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Learning Skills Is Non-Linear

Max talked about return on investment for learning. E.g. at 1% improvement per day, you can double your skill in 70 days. It’s around 2 years for 0.1%. If you always spend half your time learning instead of working, then your productivity (stuff accomplished per day) will be ahead once you double your skill.

I want to talk about some problems with that linear skill model. I think it’s misleading and understates the value of learning.

Learning Is Non-Linear

There are non-linear jumps in performance when learning. It’s like jumps to universality. There are discontinuities.

Put another way, some learning crosses an important breakpoint and results in a major jump in performance. And some doesn’t.

If you don’t make some kind of significant breakthrough, Max’s simplified model may overestimate the effectiveness of learning. But a single breakthrough can be worth a ton of effort.


Also, people often fail at things. One of the results of learning is more ability to succeed rather than fail. Learning more can often make the difference between success and failure. There are lots of things you just can’t do successfully unless you learn enough. Learning reduces errors.

Not a Matter of Speed

David Deutsch said:

The thing that people call intelligence in everyday life — like the ability of some people like Einstein or Feynman to see their way through to a solution to a problem while other people can't — simply doesn't take the form that the person you regard as 'unintelligent' would take a year to do something that Einstein could do in a week; it's not a matter of speed. What we really mean is the person can't understand at all what Einstein can understand.

This is related to non-linearity again. You can’t just take 100 people who did less learning and have them do the same work as 1 guy who learned enough to be 100x as effective. Even if you set aside the overhead for coordination between the 100 people, it still doesn’t work. You can’t replace an Einstein or Feynman with even a million ordinary people and get the same work accomplished.

The 100 people have some advantages too. Learning doesn’t give you a big effectiveness gain at all work. The advantages from learning are unequally distributed. This is often mitigated by helpers. A genius can hire help or work at a company with a bunch of other manpower.

But if you imagine the genius alone on a desert island, and then imagine a second desert island with 100 average people, you’ll see some advantages and disadvantages for each island. (The desert island scenario prevents the genius from having any helpers.)


IMO, it’s pretty hard to go wrong investing in learning if:

  • your learning is effective
  • you’re reasonably young
  • you’re learning general purpose stuff

Learning stuff that’s only useful for a few purposes is more risky. You might stop using it later. And failing to learn or getting stuck or learning wrong ideas are common problems. And you probably shouldn’t learn to code and try to switch careers when you’re 90.

Learning effectiveness is the condition that concerns me the most. Lots of times people try to learn stuff and it doesn’t work. This is especially true for more general purpose stuff like philosophy. Learning really specific skills is more reliably successful. But most people aren’t very successful at learning about epistemology. (That’s a problem I’ve been working on.)

Elliot Temple on April 3, 2021

Messages (3)

I think I agree with your post. Some of what you said isn't clear to me, tho, so I wanted to write out my new thoughts for my own clarity and to expose them to crits.

> I want to talk about some problems with that linear skill model.

You use the word *linear*. There are two meanings that I think you mean by this:

1. Learning a new skill has breakpoints, so the pattern is more like *growth -> plateau -> growth -> plateau -> ...* rather than *add 1% -> add 1% -> add 1% -> ...*. Both of those patterns are nonlinear in that they're not `y = mx + b`, so what's not linear? The growth rate; there are discontinuities b/c of rapid progress via breakpoints and breakthroughs. Mb another way to say that is that *the increase in effectiveness via learning isn't smooth*.

2. Skills interact, so focusing on one skill in isolation isn't optimal/effective learning. Learning different (and particular) skills lets you combine them and get a ~synergy type boost to your productivity and/or capabilities.

As an example for (1): say you wanted to manage a resource like water where you have some incoming rate and an outgoing rate. You could get better at that task by getting better at doing arithmetic and computation, i.e., manually calculating incoming and outgoing figures. Maybe you do that by focusing on speed of computation and you get like 1% better each day. But you could also learn new methods of doing arithmetic (e.g. some of the clever ways of doing multiplication) and get *much* better in a short space of time. That's a breakpoint but it's like a 100% improvement and then you'd plateau. *Or, a third option,* you could learn calculus. That's also a breakpoint -- but much more like the jump to universality: if you know calculus you have *qualitatively new* methods of analysis. Not only can you do the stuff you used to do *much* faster (e.g. 10x faster or 100x faster), but you can also find new relationships that allow you to know stuff that *you never could have* using the previous methods (like finding critical points algebraically).

I guess that's also an example for (2); there were two paths you could have taken (faster computation or a new method), and learning that new method (calculus) lead to a breakthrough.

It occurs to me: if you can do effective learning (particularly with some static or dynamic guidance -- e.g., an organized course or tutoring, respectively), then your rate of progress can go way faster than exponential growth. Mb this is b/c *the benefit you get from learning is not based on your previous performance, it's based on the significance/reach/universality of the new ideas*.


I agree with the rest of your post, too, but didn't feel there was a need to quote or discuss other points -- the above was enough.


> I think it’s misleading and *understates the value of learning*.

I think I agreed with this after I read your post (before writing this), but, up until I wrote this reply, I didn't realise just how misleading it was and to what extent it understated the value of learning.

Max at 8:04 PM on April 4, 2021 | #1 | reply | quote

I agree that "linear" was the wrong word.

curi at 12:18 PM on April 5, 2021 | #2 | reply | quote

> And you probably shouldn’t learn to code and try to switch careers when you’re 90.

I tried to learn coding at 40 and I failed. I hate my job.

Anonymous at 12:16 PM on April 6, 2021 | #3 | reply | quote

Want to discuss this? Join my forum.

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