sfpotter

12 ms·

151.
by sfpotter 1y ago
The wealthy use a progressively more and more marginal amount of their income for necessities. Consequently, their income gets pumped into assets, which produce still more wealth for them. There are different ways of taxing people. You can
152.
by sfpotter 1y ago
Sure. Let's just not give a giant handout to the wealthy.
153.
by sfpotter 1y ago
I read it and it made me pretty upset... Wallace clearly got way out over his skis and simply shouldn't have been writing about the topic. There were way too many moments interspersed throughout the book where it was obvious that he di
154.
by sfpotter 1y ago
Terrible on every front? I'm sorry, but it's hard to take this seriously. I've been daily driving Fedora with Cinnamon for the past 4 years and it works just fine. I use Mac and Windows on a regular basis and both are chock f
155.
by sfpotter 1y ago
Something interesting here is that although Clenshaw-Curtis rules with N nodes only exactly integrate degree N-1 polynomials while Gauss rules integrate degree 2N-1, they are frequently competitive with Gauss rules when integrating general
156.
by sfpotter 1y ago
Ah, shucks. I can see you're getting upset and defensive. Sorry... Yes, it should be clear from everything I've written that I'm quite clear on the definition of these. If you would like to read what I'm saying but from
157.
by sfpotter 1y ago
I would check out "An Introduction to Numerical Analysis" by Suli and Mayers or "Approximation Theory and Approximation Practice" by Trefethen. The former covers all the major intro numerical analysis topics in a format
158.
by sfpotter 1y ago
Which topic?
159.
by sfpotter 1y ago
No, I am not confused. :-) I am just trying to help you understand some basics of numerical analysis. > What you do not understand is that this is the same thing. It is not the same thing. You can express an analytic function f(x) in a c
160.
by sfpotter 1y ago
If there is, I'm not aware of it. Orthogonal polynomials come up in random matrix theory. Maybe there's something there? But your last paragraph is exactly it... it is a "basic" fact but the consequences are profound.
161.
by sfpotter 1y ago
What you're saying isn't wrong, per se, but... There are polynomials that aren't orthogonal that are suitable for numerics: both the Bernstein basis and the monomial basis are used very often and neither are orthogonal. (Well
162.
by sfpotter 1y ago
Chebyshev polynomials are useful in approximation theory because they're the minimax polynomials. The remainder of polynomial interpolation can be given in terms of the nodal polynomial, which is the polynomial with the interpolation n
163.
by sfpotter 1y ago
Nothing to do with what you said? This is true for any curve... If your curve is continuous, it is locally linear. Hmm... Sometimes naive approximations are all you've got; and in fact, aren't naive at all. They're
164.
by sfpotter 1y ago
For a function to be locally linear at a point, it needs to be differentiable at that point... |x| isn't differentiable at 0, so it isn't locally linear at 0... that's the entirety of what I'm saying. :-)
165.
by sfpotter 1y ago
A curve isn't necessarily locally linear if it's continuous. Take f(x) = |x|, for example.
166.
by sfpotter 1y ago
Never heard of it. Got a reference? I can investigate.
167.
by sfpotter 1y ago
Yeah, I'd generally agree with that. One thing to bear in mind, though: there are numerical algorithms which are stable and unimpeachably useful but which are unstable in interval arithmetic owing to the natural interval inclusion be
168.
by sfpotter 1y ago
Yeah that's it. There might be a couple others? That paper should also have references back to earlier papers on higher order inclusion functions.
169.
by sfpotter 1y ago
For what it's worth, what you originally said was: "This is total nonsense." The points you're making are valid, but it isn't "total nonsense". Something not being exactly factually correct doesn't me
170.
by sfpotter 1y ago
This is a great point... and Rademacher's theorem is one of my favorites. But this is in the context of a numerical algorithm which proposes to replace interval arithmetic with a direct evaluation of a gradient. For an SDF, the gradien
171.
by sfpotter 1y ago
The concept of a Lipschitz function comes from mathematical analysis; neither computer graphics nor numerical analysis. It's straightforward to find the definition of a Lipschitz function online, and it is not in terms of its derivat
172.
by sfpotter 1y ago
The point of interval arithmetic isn't really to deal with numerical stability, per se... it's to make it possible to do rigorous and validated computations on a computer. Numerical stability is a different concept that is somewha
173.
by sfpotter 1y ago
Cool post. The Lipschitz trick here relies on the assumption that the gradient has magnitude 1 everywhere. Evaluating the SDF in a box and using the Lipschitz property lets you get some quick estimates on the range of the SDF over the box.
174.
by sfpotter 1y ago
Worth pointing out that these ideas were already well known by Moore, the founder of interval arithmetic. Chapter 3 of his monograph "Methods and Applications of Interval Analysis" has the basic ideas worked out. The folks working
175.
by sfpotter 1y ago
Because in many cases no "troll" has been found at all; and discouraging people from witch-hunting leads to a more positive environment that's conducive to interesting conversations. Often the witch hunter is just salty about
176.
by sfpotter 1y ago
Said with sadness, not sneeringly.
177.
by sfpotter 1y ago
Paul Graham, as a writer who writes sentences that sound bad and who promulgates ideas that are stupid, is an expert in neither good sounding sentences nor sound ideas, hence is unqualified to hold forth on the topic.
178.
by sfpotter 1y ago
It actually isn't that hard to come up with something better than what's in a standard library, but that requires understanding what better means for what you're working on. That's the hard part. In my experience, people
179.
by sfpotter 1y ago
So many bitter and jaded people in this thread.
180.
by sfpotter 1y ago
Just because you've never felt the need doesn't mean you aren't stuck in a local minimum.

More ›