The Mathematics of the 21st Century

 

Check out the video of my talk, the first in the Applied Category Theory Seminar here at U. C. Riverside. It was nicely edited by Paola Fernandez and uploaded by Joe Moeller.

Abstract. The global warming crisis is part of a bigger transformation in which humanity realizes that the Earth is a finite system and that our population, energy usage, and the like cannot continue to grow exponentially. If civilization survives this transformation, it will affect mathematics—and be affected by it—just as dramatically as the agricultural revolution or industrial revolution. We should get ready!

The slides are rather hard to see in the video, but you can read them here while you watch the talk. Click on links in green for more information!

12 Responses to The Mathematics of the 21st Century

  1. Stasheff, James says:

    The graphics are almost invisible. ☹
    Are they available on line elsewhere?
    Jim

  2. Ishi Crew says:

    Good lecture—half would be comprehensible to some people I know.

    H Odum’s diagram shows up—a local group i’m slightly involved with uses some of these qualtitative ‘complexity theory’ and ‘systems design thinking’ diagrams to try to deal with some very basic local issues (how to get mothers to get to a milk breastfeeding place, ‘rodent control’ —how to get people to put trash in a trash can and not throw it in the alley).

    The ‘social contagion network’ paper I view as midway in complexity between qualtitative reasoning and applied category theory. (I tried to take the online class, but only made it partway through—there is a steep learning curve for me.)

    Since my music event was canceled last nite, instead i made some money putting salt on the street—i can see that even so there is enough snow that all that ‘work’ was for naught—and i dont even like putting all that salt down (much less carrying it around—its pollution).

    I only have taken a plane once in last 10 years to visit a relative in Hawaii—i stayed 2 1/2 months. I wasnt going through all that hassle for a weekend. (When i came back i realized my apt had been burglarized like all the other ones in my building. I didnt lose anything since there is little to steal of value except this computer and a guitar.) A relative of mine recently graduated from undergrad at MIT and now has a job in UK at FB. I had an interesting visit there and got in a bit of trouble——i went wading or swimming in atlantic—and was thinking of swimming to UK—but people called the police who drove me back where was staying. My family did not appreciate that.

    ( Ishi is a nickname i use— see wikipedia )

    • John Baez says:

      Ishi wrote:

      H Odum’s diagram shows up—a local group i’m slightly involved with uses some of these qualtitative ‘complexity theory’ and ‘systems design thinking’ diagrams to try to deal with some very basic local issues (how to get mothers to get to a milk breastfeeding place, ‘rodent control’ —how to get people to put trash in a trash can and not throw it in the alley).

      How much do these diagrams help those people? And in what ways are they helpful? I’m always curious about such questions.

      • Ishi Crew says:

        I passed the link to your lecture above to the person leading the i group i’m in—-i don’t know if he’ll look at it, but perhaps.

        the link below is by a U Wash professor of engineering (seems to be pretty ‘hardcore’—mostly applied, but his Duke PhD was on chaos in Duffing’s equation. )

        He does this blog ‘on the side’—very nontechnical, but similar to the kinds of presentations i’ve seen in activist trainings and in community action trainings.

        https://empathy.guru/fundamental-set-of-knowledge-structures

        As you say out programmers, many can write a program in a day , and other people can make very complex diagrams also in a day , and some can actually translate those diagrams to calculate something (eg Feynman diagrams). Some of us are not good at much of anything.

        (Turned out we got from 9 to 12 inches of snow today. Nice, but not a good advertizement to act on AGW.

        Besides the 'green new deal', other peole are talking about  industrial agriculture and universal basic income---though many of the proposals for UBI---eg the one by Chris Hughes of Facebook or Van Parijis in Belgium---are poorly thought out--almost look like trojan horses.  The best 'basic income'  proposals seem to be  based on Thomas Paine and  Henry George style property/land/resource taxes, and a Negative income tax.   )
        
  3. Rif A. Saurous says:

    Non-mathematical question. You mention flying less as being a key thing folks can do. What’re your thoughts on carbon offsets vs. just not flying?

    • John Baez says:

      I’ve repeatedly tried to find out how well carbon offsets actually work: it’s hard. There are organizations devoted to this question, for example:

      American Carbon Registry

      You should only use carbon offsets that are accredited with some reputable organization of this sort. But even so, I’ve read stories about people planting lots of trees but then not taking care of them well enough: this sort of things needs constant monitoring. The great advantage of just not flying is that it’s so much simpler!

  4. mirskontsa says:

    Nice overview!

    My understanding is that you want to save the planet with you research, right? I can’t yet understand, how category theory can help here.

    or, asking differently,

    What is the grand idea or vision behind applied category theory (aka, what’s the point)?
    Is there any goal that you want to achieve in the end?
    Do you want to find/construct a unified language for all the diverse topics you discuss on the slides and on the seminar?
    Do you want to introduce concepts from category theory into these topics?

    • John Baez says:

      The grand vision is to develop a language for science which is suitable for understanding and designing open systems and networks of all kinds. This is a step towards ‘ecotechnology’: technology that works like nature and works with nature instead of gobbling up resources and spewing out waste.

      Concepts from category theory already play a role in most of the topics being discussed in the seminar. The one place where it’s not completely apparent is “social contagion on networks”, but that’s just because the people working on that probably don’t realize how natural it is to study contagion processes on open networks using category theory: this is the sort of thing my students and I could easily do.

      For just a tiny bit more information, try my manifesto from 2011. This is the first of a long series of articles, but we’ve done a lot more by now so scanning our papers might be a next step.

    • Todd Trimble says:

      The phrase “applied category theory” is ambiguous. There are a lot of things that could be called “applied category theory”, and taking those into account, it wouldn’t be right to say “the grand vision of [applied category theory] is to develop a language for science which is suitable for understanding and designing open systems and networks of all kinds”. There are huge swaths of interface between category theory and computer science which deserve to be considered applied category theory, for example.

      Words matter, and I really wish people would make an effort to find a less ambiguous term for this burgeoning area. A number of people have urged this, but maybe it’s already too late?

      • John Baez says:

        Applied category theory is very general, so it’s hard to fully capture it without writing something extremely long. But my students and I have specific reasons for working on it. That’s what this seminar is about. That’s what my talk was about. And that’s what I thought the question was about: not generalities, but what we’re actually doing here.

        The questioner did, after all, also ask:

        Is there any goal that you want to achieve in the end? Do you want to find/construct a unified language for all the diverse topics you discuss on the slides and on the seminar?

        The short answers are “yes: saving the planet” and “yes: and indeed we’ve partially done this and want to continue”. I wanted to give a slightly longer answer, with links to even longer ones.

  5. Scott Hotton says:

    That is a great overview of the global warming
    crisis. Full of facts to put the issue in context.

    A study came out in the PNAS last year
    entitled “The biomass distribution on Earth”.
    I found some of its results surprising. For
    the last 20 years i thought subterranean
    prokaryotes constituted the bulk of the
    Earth’s biomass. Before that i thought it
    was plankton. According to this study plants
    make up over 80% of the Earth’s biomass.

    If true it would put a different perspective
    on all sorts of human-plant interactions.

    https://www.pnas.org/content/115/25/6506.short

    I hesitate to add that it seems that plants
    make up the bulk of the biomass on the Moon
    today.

    https://www.forbes.com/sites/jonathanocallaghan/2019/01/15/china-is-growing-life-on-the-moon-for-the-first-time-in-history/#510642b62a2b

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