That some "horns" have a threshold beyond which the standard diminishing returns formula is the wrong way to think about it, and that once this threshold is crossed you open up a whole slew of new parameters to toy with, as if you'd just started on something entirely new (which is often the case in some sense).
(paragraphs 1-2) This idea that there's a transition point where suddenly returns start increasing appears nowhere in the physical instance of a powder horn (when you finally turn it over, do you get even more powder than your first easy scoop?) which even implies that returns will hit zero the instant after you turn over the horn (because now the horn is completely empty).
(paragraphs 3-4) OP then claims that some things aren't horns because there is some transition effect where returns suddenly start increasing with more investment. But the claim comes off completely flat because exactly one example is given, and a pretty dubious one at that.
Basically, the guy who stopped trying to learn more about poker rules because he saw diminishing returns and never pushed forward enough to "get" the things that lead to counting cards and deception and metagame will have missed out on the point of poker entirely.
Those may be interesting and complex, but your description matches up fine with diminishing returns.
At least, if I'm interpreting the main article correctly, there are some fields of knowledge which behave in a similar fashion, and we might benefit from having good heuristics for figuring out which fields will behave like this so that we can improve our research efficiency... or something.
At this point in the discussion, I think we would benefit more from establishing that there are such fields at all.
Yes, all good points, but one minor bump when I read your comment:
Those may be interesting and complex, but your description matches up fine with diminishing returns.
I don't quite understand what you mean. Given that an agent values having the kind of fun given by playing poker on more advanced levels, I do see a point at which poker suddenly starts generating more fun-returns for each unit of learning-to-play-poker, just before which diminishing returns still applied.
Then a bunch of increments give high value before diminishing returns start being a...
Some time ago I learned of the metaphor of 'digging the bull's horn'. This might sound a little strange, since horns are mostly hollow, but imagine a bull's horn used to store black powder. In the beginning the work is easy and you can scoop out a lot powder with very little effort. As you dig down, though, each scoop yields less powder as you dig into the narrow part of the horn until the only way you can get out more powder is to turn the horn over a dump it out.
It's often the same way with learning. When you start out in a subject there is a lot to be learned (both in quantity of material you have not yet seen and in quantity of benefits you have to gain from the information), but as you dig deeper into a subject the useful insights come less often or are more limited in scope. Eventually you dig down so far that the only way to learn more is to discover new things that no one has yet learned (to stretch the metaphor, you have to add your own powder back to dig out).
It's useful to know that you're digging the bull's horn when learning because, unless you really enjoy a subject or have some reason to believe that contributing to it is worthwhile, you can know in advance that most of the really valuable insights you'll gain will come early on. If you want to benefit from knowing about as much stuff as possible, you'll often want to stop actively pursuing a subject unless you want to make a career out of it.
But, for a few subjects, this isn't true. Sometimes, as you continue to learn the last few hard things that don't seem to provide big, broadly-useful insights, you manage to accumulate a critical level of knowledge about the subject that opens up a whole new world of insights to you that were previously hidden. To push the metaphor, you eventually dig so deep that you come out the other side to find a huge pile of powder.
The Way seems to be one of those subjects you can dig past the end of: there are some people who have mastered The Way to such an extent that they have access to a huge range of benefits not available to those still digging the horn. But when it comes to other subjects, how do you know? Great insights could be hiding beyond currently obscure fields of study because no one has bothered to dig deep enough. Aside from having clear examples of people who came out the other side to give us reason to believe it's worth while to deep really deep on some subjects, is there any way we can make a good prediction about what subjects may be worth digging to the end of the bull's horn?