Except that all the meaningful combinations are already being competed on, while all the meaningless combinations are not.
The amount of meaningful combinations is not , but much lower. This website lists 12.000 career paths. I'd wager that the true number is not more than an order of magnitude away from it. If we take a (totally arbitrary) upper bound guess of 100.000 career paths, that means to be world class you still have to compete with 80.000 people.
Of course you can try and invent a new meaningful combination of skills, but that's just another skill combination, and it's one that a lot of people are already competing on.
There are other points in support of your counter argument too. Defining the boundaries of a “skill” is arbitrary. Are we comparing ourselves to professionals or laypeople, and what counts as a useful level of achievement?
This same objection comes up on this website every time this argument gets made. You can find it in some of johnswentworth’s posts. The motion of the argument is always from the “combinations of skills makes you world-class” -> “the good ones are all taken,” not the other way around.
The central point, unstated here, is that we need to find ways of sparking our imagination to see how we can get beyond imitation and into innovation.
It’s hard to go from a combination of very general skills (cooking, tractor repair, math, stand up comedy, arctic exploration) to a concrete idea for a job, invention, or research project.
Instead, focusing on the most important, tractable ideas pushes people to gain new skills outside their specialty. Those who hyper-specialize limit themselves to projects that are tractable within their current skillset. Those who are willing to learn in an open-ended way to pursue the most interesting goals acquire targeted micro-skills outside their main discipline.
This suggests an association between having a variety of skills and significant, world-class achievement. But it’s not that achievement will consistently follow from arbitrary skill combinations, but rather that the remaining available achievements can only be unlocked by mastering previously unknown skill combinations.
There’s an unstated call to action here. If you’re choosing between a moderately interesting project that’s fully within your skillset, and a very interesting one that requires learning some far-afield skills, choose the latter.
The central point, unstated here, is that we need to find ways of sparking our imagination to see how we can get beyond imitation and into innovation.
My personal approach is to deliberately master a variety of orthogonal skills and wait for my unconscious to ask "Why doesn't someone do ?" because good cross-disciplinary ideas are often obvious to specialists and invisible to everyone else.
If you're a database expert, don't build a chat app for teenagers (unless you're also a teenager). Maybe it's a good idea, but you can't trust your judgment about that, so ignore it. There have to be other ideas that involve databases, and whose quality you can judge. Do you find it hard to come up with good ideas involving databases? That's because your expertise raises your standards. Your ideas about chat apps are just as bad, but you're giving yourself a Dunning-Kruger pass in that domain.
―How to Get Startup Ideas by Paul Graham
Exactly. Really, the title should be "Six specializations makes you world-class at a combination of skills that is probably completely useless." Really, productivity is a function of your skills. The fact that you are "world class" in a random combination of skills is only interesting if people are systematically under-estimating the degree to which random skills can be usefully combined. If there are reasons to believe that, then I would be interested in reading about it.
Another interpretation of that website would conclude (though I think just using the big categories works better). Thank you for the link. I originally thought might be too high but now I feel it might be too low.
Looking for pre-existing career paths is doing the opposite of what my article recommends because pre-existing career paths are, by definition, domains with competition. To follow the advice in this article, you usually must discover or "invent a new meaningful combination of skills".
Many meaningful combinations are not being competed on. For example, nobody is writing good Harry Potter Rationalist fanfiction right now and that's just (fiction writing and rationalism).
Our double crux seems to be about the feasibility of finding new combinations that are meaningful.
Using previously discovered combinations as examples doesn't count, because discovery is easy in hindsight.
Could you come up with a bunch of novel combinations, right here and now, that sound like they might be useful to the world at large?
Could you come up with a bunch of novel combinations, right here and now, that sound like they might be useful to the world at large?
I could, but that would be a recipe for ideas that sound good but are actually bad.
Maybe there are better ways to come to agreement on the feasibility of discovery. Perhaps we should look at the success rate of startups? Do you have other ideas?
From lsusr's response to my comment above, I think they're saying that learning new skills makes you more able to recognize the right problems to solve, as well as to execute on potential solutions.
So there is a prediction here. Learning a new skill will be more positively correlated with identifying better ideas than they had before, as compared with an equal investment of time deepening a skill they already possessed.
How can we operationalize this?
One way is that we could create a dataset of startup founders. We'd look at their age and the number of previous companies they'd founded or worked for. Optimally, we'd find a way to quantify how different from each other these companies were.
lsusr's framework might predict that, controlling for age, founders who'd worked for a greater number and diversity of companies would achieve greater personal wealth than those who'd worked for a smaller number and less diverse range of companies.
Because this is a loose heuristic, with a solid argument in both directions, I think we should insist on careful data-gathering in a carefully operationalized manner before we accept anything as more substantial evidence than the plausibility-supporting anecdotes we already have access to here.
I base my estimate of the feasibility of discovery on my personal experience of startup (and non-startup) entrepreneurship. The number of worthwhile projects I can pursue is way higher than the number of projects I have time to pursue. For example, I coded and deployed an ML-based language learning app that I use for self-study but I don't open it up to the public because I'm working on more important projects.
Of course you can try and invent a new meaningful combination of skills, but that's just another skill combination, and it's one that a lot of people are already competing on. Caveat: this may not be very true (outside not-completely-incompetent entrepreneurship).
This is heavily supported by my experience/intuition; if I were to rank the people I know and/or admire according to total awesomeness or similar, I believe it is the case that very nearly all of the top twenty are on the list because of being 99.9th+ percentile in three or more things.
Only one of them is 99.999th percentile in a single thing.
I think there are 2 mistakes here. First you are missing an n!. There are only ~ 10,000 skill pairs if (physics , writing) is different from (writing , physics). There are ~ 5,000 unordered pairs.
Secondly is the assumption that no one else can have more skills than you. If everyone picks 5 skills to get good at, you can be the only person in the world with that combo of skills. If you get to pick 5 skills. And some other people are good at all 100, you don't get a unique combo. If 32 people each have 50 skills, then you probably don't have a unique combo.
Thank you for the correction. Adding the missing factorial increases the answer from five to six.
You don't need a unique combination. You just need combination nobody else is competing at. If someone has more skills than you then there is a combinatorial explosion in the possibility space available to zem. The odds zir work collides with yours goes down fast as the number of skills your superior has goes up. Ze likely have better things to do than compete with you.
I can follow the idea that "combining six skills at random makes you so specialized that literally nobody in the world is competing with you", and that this would translate to "something extraordinary" (for some definition of extraordinary). However, I don't think that it necessarily follows that "You can make a lot of money" just by doing this.
It seems to me that by hyper-specializing, you are moving your skill-set to an area where the effective supply of the combination of such skills is low. However, from an economic perspective, if we want to "make a lot of money", we need to also consider the demand for such a hyper-specialized skill-set.
That being said, I think that the insights gained by being top-tier at a skill can provide a competitive advantage in a field that requires another different skill.
Specialization is typically framed as "narrowness of skill," and I think lsusr and others are pointing out that this is the wrong frame by which to understand it. Instead, I think they're pointing out that "narrowness of problem" is a better way to define specialization. A wide range of skills may easily be necessary to tackle the most valuable problems.
lsusr is also pointing out in the comments that we may not be able to figure out what problems exist until we've gained some relevant skills.
My sense is that it's the arbitrariness of combining skills at random that is bothering a lot of commenters, here and elsewhere. I think that's important. I also think there's a synthesis.
It seems to me that navigating toward interesting problems involves reasoning under uncertainty.
"If I spend another 3 months improving my skills, should I learn something new (say, immunology) or something I already know how to do (say, machine learning)?"
People are making a prediction partly on whether learning immunology or more ML will be useful for the problem they're already focused on. But they're also predicting which investment is more likely to expose them to a new and more valuable problem to solve.
lsusr's arguing that people tend to focus on the problems they already know about. Having 3 months of ML under your belt makes you aware of the problems you could solve with 6 months of ML experience. That may incline you to invest in another 3 months of ML learning. But if you considered all the unknown unknowns you'd be exposed to if instead you spent those 3 months focused on immunology, you might find that broadening your skill base tended to result in counterfactually more valuable exposure to problems and opportunity to create value for others.
So we don't have to imagine that the new skills are chosen arbitrarily. That's sort of what the post implies, but I don't think it's core to the argument. Instead, the new skills can be chosen based on what seems like it offers the most potential for cross-fertilization. Even so, you're still making a choice between acquiring that novel skill, or improving a skill you already possess.
If the choice between investing equal amounts of time into a new vs. old skill seems intuitively to offer about equal value, choose to acquire the new skill. Most of the value in improving the old skill is apparent when you're making the decision. Most of the value of learning the new skill will become obvious only after you've learned it. So there's a systematic bias against broadening your skillset, and it takes a rule like this to overcome that bias.
Well-put! Your comment was valuable because I tend to think / read about problems in a particular field that were able to be solved in a unique / unorthodox fashion due to skills acquired in another field (discovering new solutions), but your point about discovering new problems that only can be realized by having expertise in multiple fields is something to think about as well.
Some of johnswentworth's posts and sequences touch on something related, I think: Specializing in Problems We Don't Understand, the Framing Practicum sequence, and the Gears Which Turn The World sequence.
This is a shot in the dark, but I recall there was a blog post that made basically the same point visually, I believe using Gaussian distributions. I think the number they argued you should aim for was 3-4 instead of 6. Anyone know what I'm talking about?
I don't recognize the exact blog post you reference but in my personal experience the actual number of skills that put me on a useful Pareto frontier is indeed closer to 3-4. To be clear, I don't get there by just learning 3-4 different skills. I learn like 8-10 and then a subset of 3-4 gets me to the Pareto frontier.
You can make a lot of money by being the best at a scalable domain because leverage feeds winner-take-all dynamics.
The problem is there are P=8×109 people on Earth. To be the best, you have to be better than every single one of them. It's not hard to get into the top 0.1 or even 0.01 of people at many skills but it is hard to get into the top 1P=.0000000001.
There are many different skills you can learn e.g. mathematics, sales, drawing, management. Suppose there are S=100 basic skills. You can become the best in the world by being the best at any one of them. But to be the best at one of S=100 different skills you must compete against PS=80,000,000 people. Competing against eighty million people is easier than competing against eight billion but it is still hard.
Many real-world competitions require more than one skill. Suppose you want to be the best author of physics books. You must combine two skills: writing and physics. There are S(S−1)2=100(100−1)2≈5,000 different pairs of skills. Instead of competing against the rest of mankind in 100 domains you are competing in 5,000 different domains. On average, you will compete against 2PS(S−1)≈2PS2=1,600,000 people.
For n randomly-selected skills there will, on average, be only Pn!Sn people competing at the intersection. You are one of those people. At what n is there zero competition (besides yourself)?
Pn!Sn=1P=Snn!lnP=nlnS−ln(n!)≈nlnS−(nlnn−n)≈n(1+lnS−lnn)
lnn≈2 when 5≤n≤10.
lnP≈n(1+lnS−2)≈n(lnS−1)n≈lnPlnS−1≈ln(8×109)ln100−1≈6
Six. If S=100 then combining six skills at random makes you so specialized that literally nobody in the world is competing with you. The equation is weakly dependent on our choice of S. If S=50 then you need seven skills instead.
Six arbitrary skills may not be, in general, synergistic. But if your work combines six or more skills then you should not be surprised if you are the best in the world.