Thanks for the explanation. I accept your usage of “abstraction” as congruent with the common use among software engineers (although I have other issues with that usage)). Confusingly, your hierarchy is a hierarchy in g required, not a hierarchy in the abstractions themselves.
I am well-read in Joel Spoelsky, and my personal experience matches the anecdotes you share. On the other hand, I have also tutored some struggling programmers to a high level. I still find the claim of a g-floor incredible. This kind of inference feels like claiming the insolubility of the quintic because I solved a couple quintics numerically and the numbers look very weird.
Sidenote: I find your example discussion of human learning funny because I learned arithmetic before writing.
It’s that the general form is unsolvable, not specific examples, without better tools than the usual ones: +, -, *, /, sqrt, ^, etc. I’ve heard that with hypergeometric functions it’s doable, but the same issue reappears for polynomials of higher degree there as well.
This kind of inference feels like claiming the insolubility of the quintic because I solved a couple quintics numerically and the numbers look very weird.
I think it is more like the irreversibility of the trapdoor functions we use in cryptography. We are unable to prove mathematically they are secure. But an army of experts failing to break them is Bayesian evidence.
Thanks for the explanation. I accept your usage of “abstraction” as congruent with the common use among software engineers (although I have other issues with that usage)). Confusingly, your hierarchy is a hierarchy in g required, not a hierarchy in the abstractions themselves.
I am well-read in Joel Spoelsky, and my personal experience matches the anecdotes you share. On the other hand, I have also tutored some struggling programmers to a high level. I still find the claim of a g-floor incredible. This kind of inference feels like claiming the insolubility of the quintic because I solved a couple quintics numerically and the numbers look very weird.
Sidenote: I find your example discussion of human learning funny because I learned arithmetic before writing.
It’s that the general form is unsolvable, not specific examples, without better tools than the usual ones: +, -, *, /, sqrt, ^, etc. I’ve heard that with hypergeometric functions it’s doable, but the same issue reappears for polynomials of higher degree there as well.
I think it is more like the irreversibility of the trapdoor functions we use in cryptography. We are unable to prove mathematically they are secure. But an army of experts failing to break them is Bayesian evidence.
Sidenote: Lol.