I just finished reading lots of Stephen Witt quotes on goodreads. He comes across as a white Malcolm Gladwell, except that he actually does know what "Igon values" are so I don't know what his excuse is.
Is Matrix Multiplication Ugly?
61–70 of 113 posts
Re: Is Matrix Multiplication Ugly?
#62Earlier quoted context omitted.
The first two results from Google with "Voronoi astro" gave two different uses than the one I knew about (sampling fibre bundles): https://galaxyproject.org/news/2025-06-11-voronoi-astronomy/ https://arxiv.org/abs/2511.14697
Astronomy is pure research and is performed almost exclusively by academics. I’m not saying these things have zero utility, it’s just that they’re used far less frequently in industry than academics imagine.
And astronomy tends to throw up technology that becomes widely used (WiFi being the obvious example) or becomes of "interest" to governments. I expect that AMR code will be used/ported to nuclear simulations if it proves to be useful. Do I expect it to be used in a CRUD app? Obviously not, but use by most software shops isn't a measure of importance.
Re: Is Matrix Multiplication Ugly?
#63> But matrix multiplication, to which our civilization is now devoting so many of its marginal resources, has all the elegance of a man hammering a nail into a board. Elegance is a silly critique. Imagine instead we were spending trillions on floral bouquets, calligraphy, and porcelain tea sets. I would argue that would be a bad allocation of resources. What matters to me is whether it solves the problems we have. No…
You're right. It's all about solving problems.
Maybe we need a word that, when applied to mathematical concepts, describes how simple, easy to understand and generally useful a solution or idea is.
I wonder what that word could be.
Re: Is Matrix Multiplication Ugly?
#64maybe the issue boils down to overloading the term "multiplication". If mathematicians instead invented a new word here, people would get tripped up less (similarly for 'dot' and 'cross' "products")
i think a lot of issues arise from using analogies. Another one us complex numbers as 2D vectors. Its an ok analogy.. Except complex numbers can be multiplied where are 2D coordinates can not. Your weird new nonvectors are now spinning and people are left confused
Re: Is Matrix Multiplication Ugly?
#65IIRC, working with matrices was much easier using FORTAN, I would expect modern fortran kept that 'easiness'.
Re: Is Matrix Multiplication Ugly?
#66I think this sentence: > But matrix multiplication, to which our civilization is now devoting so many of its marginal resources, has all the elegance of a man hammering a nail into a board. is the most interesting one. A man hammering a nail into a board can be both beautiful and elegant! If you've ever seen someone effortlessly hammer nail after nail into wood without having to think hardly at all about what they're…
A somewhat more beautiful matmul for neural networks is given by the Monarch paper: https://arxiv.org/abs/2204.00595 Generally, low-rank and block-diagonal matrices are both great strategies for producing expressive matmuls with fewer parameters. We can view the FFT as a particularly deft example of factorizing one big matmul into a number of block-diagonal matmuls, greatly reducing the overall number of multiplicati…
Do low rank/block diagonal matrices come up in LLMs often? What about banded or block tridiagonal? Intuitively banded matrices seem like they ought to be good at encoding things about the world… everything is connected but not randomly so.
Re: Is Matrix Multiplication Ugly?
#67Earlier quoted context omitted.
the aesthetics of math and physics is by far the most boring discussion that can be had. i used to be utterly repulsed by such talk in undergrad - beauty this and that. it absolutely always felt affected and put on - as if you talk about it enough, you'll actually convince people outside of the major to give you the same plaudits as real artists.... yea right lol.
That’s the opinion of one person. There are many mathematicians who find beauty in the maths they are studying.
I will emphasize your point more forcefully. All mathematicians I know work on what they work because of the beauty and aesthetics in their field.
Much like sex. Sex has reproductive utility but that's not why most people engage in it. Those who do are are missing much.
Notion of beauty for a mathematician is quite specialized. It's the difference between spaghetti code that works and an elegant and efficient code that is correct. They are easy to build upon efficiently.
Re: Is Matrix Multiplication Ugly?
#68Earlier quoted context omitted.
I think you're right that the inelegant part is how AI seems to just consist of endless loops of multiplication. I say this as a graphics programmer who realized years ago that all those beautiful images were just lots of MxNs, and AI takes this to a whole new level. When I was in college they told us most of computing resources were used doing Linear Programming. I wonder when that crossed over to graphics or AI (or…
> When I was in college they told us most of computing resources were used doing Linear Programming. I seriously doubt that was ever true, except perhaps for a very brief time in the 1950s or 60s. Linear programming is an incredibly niche application of computing used so infrequently that I've never seen it utilised anywhere despite being a consultant that has visited hundreds of varied customers including big busine…
3d modelers would like to have a word with you.
Part of the reason why linear programming does need t get used as often is that there are no industry standard software implementation that is not atrociously priced. Same deal with Mathematica.
Re: Is Matrix Multiplication Ugly?
#69I doubt anyone of the past or present could fully describe what a matrix is, and what its multiplication is. There are many ways people looked at it so far - as a spatial transformation, dot products and so on. I don't think the description is complete in any significant way. That's because we don't fully understand what a number is and what a multiplication is. We defined -x and 1/x as inverses (additive and multipl…
This is just low brow philosophical sounding rubbish of the same variety as "what is 'is'" nobody knows. Sounds profound though.
Matrix is just one way to organize data. When linear operators are organized this way composition of linear operators map to matrix multiplication.
But that is just one of the ways that multiplication may be defined on matrices, Hadamard products, Tensor product, Khatri-Rao product are some of the other examples. They all correspond to different mathematical structures one wants to explore or use. If linear algebraic structures is what ones to explore or use then one gets matrix multiplication.
Re: Is Matrix Multiplication Ugly?
#70Maybe I'm just being ai-phobic or whatever but I strongly suspect the original article is written by grok based on how it goes off on bizarre tangents describing extremely complicated metaphors that are not only inaccurate but also wouldn't in any way be insightful even if they were accurate.