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Is Matrix Multiplication Ugly?

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Re: Is Matrix Multiplication Ugly?

#31

Post by tiagod »

Honestly, in a purely technical sense, I do find it beautiful how you can take matrix multiplication and a shit-ton of data, and get a program that can talk to you, solve problems, and generate believable speech and imagery.

There are many complications arising from such a thing existing, and from what was needed to bring it into existence (and at the cost of whom), I'll never deny that. I just can't comprehend how someone can find the technical aspects repulsive in isolation.

It feels a lot like trying to convince someone that nuclear weapons are bad by defending that splitting an atom is akin to banging a rock against a coconut to split it in two.

Re: Is Matrix Multiplication Ugly?

#33

Post by JanNash »

hobs wrote: post #17
sfpotter wrote: post #4

I 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…

https://www.youtube.com/watch?v=Ruf-cLr2PZ8 I always think of this when thinking about the gracefulness of a hammer.

Wow, thank you for this gem!!!

Re: Is Matrix Multiplication Ugly?

#34

Post by Filligree »

o11c wrote: post #21

Matrix multiplication libraries are ugly. They either give up on performance or have atrocious interfaces ... sometimes both. Using matrix multiplication is also ugly when it's literally millions of times less efficient then a proper solution.

What’s the proper solution for computing the voltage and current flows in a component network, order than modified nodal analysis?

Re: Is Matrix Multiplication Ugly?

#35

Post by almostgotcaught »

janalsncm wrote: post #18

> 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…

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.

Re: Is Matrix Multiplication Ugly?

#36

Post by stackghost »

>Matrix algebra is the language of symmetry and transformation, and the fact that a followed by b differs from b followed by a is no surprise; to expect the two transformations to coincide is to seek symmetry in the wrong place — like judging a dog’s beauty by whether its tail resembles its head.

The way I've always explained this to non-algebra people is to imagine driving in a city downtown. If you're at an intersection and you turn right, then left at the next intersection, you'll end up at a completely different spot than if you were to instead turn left and then right.

Re: Is Matrix Multiplication Ugly?

#37

Post by o11c »

Filligree wrote: post #34
o11c wrote: post #21

Matrix multiplication libraries are ugly. They either give up on performance or have atrocious interfaces ... sometimes both. Using matrix multiplication is also ugly when it's literally millions of times less efficient then a proper solution.

What’s the proper solution for computing the voltage and current flows in a component network, order than modified nodal analysis?

I'm not familiar with that particular problem, but I did use a load-bearing "when".

Re: Is Matrix Multiplication Ugly?

#38

Post by chris_wot »

almostgotcaught wrote: post #35
janalsncm wrote: post #18

> 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…

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.

Re: Is Matrix Multiplication Ugly?

#39

Post by chris_wot »

o11c wrote: post #37
Filligree wrote: post #34

Earlier quoted context omitted.

What’s the proper solution for computing the voltage and current flows in a component network, order than modified nodal analysis?

I'm not familiar with that particular problem, but I did use a load-bearing "when".

Can you give an example of when it is not appropriate?

Re: Is Matrix Multiplication Ugly?

#40

Post by card_zero »

So, Hardy focused on good explanations, and that was what he meant by beauty. Fair enough. The best objective definition of beauty I know of is "communication across a gap". This covers flowers, mathematics, and all kinds of art, including art I think is ugly such as Lucian Freud and Hans Giger I guess. So now I'm describing some things as beautiful and ugly at the same time, which betrays that there's a relative component to it (relative, objectively). That means I wish some things - including mathematics, which is usually tedious - communicated better, or explained things that seem to me to matter more: I feel in my gut that there's potential for this. So I don't rate mathematics as beautiful, any of it, personally.

But I'll admit its barely beautiful. Within which context, I guess the article's lawyering for the relative beauty of a matrix was a success, but I always liked them better than calculus or group theory anyway.

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