wwalker3

5 ms·

1.
by wwalker3 4y ago
That's a great article! 1) I'd seen a lot of other cool stuff from the same author over the years (see https://math.ucr.edu/home/baez/README.html ), but had somehow missed this one. 1) "Struggles wit
2.
by wwalker3 4y ago
If you use the theory of nonlinear partial differential equations to analyze the behavior of compressible materials, you can find what are called the "characteristic" speeds, which are the speeds that various types of waves propag
3.
by wwalker3 4y ago
If mathematicians could solve these kinds of problems, they could answer valuable questions like "Will this equation always have a physically meaningful solution?" If the answer was "No", then we would know that the equa
4.
by wwalker3 4y ago
It's the equations themselves that are singular. When we write simulators, we usually have to paper over the singularities that are inherent in the math. For example, if you're simulating charged particles moving around, and you u
5.
by wwalker3 4y ago
The density can be constant, but it doesn't have to be. If the density field starts out with some variation in it, then those variations move around as the fluid flows. Incompressibility just means that those density variations can&#x2
6.
by wwalker3 4y ago
Pretty much any mathematical model of a real phenomenon can have some sort of singularity or discontinuity in it. If you model atoms as dimensionless points (1), then any kind of force law with the distance between atoms in the denominator
7.
by wwalker3 4y ago
Wow, I'm honored :) These days, I try to only comment when an article is really in my wheelhouse, but that's not very often, given my narrow interests in fluid dynamics and computational physics.
8.
by wwalker3 4y ago
The incompressible Euler equations model a fluid as a two-valued field. This means that at every point in space, the field has two values, density and velocity (1). To me (2), a singularity in a field like this means that one or more of the
9.
by wwalker3 4y ago
The question that the referenced paper (1) is trying to answer is "do the 3D incompressible Euler equations develop a finite time singularity from smooth initial data of finite energy?" This is an important question in the theory
10.
by wwalker3 7y ago
That's a good point. Guess-and-verify could be a handy additional heuristic method if Mathematica's other methods came up empty on a problem. I've also heard of machine learning being used to choose between internal algorithm
11.
by wwalker3 7y ago
The authors have shown a very nice and (to me) non-intuitive result. But they're playing a little fast and loose with their comparison to Mathematica. They're comparing their algorithm's accuracy (solution correctness vs. inc
12.
Talent, luck and success: simulating meritocracy and inequality(medium.com)
156 points by wwalker3 9y ago|189 comments
13.
by wwalker3 14y ago
I suspect that at least some of these "flaws" are intentional, and are meant to make programming easier, at the expense of some performance. For example, three of the poster's points (not allowing device property querying, not allowing the
14.
by wwalker3 14y ago
It does look like mobile GPU vendors are about to start offering OpenCL support. For example, ARM submitted OpenCL 1.1 Full Profile conformance test results for the Mali-T604 last year ( http://blogs.arm.com/multimedia/775-opencl-with-arm-m
15.
by wwalker3 14y ago
When I saw the TEDx guys' caution about a "physics-related speaker [who] has a degree in engineering, not physics", it struck a bit of a nerve for me. My Ph.D. is in electrical engineering, not physics. I recently got a computational physic
16.
by wwalker3 14y ago
I work in the R&D division of a microprocessor company. Most of what we do, I would call "research", but not quite "science". We investigate things that are too risky or time-consuming for our product design groups to look into, with an
17.
by wwalker3 14y ago
Stross' comparison between Cray 1 performance and that of a modern smartphone seems off. He says: "A regular ARM-powered smartphone, such as an iPhone 4S, is some 12-13 orders of magnitude more powerful as a computing device than a late 197
18.
by wwalker3 15y ago
It sounds like the NCSU guys are using the CPU as a prefetcher to speed up GPU kernel execution, not using the GPU to speed up normal CPU programs as the ExtremeTech article implies. The CPU parses the GPU kernel and creates a prefetcher pr
19.
by wwalker3 16y ago
Humorously enough, early television in the UK (from 1929-1935) had only 30 lines of resolution and so could be recorded at audio frequencies onto a "Phonovision" disk. You can see some examples at http://www.tvdawn.com/recordng.htm of the
20.
by wwalker3 16y ago
Having to reject someone can be a very stressful experience. I don't like the idea of purposefully inflicting that stress on others unless there's a chance we both could benefit. "Getting rejected on purpose" sounds like I'd be picking situ
21.
by wwalker3 16y ago
It looks like a big linear motor like in the video is probably $1000 to $2000 dollars. Angle sensors are pretty cheap (just a few bucks). Then you'd need an A/D-D/A board to control it with ($500 to $1000).
22.
by wwalker3 16y ago
The guy whose thesis this was comments on it here: http://www.reddit.com/r/math/comments/ebql6/double_inverted_... I had guessed they were using visual sensing because of how the two halves of the pendulum were painted in contrasting, bri
23.
by wwalker3 16y ago
I agree that component count and the price of other logic chips were important too. Woz was a genius at that kind of design where you have to do something super-creative to save that last tiny bit of cash. However, I think I can make a good
24.
by wwalker3 16y ago
It's true that the Apple ][ was double-buffered, but as another commenter mentioned, it wasn't a game console :) But the Apple ][ is actually a good illustration of my point. Due to the cost of memory back then, Wozniak had to make many com
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by wwalker3 16y ago
I liked how today's low memory prices completely changed the hardware design tradeoffs. This system uses only 1980s-level technology, but you could never have afforded to build a bank-switched double-buffered memory system like this for a h
26.
by wwalker3 16y ago
The founder's thesis mentions that they use a linearizer in their analog circuit, but all that does is give the same precision over the entire logical value range from 0 to 1 (by that I mean the same amount of voltage swing equals the same
27.
by wwalker3 16y ago
I think it is likely we will see more of these. But this probability chip sounds more like an analog computer than what D. E. Shaw has done. The Lyric web site says that they "model relationships between probabilities natively in the device
28.
by wwalker3 16y ago
It would be very hard to accurately account for a microprocessor's out-of-order instruction issue in a compiler. A modern desktop-class microprocessor can have scores of instructions "in flight" at once. Each new instruction that's decoded
29.
by wwalker3 16y ago
That might very well fix the anisotropy problem (I haven't seen it done yet, but it sounds reasonable). However, that leaves you with another problem -- how do you create a stable particle-like pattern that can travel over a randomly-connec
30.
by wwalker3 16y ago
You're right, NKS does cover more than cellular automata, like network systems (as your reference shows). But all the examples Wolfram gives of network systems have the same anisotropy problem as a cellular automaton. He uses mostly hexagon

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