BILL: A computer program (or an AI or an ML or whatever) found a BETTER way to do matrix mult! Its in the same spirit as Strassen. I've always wondered if Strassen was practical since it is simple, and computers have come a long way since 1969, though I suspect not (I WAS WRONG ABOUT THAT). I'll blog about and ask if Strassen will ever be used/practical (I did that post here).

READERS: Uh, Bill, (1) Strassen IS used and practical and (2) the new algorithm only works in GF(2). (Lance did a post about the new algorithm where he makes this explicit here.) Some readers claimed it was GF(2^k) and some that it was fields if char 2. In any case NO it is not a general algorithm.

BILL: There is good news and what others might consider bad news but I do not.

GOOD NEWS: I learned that Strassen IS practical and used, which I did not know.

GOOD NEWS: I learned that I was WRONG about the new algorithm since I just assumed it worked in general, and updated the post so others would not be deceived.

BAD NEWS: Darling asked if I was embarrassed to be wrong. If I am embarrassed that easily I would have quit blogging in 2009.

DARLING: So Bill, how did you get it so wrong?

BILL: Well obviously my bad for not doing my due diligence. But that's not what's interesting. What's interesting is that if you read the articles about it for the popular press you would have NO IDEA that it only works for mod 2. Its like reading that quantum computing will solve world hunger.

DARLING: It won't?

BILL: No it won't.

DARLING: I was being sarcastic.

BILL: Anyway, the coverage pushed two points

a) IMPRESSIVE that a computer could FIND these things that humans could not. This is TRUE (gee, how do I know that? *The Gell-Mann Effec*t, is that people disgusted when they read a newspaper article on something they know about and find the mistakes later assume that the other articles are fine. SHOUT OUT to Jim Hefferon who telling me the name *Gell-Mann Effect* and left a comment with a pointer. The original version of this post had a BLANK there.)

b) The algorithm is practical! They did not quite say that but it was implied. And certainly there was NO mention of it only working in GF(2). And I was fooled into thinking that it might be competitive with Strassen.

READERS (of this blog entry, I predict) Uh, Bill, the popular press getting science news wrong and saying its more practical than it is probably predates the Bible. I can imagine the Cairo Times in 2000BC writing *`Scientists discover that in any right triangle with sides a,b,c a^2+b^2=c^2 and this will* *enable us to build food silos and cure Hunger*. In reality they knew that the 3,4,5 triangle was a right triangle, were no where near a proof of a general theorem, and I doubt it would have helped cure hunger.

BILL: This time the news was REALLY CLOSE to what I do (if R(5) is found by a computer and the media claims its practical I'll either have a very angry blog or repost my April Fools' day article on Ramsey Theory's application to History) AND I posted incorrectly about it. So, to quote many a bad movie

**THIS TIME ITS PERSONAL!**

FWIW A matrix multiplication algorithm over GF(2) can be turned into a matrix multiplication algorithm over GF(2^k): treat elements in GF(2^k) as polynomials over GF(2) and consider polynomials with matrix coefficients modulo the minimal polynomial. To multiply coefficients, you then use the GF(2) multiplier. See https://arxiv.org/pdf/0901.1413.pdf and https://dl.acm.org/doi/10.1145/2442829.2442838

ReplyDeleteThanks!

DeleteIn place of BLANK you mean Gall-Mann; see https://en.m.wikipedia.org/wiki/Michael_Crichton#GellMannAmnesiaEffect.

ReplyDeleteThanks!- YES I knew it had a name but I could not find it, so I put in the BLANK. I will edit the post now.

DeleteIt should be Gell-Mann, not Gall-Mann

ReplyDeleteNow you made me wonder about that...

ReplyDeletehttps://english.stackexchange.com/questions/289485/a-word-for-a-typographical-illusion-or-typo-blindness

Typoglycemia is certainly evocative.

Not exactly about typo-blindness, but vaguely related:

ReplyDeleteThere's also Muphry's Law: the more obnoxiously one complains about typos in someone else's writring, the more likely it is that there will by typos in that complaint itself.