# Abstraction, Beauty, Math and Applied Category Theory

January 1, 2019 2:34 AM Subscribe

A quest for beauty and clear thinking. Interviewing John Baez - "John Baez is an American mathematical physicist, and a professor of mathematics at the University of California Riverside, and an activist for the environment. I have been in touch with him via email and through his online course on category theory. Recently, I had the pleasure to met him in person in London, during a conference about Physics and Philosophy dedicated to Emmy Noether."[1,2,3]

Chaos Makes the Multiverse Unnecessary - "Rather than looking at the real numbers as central and the octonions as strange larger number systems, think of the octonions as fundamental and all the other number systems as just special subsets of octonions."[7,8]

The Friendship That Made Google Huge - "Jeff and Sanjay gave Google what was arguably its biggest single upgrade in the course of four months in 2003. They did it with a piece of software called MapReduce. The idea came to them the third time they rewrote Google's crawler and indexer. It occurred to them that, each time, they had solved an important problem: coördinating work in a vast number of geographically distributed, individually unreliable computers. Generalizing their solution would mean that they could avoid revisiting the problem again and again."

Evolutionary algorithm outperforms deep-learning machines at video games - "It starts with code generated entirely at random. And not just one version of it, but lots of versions, sometimes hundreds of thousands of randomly assembled pieces of code... The evolved code has another advantage. Because it is small, it is easy to see how it works. By contrast, a well-known problem with deep-learning techniques is that it is sometimes impossible to know why they have made particular decisions, and this can have practical and legal ramifications."

Mathematics seems to attract people who enjoy patterns, who enjoy precision, and who don't want to remember lists of arbitrary facts, like the names of all 206 bones in the human body. In math everything has a reason and you can understand it, so you don't really need to remember much. At first it may seem like there's a lot to remember - for examples, lists of trig identities. But as you go deeper into math, and understand more, everything becomes simpler...Mathematics in the 21st century - "I'll give an updated synthesized version of these earlier talks of mine, so check out these slides and the links." also btw, brute force, logic and evolution...

[M]athematicians, like everyone else, need to think about global warming and what we can do about it: it's the crisis of our time. I spent some time learning the basics of climate science and working on some projects connected to that. It became clear that to do anything about global warming we need new ideas in politics[4] and economics.[5,6] Unfortunately, I'm not especially good at those things. So I decided to do something I can actually do, namely to get mathematicians to turn their attention from math inspired by the physics of the microworld - for example string theory - toward math inspired by the visible world around us: biology, ecology, engineering, economics and the like. I'm hoping that mathematicians can solve some problems by thinking more abstractly than anyone else can...

If this were a war, and these were humans dying, this would be the worst war the world has ever seen! But these changes will not merely affect other species; they are starting to hit us too. We need to wake up. We will either deliberately change our civilization, quite quickly, or we will watch as our cities burn and drown. Isn't it better to use that intelligence we humans love to boast about, and take action?

Chaos Makes the Multiverse Unnecessary - "Rather than looking at the real numbers as central and the octonions as strange larger number systems, think of the octonions as fundamental and all the other number systems as just special subsets of octonions."[7,8]

The Friendship That Made Google Huge - "Jeff and Sanjay gave Google what was arguably its biggest single upgrade in the course of four months in 2003. They did it with a piece of software called MapReduce. The idea came to them the third time they rewrote Google's crawler and indexer. It occurred to them that, each time, they had solved an important problem: coördinating work in a vast number of geographically distributed, individually unreliable computers. Generalizing their solution would mean that they could avoid revisiting the problem again and again."

Evolutionary algorithm outperforms deep-learning machines at video games - "It starts with code generated entirely at random. And not just one version of it, but lots of versions, sometimes hundreds of thousands of randomly assembled pieces of code... The evolved code has another advantage. Because it is small, it is easy to see how it works. By contrast, a well-known problem with deep-learning techniques is that it is sometimes impossible to know why they have made particular decisions, and this can have practical and legal ramifications."

Cool. I knew John Baez first as the author of the Crackpot Index which is one of those niche things that really rings true if you've spent any time as a professional scientist (particularly in physics or astronomy). He also has written some excellent descriptions of complex physics topics.

posted by Betelgeuse at 7:30 AM on January 1, 2019 [1 favorite]

posted by Betelgeuse at 7:30 AM on January 1, 2019 [1 favorite]

I'm committing in 2019 to learn category theory as a stepping stone to being versed in formal verification tools and thus stay relevant and employabvle as a QA-oriented programmer.

So these links are relevant to my interests and I would like to subscribe to your newsletter.

posted by ocschwar at 5:25 PM on January 1, 2019 [3 favorites]

So these links are relevant to my interests and I would like to subscribe to your newsletter.

posted by ocschwar at 5:25 PM on January 1, 2019 [3 favorites]

I'm just here to confirm that John Baez

posted by atoxyl at 8:48 PM on January 1, 2019 [1 favorite]

*is*related to Joan Baez, via Albert Baez. Maybe everybody else already knew that.posted by atoxyl at 8:48 PM on January 1, 2019 [1 favorite]

I've found John Baez to be one of the most approachable mathematicians to read, perhaps because like he mentions, he tries to make his efforts directly and immediately relevant to pressing social / environmental / engineering problems. Not only is his writing enjoyable, his approach to math in society is arguably seen much too infrequently.

And the crackpot index is desperately funny. (It reminds me of a similar "index" floating around maybe the sci.crypt newsgroup a long time ago, where points were awarded for claiming an unbreakable encryption method that wasn't a one-time pad, points were awarded for claiming an unbreakable encryption method but refusing to provide algorithms or source code, and so on.)

posted by iffthen at 3:17 AM on January 2, 2019

And the crackpot index is desperately funny. (It reminds me of a similar "index" floating around maybe the sci.crypt newsgroup a long time ago, where points were awarded for claiming an unbreakable encryption method that wasn't a one-time pad, points were awarded for claiming an unbreakable encryption method but refusing to provide algorithms or source code, and so on.)

posted by iffthen at 3:17 AM on January 2, 2019

Don't miss John Baez's homepage... there is surely something there for everyone to get lost in all day.

I remember Baez from sci.math and sci.physics back in the '90s— always very smart and understandable.

posted by zompist at 3:56 PM on January 2, 2019

I remember Baez from sci.math and sci.physics back in the '90s— always very smart and understandable.

posted by zompist at 3:56 PM on January 2, 2019

Applied Category Theory 2019 School :P

"If you attend the Applied Category Theory 2019 school you'll have a chance to work with the one and only BARTOWSZ MILEWSKI, author of Category Theory for Programmers!"

posted by kliuless at 7:03 PM on January 24, 2019

"If you attend the Applied Category Theory 2019 school you'll have a chance to work with the one and only BARTOWSZ MILEWSKI, author of Category Theory for Programmers!"

posted by kliuless at 7:03 PM on January 24, 2019

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