Hello!  This is the official blog of the Azimuth Project.

You can read about many things here: from math to physics to earth science and biology, computer science and the technologies of today and tomorrow—but in general, centered around the theme of what scientists, engineers and programmers can do to help save a planet in crisis.

Feel free to ask questions or continue discussion on the many blog articles—it’s never too late! Or, if you have general questions about this blog or the Azimuth Project, please ask them here.

138 Responses to About

  1. adamm says:

    I followed your writings over the past few years, including the circuit modeling items. Azimuth: interesting choice, the word appears in this paper also:

    The Pocklington Equation via Circuit Theory 45-69

    Click to access V16N4BAR.pdf

    Enjoy Singapore, and surrounding areas. And DONT become an expat…. live local. My 2 cents.

  2. Steven Shippee says:

    I’ve really enjoyed your [tireless] efforts with http://math.ucr.edu/home/baez/ – please keep up those types of posts when you can.

    Steven Shippee
    Olympia, Washington

    PS: I did 30 years in the Marine Corps and was in Singapore in 1981 for a time – I’d also appreciate hearing how much it has changed since then.

    • John Baez says:

      I’m glad you like my stuff, Steven. Which type of posts do you want me to “keep up”?

      If you want to read about Singapore, go to my diary.

      Singapore is a fascinating place!

  3. Todd Olson says:

    David MacKay (David JC MacKay FRS / Professor of Natural Philosophy, / Department of Physics, / University of Cambridge) has a good extensive analysis of ‘Sustainable Energy’ at http://www.withouthotair.com/

  4. Mark Meckes says:

    If you don’t already know about it, you may be interested in this workshop for mathematicians on sustainability problems.

  5. I’ve been thinking about joining or creating an social network expert commnity-driven site for some time now and as I’ve followed your writings for some time I also decided to instead put my efforts on Azimuth which is the closest to what i had envisioned so far. So I’ll be able to dedicate my efforts towards Azimuth instead. I’ll join and see what is in the pipeline on the site or you might inform me what is prioritized.

    • John Baez says:

      Great! I’d love it if you’d join the Azimuth Project. I see you’ve become a member of the Forum — good start!

      Right now the top-priority projects seem to be:

      • Working through some well-known plans of action — strategies for dealing with global warming — and summarizing them, discussing them here on the blog, critiquing them, and eventually maybe trying to formulate our own.

      • Making it easier for scientists, engineering and computer people to understand climate models.

      There are also a lot of other projects to do, and I think it’s good for everyone to work on things that are fun and take advantage of their special skills.

      We can talk more about this on the Forum if you like.

  6. Robert J. Guercio says:

    Hi John,

    I’m not sure if I’m going about this correctly but if not, please accept my apologies.

    I wrote a blog explaining how greenhouse gases cause the stratosphere to cool. Here I offer a summary:

    Temperature is a measurement of the translational Kinetic Energy (KE) of the particles. When CO2 and other particles collide with each other, some of the translational KE is converted into vibrational KE of the CO2. The loss of translational KE lowers the temperature and thus excites the CO2 molecules.

    Nature prefers the lowest energy state and the excited CO2 molecules give up the vibrational Kinetic Energy by returning to the unexcited ground state. In so doing, they emit Infrared radiation. In the rarefied atmosphere of the stratosphere, this radiation does not impinge on stratospheric particles and simply escapes into space.

    If the CO2 level of the stratosphere increases, there are more of these reactions and the temperature is lowered.

    For a complete explanation, please see my blog:


    Please consider posting this blog on your site.

    Thank you,


  7. joestudent says:


    nothing to do with the climate, but I remember you were interested by the Voynich manuscript, so just in case you didn’t see the news: it has finally been carbon-dated, and was written between 1404 and 1438 (so about a century later than expected) http://uanews.org/node/37825


  8. I’ve rediscovered your work. Used to visit the UC Riverside posts, now connected to the current blog.

  9. s. vik says:

    “Azimuth Code Project, which is a way for programmers to help save the planet!”

    I am a programmer with math and phys. What can I do other than “burn more coal” simulating it?


    • John Baez says:

      Hi! Sorry to take a while to reply…

      There are lots of ways you could help us. Some are listed here:

      Azimuth Code Project.

      The easiest programs to write are educational: I used some to help explain issues in week308 and week309, and I plan to do more of that. One of the more exciting projects of this sort would be to develop models of the glacial cycles and how they might be caused by variations in the Earth’s orbital parameters. I have the data, I have the math, I just need someone to write the programs!

      You can also see ideas for more ambitious projects that might have a bigger impact.

      We can talk about this stuff here or on the Azimuth Forum…

      • S. Vik says:

        Re: “Glacial cycles” and “variations in the Earth’s orbital parameters”.

        That would be quite interesting if there is a connection. In fact I would almost expect it!

        Send me some details, equations and some data, and I’ll get started. I do have a day job but I should be able to make reasonable progress after hours and on weekends.

        S. Vik, bmath, Kitchener/Waterloo, Ontario.

        • John Baez says:

          S. Vik wrote:

          Send me some details, equations and some data, and I’ll get started.

          That would be great!

          Staffan Lilgeren is also interested in writing simple climate models to study the effect of variations in the Earth’s orbit on glacial cycles. But I don’t know how much he’s done yet.

          The project has a number of aspects, so there’s surely enough work to keep us all busy—the more of us, the merrier! But, it would be nice to coordinate a bit, so we don’t have two people doing the same thing.

          I explained some details on the Azimuth Forum, and said that I’d love to discuss things and answer questions if I can.

          So, I really urge you to join the Azimuth Forum by following these instructions, so you can post comments there, and we can talk about this more there.

          The instructions for joining the Azimuth Forum look a bit long—but that’s just because I spelled them out in so much detail that even idiots like me could follow them, step by step. It doesn’t take long at all, except waiting for me to wake up (I’m in Singapore, I guess you’re on the other side of the world) and approve your application.

          Please use your real name, or at least “S. Vik”, as your username.

          It would be wonderful to have you try this project!

      • S. Vik says:

        I looked up a Scientific American article I read some time ago:

        How Did Humans First Alter Global Climate?; March 2005; Scientific American Magazine; by William F. Ruddiman; 8 Page(s)

        His theory is that rice and beef growth over the last 8000 years has actually warmed the earth and delayed the next ice age (which should have come already).

        If true we have to eat less beef and more potatoes. The question is how much less??


        Right now I better go and eat some beef while I still can. :)

        s. vik

        Hope you all have a sense of humor.

        • streamfortyseven says:

          On this weblog people often ask “Where’s the beef” with regard to a lot of the topics that get bandied about here … so now we know – and we’ll send them your way. I hope you don’t have a beef with that.

        • Tim van Beek says:

          Humans had a global impact for quite some time on this planet, I think that some of the items on our recommended reading list elaborate that point.

          You know, there are two things that I really like, and that I sadly miss in the climate discussion:

          – well informed, valid, enlightening, constructive comments,

          – humor.

          I’m very thankful for either of them.

  10. Ruth Williams says:

    Hi John. Congratulations on a brave decision. I agree completely with what you say in your introduction to your new blog, and I shall be following it with interest. We were in Singapore recently and met one of my former (undergraduate) students, who is now a Minister of Finance there – she talked a lot about sustainability.

  11. ateixeira says:

    I don’t know if you already know this but there is a python script that allows one to write a .tex file that is converted into .html

    This way the endless hardships of writing a good post for wordpress.com are severely shortened.


  12. Intriguing subject, octonions. The 8X8 matrix field shows up in connecting the nucleotides of the genetic code, and the hexagram logic of the I Ching. Is the mathematic/vector space of Octonions applicable to these other 8X8 fields? Some aspect of deep quantum string reality that resonates at different levels?

  13. Dear Prof. Baez,

    I note with some interest that you will be attending Macquarie University in Sydney to give a lecture, and that I will be attending.

    These updates you send me regularly are quite interesting and I take the time to forward them to my father in the Graduate School of the Environment.

    I was not initially aware that you were a mathematical physicist, but now that I am, I may have something that might interest you. Are you familiar with the field of time optimal quantum control a.k.a. Time Dependent Quantum Mechanics?

    Unfortunately for me it seems to be a somewhat sensitive topic (think the War of the Currents on a nanoscale) and it has proved to be quite impossible to find a PhD scholarship in Australia in this area. Do you know of anybody who would be interested?

    Anyhow, links to my master’s research on time optimisation is contained at http://www.quantumcontrol.wikidot.com/start free to distribute and copy. Let me know if you can help me with my concerns. All I dream of is a time optimal computer!

    Look forward to hearing from you. My father and I disagree on the whole Elsevier issue (he’s with them and Springer, I’m a “free-to-all” kind of guy!), we are always debating the best way of disseminating information.

    Thanks, and have a happy day!

    Pete Morrison BSc. MSc.

    • John Baez says:

      Hi! There are lot of people working on quantum control at Australia National University—see this—so if you can’t get a Ph.D. scholarship in that area there, I’m not sure where to suggest. I don’t work on it myself, but you might look at the CQT website and see if anyone there does.

      I’ll actually be giving three talks at Macquarie starting tomorrow. First I’ll be giving the Mathematics Colloquium at 1 pm Monday 6 February 2012, in E7B T2:

      Probabilities versus Amplitudes

      Some ideas from quantum theory are just beginning to percolate back to classical probability theory. For example, there is a widely used and successful theory of “chemical reaction networks”, which describes the interactions of molecules in a stochastic rather than quantum way. If we look at it from the perspective of quantum theory, this turns out to involve creation and annihilation operators, coherent states and other well-known ideas – but with a few big differences. The stochastic analogue of quantum field theory is also used in population biology, and here the connection is well-known. But what does it mean to treat wolves as identical bosons?

      Then Tuesday the 7th at 1 pm in E7B T2 I’ll be giving this talk:

      Energy, the Environment and What We Can Do

      Our heavy reliance on fossil fuels is causing two serious problems: global warming, and the decline of cheaply available oil reserves. Unfortunately the second problem will not cancel out the first. Each one individually seems extremely hard to solve, and taken together they demand a major worldwide effort starting now. After an overview of these problems, we turn to the question: what can we do about them?

      Finally, Wednesday the 8th at 2 pm in E7A 333, after lunch with the category theorists, I’ll be giving this talk in the Australian Category Seminar:

      Symmetric Monoidal Categories in Chemistry and Biology

      Chemists use “chemical reaction networks” to describe interactions between things of different types. In population biology and the study of infectious diseases, “stochastic Petri nets” are sometimes used for the same purpose. In fact chemical reaction networks and stochastic Petri nets are essentially the same thing. The theory of symmetric monoidal categories can help us understand what this thing is, and how to work with it.

  14. Unfortunately for everyone involved, especially ANU, they only study closed loop control, whereas I am focused on open loop control (time optimal, no feedback).

    My PhD application, while impeccable in my eyes, had sufficient “inconsistency” for them to can the whole project. I have literally run through an exhaustive search of all Australian prospective supervisors, and none will touch a project that proposes time dependent matrix control.

    It’s hard not to see jealousy in those academic eyes.

    (Time taken)x(Energy Invested)= a constant

    At best; and often a whole lot worse, provably for a closed loop control. Why would you bother with an adiabatic computer when you could do things time optimally?

    • John Baez says:

      In my advice for young scientists, one thing I hint at but don’t quite emphasize enough is that it’s wise to pick an advisor because they’re smart, well-connected, friendly, help their students get jobs, and do interesting work. And then, after you pick one, work on what they’re interested in. You can’t expect a supervisor to switch over to thinking about what you’re interested in: they’re the boss in this situation. There’s no point in feeling angry or rebellious about this. A Ph.D. is an apprenticeship, after all: it’s good to take advantage of that rather than fight against it. Once you get a degree, then it’s a good time to pursue your own research agenda.

  15. Anton says:

    This is quite a good lecture on palaeoclimatology.

    The biggest control knob; Carbon Dioxide in Earth’s Climate History by Richard B. Alley


  16. […] I plan to talk about many things on this blog: from math to physics to earth science and biology, […]

  17. Dr J R Stockton says:

    Can you, or your supplier, do something about those meaningless times on comments? Without an indication of offset from GMT, they cannot be understood. Also, in an international medium, the 24-hour clock is better – those who do not understand it need to learn.

    This will be sent at about 10:05 local, 09:05 GMT; we’ll see what you put.

  18. Dr J R Stockton says:

    So it’s GMT. That’s good; but it needs the GMT (or UT, UTC) to be visible. But who not go the whole ISO 8601 hog and use YYYY-MM-DD hh:mm ? Sending at 10:07:45 now.

    • John Baez says:

      I can’t get it to say “GMT” or “UTC”. I perhaps suboptimally chose the DD-MM-YYYY format for dates of news articles referred to on the Azimuth Wiki, so I’m using that too here. I apologize for my suboptimality.

  19. Daniel Johnson says:

    To help our abused planet, I suggest that we need to reframe our view of the issues. I am writing an Occupy Wall Street User Manual. The first part (and summary) can be found here: http://www.salem-news.com/articles/april212012/ows_part_1.php

  20. Vijay Sharma says:


    Nothing related to this post.
    I want to discuss more about Azimuth project with you.
    I am based in India and would like to put some projects here.

    Waiting for your inputs.


  21. Vijay Sharma says:


    Basically to extent the ideas which you are building at Azimuth.
    One thing I am already working at is related enhancing bio-diversity at villages.


  22. konst says:

    You must know about this since Barry Brooks blog appears on your blogroll list but to anyone interested he wrote a series of reports on renewables called TCASE (Thinking Critically About Sustainable Energy)


    It might clear up some misconceptions that I’ve seen in the comments by some thinking solar is the answer to the mysteries of the universe of our energy needs.

  23. Hi John,

    I’d like to introduce you to some ideas and sources you might not be aware of, related to the issue you’re grappling with: how you should personally respond to anthropogenic climate change. The most important of these is antihumanism.

    Antihumanism is a relatively new philosophy, which emerged along with critique of industrialism in the modern era, particularly after WWI. Antihumanism gathered strength from the nihilism of post-1960s counterculture and is now evolving rapidly, so there’s already a wide spectrum. At the moderate end are mainstream novelists such as Kurt Vonnegut (“Breakfast of Champions”), Margaret Atwood (“Oryx and Crake”), and Paul Theroux (“O-Zone”). All of these books contain antihuman concepts and observations, though their authors probably wouldn’t use the word. There are also many antihuman movies, too many to list, but at a minimum “Eraserhead” by David Lynch, “THX-1138” by George Lucas, and “Soylent Green” should be mentioned. At the extreme end are actual organizations such as The Church of Euthanasia, VHEMT (Voluntary Human Extinction Movement), and GLF (Gaia Liberation Front).

    In the sciences antihumanism is usually expressed by paleontologists and biologists, and increasingly by climate scientists. Some current examples are Jeremy Jackson and Kevin Anderson (see links below). Edward O. Wilson is best known for his work on biological diversity, but he was also the first biologist to seriously propose that intelligence snuffs itself out, and that this solves Fermi’s paradox: we don’t receive messages from the stars because by the time an alien life form has enough power to transmit that far, it’s already on the threshold of annihilating itself, and the odds of its brief blaze of glory lining up with ours are infinitesimal. This is closely related to the view that life (particularly human life) creates short-term order at the cost of accelerating the entropy of its environment, in stark contrast to the idealistic Gaia theory. For example paleontologist Peter Ward’s “Medea Hypothesis” demolishes the notion that life is self-regulating, and compares life to a drunk stumbling around in a darkened room.

    Antihumanism can be usefully contrasted with humanism. Humanism derives from the ancient Greek notion that man is the measure of all things, and that without human existence nothing would have value. Concealed within this is the assumption that only humans experience value. This assumption has no basis in biology, but is nonetheless one of the pillars of modern civilization, because it provides justification for extermination of other species. The denial of intrinsic value to non-human life is the essence of speciesism, and is closely related to the dogma of dominion, i.e. that it’s man’s destiny to subjugate all other living things (a concept that Edward O. Wilson attacked in his “Consilience”).

    Beyond humanism is transhumanism, sometimes known as futurism or extropianism. This is the belief that not only is man the measure of all things, but the only part of him that matters is his mind, and the sooner his mind is freed from the limitations of biology the better. The moderate form is life extension and cryogenics, while the extreme form is downloading human intelligence into robots and conquering outer space, like the Daleks on Dr. Who. Famous transhumanists include Ray Kurzweil, and Stephen Hawking who recently stated that humanity’s only hope is to escape to other planets before we destroy this one. Antihumanists regard transhumanists as archenemies due to their flagrant disregard for non-humans. From the antihuman point of view, transhumanism bears a striking resemblance to Christianity. Both are escapist, characterized by unshakable belief that humans belong somewhere else, i.e. Heaven/Outer Space. Both express hatred for biology, e.g. Catholic repression of sexuality, and transhumanist use of derogatory terms such meatspace. Both are motivated by fear of death, and presumably of life too, since one engenders the other (literally via natural selection). Both reject the limits of existence on earth, and promulgate a fantasy that justifies exceeding those limits. The danger isn’t that the fantasy will be realized, but that deluded people will make earth unsuitable for life far sooner than would have otherwise been the case.

    Unlike mere misanthropy, antihumanism is distinguished by reverence for non-human life. Biological diversity is considered an axiomatic value, and contrasted with the ugliness and sterility of human monoculture. Earth is described as a “wrecked planet” (Kurt Vonnegut), and various measures are called for to prevent further damage, the most obvious being drastic reduction or elimination of the human population. The pre-human fecundity of earth is idolized, and provides a reference for demonstrating impoverishment of ecosystems. This relates to the shifting baseline syndrome posited by Jeremy Jackson and others, in which each successive generation incorrectly assumes the degree of biological diversity they observe was also seen in previous generations.

    The central paradox of antihumanism is that humans evolved, and are arguably no more or less natural than any other living thing. Stephen Jay Gould argued convincingly that evolution doesn’t converge on anything except fitness for conditions: there are no good or bad organisms, just ones that survive, and mostly ones that don’t. Richard Dawkins went even further and described organisms as mere transport for genes, in which case the DNA we share with all other eukaryotes is the winner, regardless of what humans do. One proposed resolution is that humans are malignant life, as argued by A. Kent MacDougall in “Humans As Cancer”. This sidesteps the problem however, because cancer is also natural, and is closely related to viruses. The higher-order question is ethical: why is malignancy bad, and from what point of view is its badness determined?

    The paradox of human naturalness could possibly be resolved by arguing that sentience is not intelligence but the ability to feel pain and pleasure. What distinguishes humans from other primates is the existential suffering that results from self-knowledge, particularly fear of death. Since humans have such capacity for suffering, we should have equally developed empathy, but instead we succumb to corruption, creating hellish conditions for humans and non-humans alike. Thus despite our naturalness, humans can and should be blamed for wrecking the planet, precisely because we’re capable of feeling remorse for having done so. If we’re unable to reform ourselves, as seems increasingly to be the case, we should have the decency to step aside and give other organisms a chance. Apes might re-evolve back into us, but they might not, and either way it won’t be our fault.

    Dan Miller: “A REALLY Inconvenient Truth”

    Peter Ward (The Medea Hypothesis):

    Professor Kevin Anderson, Tyndall Centre for Climate Research – Climate Change: Going Beyond Dangerous

    Brave New Ocean – Jeremy Jackson

    Church of Euthanasia

    The Voluntary Human Extinction Movement

    • Paul Mackilligin says:

      Interesting. Cancer is a pretty good analogy for civilisation I think. Not for humanity as such, but specifically civilisation, where humans create cities and practise agriculture. Part of a system growing ‘exponentially’ for the sake of growth itself, and consuming resources without regard for the whole. Also, if you look at a photograph of a grey, necrotising cancer tumour embedded within healthy pink tissue, and then at a photograph of a grey city embedded within a healthy green environment and ‘squint’ a bit, they do look strikingly similar (if you allow for a shift from green chlorophyll to red haemoglobin), …right down to the development patterns along arterial routes. You can even see ‘metastasis’ happening in the form of colonisation along trade routes. The same pattern of overconsumption being propagated remotely as well as locally.

      Whilst I share the view that natural biodiversity, complexity and beauty are absolute goods or values, which deserve admiration, respect and protection irrespective of human purposes and benefits, and whilst I also share a certain ‘pessimism’ about human nature and the chances of averting massive ‘ecocide’ (..and further, I would say that the world human population should be reduced gradually but very considerably to about the population density of Canada or Australia or Sweden) …I am still very much a fan of humanity as a species.

      I think we are in a collective mental rut though and desperately need some new models.

      As far as I can see, the only way to change an outmoded model (or underlying, behaviour-driving belief system?) is to thoroughly examine the model in its entirely and in its full complexity, thus revealing its inner contradictions, its over-simplifications, its limits of applicability, etc. I don’t think that process can be short-circuited. (I mean there is no short-cut. Human history is littered with attempts to change things without understanding them first and that hasn’t worked.) The difference between internally coherent, ‘responsible’ (responsive to the needs of the whole system) models, and internally incoherent and irresponsible models, is that the former can withstand thorough scrutiny and the latter cannot. This difference can perhaps be exploited in the same way that the difference between normal cells and cancer cells can be exploited with chemotherapy (…in that normal cells retain the ability to repair DNA damage caused by chemotherapy drugs and cancer cells do not.)

  24. Jimmy says:

    Hello John,

    I appreciate your work and share your thinking on what the planet needs. I was looking for your notes on economics but the link on your website does not work. Is there a way I can find those? I would be interested to read your view on that.



    • John Baez says:

      Where do you see a broken link? You can get to my economics diary here.

      • Jimmy says:


        Thanks for the link; this is what I was looking for. I appreciate your efforts by talking about what scientists can do to help the planet. I am also of the opinion that the problem lies at the heart of how governments frame policies that, in turn, shape the world. The classical economic model of ‘wealth maximization’ needs to be replaced with policies that support resource sustainability rather than unnatural growth fueled by liquidity and debt. Sensible policies would allow a natural balance between the environment and economic prosperity. By framing the policies with just one objective in mind (growth), we have created a state of artificial demand that has resulted in the current mess.

        Nature has a mechanism to keep things in balance. With the establishment of the current socio-economic system, the planet does not have a natural way to control human population.The false sense of economic prosperity and wealth creation portrayed by aggressive expansionary economic policies have allowed the human population to burgeon. It is imperative that we think of the restrictions on the supply side. The governments have allowed expansionary policies over years to create the situation we face today. In my view, economic policies should aid resource sustainability instead of focusing on perennial growth – the main reason why the planet is in danger today. By promoting policies that keep a check on exploitation of resources, the governments could help keep an implicit check on global population. The idea may sound offbeat but there is a remote chance of improvement until the officials take the lead.


        • John Baez says:

          I agree that we need to slow the exploitation of resources, but most governments are set on doing the exact opposite. So, the trick is to figure out how to persuade governments to change their policies. Replacing GDP with some sort of ‘genuine progress indicator’ might help. That’s why we have this page:

          Genuine Progress Indicator, Azimuth.

          And I’ll repeat my question: “Where do you see a broken link?” I always want to fix broken links on my website.

        • Jimmy says:

          Sorry I missed to address your question last time. I got the broken link for eco here:

          http://math.ucr.edu/home/baez/NASTY.html .

          However, it seems to work when I check now. Maybe I encountered a technical problem then.

          Regarding ‘Genuine Progress Indicator’, it’s a good concept but it may not work on a standalone basis. GDP incentivizes investors to provide funds and this reduces the cost of capital, pushing up asset prices. Genuine Progress Indicator may deduct various costs from the GDP but these are intangible in nature; the investors may discount these and the net effect would be marginal. I think such an index needs to be supplemented with a shift in the taxing policies to restrict activities hazardous to nature.

          I visit your blog twice a week and I intend to continue doing so. I hope you continue with your commendable work and I look forward to learning more about your views.



  25. Andrew says:

    Hi John,

    I have been enjoying reading through your blog posts on topical developments in physics, and will take up perusing posts on other topics of interest here as well when I can.

    With the publication of the WMAP data, and now, the fantastic results obtained in the Planck project, a question has come to mind that I have not seemed to be able to find an answer to.

    It is, of course, the case that all the data we receive about the universe and the state of matter within it is through the detection of EM radiation (light). It is my understanding that our insight into the physical significance of this data is necessarily governed by the model of the universe we use to interprete the data.

    The question that comes to mind, for which I have yet to find an answer (google search and all), is: Has there ever been an attempt to perform a model independent experiment to calibrate the propagation of light over cosmologically relevant distances?

    My understanding is that the luminosity-distance correlations, (and other methods for establishing distance relationships of celestial objects assume that light propagates across large distances (in an unobstructed field free static space), according to a metric that is Minkowskian. But, I cannot seem to find any information about any empirical experiment to verify that this assumption is correct.

    I am hoping that you can point me to where I can find information on what our current state of knowledge is on this subject, and more particularly, any results obtained from model independant empirical experiments that confirm .

    In reading through all the newly published papers produced by the researchers working on the Planck project and the stunning findings they have reported, the notion of asking, at this late date, if anyone has ever undertaken an experiment capable of “calibrating” how light propagates over great distances carries with it a note of some wonderment.

    One would think, if it has not already been done, that the results of an empirical test which would be the physical “analog” of the Michelson-Morley experiment* on an astronomical scale, or some other model independant test that would directly calibrate how light propagates over cosmologically relevant distances, would be of compelling interest to astronomers, astrophysicists and cosmologists, and that it would be a matter of some priority to establish.

    Thank you again for Azimuth. Its a great resource and a huge service for those of us who are interested in ideas about the “world” we live in.


    * I refer to the M-M experiment losely. But the concept I hope is illustrative of the idea of conducting an experiment to determine whether light traveling over great distances would produce data that would give a null result in the M-M experimental model.

  26. pendantry says:

    You may find some resources of use/ interest at the Manpollo Project.

  27. Marcia says:

    Hi John, I did a paper on the Beal’s Conjecture and would like to submit it to be included in your column called “This Week’s Finds in Mathematical Physics”. How do I submit?

  28. […] scientists, engineers and programmers trying to help save the planet. On the Azimuth Wiki and Azimuth Blog we are trying to explain the main environmental and energy problems the world faces today. We are […]

  29. As I’ve mentioned previously, one of the amazing features of the internet is that you can take almost any idea and find a community obsessed with it. Thus, it isn’t surprising that there is a prominent subculture that fetishizes rationality and Bayesian learning. They tend to accumulate around forums with promising titles like OvercomingBias and Less Wrong. Since these communities like to stay abreast with science, they often offer evolutionary justifications for why humans might be Bayesian learners and claim a “perfect Bayesian reasoner as a fixed point of Darwinian evolution”. This lets them side-stepped observed non-Bayesian behavior in humans, by saying that we are evolving towards, but haven’t yet reached this (potentially unreachable, but approximable) fixed point. Unfortunately, even the fixed-point argument is naive of critiques like the Simpson-Baldwin effect.

  30. Jzal says:

    For a topic, I would love to see you guys do a book review of this book. I thought he put a lot forward with his account of the second law applied to cosmology which I found very accessable and well presented. He points out some inconsistancies of existing mainstream theory that I thought were fascinating. But overall just a really cool geometry of the universe that I thought I would share with your blog.


  31. NNK says:

    Dear Mr Baez,

    Your initiative of scientists pitching in to save our precious planet is indeed inspiring to me!

    I am bouncing to contribute to this noble effort as well: I am a practicing engineer in computer & machine vision and computational photography; with some experience in applied machine learning.

    Please let me know how I can join in……..

    • John Baez says:

      I’m glad you’re eager to help! One way to get started is to join the Azimuth Forum, where we talk about what we’re doing. You can do this by clicking the link and following the directions, which look more complicated than they are. Please choose your real name as username.

      David Tweed also has experience in machine learning and he is interested in simple ways of trying to understand global warming, which do not use detailed global climate models. This is a bit similar to what the Berkeley Earth project is doing.

      We have a number of computer-related projects underway which you can read about here. Unfortunately we are moving rather slowly on these.

      But we are also doing lots of other things. You can look at the Azimuth Forum even before you join it, to see what some of these are.

  32. anitachowdry says:

    Dear John Baez,
    I continue to find your posts inspiring, and I would like to share with you the completion of the first stage of my harmonograph-as-a-work-of-art project, documented on my new site anitachowdry.com. Here is a page of drawings that the beast has produced : http://www.anitachowdry.com/iron-genie-drawings/4582085804 I couldn’t begin to describe the maths in them, but they do inspire me with an almost Pythagorean sense of awe.
    The machine is now ready to be loaned/hired out for for public appearances, so if anyone has any ideas about institutions that would like to have it for a period of public engagement, I would be most interested to hear from them.
    I hope you enjoy the Iron Genie beast, Anita

    • John Baez says:

      Nice pictures, Anita! Let me post a little one here so people are tempted to visit your site:

      I have another blog, Visual Insight, which is about explaining math through beautiful images. I’m tempted to ask you for a nice image made by your harmonograph! The problem is that without a detailed description of how the machine works, I can’t figure out the physics, and then the mathematics, that lurks beneath the beautiful surface of these images.

      I hope you’ve been enjoying the nice pictures of rolling motions created by Greg Egan and others… the pentagram of Venus is reminiscent of your harmonograph patterns, and probably related, mathematically speaking.

      I will try to think about institutions that might like the harmonograph. Does it need a trained person to operate it? Does it need you?

      By the way, I’ll be in Oxford from February 21 to March 14, visiting the computer science department. I’m afraid I won’t have the time to go into London, though…

    • Todd Trimble says:

      Anita, I was intrigued by your posts a few months back describing your plans for the harmonograph, and am very pleased to see this machine has been brought into being! It’s quite beautiful — really the most elegant harmonograph I’ve seen (and of course its products are fascinating as well). Congratulations!

      I had mentioned your name (and sent a link to your blog) to an artist who lives in my town, Jane Philbrick, who is also intrigued by the idea of bringing mathematics and visual art together. One of her recent projects involved the re-creation of a sculpture (Marta Pan’s Sculpture Flottante I) into different media, including sound waves. The rough idea here, as I understand it, was to represent the characteristic sound forms of the sculpture (cf. “can one hear the shape of a drum?”) mathematically, and then render this representation sonically, to suggest possible “evolutions” of the shape (which were finally compiled into a sculptural “swan song”). This also wound up being the basis of a mathematics paper on the arXiv, which John might find intriguing as well. Curious stuff!

      • nad says:

        Interesting project.
        It’s great that the Central Saint Martin’s college of Art and Design workshop is open for all sorts of arts projects.

      • anitachowdry says:

        Dear Todd, Thankyou for your kind comments – very gratifying! Jane Philbrick’s work sounds intriguing, and reminds me of another collaborative project by a French artist called Anais Tondeur (visualizing the sound of graphite).

        The movement of collaborations between artist and scientists keeps gaining greater momentum, and I think it very fruitful – in fact many of last year’s new intake on the Central Saint Martin’s M.A. Art & Science had scientific – mostly biological or earth sciences – (& not art) training – so the boundaries are ever more blurred. In fact, I tend to think that maths is in many ways an arts/philosophy discipline.

        In this respect I am very grateful to John Baez for providing such a lively platform for sharing and discussing such ideas.

  33. anitachowdry says:

    Many thanks for your interesting reply John, with so many suggestions. Just clicked through to Visual insight – thanks for pointing me to that , I intend to browse in more detail.
    I would be very happy to give you as many images as you wish.

    John Martineau, founder & director of Wooden Books http://www.woodenbooks.com/ came & had a look at it and explained how to count the beats of the pendula with a stopwatch to get approximate ratios that create distinctive classes of drawings, so I can try & make notes with the next batch. But unlike a computer programme, the Genie is full of crazy unpredictable variables!

    Not much training required for the Iron Genie – the whole point is that audiences can have fun making the drawings themselves – I just watch & explain initially what to move. An intern could even help with that. (That’s why I had a young girl demonstrating in the video)

    I am delighted to hear that you will be visiting Oxford – I can come & see you if you have time for a drink. If that is a possibility could you e-mail me?


    • John Baez says:

      Sure, it would be great to meet in Oxford, and I’ve emailed you about that.

      Clearly you are getting some fans here on Azimuth. The beautiful design of the Iron Genie is just as attractive as the images it draws, maybe even more so.

  34. anitachowdry says:

    The video on http://vimeo.com/83773739 might give you an idea of its workings – its very simple in principle – it all comes from the pendulums.

  35. rly1987 says:

    Looking for science and tech writers with spiritual and humanitarian outlook:


  36. Alexander says:

    Dear Dr. John Baez!
    What is your opinion about the new information about the Planck length in Wikipedia (in the 2 proofs) at https://en.wikipedia.org/wiki/Planck_length ?

  37. Alexander says:

    What about the content of the evidence?

    • John Baez says:

      Sorry, I don’t want to encourage people to use Wikipedia as a way to publish their own research, so I don’t want to discuss work published that way.

      • Alexander says:

        I agree with you. I note only that this material was published in an unknown physical journal FIZIKA B (Zagreb) (“Physics B”, Croatia).

  38. Frankie says:

    I thought you might be interested in this recent video featuring mathematician Peter Cameron, cosmologist George Ellis and physicist David Tong – http://iai.tv/video/the-hunt-for-dark-energy

  39. Jim Adams says:

    John, I have a chapter, no. 5, of an eBook called Superexponential algebra being written up on my website, which is in violation of the ‘non-existence of elements of Hopf invariant one’, and I was wondering if you would like to comment on it, since you have written on division algebras?

    • John Baez says:

      Hi! If you’re claiming to have found a counterexample to a famous theorem, I probably don’t have the energy to look into it and see if there’s a mistake somewhere.

      • Jim Adams says:

        Hello John

        Yes you are right, and I am not saying this anymore.

        However, if you make the assumption that the scalar part is nonzero, then there do exist such objects. I call them novanions, and they are in chapter 5 of the eBook in preparation called Superexponential Algebra. There is more than one type, and the theory is not now in conflict with any well-established mathematical result.

        Jim H Adams

  40. Ivan Pencoff says:

    Hello John, It’s Ivan from our Stratford Landing School days in Springfield, Virginia. I just wanted to pop in and wish you a Happy Super PI day today… 3.14.15 9:26:53. So have a happy day!!! :)

  41. James K. Finley says:

    Hello John, My son, who is studying Earth Sciences at UVic B.C. noted that the New Scientist article about Leap Seconds (June 27-July 2015) could not be correct by his calculations. E.g. the Earth travelling 29,800 km per second. I never really thought about it but obviously his math is correct. The ONLY contradiction to this is your article. I’m astounded that such prestigious magazine could make such a colossal blunder but cannot find any correction. Has anyone acknowledged your correction ?

    • John Baez says:

      I was not the only one to make a correction. I got an email from Greg Egan saying:

      Other readers noticed those errors, and New Scientist published a correction in the print magazine a couple of issues later. I don’t know exactly when the online version was corrected, but it currently carries the interesting claim:

      Article amended on 26 December 2014
      Since this article was first published, the figures in “The world in one second: Distance” have been corrected.

      Perhaps their web site couldn’t cope with the leap-second, so they had to shift their clocks back by six months.

      (That’s a joke about their claim that the correction appeared about half a year before the article.)

  42. cristhian luque says:

    Hey John! greetings from Bolivia, I liked very much the work you do, congrats. Respect to the Azimuth Project, you should take a view of what´s is going on here in south america, more precisely here in Bolivia, there was a great lake called Poopó that recently became as dry as a desert……. I hope you get my message… and congratulations for your work!!!! and let me know if I can participate in your initiative… I am an civil and electromechanical engineer and I would be really happy if I can join to the initiative…

    • John Baez says:

      Hi! Right now I’m interested in concepts like stability, observability and controllability and how they either are or aren’t preserved when we ‘compose’ networks, i.e.., build bigger networks out of smaller parts. My student Jason Erbele is working on this using the formalism here:

      Categories in control.

      But it would be helpful to have an expert with a good intuition for these things.

  43. Rob Superty says:

    Hi John!

    I’ve just stumbled on your blog and am absolutely loving the series on symmetry and the fourth dimension. Any plans to revisit? Can’t wait to hear about the other 4D solids. Definitely one of the clearest explanations of the topic I’ve seen!

    Thank you so much

  44. Jim H Adams says:

    Hello John
    My website at http://www.jimhadams.com contains a popularisation of climate catastrophe issues in the free eBook ‘the climate and energy emergencies’. This was written in 2014, an update with pictures of the 2009 edition.
    I support what you do.

  45. Priyakant Sharma says:

    Hello Sir, Your blogs are mind blowing. I am an engineering student and me respective branch is Mechanical Engineering. Day by day my love towards physics is increasing. Please suggest me a project work.

  46. Jim H Adams says:

    Hello John
    Sorry, I sent you what was claimed to be a proof of the generalised Riemann hypothesis. Simply, it isn’t.
    With best wishes
    Jim H Adams

  47. Raymond Lutz says:

    Hi, Mr Baez.

    Did you cross Gail Tverberg’s essays about networked economy?

    In this post (and others) she writes about increased complexity in our societies (and their impending collapse?)


    Merci pour votre effort de vulgarisation!

  48. Kent Palmer says:

    John Baez–

    See “What Special Systems Theory is about . . . Life, Consciousness and the Social”


    See also https://www.academia.edu/3795281/Special_Systems_Theory


    https://works.bepress.com/kent_palmer/4/ Reflexive Autopoietic Dissipative Special Systems Theory

    More information at http://schematheory.net

    Thanks for your work. Have been following it for years. I have learned a lot. And have included some references to it in my dissertation. http://emergentdesign.net

    Kent Palmer

  49. Tom Fuchs says:

    Here is a suggestion for a physics topic that I haven’t seen covered elsewhere. See the chart at the bottom of The Relativistic Rocket page, that you host at http://math.ucr.edu/home/baez/physics/Relativity/SR/Rocket/rocket.html. It’s a height-over-time chart of a stone thrown upward at close to c in a uniform gravitational field, in the frame of the thrower. T is in years and h is in light years. Where the plot is close to the x-axis the stone is moving at close to c, so there it’s a proxy for the path of light.

    It seems to me this chart shows that, in the frame of a ground-based observer, light shone upward accelerates away, and light received from above decelerates to reach the observer at c (presumably decreasing its wavelengths to cause a blueshift). When the chart is extended below the x-axis, it shows that light shone downward decelerates away, and light received from below accelerates to reach the observer at c (presumably increasing its wavelengths to cause a redshift).

    This behavior expounds on gravitational time dilation. For example, the Lunar Laser Ranging experiment finds the Earth-Moon distance by measuring the round-trip time of light shone from Earth toward a reflector on the Moon, and multiplying half of this time by c. In the frame of an astronaut on the Moon that round trip takes longer, since clocks on Earth run slower than the astronaut’s wristwatch. The astronaut could thereby reckon that the Earth-Moon distance is greater than what the Earth-based observers found. There is only 1 tape-measured distance, of course, between the other 2 values.

  50. Susie Coles says:

    My late brother David Tweed, recently chose to leave the world. His dying wish was to make sure you received his donation of $500. Is there anyway you can see if this was received. I believe he would have sent it on 12/1/2017.

    Thank you

  51. Tom Fuchs says:

    Here’s another suggestion for a physics topic. I propose that a better metric for Schwarzschild geometry is (in geometric units):

    ds^2 = - \left( \frac{r}{r + r_s} \right) dt^2 + \left( \frac{r}{r + r_s} \right)^{-1} dr^2 + r^2 do^2

    where the variables are defined at http://casa.colorado.edu/~ajsh/schwp.html. The reason for this change is to have a metric that fully adheres to GR’s equivalence principle (EP) and is otherwise preferred by Occam’s razor.

    Be in free fall, initially straddling the horizon of a black hole (massive enough that you don’t detect a tidal force), beside a freely falling stone that’s above the horizon and escaping to infinity. GR predicts that the stone is passing you in the outward direction, away from the black hole. If GR adhered to its EP I’d be able to add the condition “Let the stone be passing you in the inward direction”, or even “Let the stone completely pass you in the inward direction at a speed close to c as you measure”, for in some other locally inertial frame that freedom of relative movement is possible. Which is to say, the laws of physics in your local frame differ from those in some other locally inertial frame. Note I didn’t specify that you’re falling through the horizon.

    In the river model of black holes (http://jila.colorado.edu/~ajsh/insidebh/waterfall.html) an analogy is made that a fish is inexorably swept to the bottom of a waterfall when the water falls faster than the fish can swim through it. The problem with GR working analogously is that there’s no EP for rivers. The page says “[In] general relativity, space itself can do whatever it likes.” A theory of gravity that postulates the EP is thereby constrained on what space itself can do.

    A solution is to limit escape velocity to less than c everywhere. The escape velocity embedded in the metric above is:


    No test that I know of rules out the equations above. For example the new metric still predicts 42.98 arcseconds per century for Mercury’s anomalous perihelion shift. The problems around black holes vanish, including incompatibility between GR and QM regarding singularities, which for the new metric can be a limiting case.

    If you allow it, later I’ll suggest how the new metric can solve the mystery behind dark matter, without making new assumptions. I apologize if my comments are out of line here.

  52. AS says:


    I am a programmer and I do programming in Python, PHP etc. How can I participate?

    Check my details at http://adnansiddiqi.me


    Karachi, Pakistan

  53. Xenophon Philippousis says:

    Hello Mr Baez,
    I have watched on YouTube some of your lectures about numbers (University of Glasgow). Enjoyed your way to explain in a simple way some very complex ideas ( even though some were beyond my knowledge ). I would be grateful if you could spend some of your time and watch a short animation.

    This started as a experiment on a geometrical construction and ended as a motion graphics clip. Starting with a circle of radius 1 we end up with a square having a specific side length (the title I gave to my animation). I concluded that this is the number by using the Geozebra application for geometry. My question is if this can be proved using the exact construction and if there is any interesting property about this number. Unfortunately even though I was good at school in geometry (it’s been a long long time ago) now I am incapable to think a way to find a prove, if there is one.
    Hope you find it interesting and thank you a lot for your time.
    Xenophon Philippousis

  54. Abhishek Bijalwan says:

    Hey, I read your stuff about end of the Universe. I want to save the planet so i am dropping this comment. Hope you will notice me.

  55. Hi Dr. Baez, An Invitation.

    We’re organizing an AMS special session on Quaternions at the 2018 Joint Math Meetings in San Diego (Jan 10 – 13).

    We’ll be having a diverse group of presentations related to Quaternions.

    Presenters include mathematicians, physicists, and a biologist.
    Some of the talks will be on Clifford Algebras and Octonions.
    There will also be some talks on historical questions.

    One of the presenters will be David Hestenes of Geometric Algebra fame.

    We hope some of your blog’s readers might find our sessions interesting and we’d like to invite them to attend!

    We’ve emailed you a personal invitation to present as well.

    More information can be found at our website Quaternion Notices:

    Dr. Chris McCarthy cmccarthy@bmcc.cuny.edu
    Dr. Johannes Familton
    Dr. Terrence Blackman

    • John Baez says:

      Thanks very much for your invitation! I tend not to go to the Joint Math Meetings—they happen right when winter classes are starting at my university, and I think it makes a bad impression to sneak off on the second week of class. However, I’m glad you’re having a session on quaternions, and I wish you luck with it.

      • Jim H Adams says:

        Hello John

        I have just now sent this email to Chris McCarthy:

        Following an email from the Azimuth site concerning quaternions, I would like to initiate a conversation with you.

        I think what I have to say on the mathematics part of my website, which contains new work on quaternions and developments from them, is interesting. These new developments have also, I believe, applications to physics, which is also on this website, http://www.jimhadams.org.

        I cannot go to your conference, but I would like to present to you in this email an introduction to these ideas, and where they lead. I have only just read the email from John Baez at Azimuth, so this communication is an improvisation.

        The mathematics part of the website contains three eBooks of relevance, these are, Innovation in mathematics, written in 2014, Superexponential algebra, which considerably expands the material in Innovation in mathematics for which Innovation in mathematics might be thought of as an introduction or prequel, this was written mainly in 2015-2016, and a sequel to Superexponential algebra, Number space and logic, which is due to be finalised by the end of 2018. These document an extremely ambitious programme in mathematics to cover its foundations in an overarching view, accessible in Superexponential algebra to the undergraduate. The language is a simple as I can make it, whilst keeping technical discussion technical. An objective to to teach, if possible, the creative process, including by example. It is not an attempt to teach what I call ‘performance mathematics’. In music, an analogy is to teach composition rather than the playing of an instrument.

        A gentle introduction is to read Innovation in mathematics first.

        Superexponential algebra develops in chapter I a representation of 2 x 2 matrices which I call intricate numbers, since embedded within them are the complex numbers, and this is a similar name. These are not new: they were introduced in 1849 by James Cockle and called by him coquaternions. The most frequently known name is split-quaternions.

        Chapter II develops intricate numbers to form hyperintricate numbers (the word hyper comes from Hamilton: hypercomplex numbers) in a completely regular extension of the idea of intricate numbers.

        Chapter III includes a description of quaternions using the hyperintricate description. A careful scrutiny of indices on one of the sections on quaternions will discover that there are a number of matrix representations of quaternions. All of course are isomorphic. A proof that the only division algebras that are associative all include the quaternions is given in this chapter.

        Chapter V goes beyond associative algebras to nonassociative algebras, so you would expect to find a description there of octonions, as indeed happens. What is surprising is that I have discovered a new type of mathematical object called a novanion. These are not division algebras, they are novanion algebras, so the theory of J.F. Adams in 1960 that there are no division algebras beyond the octionions holds, but they do have the interesting property that when the scalar part is zero, they are division algebras. The chapter contains a proof of this statement using eigenvalues (although novanions, like octonions are not division algebras, and are not therefore representable by a matrix).

        A whole theory of physics is presently under construction in the physics part of the website using novanions. This is the work Universal physics, in three volumes. One of the features of this theory is that time is represented by a scalar and the novanionic imaginary dimensions are space-like. Then a time t = 0 novanions can be created out of nothing, but the creation process is irreversible after t = 0, and conservation laws on novanions then hold.

        Novanions may have implications for the classification of simple groups. This is mentioned in Number, space and logic.

        With best wishes

        Jim H Adams

      • I know what you mean feeling guilty about sneaking off during the semester. Although usually my students tend to encourage me to go, so they get a day off. :-)

        Anyway, after the conference, we’ll be posting the slide shows (the power points) of the presentations on our website:

        Thanks for well wishes!

        Chris McCarthy

  56. Jim H Adams says:

    Slight correction here: I should have said ‘when the scalar part is not zero, they are division algebras’.

  57. a.lie says:

    Hey John! Love your blog, it’s consistently insightful and entertaining!, a rare combo among scientific writers. I was wondering if you could write a blog post about the Self-Organized Criticality. I’ve seen you mentioned it in passing in several blog posts, but was wondering why you never got to dedicate a post on it since its quite a big topic in complexity science. There are several nice articles/books regarding SOC’s, but after reading through some of them a sense of greater confusion arose instead of a better understanding. I guess a big part of that has to do with our inherent not-understanding of it, but despite that it still seems to hold a lot of intuitive appeal and power. I was wondering if you could shed some light on the topic.

    • John Baez says:

      Alas, I don’t have any special insights into self-organized criticality that would lead me to write a blog article on it. What about it do you find puzzling? I can easily imagine there are a lot of open questions in this subject, like: under what conditions does a system spontaneously move toward a critical point?

  58. Alex says:

    Hi Prof. Baez

    You interviewed Eliezer Yudkowsky about potential risks from advanced AI five or six years ago, and I believe you said there that you would consider working in this area a few years down the road. Now, the topic become a mainstream, and AI Safety research is more talent constrained than funding constrained. Do you still consider this option as possible? If so, I’d love to know more details :)

  59. Gregor Kölsch says:

    Dear Prof. Baez,
    I am a biology teacher. I am interested in the simulations mentioned in This Week’s Finds (Week 309). That was some time ago, right. There is a figure showing the time course of a prey and a predator population, respectively. You compare it to the real world example of the hare and the lynx. I would greatly appreciate a high resolution copy of that figure – and your ok to use it in an exam.
    Please answer soon, because I have to prepare all the materials for the exam these days.
    Thank you very much in advance.
    Yours sincerely,
    Gregor Kölsch

    • John Baez says:

      You’re free to use the computer-generated pictures on week309, since they were created by my colleagues in the Azimuth Project. I don’t have the rights to the picture of historical data from MacLulich’s classic 1937 paper “Fluctuations in the numbers of the varying hare (Lepus americanus)”, but I won’t tell anyone if you use it. I don’t have higher-resolution versions of these pictures. (In general, I make available the best versions of whatever I’ve seen.)

  60. Justin Hilburn says:

    Dear Prof. Baez,

    I was looking to refer an undergraduate student to some old This Week’s Finds when I noticed that your page at Riverside has disappeared. Do you have any plans to make them available online again?


    • John Baez says:

      The server hosting math.ucr.edu went down about 3 weeks ago due to a power outage, along with all other computers at U. C. Riverside. Unfortunately this particular server was unable to reboot so they had to replace it. The machine has been replaced, but only yesterday was I able to log in and tell them where in the directory hierarchy my website was located, so they could make it visible to the world. They are trying to do that now. So, in a few hours, or days, or weeks, my website and all the images it hosts should reappear.

  61. Richard Taylor says:

    I’m am independently wealthy investor who’d like to know more about your project and if you’re interested in funding or investors. How can we go about this?

    • John Baez says:

      I don’t need any money, and you probably shouldn’t invest in me since I don’t plan to make any more than I need. Unless, of course, you want to help save the planet.

  62. Craig Morgan says:

    I’ve followed your math/physics writings for a short while now. And I’ve often wondered what, if any, relation there might be between you and my freshman physics text author. With your post “Algebraic Geometry”, now I know! Thanks for the story.

  63. Dear Prof Baez

    since you both work in math but also are concerned with the environment (Azimuth project) I thought that a new book may interest you and perhaps others in this blog too


    It is a product of the collaboration of an artist an architect and a historian of science. It is connected with efforts to adress issues related to the environmental change, but it is also an exploration of new representations of space and time. It seems to me that there is interesting mathematical content in their work (although they are not using expicitely the mathematical concepts that are more readily available in mathematicians).

    I also add some video related to this work


  64. … παρακολουθώ με ενδιαφέρον τον John Baez και το Azimuth …

    [… I watch John Baez and Azimuth with interest …]

  65. John Baez, I read your Azimuth posts (I have subscribed through email). Thanks for taking the time to create these wonderful posts. I enjoy reading on these varied topics and your refreshing approach to writing about math/physics/etc.

  66. Prashanta says:

    I’m a lover of science and technology who caught the social service bug at sixteen. Now I’m a yogi currently working on curating the knowledge of different wisdom traditions. I’m a devotee of the Renaissance and it’s championing of art and music, of what is abstractly beautiful. So my question is how can we protect the subtle assets of our world? I miss the world science fiction foretold in the Sixties and peaking with positivity of TNG. After fifty years I need to be able to be able to present to my friends and family what is going on in the world. I know children that I want to have a good shot of thriving and prosperity.
    I also serve as an organizer among the tetration and hyperoperations community. I specialize in iterated smooth functions f^n(x) , which is more general than Arnold’s measure preserving definition of dynamics. A main focus has been working on the question, “do maps in general have flows?”, with application to the hyperoperators.
    My applied category question is given f(g(x)) being associated with the integer and set partitions through Faa Di Bruno’s formula, it is easy to demonstrate the association of f^n(x) to total partitions (Stanley), hierarchies(Flajolet) and Schroeder’s Fourth Problem.
    Question – given the connection between set partitions and total partitions (not proved here), and the relationship of total partitions to Classification Theory, can the laws of physics be viewed as a classification engine? R. Aldrovandi and L. P. Freitas, Continuous iteration of dynamical maps, J. Math. Phys. 39, 5324 (1998) discuss the flow of dynamics through channels of greater and greater detail.

  67. Darrin Meyer says:

    There is a practical solution to many of the problems created by Climate Change.
    Due to increased glacier melting and thermal expansion, the Ocean is rising 3-4 mm per year – equivalent to 300 trillion gallons per year. At the same time, rivers pour hundreds of trillions of gallons of fresh water annually into the Ocean.
    For example, the watershed feeding James Bay, connected to Hudson Bay, pours 85 trillion gallons of fresh water into the Ocean per year; and the Columbia River in Oregon adds 65 trillion gallons annually.
    Even with continuing excess glacier melt, diverting 150 trillion gallons of water per year from these two sources will reduce the rate of sea-level rise by half.
    The water from James Bay can be diverted by canal to irrigate 500,000 sq. kilometers (125 million acre) of arid/semi-arid land stretching from Montana to Texas. The irrigation will approximate 18-24 inches per year of precipitation over the region.
    The Columbia River water can likewise be diverted by canal to irrigate the San Joaquin Valley in California (5-10 trillion gallons); and 300,000 sq. kilometers (75 million acres) in the arid part of Northern Nevada and Utah.
    The irrigated land in both regions can be used to grow billions of trees. Using half of the combined areas would create 100 million acres of new forests, which would recapture 60-80 tons of carbon per acre, or a total of 6-8 Billion tons per year – more than the total annual carbon output of the U.S.
    80 million acres (40% of the combined regions) could be set aside to revive small family farming. The remaining 20 million acres could be divided into 3,000 communities (+30 million people) drawing remote employees from tech industries and disadvantaged people who are frightened and sickened by life in decaying cities. The increase in land value of $8-10,000.00 per acre (approx. $2 Trillion) will more than offset the cost of building the canals.
    Darrin F. Meyer, Esq.

  68. Just read your Azimuth piece about discounting. IMO valuation of money may be temporally non-linear but should be integrable, contra Marx and other systems that ban interest. Rates are semiotic signals of the time value of money, something Marx denied. USUALLY people value ‘a bird in hand’ more than ‘a bird in the bush,’ but not always. So the usual thing, as with bonds, is that rates vary directly (or polynomially?) with duration. Best wishes!

  69. sostentech says:

    Hey John! its been sometime since we worked at the Torino’s category school with David, Jacob and all the other friends! Just saying hi

    -Edgar Valdés

  70. You seem to have moved a bit back to physics from the Azimuth project, but that is based only on what I’ve read here recently.

    Since Max Tegmark has moved from physics to AI, with the main goal to make AI safe, and is otherwise interested in saving the planet and so on and is in a position to actually influence some people, it seems that you should investigate possible synergy,

    • John Baez says:

      For the last 5 years my main work on the Azimuth Project has been on “applied category theory”: a project to get category theorists doing more practical things, and to use category theory to develop systems thinking in a more rigorous way. This seems to be working well, so let me show off a bit.

      There’s now an annual conference and school on Applied Category Theory! The 2021 school includes two courses that use my work on “structured cospans”. One of them uses structured cospans as part of a software tool that allows one to quickly build models from smaller parts:

      Applied Category Theory 2021 Adjoint School.

      Also, my former student Brendan Fong has teamed up with David Spivak to set up a new institute, the Topos Institute, for work along these lines. They have $3.1 million in funding so far, but they’re just getting started.

      I am not particularly interested in working on AI and AI risks, since so many smart people are already doing that, and I don’t feel I have any special skills in that area. But it would definitely be good to talk to Tegmark.

      After I retire in July, and already starting now, I plan to spend more time explaining math and physics… especially polishing up and packaging the explanations I’ve already written in This Week’s Finds and course notes. My attempt to update the FAQ which you’re seeing here on Azimuth, is part of that. But I actually got pulled into that particular little project because I was trying to understand neutrinos a bit better, to continue my project on octonions and the Standard Model.

  71. Taisiia says:


    I’ve seen a few of your posts and it looks like you are not indifferent to the situation with our planet and humanity. I want to invite you to a very important event for every human being.

    On Dec 4, an online conference “Global Crisis. Time for the Truth” will take place. The event is organized by volunteers from 180 countries on the Creative Society platform and will be interpreted into 100 languages.

    This conference is dedicated to the climate change topic and the absurdity of the consumerist format of our society. The true causes of everything that is happening will be voiced by honest scientists and specialists, and what is MOST IMPORTANT, – solutions to these problems will be offered.

    Please, join watching!

    You can also share this information on your page and easily stream this conference on personal network platforms.

    If you like to stream the event on your YouTube channel and other possible platforms, I’ll be happy to give you more information.

    Best regards,
    Taisiia Korchak
    Volunteer of the Creative Society Project

  72. Keith Harbaugh says:

    I have a suggestion for two posts in the Azimuth blog.

    How is the energy crisis affecting people personally?
    There are articles in the news media about this,
    but I wonder how readers of this blog have been affected.
    Sanctions have been imposed on Russia,
    and Russia has retaliated in various ways.
    This is not the place to argue who is right and who is wrong on this issue.
    However, there is something objective that I believe can and should be discussed.

    Various changes to energy policies may be implemented.
    While the economic consequences of these alternatives are often emphasized,
    what does not seem to be so emphasized is
    the effect of each alternative on the struggle to limit global warming.

    E.g., people have proposed the use of biomass as a replacement for Russian natural gas.
    What does that mean for CO2 emissions?
    Is the claim
    “the transition from imported gas to local biomass fuel
    has resulted in a cost reduction for consumers
    as well as in a reduction of the emissions of CO2
    in this article

    That is just one example.
    All this is a complex issue, weaving together economics and ecology.
    The issues are too complex to be adequately discussed here.
    But what could be usefully done here is
    the posting of links to good articles and reports that discuss this important topic.

    • Keith Harbaugh says:

      In my original text, each proposed post was numbered, thus
      “1. How is …’ and
      “2. Sanctions…”,
      with a paragraph break between.
      However in the published version the numbers and paragraph break were omitted, at least on my computer, perhaps I confusion.

  73. Karen says:

    Hello, I found your blog site due to my interest in climate change and environmental activism. Thank you for elevating and sharing your ideas.

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