> Well, it's not just any arbitrary definition, it's the projection of f onto g.
> Well, it's not just any arbitrary definition, it's the projection of f onto g. 'Projection' also has no intuitive (EDIT: I meant 'intrinsic') meaning; "inner product" is the same structure as "projection + norm" (subject to appropriate axioms). Anyway, I didn't mean to claim that the definition was arbitrary, but rather that there was no way to argue against it: definitions can't be wrong (at worst, they can be infelicitous, uninteresting, or uninhabited). > Intuitively, sum(f_i * g_i). I think rndn ( https://news.ycombinator.com/item?id=9621422 )'s objection applies to this intuition: to get a reasonable approximation of the integral, you need a lot of sample points, and any sum that doesn't take into account the spacing of those sample points has a good chance of diverging. (Consider f = g = 1, so that the sum is just a count of the number of sample points!) Once you write sum(f(x_i) * g(x_i) * (dx)_i), of course, this becomes just notation for (a sequence of) Riemann sums, whose limit is by definition the integral (for continuous functions).
Posted by JadeNB on May 29, 2015, 1:40 AM
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I mean that's the problem though.
I've always believed the opposite: get conditionals deep in your code so that the higher level control flow is regular.
The biggest problem with AI isn't being able to do things.
I am a 3D printing maker type nerd (I make my own tools for other creative tasks, rather than as their own outcomes) and I saw an incredi...
Of course not, those are clearly scams.
Claude makes more detailed plans that seem better if you just skim them, but when analyzed, has a lot of errors, usually.
Effectively everyone is building the same tools with zero quantitative benchmarks or evidence behind the why / ideas … this entire s...
> creating and operating a small company in Germany is a nightmare To be fair, I think the problem operating in Germany is its federated...
> Well, it's not just any arbitrary definition, it's the projection of f onto g.
> Well, it's not just any arbitrary definition, it's the projection of f onto g. 'Projection' also has no intuitive (EDIT: I meant 'intrinsic') meaning; "inner product" is the same structure as "projection + norm" (subject to appropriate axioms). Anyway, I didn't mean to claim that the definition was arbitrary, but rather that there was no way to argue against it: definitions can't be wrong (at worst, they can be infelicitous, uninteresting, or uninhabited). > Intuitively, sum(f_i * g_i). I think rndn ( https://news.ycombinator.com/item?id=9621422 )'s objection applies to this intuition: to get a reasonable approximation of the integral, you need a lot of sample points, and any sum that doesn't take into account the spacing of those sample points has a good chance of diverging. (Consider f = g = 1, so that the sum is just a count of the number of sample points!) Once you write sum(f(x_i) * g(x_i) * (dx)_i), of course, this becomes just notation for (a sequence of) Riemann sums, whose limit is by definition the integral (for continuous functions).
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