kmill

47 ms·

361.
by kmill 7y ago
I'm glad someone posted this again, since a couple weeks ago I was trying to remember exactly how it worked! (Not for any particular purpose, but I had just remembered it being a nice design for a combinatorial feedback loop.)
362.
by kmill 7y ago
I tend to think of math as having two parts: a way of thinking along with all the things people thought up by thinking that way. To learn the first, you have to study the second. Examples of the second are calculus, group theory, algebra,
363.
by kmill 7y ago
I can't find it at the moment --- it was an essay about a Russian mathematician's experiences coming to the United States and the culture shock with respect to education --- but in it he offered that Soviet academics' relatio
364.
by kmill 7y ago
This is the Henry Cohn that recently received recognition for his work on optimal sphere packings in 8 and 24 dimensions: http://www.ams.org/journals/notices/201804/rnoti-p463.pdf
365.
by kmill 7y ago
> Mathematica It's derived from Wolfram's conception of Macsyma, and it is designed so that all code is made out of numbers, strings, symbols, and arrays (sure, not cons cells). I guess it's nice to know you wouldn't
366.
by kmill 7y ago
I'm not sure what the relationship between fexprs and homoiconicity is supposed to be. If anything, the arguments to an fexpr in a Lisp with lexical scoping are opaque and cannot be manipulated, since they are wrapped up in a closure
367.
by kmill 7y ago
Here's a small toy to play with the heat equation: https://math.berkeley.edu/~kmill/toys/heat/heat.html (it probably doesn't work on mobile---sorry!) It shows the Fourier transform of the curve you
368.
by kmill 7y ago
It certainly does explode to infinity as a series. What's going on in the factoid (though I'm a bit weak in analysis) is that the series zeta(s) = sum(k^(-s) for k in 1:Infinity) converges for all complex s whose real part
369.
by kmill 7y ago
(One of the copy editors was Leslie Lamport himself! Took me a little digging to get the joke.)
370.
by kmill 7y ago
> Among other things, this paper is not about an implementation methodology that ensures the GCD algorithm will take exactly the same amount of time regardless of the input. The introduction to the paper talks about the importance of dev
371.
by kmill 7y ago
One might argue that calling O(1) just "constant time" in asymptotic complexity theory is click bait itself! Calling O(1) bounded time would have been better terminology, in my mathematical opinion. Sometimes people actually co
372.
by kmill 7y ago
I don't work in the field, but I did a little reading about the theory last year. (I can't say anything about how any of this is applied---I have been wondering for a while whether it does anything beyond giving really nice looki
373.
by kmill 7y ago
I was wondering about having a special message to indicate the end of the buffer while reading the article, so thanks for pre-emptively answering my question! Another thing I was wondering about is using a simple buddy allocator with the ri
374.
by kmill 7y ago
Or UC Berkeley's math department, which doesn't require submitting anything for publication at all.
375.
by kmill 7y ago
I use my university Mathematica license rather than use WolframAlpha because I can never figure out exactly what the latter can do. Wolfram Language, in contrast, has ok enough documentation and a predictable programming model. (It's n
376.
by kmill 7y ago
Thanks, that's right. (I had the Lie algebras in mind with that statement. The Lie brackets are placed at the vertices in the construction.)
377.
by kmill 7y ago
Speaking as someone who uses this tensor notation quite a lot: putting multiple objects into the same diagram is what a tensor product is, and a great thing about the notation is that it reveals that a tensor product of two matrices is no
378.
by kmill 7y ago
Yeah, cross product is the determinant with "one strand bent back." If you take a 3-regular planar graph and put the determinant/Levi-Civita tensor on each vertex, you get plus-or-minus the number of edge-3-colorings of that
379.
by kmill 7y ago
Maybe you mean something like a simplicial complex? I don't understand how you can do very much with a single simplex (which is a generalization of a triangle and a tetrahedron in the language I'm used to).
380.
by kmill 8y ago
The lab apparatus they used to compare against the coffee maker might be a Soxhlet extractor.
381.
by kmill 8y ago
Yeah, it does not completely replace quasiquotation, but in my experience the main things quasiquotation solves are (1) not having to write quote marks in front of every symbol and (2) not having to append lists yourself. MDL handles the f
382.
by kmill 8y ago
Thanks! (And thanks for having those docs up, they have been useful to me the past couple days.) Another thing I couldn't find is exactly what a trailer with an empty OBLIST means. Does it use <ROOT>? It shows up in TELL for the
383.
by kmill 8y ago
I meant list literal in the Python-like sense, so apologies for the confusion there. In MDL, parens and angle brackets denote LISTs and FORMs, respectively. These are both objects with the same PRIMTYPE (a linked list) but are tagged differ
384.
by kmill 8y ago
In MDL, (1 <+ 2 3> 4) -> (1 5 4) '(1 <+ 2 3> 4) -> (1 <+ 2 3> 4) '<1 <+ 2 3> 4) -> <1 <+ 2 3> 4> <1 <+ 2 3> 4> -> an error (probably that 5
385.
by kmill 8y ago
Looking through a bunch of code in the archive, it was interesting to come across the macro for TELL, which is used everywhere in games as a sort of printf, and it has some special printf-like codes to print out names of objects and such.
386.
by kmill 8y ago
Angle brackets set out FORMs, parens set out LISTs. In English: FORMs are to function calls as LISTs are to list literals. A translation from MDL to Python would look like this: <a b c> -> a(b, c) (a b c) -> [a,
387.
by kmill 8y ago
The article claims so, though the generic usage must have died out long ago: > the company quickly became best known for its electronic switches, particularly its microswitches, which (despite not being first to market) became commonly k
388.
by kmill 8y ago
In particular, determinants are born from matrices. Sylvester used grids of numbers to organize the calculation of determinants, which were useful in solving systems of n equations with n unknowns. Matrix multiplication and addition, or e
389.
by kmill 8y ago
It's a Klein bottle as an abstract surface, where an abstract surface roughly speaking is anything that is locally 2D. In this case, it is a "flat" Klein bottle, due to the kinds of straight lines (geodesics) the surface has
390.
by kmill 9y ago
The way I've thought about this is that it's about whether an index is the name or the offset of an element of an array. Indices have a torsor-like structure, where you can subtract indices i and j to get an offset j-i from i

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