Azimuth News (Part 4)


Happy New Year!

I’ve been rethinking my approach to life. Nothing major, just some small course corrections.


First, I’ve decided to stop posting so much on Google+, and post more here on Azimuth. I explain why here:

New Year’s Resolution.

I want a vibrant, lively online environment where people talk about things in serious, almost obsessive ways. At times this blog has been like that. So was the n-Category Café, back when a core group of people were all focused on roughly the same thing.

Lately I’ve been posting very little here on Azimuth. Instead, I’ve been working hard with a team of grad students to figure out how network theory can organize our understanding of circuits, control theory and nonequilibrium thermodynamics. My more general posts on ecological issues and science in general have been going to Google+. I now suspect it’s bad to split up my blogging that way. If I write more stuff in the same place, I hope more people will come here to talk.


Second, I have slowly come to realize that my talents lie in highly theoretical work—for example, network theory—rather than data-driven work like climate science, or the practical task of figuring out what to do about global warming. I still think that adapting to the Anthropocene and developing an ‘ecotechnic civilization’ is the challenge of the century for
civilization as a whole and scientists in particular. But I think the more urgent aspects of this—the ones that need to be done really soon—are not the ones I’m good at. The stuff I’m good at will help later, if at all. And yet, it doesn’t pay for me to do things that other people are already doing better.

There’s been a big change since I started this blog in 2010! Back then, it seemed only a few people knew quite how serious global warming would be, so I felt the need to shout an alarm. This December, thousands of politicians from around the world met in Paris to do something about it—and while they haven’t done enough yet, they all know the basic facts that had me so worried: for example, that we need to leave most of the world’s fossil fuels unburnt in the ground, in part because if we don’t, the effects will last for thousands of years:

More generally, there’s been a huge shift towards recognizing that we have to change our habits, quickly. In 2013, Copenhagen announced it will try to go carbon-neutral by 2025. In October of this year, California passed a law requiring the state to obtain 50% of its electricity from renewables by 2035. In December, San Diego became the largest city in the USA to require that all of the city’s power to come from renewables—again, by 2035.

And so on. The battle has not been won, but it has been joined. Countries, localities, cities and individuals around the world are volunteering to tackle this problem.

I can serve as a cheerleader for this trend, but I’m not really a politician, an engineer or even an experimentalist. Mathematicians, too, have their part to play. So, this year I’ll keep talking about network theory, and push it toward the ‘green mathematics’ I’ve been dreaming about, by getting serious about its applications to biology and ecology.

More on that soon!

27 Responses to Azimuth News (Part 4)

  1. Jon Awbrey says:

    Happy Vita Nova❢ You may wish eventually to look into the way that networks, or graphs, can be used to do logic. Doing that requires getting beneath purely positive connections to the varieties of negation that can be used to generate all the rest. Peirce was a pioneer in this pursuit, as evidenced by his logical graphs.



  2. cclingen says:

    Happy New Year to you too! May your new focus bring you much progress and success in the coming year. One other thing that you excel at — teaching and explaining difficult concepts to non-experts. Sometimes it seems that clearly explaining and communicating a complex abstraction is more difficult than discovering/creating it in the first place. But there’s no doubt that you will continue to do so — it’s in your blood! I hope to enjoy this new venture as much as you will!

    • Bruce Smith says:

      I second that! You (John) are great at teaching and explaining not only technical concepts, but more or less any story that you understand and that excites you. A lot of your “generalist” readers (and me too) probably skim most of the technical stuff in order to get to the great stories and explanations! So even if you sometimes feel like “just a single neuron in the global brain”, you are an important, unique, and appreciated one!

  3. Happy New Year to you!

    RE: Your blog vs. G+, what if I told you that you might have your cake and eat it too? I too have a WordPress blog, but I’ve tacked a few bits on to the back end and this allows me to use my blog as the primary hub for my work as you’re suggesting you plan on doing. I then use platforms (walled silos) like Google+, Twitter, and Facebook to syndicate my material out to allow for a broader reach by leveraging social networks effects to my benefit. Even better, I’ve got things set up so that comments on platforms like Google+ feed back to my blog, which allows me to not only live on my own site, but it also allows me to “own” all of the content and commentary that’s generated from it. (This way if Google+ is shut down next month, I’d still have all of the generated commentary, which could live indefinitely on my own site.) Thus your followers who prefer to read your material on other platforms (G+, in your case) aren’t left without the content you’re generating, but their commentary also appears back on the blog to add to the larger conversation.

    First, consider using the “Jetpack” module (free software built by the same company that makes WordPress) and its publicize functionality to connect your G+ account and auto-post (syndicate) your Azimuth content automatically to G+. (This also frees up a good bit of time to not have to do it manually.) If nothing else, this will help to keep some of your audience engaged.

    Second, to port the comments from the syndicated G+ post back to your original post on Azimuth (comments from G+ will show up as comments in WordPress that you can approve/delete just like other WP comments; this also prevents you from spending so much time in G+ after you turn off comment notifications) you can follow the details at the IndieWebCamp site ( to add/configure a few simple plugins as well as to connect to allow social networks to communicate with your blog.

    If you need help/assistance to make the technical hurdles a bit lower, I’m happy to help walk you through the details or even do it for you (gratis) if you’d like. All of the modules I’ve mentioned are free and open source and under very active development.

    For a simple example see the comments on this post which originated from G+

    For a brief overview, you might appreciate the opening few paragraphs of

    • John Baez says:


      In preparation for a terrorist attack on the Google servers—or just because I want control over my own writings—I’ve already transferred most of my G+ posts to my online diary. So I seem to share your philosophy, just not your know-how.

      In fact, I’m such a Luddite that when I saw something about that ‘Jetpack’ module, I completely ignored it. Now I don’t see it on my blog. When I go to their website and type in my URL, I get:

      Your site is safely hosted at which means you already have most of the Jetpack goodness right out of the box. Have you considered upgrading your Plan?

      That’s a bit ambiguous. What kind of WordPress account do I need to get Jetpack to work?

      Similarly, what sort of WordPress account do I need to “port the comments from the syndicated G+ post back to your original post on Azimuth”? That sounds really neat.

      Right now I have a free plan.

      I really appreciate your offer of help.

      • I always forget that Jetpack is essentially built-in for hosted sites. You can find the settings in your control panel under “settings” and then under “sharing” (alternately try going directly to while you’re signed in) then click on “Publicize settings” at the top which will take you to a page to configure your Facebook, Twitter, G+ and a few other social network settings.

        After this, in the admin interface ( while writing a post, you should have a new line with the “Publish” block (typically on the top right where you hit the “publish” button) that says “Publicize” next to which is an “edit” link that will allow you to individually toggle one or more of the networks you’ve set up so that you can choose to cross-post or not on each and every post you make, though most often you’ll probably just use the default setting, which is to cross-post to all the platforms that are set up.

        When it comes to WordPress there are two flavors: the WordPress hosted version (free with various paid upgrades) with or a self-hosted version via which requires that you have your own domain name and hosting service and do the upgrades yourself. To my knowledge you should be able to do the second portion under either model, though I’ve only ever done it via the self-hosted version. Your free hosted version won’t allow you as much flexibility as the self-hosted route, but by going to you should be able to click on the button and follow the set up to add the webmentions part to Azimuth. The site has some reasonable help and discussion.

        If you want the extra flexibility of a self-hosted version it’s typically $10 a year to register a domain and usually between $5-15 a month for hosting depending on who your host is.

      • John Baez says:

        Thanks! I think I’ve managed to enable Jetpack both here and on my blog Visual Insight, which is about pretty pictures of pure math. I won’t know until another article comes out.

        I’ll see what I can do with a free WordPress-hosted blog over at

  4. gowers says:

    I don’t know whether your decision is right or wrong, but I will say that you’ve had a big influence on me: as a result of your posts over the last few years I have taken climate change much more seriously than I probably would have otherwise. My guess is that many others could say the same. So thank you for doing it — I think part of the reason that the politicians are now beginning to get their act together is that thanks to people like you they know that voters care more about these issues.

    • John Baez says:

      Thanks—that means a lot to me. It’s great to hear this compliment from you, but it’s also just great getting any feedback at all. One difficulty in making decisions is that it can be hard to tell whether what you’ve been doing has been working, especially if you’re trying to shift people’s attitudes.

      I won’t stop writing about climate change. My attitude used to be that we were driving a car off a cliff without even noticing. I think now we’ve entered a more subtle phase where lots of people are trying to take significant action, yet things will continue to worsen, and we’ll be wondering if the actions being taken will be big enough, soon enough, to do much good. I.e., now we’re starting to slam on the breaks.

      There’s still no shortage of scare stories:

      • Andre Mitchell, ‘Absolutely terrifying’: Temperature climbs to 33 degrees Fahrenheit in North Pole, Life, 2 January 2016.

      • Jenny Meyer says:

        For what it’s worth, I didn’t need to be persuaded that climate change is a problem, but I’ve felt more optimistic about the ability of humans to actually respond in a sensible way after reading your posts. I know a lot of people who are vaguely concerned, but not many are thinking long and hard about the best actions to take (beyond dressing up in polar bear suits and picketing politicians, or buying a Chevy Volt).

        So I’m glad you’re going to stay with it, especially now that the post-Paris euphoria is over and we get to think about how to achieve those goals even as the North Pole is turning to slush.

        • John Baez says:

          Hi, Jenny. I’m very glad my posts made you feel more optimistic. For the first few years of Azimuth they often made me feel less optimistic! A careful analysis of a problem, with lots of helpful comments from people clarifying different issues, would give me the sense that humanity was not responding with anything remotely like the required actions. We were replacing lightbulbs when we should be shutting down coal-fired power plants.

          I always felt we could solve the problem… but only if everyone in the world had a personality transplant, including me.

          But now I’m starting to see people line up, promising to do dramatic things. A worldwide change of heart seems to be underway.

          Is it for real? Will it happen fast enough? We’ll see. This is going to be interesting.

  5. Patrice Ayme says:

    Happy New Year! How to predict and respond to the GreenHouse Gas (GHC) crisis goes well beyond “data driven”. It implies also high level theoretical work, in politics, mass psychology, individual psychology, the theory of mind, ethics, philosophy, economics, and even mathematics and physics (such as a generalization of the equipartition of energy theorem, which I have proposed).

    Be it in math, or physics, or even biology, research develop where (chosen) axioms and (established) institutions lead. For example, the FDA refused to allow, until 2016, trials (thus development) of anti-aging drugs on philosophical grounds. The science of tipping points or change of dynamical regime, related to morphogenesis (R. Thom) has not been developed enough, yet, for the GHC crisis.

    However the present crisis threatens civilization itself, thus intellectuals would be wise to consider it well beyond what data drives to.

  6. David Keirsey says:

    Finally into non-equilibrium thermodynamics! (from neutrinos, to Internet dynamics)

    I doubt that you will take my recommendations re: biology, but here it goes. It is important to get an wholistic overview that is science and information based. 1) Robert Rosen: Life Itself [the math for you is simplistic, but the attached semantics (the meaning) is profound], 2) Lynn Margulis: Symbiotic Planet [her last “technical” attempt, Microcosmos is the most popular], 3) Nick Lane: The Vital Question.

    • John Baez says:

      I have Robert Rosen’s Life Itself by my bed — it was given to me by a blog-reader, Tom Holroyd, when I started talking about biology. It has a nice explanation of the ideas behind physics and why they aren’t enough to handle biology, and a nice introduction to the basic idea of category theory. It has some insights into living systems… but as you say, the math here is simplistic, not enough to really be ‘the language of life’. I’ll reread it.

      I don’t know Nick Lane.

      I’m a huge fan of Lynn Margulis and her work. I blogged about her here:

      Lynn Margulis, 1938–2011, Azimuth, 24 November 2011.

      She was, however, very tough on people who tried to apply math and physics ideas to biology. Her remarks here are a warning to me:

      I work in evolutionary biology, but with cells and microorganisms. Richard Dawkins, John Maynard Smith, George Williams, Richard Lewontin, Niles Eldredge, and Stephen Jay Gould all come out of the zoological tradition, which suggests to me that, in the words of our colleague Simon Robson, they deal with a data set some three billion years out of date. Eldredge and Gould and their many colleagues tend to codify an incredible ignorance of where the real action is in evolution, as they limit the domain of interest to animals—including, of course, people. All very interesting, but animals are very tardy on the evolutionary scene, and they give us little real insight into the major sources of evolution’s creativity. It’s as if you wrote a four-volume tome supposedly on world history but beginning in the year 1800 at Fort Dearborn and the founding of Chicago. You might be entirely correct about the nineteenth-century transformation of Fort Dearborn into a thriving lakeside metropolis, but it would hardly be world history.

      By “codifying ignorance” I refer in part to the fact that they miss four out of the five kingdoms of life. Animals are only one of these kingdoms. They miss bacteria, protoctista, fungi, and plants. They take a small and interesting chapter in the book of evolution and extrapolate it into the entire encyclopedia of life. Skewed and limited in their perspective, they are not wrong so much as grossly uninformed.

      Of what are they ignorant? Chemistry, primarily, because the language of evolutionary biology is the language of chemistry, and most of them ignore chemistry. I don’t want to lump them all together, because, first of all, Gould and Eldredge have found out very clearly that gradual evolutionary changes through time, expected by Darwin to be documented in the fossil record, are not the way it happened. Fossil morphologies persist for long periods of time, and after stasis, discontinuities are observed. I don’t think these observations are even debatable. John Maynard Smith, an engineer by training, knows much of his biology secondhand. He seldom deals with live organisms. He computes and he reads. I suspect that it’s very hard for him to have insight into any group of organisms when he does not deal with them directly. Biologists, especially, need direct sensory communication with the live beings they study and about which they write.

      Reconstructing evolutionary history through fossils—paleontology—is a valid approach, in my opinion, but paleontologists must work simultaneously with modern-counterpart organisms and with “neontologists”—that is, biologists. Gould, Eldredge, and Lewontin have made very valuable contributions. But the Dawkins–Williams–Maynard Smith tradition emerges from a history that I doubt they see in its Anglophone social context. Darwin claimed that populations of organisms change gradually through time as their members are weeded out, which is his basic idea of evolution through natural selection. Mendel, who developed the rules for genetic traits passing from one generation to another, made it very clear that while those traits reassort, they don’t change over time. A white flower mated to a red flower has pink offspring, and if that pink flower is crossed with another pink flower the offspring that result are just as red or just as white or just as pink as the original parent or grandparent. Species of organisms, Mendel insisted, don’t change through time. The mixture or blending that produced the pink is superficial. The genes are simply shuffled around to come out in different combinations, but those same combinations generate exactly the same types. Mendel’s observations are incontrovertible.

      So J. B. S. Haldane, without a doubt a brilliant person, and R. A. Fisher, a mathematician, generated an entire school of English-speaking evolutionists, as they developed the neo-Darwinist population-genetic analysis to reconcile two unreconcilable views: Darwin’s evolutionary view with Mendel’s pragmatic, anti-evolutionary concept. They invented a language of population genetics in the 1920s to 1950s called neo-Darwinism, to rationalize these two fields. They mathematized their work and began to believe in it, spreading the word widely in Great Britain, the United States, and beyond. France and other countries resisted neo-Darwinism, but some Japanese and other investigators joined in the “explanation” activity.

      Both Dawkins and Lewontin, who consider themselves far apart from each other in many respects, belong to this tradition. Lewontin visited an economics class at the University of Massachusetts a few years ago to talk to the students. In a kind of neo-Darwinian jockeying, he said that evolutionary changes are due to the Fisher–Haldane mechanisms: mutation, emigration, immigration, and the like. At the end of the hour, he said that none of the consequences of the details of his analysis had been shown empirically. His elaborate cost-benefit mathematical treatment was devoid of chemistry and biology. I asked him why, if none of it could be shown experimentally or in the field, he was so wedded to presenting a cost-benefit explanation derived from phony human social-economic “theory.” Why, when he himself was pointing to serious flaws related to the fundamental assumptions, did he want to teach this nonsense? His response was that there were two reasons: the first was “P.E.” “P.E.?,” I asked. “What is P.E.? Population explosion? Punctuated equilibrium? Physical education?” “No,” he replied, “P.E. is `physics envy,'” which is a syndrome in which scientists in other disciplines yearn for the mathematically explicit models of physics. His second reason was even more insidious: if he didn’t couch his studies in the neo-Darwinist thought style (archaic and totally inappropriate language, in my opinion), he wouldn’t be able to obtain grant money that was set up to support this kind of work.

      The neo-Darwinist population-genetics tradition is reminiscent of phrenology, I think, and is a kind of science that can expect exactly the same fate. It will look ridiculous in retrospect, because it is ridiculous. I’ve always felt that way, even as a more-than-adequate student of population genetics with a superb teacher—James F. Crow, at the University of Wisconsin, Madison. At the very end of the semester, the last week was spent on discussing the actual observational and experimental studies related to the models, but none of the outcomes of the experiments matched the theory.

      • Eugene says:

        Hi John,

        It’s an interesting quote. Where is it from?

      • David Keirsey says:


        Re: Rosen. — Actually the book Life Itself is the introductory book I try to get my “scientist” friends to read, HOPING, that they will look further into his other books and articles. His previous books Anticipatory Systems, Dynamical Systems Theory in Biology, Fundamentals of Measurement have more mind numbing (but very important insights) into the advantages [but more importantly the disadvantages] of modeling natural processes (including physics) via conventional mathematics (calculus and probability).

        Re: Margulis. — along with Rosen she points out [concretely in biology] for the need to look at systems AND their surrounding contexts (Formal [formal cause], ConFormal [efficient cause], and SubFormal [material cause]) The point being if you don’t know what the semantics (the “meanings” of the “ding auch sich”) you are just mimicking the “thing” on the thin surface features [like Topologists ;-) ]

        Re: Lane — His latest book The Vital Question, which delves into the origins of life [from partly a non-linear “thermodynamic” perspective]. You might need to learn some more chemistry [or learn it on the fly] to get something out of it. I use my insights that I learned from the origins of life to guide me in better understanding of General Relativity and four gauge “forces”. I have realized that general and specific abstractions like category theory and group theory are limited so I need to look, for example, at semigroups, quasigroups, non-associative Moufang loops, the Sporadic groups: as both as Syntactic and Semantic models too.

  7. Brad Venner says:


    Happy belated new year! I’ve been a long-time fan of your work, but haven’t commented before.

    One obvious link between your climate change interests and your theoretical interests is the “smart grid.” I agree that we’re rapidly moving from the question of “is climate changing” to “what do we do about it.” Evolution of the smart grid is one of the most important enabling technologies to doing something about climate change. All work, including theoretical work, is very important.

    Your work on applying category theory to control systems and digital circuits are promising first steps, but as you noted previously are still a long ways away from engineering practice. But I hope that theoretical breakthroughs in the study of networks have profound impacts on engineering practice, as they are badly needed.

    One interesting group studying networks broadly and smart grids in particular is at Caltech. They have a group blog at John Doyle is a member – you’ve mentioned wanting to read one of his papers previously ( He has broad and ambitious goals of understanding networks in general that are similar to yours but with a more engineering bent. Steven Low has some very interesting and accessible articles comparing communication and power networks. They recently got a large grant from ARPA-E for smart grid research. I hope you check them out sometime.

    • John Baez says:

      Thanks for the tip—especially because Caltech is close, so I can imagine visiting that group and talking to them.

      I am surprisingly content doing work that’s far from practical engineering. I really feel I’m making lots of progress toward a general theory of networks. The specific examples of control theory and circuits are just ‘test cases’ as far as I’m concerned: I’m not doing anything that would excite experts on those particular subjects, but that’s not my goal. I’m now getting into a bit of biochemistry, mainly because it’s a great example of the nonlinear nonequilibrium thermodynamics of open systems. I’m expecting it to take a few years or a decade before enough mathematical infrastructure is worked out to reach really exciting applications… but by that time, I hope to have a pretty thorough view of things.

      Nonetheless, it’s always good to hear about specific concrete problems that ‘hands-on’ folks are interested in. So, I should get to know that group at Caltech.

  8. Brad Venner says:

    Well, the Caltech group puts smart grid development as a 20 year engineering challenge, so your timeline is right on…

    The move to non-linear systems might be a good one vis-a-vis eventual smart grid applications. Steven Low points out that the big difference between communication networks (such as TCP-IP) and power networks is the non-linearity of Kirchhoff’s laws. This non-linearity makes it hard to isolate “layers” from each other. He states

    I feel that the most important layering concept for power must allow us to insulate higher-level mechanisms from the physics of power flows. But it is not clear what that can be.

    Some insights from biology might be greatly appreciated! Biological control systems must obviously deal with non-linear chemical systems. John Doyle has made similar moves in looking to biological systems for insights into network architectures.

    Nonetheless, I’d still love to see your circuit work expanded to include active components!

    • Brad Venner says:

      Oops, both markdown and reply fails! Where is the preview function!

      • John Baez says:

        Markdown works; to a reply to a given comment you click reply on that comment or (often better) the one above it on the comment tree.

        Sorry, no comment previews.

    • John Baez says:

      Brad wrote:

      I’d still love to see your circuit work expanded to include active components!

      Including voltage sources and current sources should be very nice—mathematically beautiful. My team has more mathematical tools now than when Brendan and I wrote A compositional framework for passive linear networks, so we should be able to do it in a slick way. Thanks for nudging me!

      Thanks for the link to Steven Low’s writings. Steven Low wrote:

      I feel that the most important layering concept for power must allow us to insulate higher-level mechanisms from the physics of power flows. But it is not clear what that can be.

      This is interesting because it requires looking at networks from a ‘hierarchical’ perspective, so we can define ‘layers’ or ‘levels’. One approach might be to define morphisms between networks, where f : X \to Y means that Y is a ‘coarse-grained view’ or ‘higher-level view’ of X, where we omit some details.

      I don’t know what you mean by ‘the non-linearity of Kirchhoff’s laws’. Kirchhoff’s laws are a set of linear equations.

      • Bruce Smith says:

        Studying the ways in which one network can be a coarse-grained view of another one seems really useful for at least two purposes — studying how low and high level models or histories of one system should relate, and studying good ways of summarizing a complex network being presented to a human viewer (which is a big practical need in implementing “Overlaid Personal Semantic Networks”).

      • John Baez says:

        One thing that Blake Pollard and I had planned to study is coarse-graining Markov processes. The goal is to systematically understand the process of replacing one description of a random process by another, coarser description. People study this a lot, but apparently not quite as formally as I’d like.

        We think of a Markov process as a graph with ‘states’ as vertices and ‘transitions’ as edges, with a ‘rate constant’ assigned to each edge. We can ‘coarse-grain’ this by mapping it to another Markov process in an onto but typically many-to-one way.

      • Brad Venner says:

        Sorry I haven’t gotten back sooner. You’re a hard man to keep up with!

        Low is trying to solve the AC smart grid problem:

        From Wikipedia:

        An alternating current power-flow model is a model used in electrical engineering to analyze power grids. It provides a nonlinear system which describes the energy flow through each transmission line. The problem is non-linear because the power flow into load impedances is a function of the square of the applied voltages. Due to nonlinearity, in many cases the analysis of large network via AC power-flow model is not feasible, and a linear (but less accurate) DC power-flow model is used instead.

        Low also discusses the AC frequency regulation problem, which has some similarities to a nonlinear thermodynamics problem. I need to study this to see if there is more than a superficial analogy here. This needs one of those Baez analogy tables!

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