curves”[0]. Even if you’re taking over the entire physical universe, eventually you run out of some limiting growth factor like “total addressable market” or “particles in the the reachable universe.” This isn’t a purely nitpicky point - epidemics and “viral ideas” initially have little interference like this, but when they grow enough they run into interference from immune or previously infected individuals being much harder to infect. Tiktok for example surely had an exponential growth phase among the 14-24 demographic in the US, but by now everyone in that demographic has at least heard of it, and if it did near total penetration into that demographic it’d eventually be limited by the actual number of people able to use their app.
There are also log returns, which look superlinear (not really exponential technically) but eventually taper. For example, a skilled aerospace engineer could probably make a crappy paper plane for $0.1, a really good one for $100. But for $10000 it probably wouldn’t be that much better than the $100 if at all. Plenty of things are like that, it’s called diminishing returns…
Finally, there are definitely quadratic curves in real life. If you’re looking at communications it’s everywhere, usually as an upper bound or worst case. Additional leaf connections may have their diminishing marginal utility countered by the fact that existing and new connections become incrementally more valuable as the network grows.
You see it in processes where something spreads to its vicinity.
This isn't really a natural example, but if you draw a square on a sheet of graphing paper. Next iteration you fill in each adjacent square. Repeat this process until you get tired of it. The radius increases linearly at a constant rate, but the area, the number of squares, as a function of each iteration, is growing quadratically.
Take a circular forest in a place where there are no fires and no logging. Its rate of growth is proportional to its circumference, which is proportional to its radius. Its area as a function of time is a quadratic function.
Suppose the value of a network to an individual user is proportional to the number of users. Then the total value of the network, summed across all its users, is proportional to the square of the number of users.
Of the two sources of superlinear returns here I find step functions the easier one to steer my life happily by. Graduating college is a step function: You go from 0 sheepskin effect to 1 sheepskin effect, and all future employment barriers are made significantly easier to scale. SOC2 compliance is a step that lets you sell 1/10 the feature set to 10 times the enterprises at 100 times the subscription price. An exponential return is the fundamental driver, for sure, but the way you get there is often by hurtling over a sequence of steps.
One huge example for me: Marriage. I went from a long time with 0 wives, and now I have 1 and everything is much much better. What a step! If this is what PG means by a superlinear return sign me up!
Can you say more about the impact of SOC2 certifications? We’ve been selling to enterprises for years without any certifications, but with long and intricate security questionnaires needing to be filled out. Does that go away if you have a certification? Our sector isn’t very regulated (video games industry), but the question for SOC2 does come up regularly - however never as a blocker.
Only in general terms I'm afraid. You're right that it varies by industry: My experience is coming out of banking tech and medical software, where the industries are much more heavily regulated. At my first job out of college I had to do all of my development work 3 VMs deep on a separate laptop partly just so I could comply with all of them -- but we also made total bank because we were the only game in town.
Great points. One thing that is worth underlying, as unpopular a subject as it may be with this crowd, is the impact structural disadvantages in our society have.
It comes down in many ways to, "how many turns at bat do you get?" As a parent, I think providing my kids with as many turns at bat is a better heuristic than what college they get into, etc.
To Paul's point, there are actually ways to "earn" more times at bat — learning to read, or to draw, or to code. In America, that's something that most parents can provide — but worth emphasizing that even there, structural disadvantages come into play.
This is why I support a universal basic income and disagree with the idea that everyone would become lazy and depressed. I actually think giving people more turns at bat wouldn't just set them up for potential success — it also would benefit society. As Paul points out — there are likely to be discoveries from unexpected people and places.
There are a lot of brilliant people in the world, and they don't all look the way you'd expect, or come from places you'd expect. But in a world where institutions and organizations are less predictive of success, this diversity is worth keeping in mind.
Great essay, but I'd add one thing that I think Paul has actually touched on before and is somewhat implicit here — it's often surprising just how little one needs to rise above average to hit that step function. Consistency, consistency, consistency.
Exponential growth tends to work at the beginning of "something". Since the world is finite, at some point new somethings need to be created or discovered for an exponential growth, quite possibly eating the last thing that was exponentially growing at one point. So part of the trick is to be in on the exponential growth phase and sell off / reduce exposure to the thing when that tapers off.
Yup, and that's why I'd consider this a "101" essay. The larger exponential-growth trends (e.g. Moore's Law) practically always have a microstructure with many sigmoid curves. After you've encountered your first exponential, the "201" lesson about saturation becomes important.
And then generally all the smaller S-curves build on each other to make a curve that looks exponential for much longer, but ultimately turns out to be a sigmoid as well. One thing I muse on occasionally is whether the same will ultimately be true for technological progress as a whole.
When you have new tech that will “capture the light cone of all future value” [1] you’ll attract a herd of followers, and that’s where the outsized ROI comes from. The gain is from collecting and arbitraging disciples. The product doesn’t necessarily need to lead those disciples to a better place.
Some people might argue that it is a hollow phrase to make OpenAI sound more important than it is. ;-)
On the other hand: since we are, of course, nearing the AI singularity, we are in the situation where we cannot even predict what will have value in the coming future - will it be money, or will it be some completely alien concept that no one today can even imagine? Luckily, OpenAI is already prepared for this kind of future by its capability to capture the light cone of value.
It's any value that's created at some point, and any value that will ever be created from that point onwards. A light cone starts at a point in space and time, and covers everything in space-time that point could causally interact with; speed of light is the speed of causality, hence "light cone".
Definition of "value" is the usual fuzzy one - both money/wealth and all kinds of things humans value that are not expressed in dollars.
The fact that this site doesn't serve HTTPS(correctly) remains a head-scratcher for me.
The certificate isn't valid for paulgraham.com, hence the error. It is valid for *.store.turbify.com, among other SANs, which seems to indicate that the site is hosted by Yahoo[0] and has HTTPS misconfigured.
Yeah it's weird: I've got my Firefox configured to never load HTTP sites but I'm too sure why it then tries to load the HTTPS one when a HTTP URL is given.
Paul is "not wrong"[1], but he overlooks that all of this is only the way it is due to a variety of (well guarded) social conventions (as opposed to some immutable nature of reality, as he implies)...but most every defense has holes.
“overlooks” doesn't seem right to me. He states within the first few paragraphs:
> It's obviously true that the returns for performance are superlinear in business. Some think this is a flaw of capitalism, and that if we changed the rules it would stop being true. But superlinear returns for performance are a feature of the world, not an artifact of rules we've invented.
You say “conventions” rather than “capitalism” here, but without more details it seems like you're targeting substantially the same distinction re social determination. So it sounds more like you disagree with him about that statement than that he just didn't take it into account.
Any claim that superlinear returns for performance are a feature of the world and not of some rule set really needs to come with some strong supporting evidence.
Did you see the unconventional events in the Middle East in the last few weeks? That demonstrates that while Paul may be usually correct, what he's describing is not fundamental.
The people running the show are well aware of such things and have them under control though so I wouldn't expect anything to change wrt distribution of fruits of labor in our part of the world...but the potential is always there.
Readit News
Many, if not most when taken to pedantic conclusions, seemingly-superlinear phenomena are logistic “s-curves”[0]. Even if you’re taking over the entire physical universe, eventually you run out of some limiting growth factor like “total addressable market” or “particles in the the reachable universe.” This isn’t a purely nitpicky point - epidemics and “viral ideas” initially have little interference like this, but when they grow enough they run into interference from immune or previously infected individuals being much harder to infect. Tiktok for example surely had an exponential growth phase among the 14-24 demographic in the US, but by now everyone in that demographic has at least heard of it, and if it did near total penetration into that demographic it’d eventually be limited by the actual number of people able to use their app.
There are also log returns, which look superlinear (not really exponential technically) but eventually taper. For example, a skilled aerospace engineer could probably make a crappy paper plane for $0.1, a really good one for $100. But for $10000 it probably wouldn’t be that much better than the $100 if at all. Plenty of things are like that, it’s called diminishing returns…
Finally, there are definitely quadratic curves in real life. If you’re looking at communications it’s everywhere, usually as an upper bound or worst case. Additional leaf connections may have their diminishing marginal utility countered by the fact that existing and new connections become incrementally more valuable as the network grows.
[0] https://en.m.wikipedia.org/wiki/Logistic_function
This isn't really a natural example, but if you draw a square on a sheet of graphing paper. Next iteration you fill in each adjacent square. Repeat this process until you get tired of it. The radius increases linearly at a constant rate, but the area, the number of squares, as a function of each iteration, is growing quadratically.
Take a circular forest in a place where there are no fires and no logging. Its rate of growth is proportional to its circumference, which is proportional to its radius. Its area as a function of time is a quadratic function.
See also https://en.wikipedia.org/wiki/Network_effect .
One huge example for me: Marriage. I went from a long time with 0 wives, and now I have 1 and everything is much much better. What a step! If this is what PG means by a superlinear return sign me up!
So, they will be happy you have it, but will make you do all the questionnaires anyway.
It comes down in many ways to, "how many turns at bat do you get?" As a parent, I think providing my kids with as many turns at bat is a better heuristic than what college they get into, etc.
To Paul's point, there are actually ways to "earn" more times at bat — learning to read, or to draw, or to code. In America, that's something that most parents can provide — but worth emphasizing that even there, structural disadvantages come into play.
This is why I support a universal basic income and disagree with the idea that everyone would become lazy and depressed. I actually think giving people more turns at bat wouldn't just set them up for potential success — it also would benefit society. As Paul points out — there are likely to be discoveries from unexpected people and places.
There are a lot of brilliant people in the world, and they don't all look the way you'd expect, or come from places you'd expect. But in a world where institutions and organizations are less predictive of success, this diversity is worth keeping in mind.
Great essay, but I'd add one thing that I think Paul has actually touched on before and is somewhat implicit here — it's often surprising just how little one needs to rise above average to hit that step function. Consistency, consistency, consistency.
There are no practical physical limits to wealth creation since ideas can be monetized with only energy expenditure.
This statement is internally inconsistent.
Imagine a bubble expanding at the speed of light bringing everything inside it under complete optimal control.
Technically speaking, the world is not finite.
[1] sama on chatgpt https://techcrunch.com/2019/05/18/sam-altmans-leap-of-faith/...
Some people might argue that it is a hollow phrase to make OpenAI sound more important than it is. ;-)
On the other hand: since we are, of course, nearing the AI singularity, we are in the situation where we cannot even predict what will have value in the coming future - will it be money, or will it be some completely alien concept that no one today can even imagine? Luckily, OpenAI is already prepared for this kind of future by its capability to capture the light cone of value.
*sarc*
Definition of "value" is the usual fuzzy one - both money/wealth and all kinds of things humans value that are not expressed in dollars.
Anybody else got some similar error?
The certificate isn't valid for paulgraham.com, hence the error. It is valid for *.store.turbify.com, among other SANs, which seems to indicate that the site is hosted by Yahoo[0] and has HTTPS misconfigured.
[0]: https://login.yahoosmallbusiness.com
[1]https://www.urbandictionary.com/define.php?term=you%27re%20n...
> It's obviously true that the returns for performance are superlinear in business. Some think this is a flaw of capitalism, and that if we changed the rules it would stop being true. But superlinear returns for performance are a feature of the world, not an artifact of rules we've invented.
You say “conventions” rather than “capitalism” here, but without more details it seems like you're targeting substantially the same distinction re social determination. So it sounds more like you disagree with him about that statement than that he just didn't take it into account.
The people running the show are well aware of such things and have them under control though so I wouldn't expect anything to change wrt distribution of fruits of labor in our part of the world...but the potential is always there.
Also everything should be a startup working towards a VC exit.