Superlinear Returns
paulgraham.com
paulgraham.com
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.
See also https://en.wikipedia.org/wiki/Network_effect .
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.
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.
Here's a sci-fi plot idea: a bubble expanding at near-lightspeed is bringing everything inside it under complete optimal control. Lagging behind it a couple years is another bubble, also expanding at near-lightspeed - that of false vacuum collapse. Will the zone of optimal control find a way to stop the nothingness that comes just behind it from consuming the universe?
Here's a universe-eating bubble for you: https://en.wikipedia.org/wiki/Schild%27s_Ladder
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.
Warning: Potential Security Risk Ahead
Firefox detected a potential security threat and did not continue to paulgraham.com.
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.
[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.
Because everything in our history shows humans will exploit (i.e. fully utilize) leverage wherever they find it: labour, capital, technology, AI.
> I don't think history shows that at all: In ancient Greece people fasted for weeks on end, for example.
So in the situation in ancient Greece, if the situation was such that superlinear returns from steam power wasn't interesting, there is already a situation where social constructs stop that "law of nature".
And even if, hypothetically, humans were always exploiting levers, still need to show that superlinear returns are a feature of nature and cannot be blocked by any social construct (as they are not the results of rules).
By the way, even your food hunting thing is incorrect as such, as humans are known to willingly starve themselves to death.
The problem with broad and sweeping claims is, that they are easily debunked unless they are very carefully researched.
That's a fantastic quote though!
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.
I read it as a warning that PG skews his arguments to prove some narrow points and you should be careful when applying them to your life, so you don't waste years chasing improbable goals. Plenty failed start-ups exemplify this.
--
[0] - 'dang described it long ago as behaving as if there was a great hash table in the sky, mapping a person's name to the simplest and most well-known fault of them, and as if commenters were somehow obliged to dereference that hash table every time some person's name is mentioned.
Eh. I think of it as a warning that younger us (or -at least- younger me) would have very, very, very much appreciated when we were first reading the essays.
Yeah, _you_ have had these realizations about how less-profound-than-they-seem the essays are, and _you_ have read the essay(s). But, like, the essays keep popping up... why not also keep mentioning that they're not as profound as they seem? There's _always_ going to be someone who's reading the essays for the first time, so why discourage folks from providing the new reader the opportunity to read valid criticism of the essays developed over the years?
Maciej? He's writing about how we shouldn't go to Mars these days. He's and excellent and very entertaining writer and I am sure he has plenty to teach me but I'd rather listen to PG. My focus is limited and I'd rather follow someone who already helped me get ahead and showed me what the possibilities truly are instead of pushing his limits onto me.
Which, I, for one, also find 100% on the money. A lot of snakeoil has been sold by Musk, Bezos, and co about the matter.
But, please indulge me, I am curious: how is this mindset serving you? Are you a happy person? Are you a balanced person? Are you a successful person? Do you have everything you need? How long have you been thinking like that? What would it take to change your mind?
Thanks for your answers.
Do you think you come out as balanced and happy by doing this?
Do you regularly think anybody that thinks differently than you, or doesn't gulp down whatever snake-oil the "succesful" sell, is problematic, unhappy, unsuccesful, unbalanced, and should "change their mind"?
Do you think that only business guru admirers or grind culture entrepreneurs are "happy"? Do you think only techno-optimists dreaming of strongmen like Musk and Bezos giving them Mars colonies are "balanced"? (And do you think either groups are anywhere close to a balanced person, as opposed merely naive and happy-go-lucky victims of Californian Ideology?)
How long have you been thinking like that?
Since you are aggressively pushing yours onto others it would be interesting to know how they work for you. Sorry if it felt as an ad hominem attack, it was never my intention, I was just curios. My apologies.
https://en.wikipedia.org/wiki/Cargo_cult
>Since you are aggressively pushing yours onto others it would be interesting to know how they work for you.
Well, it has worked fine thus far. So, there's that.
Not sure what kind of "belief system" you have deduced I have, based on that I'm against the hype of Mars missions, or I don't like VC-culture.
It hardly seems enough to deduce any general belief system, much less one that has wide consequences in personal life, as was implied. If anything, both sound more like common sense, or at least not being pro-hype or sucking up to the rich, than a belief system.
But I still interpret it as debiasing tool for those that aren't very familiar to PG's writing, so it's not really useless. After all, there must still be new HN users all the time, for which some things are worth repeating (just not too often).
“I read it as a warning that PG skews his arguments to prove some narrow points and you should be careful when applying them to your life, so you don't waste years chasing improbable goals”
They were being just as curt as nickpp. What they wrote was not as reasonable as your lines above, hence the response. From my pov, the main reason that you’re criticizing nickpp is because his opinion doesn’t match your own.
The irony here is that I’m more sympathetic to your viewpoint, but I’ll try to be constructive beyond just calling you out:
* These essays take a lot of work to write
* These essays are not hidden behind a paywall
* The essays capture the POV of a successful startup founder and more importantly a successful startup investor
* Does the advice apply to everyone? Probably not everyone 100%. I doubt many of his essays even apply to 25% of people, or even 10% depending on the topic.
* still, many people have profited off pg’s advice in some way
* If you don’t like pg’s essays, you don’t have to read them
* pg founded HN. Don’t be surprised to see people defending pg here.
So, my ...advice is for people to follow much more timeless wisdom which has worked great for billions, and not get into the cult of some rich/succesful or into cults of personality.
Optimism on the other hand and especially tech optimism is almost a slur nowadays. Very few voices support them, very few cheerleaders. And that is a shame - the whole world depends on these optimists. We need them to solve the problems facing our civilization. To have successful startups we need failed ones. Advances are not easy, they are damn hard and people willing to try are few and far in between and they need our support.
And finally in the last 20 years I met and interacted with hundreds (maybe thousands) of people in our field. The ones who TRIED - few successes but zero regrets. Even failures lead to positive outcomes in the end.
The only regrets and bitterness were predictably from the ones who for some reason or another were discouraged to try. They always have an excuse, some situation to point to that made them victims. But in the end it was a preexisting belief, an idea or opinion or mind virus that did the most damage to their you world-view.
Very few will lose trying to emulate a successful person. None will gain anything trying to follow coldtea's advice.
Not as much as the multi-trillion dollar industry for "how to make it big" advice, business and startup hussle culture, magic bullets and/or grind p0rn, and so on, all built on optimism, and aiming at an ever renewable supply of fresh naives.
So there is value in these essays. You don't have to see it or appreciate it but denigrating it just turns the question on you: who are you? what have you done? what do you have to show and teach us?
Likewise, it's possible for someone to manage a sports team, successfully I might add, even if they were never a top player in that sport. My point is, I don't need to be a billionaire or found a successful company to be able to critique Paul Graham's writing. I personally find it banal and would rather seek out writers who came up with novel ideas, like for example Carl Jung or Joseph Campbell to name a couple.
'For to everyone who has, more will be given, and he will have abundance; but from him who does not have, even what he has will be taken away' - Matthew 25:29
I wonder if other religions have similar elements.
It is understandable that both the size of an army, and the wealth of a ruler would lead to this conclusion, as PG states, but it's still surprising that it has been recognized with such clarity.
But there is something deeply wise in most religions that can have profound effects on how we live our lives.
"He also who had received the one talent came forward, saying, ‘(...) I went and hid your talent in the ground. Here, you have what is yours.’ But his master answered him, ‘You wicked and slothful servant! (...) you ought to have invested my money with the bankers, and at my coming I should have received what was my own with interest."
For that parable to be useful when it was written, common people must have understood the idea of lending your money with interest. From that, it's not a big step for them to have figured out what happens if do it again, and again, having the interest compound.
EDIT: Also, how old is that story about a smartass asking a king to give him a chessboard of grain, where on first field they have one single grain, and for every other field, 2x the amount on the previous one?
"To you it has been given to know the secrets of the kingdom of heaven, but to them it has not been given. For to him who has will more be given, and he will have abundance; but from him who has not, even what he has will be taken away."
This is harder to explain, but imo more relevant to TFA, since it seems to refer to knowledge and learning.
Read the CV of any new-minted corporate CEO almost without fail you'll find that before leaping into the C-suite they first laboured for 15 years in one big institution, building credibility and experience.
Big law firms, big financial firms, the military, academia, on and on it goes, large institutions within which career advancement depends on finding ones way through the institutional culture and comporting oneself to it, in greater and lesser ways.
That's the pretty consistent blindspot I've found in people who strongly promote that view - they are almost always blind to the institutions that are required to support someone "being independent".
What’s really interesting is that out of that entire list, only math and science are publicly funded at a level such that a person can get 5 to 7 years of guaranteed job security and funding(ie a PhD), giving you plenty of shots on goal.
From this point of view the science/math path seems obvious. Even if you don’t find gold during your PhD, you still get a PhD and have access to a host of industry, startup, or postdoc positions.
The failure path for writers, painters, or jazz musicians is more risky in my opinion.
It's fascinating how differently people react to the knowledge of this phenomenon. When I was a kid, basically as soon as I realized this was the case I started arguing with my parents that we had to have an Internet-connected computer in the house now. As soon as we got one I basically started reading Wikipedia every non-school hour of every day for 2 years straight.
I doubt I remember more than 0.1% of everything I actually read from that period of my life, but it felt formative and healing in a way I just never expected to be the case. I have also never met anyone else who did something like this and it makes me sad!
Then again I also printed the DooM FAQ out.
Rinse repeat over my high school and early university years.
Decades before, I did the same with Enciclopedia Larousse, an Atlas, the Historia Universal Aguilar, the Diccionario ideológico by Casares and some others. Those were made of paper, you know :)
I wasn't impressed with Wikipedia. But I enjoy IMDb very much. And many illegal/semilegal stuff online.
You're going to have to back this up.
Places and periods without high equality of opportunity for example appear to me to have terrible equality of outcome.
And with what I think you're referring too, which is the increase in the wealth gap between the top 10% and bottom 50%, I'd argue that's actually seen because of a decrease in equality of opportunity, because our system never resets the brackets, the only opportunities left are those not taken. It's harder than ever before to compete in existing opportunity market, since we're in an unprecedented level of market consolidation.
The relationship is nonlinear, most of a high compensation actually happens at the margins; how much better you are compared to the state of the art.
There is a very linear relationship between the maximum concentration that your bacterial culture will get to and the amount of sugar/carbon that they have to eat. Log growth is not really sustainable.
(Unless you continuously find ways to unlock new energy sources, either by luck or because you set aside resources for research/generation of diversity.)
For markets, it would be also good to mention that the price of an asset is not necessarily tied to the value of the asset, and this made worse by markets of low or unknown liquidity. And I would guess that it's also made worse when the valuation of group of assets is calculated by extrapolating from the price of a small number of units of the same kind of asset (i.e. stocks).
It doesn't last forever, but nothing does! Instead there's an exciting idea in place: instead of committing your entire life to trying and getting "one thing" to be as big as possible, you can kickstart many things! As someone who likes a bit of variety in my life, that sounds way more exciting to me.
And of course, sell the idea that "the next big idea" is exponential at 30x..... Until you hit the top of the sigmoid.
Wash, rinse, repeat.
EDIT: Whoops, I forgot to fellate venture capital. You know, the group of companies that would rather leave smoking ruins rather than happily sustainable to 5x companies, and deign to get anything less than 20x companies... and ideally 30x companies.
This is the same group of companies that destroyed Bed Bath and Beyond, Instapot, Toys-R-Us, and loads more, all to cash out and get a jackpot than actually create sustainable and happily workable long term companies.
> The market is a good example of evolution in action; the try-everything-and-see-what-works approach. This might provide a perfectly morally satisfactory resource-management system so long as there was absolutely no question of any sentient creature ever being treated purely as one of those resources. The market, for all its (profoundly inelegant) complexities, remains a crude and essentially blind system, and is - without the sort of drastic amendments liable to cripple the economic efficacy which is its greatest claimed asset - intrinsically incapable of distinguishing between simple non-use of matter resulting from processal superfluity and the acute, prolonged and wide-spread suffering of conscious beings.
> It is, arguably, in the elevation of this profoundly mechanistic (and in that sense perversely innocent) system to a position above all other moral, philosophical and political values and considerations that humankind displays most convincingly both its present intellectual [immaturity and] — through grossly pursued selfishness rather than the applied hatred of others — a kind of synthetic evil.
…
> The Culture, of course, has gone beyond even that, to an economy so much a part of society it is hardly worthy of a separate definition, and which is limited only by imagination, philosophy (and manners), and the idea of minimally wasteful elegance; a kind of galactic ecological awareness allied to a desire to create beauty and goodness.
> Whatever; in the end practice (as ever) will outshine theory.
There's no such elevation. The political process ultimately decides the law (including constitutional), and the law regulates (or frees) the market.
I'd argue that those techniques put us back at the mechanistic system being elevated above other values.
and yet, black markets exists, especially in places where the law fails to provide or provision a sufficiently free market for some goods/services.
So i would argue that the law does not decide this, or you could call it law of nature that decides it.
In the end, people end up elevating the market above all, whether they want it or not, because they underestimate the power of the system they're dealing with.
(Examples: Mailchimp, anything Pieter levels makes, etc.)
Read generously, they’re compounding something not financial. Expertise, for instance.
Then... eventually sold to Intuit, which appears hell-bent on ruining the remaining reputation of Mailchimp.
They're rolling out a new UI, which is obviously not being tested internally. Buttons don't work or provide confusing terminology, preview runs off the screen, occasionally the CSS for their home page just breaks, etc. Employees are clueless and development appears outsourced.
Zombie walking...
He hadn't considered the superlinear returns attributable to being "first", a point made in the article ('thresholds'). By being 20 minutes earlier into work than others on average, I was also inevitably better prepared for the high-pressure morning meeting than anyone else.
Didn't get (that) job.
I am genuinely curious how my learning about the constitution of the Roman Republic while procrastinating will help me.
> 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. We see the same pattern in fame, power, military victories, knowledge, and even benefit to humanity.
It relies on a flimsy claim: this consequence is not caused by social conventions. Are not all of the examples given some manifestation of "rules we've invented"? Which of these things have any significance sans any sort of social context?
You're not saying why it's flimsy. Talking about "social conventions" is the wrong approach. It's more like "this is an outcome of dominant strategies". Be that strategy in the time of kings and queens to become a ruler, or a powerful subject, or in the age of capitalism gaining money by offering things people want to pay for, or in socialist countries gaining power and wealth through navigating the politics of the state, or whatever it is, some people outperform others significantly.
You just have to pick whether you want a mechanism that rewards creating value for others, that they will pay for, or one that rewards having the right connections, or being willing to do violence.
I do understand the observation and I don't disagree, per se. It's just so very noticeable that the observation is made by a person who has greatly benefited from its effects. It's then more than a little distasteful from my perspective that this person is asserting that this is "a feature of the world, not an artifact of rules we've invented".
Again, strictly speaking the observed effect is not a construct of human society; a wild cat who steals food from another wild cat is the one who gets to survive that day. But it's hard to look past who is writing this and for what audience.
To clarify, the "It" in my sentence is referring to "a pretty thinly veiled way of saying that giant corporations are a natural consequence of a healthy economy". I won't object to "natural", as the essay makes a compelling point, but "healthy" was hardly mentioned and certainly not by name. Indeed, "healthy" was dismissed as irrelevant by the passage I quoted.
You'll likely notice the same about most of PG's essays. Of course he's biased -- but most of the readers here already know this, and are not surprised to see a startup-favoring lens being used in much of his writings. His essays still get a lot of traction here, specifically because this started as a discussion board for his startup incubator, and because his essays about How To Startup / What Is a Startup are fairly commonly read in this space (or were what we read when we first discovered this space?).
Obviously many others played crucial roles, but literally none of this would be here without PG’s ideas. The fact that it is and we’re discussing how his ideas may describe effects he’s benefited from only makes them more compelling, IMO.
I agree with this statement "superlinear returns for performance are a feature of the world, not an artifact of rules we've invented", but I disagree its not a problem with capitalism. Its _THE_ problem with capitalism.
The good part of capitalism is that people are rewarded for their effort, the bad part is that those rewards tend to coalesce into a very small subset of people. Winning compounds.
We impose some rules to claw back some money so we can build a safe, stable society. (tax) The problem is, if you are already winning, you are not incentivized to change the system. (pay more tax). Whats more, winners have a lot of power to control how people think and act. We have some other rules to try and limit the power of winners, but those rules are under constant attack.
Well. They're rewarded for value provided, not effort invested. I don't care if you worked really hard on it, I'm not buying your $50 fizzy drink. I want the one that took less effort (and thus cost less) but still was a good product.
> the bad part is that those rewards tend to coalesce into a very small subset of people. Winning compounds.
This isn't exactly true. Rewards work in different ways. If people want steady, mostly-guaranteed income, they (e.g. me) get a day job with a salary. If they want a shot at doing really well, they do a risky thing and, often, it doesn't work. For the few people it does for, you still wouldn't call most of them highly rewarded. A restaurant owner might well still do worse than a salaried Silicon Valley developer. But still, for the industry, you take a risk to get big payoffs.
Also, "reward" is a poor lens to look at this through, as it's slightly infantilising. It's not a pat on the head for a job well done. It's an exchange of value between adults. Steve Jobs did very well financially with the release of the iPhone. But the only reason he did so is because millions of people got value added to their lives through owning an iPhone. They got value far above what they had before, for a price they would pay.
The problem is with looking at only the successful people as examples of the overall system. The system rewards value. If you happen, through hard work, connections, innate abilities, and a bit of luck, to provide value to other people, you do well. If what you do scales to provide value to millions of people, you do really well.
> Whats more, winners have a lot of power to control how people think and act.
I don't think that's true. No one is controlling thoughts and actions. You might say that people who own news outlets have this power, although ownership conveys less control than you might think, but this is a very specific industry. And people who control vast investment sums get to set criteria for companies to fall in line with. But both of those are under fire for this reason: money shouldn't translate into power over people's thoughts or actions. However, in the normal success case, e.g. if I own a restaurant chain, I do really well, but I don't really control anything.
Fair enough, but that's just ad hominem, right? Shouldn't we be just assessing what's said?
People always flippantly quote this without ever looking at the distribution of the actual data.
Whenever people see an uneven distribution they cite something about power laws being that natural order of things and that ends the discussion.
It turns out in many, many cases (I'm not sure if it's particular one) the observed behavior follows nothing like a power law.
A good example of this is net-worth distributions. People often say "of course there's super rich people, that's just a power law! It's not concerning income inequality, it's nature!". But if you pull up the data and do a log-log plot you see quite clearly that it is not even close to following a power-law, and does so only at the lower 90% income quantiles. Which is funny considering the fundamental argument is that unequal distribution are natural so long as they follow a power law.
Is this something that's actually beneficial?
Bizarre.
If there are tens of millions who can do this, there's no way to obtain 'geometric returns'. There isn't enough money in existence.
I do agree that the comment you're replying to is asking for too much -- "verify" and "geometric" are very strong words. But I also agree with the implication that LLMs are making it a lot easier for a person with grit to get farther, which might cross that person's personal threshold (using "threshold" as used in TFA).
For example, every doubling of oil production after WW1 took more than a decade to accomplish. And oil men were pretty well known for risk taking boldness.
The physical impossibility of real resource inputs to human civilization doubling on an even faster timeline is so obvious that I skipped pointing it out, and got straight to the point.
That it's incredibly unlikely for even money to double quickly enough.
My primary skill is as a software engineer who builds complex systems that solve difficult real world problems. That overarching skill encompasses a wide body of sub skills, from UX to doing user case studies to writing blog posts about my work. The actual writing of the code is a non-trivial portion of that, but ideally the code falls out naturally from a correctly planned approach to the problem domain.
Futzing around with some broken API that has a bunch of "gotchas" that can only be gleaned from reading a dozen blog posts on the topic (because the official documentation sucks) is a huge time sink that is not related to any of my core competencies.
I've previously spent days going through annoying stupid code doing work that an AI can do in hours.
> Why should there be multiplicative returns when you haven't actually learned anything?
I do fear this for the generation of coders coming up now. The best way to learn is to build it from scratch once, which already fewer and fewer people have a chance to do, and AI is only going to make it worse.