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The 2026 APS Oliver E. Buckley Prize in condensed matter physics was announced this week, and it's a really interesting combination of topics that, to a lay person, may seem to be completely unrelated.  

Fig. 1 from this follow-up PRB.

The key idea here is the role of vortices.  Superfluidity in helium is described by an order parameter that looks like a wavefunction - it has an amplitude, \(\Psi_{0}\), and a phase \(\phi\), so that \(\Psi(\mathbf{r}) = \Psi_{0} \exp(i \phi)\).   That order parameter is supposed to be single-valued, meaning if you go around a closed loop of some kind, that phase will either remain the same or ramp by some integer multiple of \(2\pi\).  The gradient of the phase is related to the velocity of the superfluid, so if the phase winds by \(2\pi\), that implies there is a circulation of flow and orbital angular momentum that has to be an integer multiple of \(\hbar\).  In the BKT theory, the demise of the superfluid phase as the system is warmed happens through the creation and unbinding of vortex-antivortex pairs.

On the other hand, the other recipients of the Buckley Prize were Gwendal Fève and Mike Manfra for their work (experiments here and here) regarding the braiding statistics of anyons in fractional quantum Hall systems.  I'd written about anyons here.  For electrons in 2D, the wavefunctions of excitations of the fractional quantum Hall system look like vortices.  The phase of the electronic wavefunction can wind due to circulation, and because electrons are charged, the phase can also wind due to magnetic flux attached to the little whirlpool.  It's the combination of these phase effects that can lead to those excitations acting like anyons (so that when two are physically swapped or braided around one another, the wavefunction picks up a phase factor that is not just the \(+1\) of bosons or the \(-1\) of fermions).  

As my friend Dan Arovas pointed out, there was a hope back in the early 1980s that perhaps vortices in superfluid helium would also act like anyons and have fractional statistics.  However, this paper by Haldane and Wu disproved that possibility.  

Vortex shedding, from here.

Perhaps it is fitting that I am posting this on the 85th anniversary of the Tacoma Narrows bridge collapse.  That classic civil engineering failure was caused by vortex shedding by the bridge coupling to its torsional resonance frequency.  Vortices can have big consequences!  

Scientists have different goals when they communicate, leading to different styles, or registers, of communication. If you don’t notice what register a scientist is using, you might think they’re saying something they’re not. And if you notice someone using the wrong register for a situation, they may not actually be a scientist.

Sometimes, a scientist is trying to explain an idea to the general public. The point of these explanations is to give you appreciation and intuition for the science, not to understand it in detail. This register makes heavy use of metaphors, and sometimes also slogans. It should almost never be taken literally, and a contradiction between two different scientist explanations usually just means they are using incompatible metaphors for the same concept. Sometimes, scientists who do this a lot will comment on other metaphors you might have heard, referencing other slogans to help explain what those explanations miss. They do this knowing that they do, in the end, agree on the actual science: they’re just trying to give you another metaphor, with a deeper intuition for a neglected part of the story.

Other times, scientists are trying to teach a student to be able to do something. Teaching can use metaphors or slogans as introductions, but quickly moves past them, because it wants to show the students something they can use: an equation, a diagram, a classification. If a scientist shows you any of these equations/diagrams/classifications without explaining what they mean, then you’re not the student they had in mind: they had designed their lesson for someone who already knew those things. Teaching may convey the kinds of appreciation and intuition that explanations for the general public do, but that goal gets much less emphasis. The main goal is for students with the appropriate background to learn to do something new.

Finally, sometimes scientists are trying to advocate for a scientific point. In this register, and only in this register, are they trying to convince people who don’t already trust them. This kind of communication can include metaphors and slogans as decoration, but the bulk will be filled with details, and those details should constitute evidence: they should be a structured argument, one that lays out, scientifically, why others should come to the same conclusion.

A piece that tries to address multiple audiences can move between registers in a clean way. But if the register jumps back and forth, or if the wrong register is being used for a task, that usually means trouble. That trouble can be simple boredom, like a scientist’s typical conference talk that can’t decide whether it just wants other scientists to appreciate the work, whether it wants to teach them enough to actually use it, or whether it needs to convince any skeptics. It can also be more sinister: a lot of crackpots write pieces that are ostensibly aimed at convincing other scientists, but are almost entirely metaphors and slogans, pieces good at tugging on the general public’s intuition without actually giving scientists anything meaningful to engage with.

If you’re writing, or speaking, know what register you need to use to do what you’re trying to do! And if you run into a piece that doesn’t make sense, consider that it might be in a different register than you thought.

Bogdan Georgiev, Javier Gómez-Serrano, Adam Zsolt Wagner, and I have uploaded to the arXiv our paper “Mathematical exploration and discovery at scale“. This is a longer report on the experiments we did in collaboration with Google Deepmind with their AlphaEvolve tool, which is in the process of being made available for broader use. Some of our experiments were already reported on in a previous white paper, but the current paper provides more details, as well as a link to a repository with various relevant data such as the prompts used and the evolution of the tool outputs.

AlphaEvolve is a variant of more traditional optimization tools that are designed to extremize some given score function over a high-dimensional space of possible inputs. A traditional optimization algorithm might evolve one or more trial inputs over time by various methods, such as stochastic gradient descent, that are intended to locate increasingly good solutions while trying to avoid getting stuck at local extrema. By contrast, AlphaEvolve does not evolve the score function inputs directly, but uses an LLM to evolve computer code (often written in a standard language such as Python) which will in turn be run to generate the inputs that one tests the score function on. This reflects the belief that in many cases, the extremizing inputs will not simply be an arbitrary-looking string of numbers, but will often have some structure that can be efficiently described, or at least approximated, by a relatively short piece of code. The tool then works with a population of relatively successful such pieces of code, with the code from one generation of the population being modified and combined by the LLM based on their performance to produce the next generation. The stochastic nature of the LLM can actually work in one’s favor in such an evolutionary environment: many “hallucinations” will simply end up being pruned out of the pool of solutions being evolved due to poor performance, but a small number of such mutations can add enough diversity to the pool that one can break out of local extrema and discover new classes of viable solutions. The LLM can also accept user-supplied “hints” as part of the context of the prompt; in some cases, even just uploading PDFs of relevant literature has led to improved performance by the tool. Since the initial release of AlphaEvolve, similar tools have been developed by others, including OpenEvolve, ShinkaEvolve and DeepEvolve.

We tested this tool on a large number (67) of different mathematics problems (both solved and unsolved) in analysis, combinatorics, and geometry that we gathered from the literature, and reported our outcomes (both positive and negative) in this paper. In many cases, AlphaEvolve achieves similar results to what an expert user of a traditional optimization software tool might accomplish, for instance in finding more efficient schemes for packing geometric shapes, or locating better candidate functions for some calculus of variations problem, than what was previously known in the literature. But one advantage this tool seems to offer over such custom tools is that of scale, particularly when when studying variants of a problem that we had already tested this tool on, as many of the prompts and verification tools used for one problem could be adapted to also attack similar problems; several examples of this will be discussed below. The following graphic illustrates the performance of AlphaEvolve on this body of problems:

Another advantage of AlphaEvolve was robustness adaptability: it was relatively easy to set up AlphaEvolve to work on a broad array of problems, without extensive need to call on domain knowledge of the specific task in order to tune hyperparameters. In some cases, we found that making such hyperparameters part of the data that AlphaEvolve was prompted to output was better than trying to work out their value in advance, although a small amount of such initial theoretical analysis was helpful. For instance, in calculus of variation problems, one is often faced with the need to specify various discretization parameters in order to estimate a continuous integral, which cannot be computed exactly, by a discretized sum (such as a Riemann sum), which can be evaluated by computer to some desired precision. We found that simply asking AlphaEvolve to specify its own discretization parameters worked quite well (provided we designed the score function to be conservative with regards to the possible impact of the discretization error); see for instance this experiment in locating the best constant in functional inequalities such as the Hausdorff-Young inequality.

A third advantage of AlphaEvolve over traditional optimization methods was the interpretability of many of the solutions provided. For instance, in one of our experiments we sought to find an extremum to a functional inequality such as the Gagliardo–Nirenberg inequality (a variant of the Sobolev inequality). This is a relatively well-behaved optimization problem, and many standard methods can be deployed to obtain near-optimizers that are presented in some numerical format, such as a vector of values on some discretized mesh of the domain. However, when we applied AlphaEvolve to this problem, the tool was able to discover the exact solution (in this case, a Talenti function), and create code that sampled from that function on a discretized mesh to provide the required input for the scoring function we provided (which only accepted discretized inputs, due to the need to compute the score numerically). This code could be inspected by humans to gain more insight as to the nature of the optimizer. (Though in some cases, AlphaEvolve’s code would contain some brute force search, or a call to some existing optimization subroutine in one of the libraries it was given access to, instead of any more elegant description of its output.)

For problems that were sufficiently well-known to be in the training data of the LLM, the LLM component of AlphaEvolve often came up almost immediately with optimal (or near-optimal) solutions. For instance, for variational problems where the gaussian was known to be the extremizer, AlphaEvolve would frequently guess a gaussian candidate during one of the early evolutions, and we would have to obfuscate the problem significantly to try to conceal the connection to the literature in order for AlphaEvolve to experiment with other candidates. AlphaEvolve would also propose similar guesses for other problems for which the extremizer was not known. For instance, we tested this tool on the sum-difference exponents of relevance to the arithmetic Kakeya conjecture, which can be formulated as a variational entropy inequality concerning certain two-dimensional discrete random variables. AlphaEvolve initially proposed some candidates for such variables based on discrete gaussians, which actually worked rather well even if they were not the exact extremizer, and already generated some slight improvements to previous lower bounds on such exponents in the literature. Inspired by this, I was later able to rigorously obtain some theoretical results on the asymptotic behavior on such exponents in the regime where the number of slopes was fixed, but the “rational complexity” of the slopes went to infinity; this will be reported on in a separate paper.

Perhaps unsurprisingly, AlphaEvolve was extremely good at locating “exploits” in the verification code we provided, for instance using degenerate solutions or overly forgiving scoring of approximate solutions to come up with proposed inputs that technically achieved a high score under our provided code, but were not in the spirit of the actual problem. For instance, when we asked it (link under construction) to find configurations to extremal geometry problems such as locating polygons with each vertex having four equidistant other vertices, we initially coded the verifier to accept distances that were equal only up to some high numerical precision, at which point AlphaEvolve promptly placed many of the points in virtually the same location so that the distances they determined were indistinguishable. Because of this, a non-trivial amount of human effort needs to go into designing a non-exploitable verifier, for instance by working with exact arithmetic (or interval arithmetic) instead of floating point arithmetic, and taking conservative worst-case bounds in the presence of uncertanties in measurement to determine the score. For instance, in testing AlphaEvolve against the “moving sofa” problem and its variants, we designed a conservative scoring function that only counted those portions of the sofa that we could definitively prove to stay inside the corridor at all times (not merely the discrete set of times provided by AlphaEvolve to describe the sofa trajectory) to prevent it from exploiting “clipping” type artefacts. Once we did so, it performed quite well, for instance rediscovering the optimal “Gerver sofa” for the original sofa problem, and also discovering new sofa designs for other problem variants, such as a 3D sofa problem.

For well-known open conjectures (e.g., Sidorenko’s conjecture, Sendov’s conjecture, Crouzeix’s conjecture, the ovals problem, etc.), AlphaEvolve generally was able to locate the previously known candidates for optimizers (that are conjectured to be optimal), but did not locate any stronger counterexamples: thus, we did not disprove any major open conjecture. Of course, one obvious possible explanation for this is that these conjectures are in fact true; outside of a few situations where there is a matching “dual” optimization problem, AlphaEvolve can only provide one-sided bounds on such problems and so cannot definitively determine if the conjectural optimizers are in fact the true optimizers. Another potential explanation is that AlphaEvolve essentially tried all the “obvious” constructions that previous researchers working on these problems had also privately experimented with, but did not report due to the negative findings. However, I think there is at least value in using these tools to systematically record negative results (roughly speaking, that a search for “obvious” counterexamples to a conjecture did not disprove the claim), which currently only exist as “folklore” results at best. This seems analogous to the role LLM Deep Research tools could play by systematically recording the results (both positive and negative) of automated literature searches, as a supplement to human literature review which usually reports positive results only. Furthermore, when we shifted attention to less well studied variants of famous conjectures, we were able to find some modest new observations. For instance, while AlphaEvolve only found the standard conjectural extremizer to Sendov’s conjecture, as well as for variants such as Borcea’s conjecture, Schmeisser’s conjecture, or Smale’s conjecture it did reveal some potential two-parameter extensions to a conjecture of de Bruin and Sharma that had not previously been stated in the literature. (For this problem, we were not directly optimizing some variational scalar quantity, but rather a two-dimensional range of possible values, which we could adapt the AlphaEvolve framework to treat). In the future, I can imagine such tools being a useful “sanity check” when proposing any new conjecture, in that it will become common practice to run one of these tools against such a conjecture to make sure there are no “obvious” counterexamples (while keeping in mind that this is still far from conclusive evidence in favor of such a conjecture).

AlphaEvolve did not perform equally well across different areas of mathematics. When testing the tool on analytic number theory problems, such as that of designing sieve weights for elementary approximations to the prime number theorem, it struggled to take advantage of the number theoretic structure in the problem, even when given suitable expert hints (although such hints have proven useful for other problems). This could potentially be a prompting issue on our end, or perhaps the landscape of number-theoretic optimization problems is less amenable to this sort of LLM-based evolutionary approach. On the other hand, AlphaEvolve does seem to do well when the constructions have some algebraic structure, such as with the finite field Kakeya and Nikodym set problems, which we will turn to shortly.

For many of our experiments we worked with fixed-dimensional problems, such as trying to optimally pack shapes in a larger shape for a fixed value of . However, we found in some cases that if we asked AlphaEvolve to give code that took parameters such as as input, and tested the output of that code for a suitably sampled set of values of of various sizes, then it could sometimes generalize the constructions it found for small values of this parameter to larger ones; for instance, in the infamous sixth problem of this year’s IMO, it could use this technique to discover the optimal arrangement of tiles, which none of the frontier models could do at the time (although AlphaEvolve has no capability to demonstrate that this arrangement was, in fact, optimal). Another productive use case of this technique was for finding finite field Kakeya and Nikodym sets of small size in low-dimensional vector spaces over finite fields of various sizes. For Kakeya sets in , it located the known optimal construction based on quadratic residues in two dimensions, and very slightly beat (by an error term of size ) the best construction in three dimensions; this was an algebraic construction (still involving quadratic residues) discovered empirically that we could then prove to be correct by first using Gemini’s “Deep Think” tool to locate an informal proof, which we could then convert into a formalized Lean proof by using Google Deepmind’s “AlphaProof” tool. At one point we thought it had found a construction in four dimensions which achieved a more noticeable improvement (of order ) of what we thought was the best known construction, but we subsequently discovered that essentially the same construction had appeared already in a paper of Bukh and Chao, although it still led to a more precise calculation of the error term (to accuracy rather than , where the error term now involves the Lang-Weil inequality and is unlikely to have a closed form). Perhaps AlphaEvolve had somehow absorbed the Bukh-Chao construction within its training data to accomplish this. However, when we tested the tool on Nikodym sets (which are expected to have asymptotic density , although this remains unproven), it did find some genuinely new constructions of such sets in three dimensions, based on removing quadratic varieties from the entire space. After using “Deep Think” again to analyze these constructions, we found that they were inferior to a purely random construction (which in retrospect was an obvious thing to try); however, they did inspire a hybrid construction in which one removed random quadratic varieties and performed some additional cleanup, which ends up outperforming both the purely algebraic and purely random constructions. This result (with completely human-generated proofs) will appear in a subsequent paper.

Update (Nov. 6): I’ve closed the comments, as they crossed the threshold from “sometimes worthwhile” to “purely abusive.” As for Mamdani’s victory: as I like to say in such cases (and said, e.g., after George W. Bush’s and Trump’s victories), the silver lining to which I cling is that either I’ll be pleasantly surprised, and things won’t be quite as terrible as I expect, or else I’ll be vindicated.

This Halloween, I didn’t need anything special to frighten me. I walked all day around in a haze of fear and depression, unable to concentrate on my research or anything else. I saw people smiling, dressed up in costumes, and I thought: how?

The president of the Heritage Foundation, the most important right-wing think tank in the United States, has now explicitly aligned himself with Tucker Carlson, even as the latter has become a full-on Holocaust-denying Hitler-loving antisemite, who nods in agreement with the openly neo-Nazi Nick Fuentes. Meanwhile, Vice President J.D. Vance—i.e., plausibly the next President of the United States—pointedly did nothing whatsoever to distance himself from the MAGA movement’s lunatic antisemites, in response to their lunatic antisemitic questions at the Turning Point USA conference. (Vance thus dishonored the memory of Charlie Kirk, who for all my many disagreements with him, was a firmly committed Zionist.) It’s become undeniable that, once Trump himself leaves the stage, this is the future of MAGA, and hence of the Republican Party itself. Exactly as I warned would happen a decade ago, this is what’s crawled out from underneath the rock that Trump gleefully overturned.

While the Republican Party is being swallowed by a movement that holds that Jews like me have no place in America, the Democratic Party is being swallowed by a movement that holds that Jews have no place in Israel. If these two movements ever merged, the obvious “compromise” would be the belief, popular throughout history, that Jews have no place anywhere on earth.

Barring a miracle, New York City—home to the world’s second-largest Jewish community—is about to be led by a man for whom eradicating the Jewish state is his deepest, most fundamental moral imperative, besides of course the proletariat seizing the means of production. And to their eternal shame, something like 29% of New York’s Jews are actually going to vote for this man, believing that their own collaboration with evil will somehow protect them personally—in breathtaking ignorance of the millennia of Jewish history testifying to the opposite.

Despite what you might think, I try really, really hard not to hyperventilate or overreact. I know that, even if I lived in literal Warsaw in 1939, it would still be incumbent on me to assess the situation calmly and figure out the best response.

So for whatever it’s worth: no, I don’t expect that American Jews, even pro-Zionist Jews in New York City, will need to flee their homes just yet. But it does seem to me that they (to say nothing of British and Canadian and French Jews) might, so to speak, want to keep their suitcases packed by the door, as Jews have through the centuries in analogous situations. As Tevye says near the end of Fiddler on the Roof, when the Jews are given three days to evacuate Anatevka: “maybe this is why we always keep our hats on.” Diaspora Jews like me might also want to brush up on Hebrew. We can thank Hashem or the Born Rule that, this time around, at least the State of Israel exists (despite the bloodthirsty wish of half the world that it cease to exist), and we can reflect that these contingencies are precisely why Israel was created.

Let me make something clear: I don’t focus so much on antisemitism only because of parochial concern for the survival of my own kids, although I freely admit to having as much such concern as the next person. Instead, I do so because I hold with David Deutsch that, in Western civilization, antisemitism has for millennia been the inevitable endpoint toward which every bad idea ultimately tends. It’s the universal bad idea. It’s bad-idea-complete. Antisemitism is the purest possible expression of the worldview of the pitchfork-wielding peasant, who blames shadowy elites for his own failures in life, and who dreams in his resentment and rage of reversing the moral and scientific progress of humanity by slaughtering all those responsible for it. Hatred of high-achieving Chinese and Indian immigrants, and of gifted programs and standardized testing, are other expressions of the same worldview.

As far as I know, in 3,000 years, there hasn’t been a single example—not one—of an antisemitic regime of which one could honestly say: “fine, but once you look past what they did to the Jews, they were great for everyone else!” Philosemitism is no guarantee of general goodness (as we see for example with Trump), but antisemitism pretty much does guarantee general awfulness. That’s because antisemitism is not merely a hatred, but an entire false theory of how the world works—not just a but the conspiracy theory—and as such, it necessarily prevents its believers from figuring out true explanations for society’s problems.

I’d better end a post like this on a note of optimism. Yes, every single time I check my phone, I’m assaulted with twenty fresh examples of once-respected people and institutions, all across the political spectrum, who’ve now fallen to the brain virus, and started blaming all the world’s problems on “bloodsucking globalists” or George Soros or Jeffrey Epstein or AIPAC or some other suspicious stand-in du jour. (The deepest cuts come from the new Jew-haters who I myself once knew, or admired, or had some friendly correspondence with.)

But also, every time I venture out into the real world, I meet twenty people of all backgrounds whose brains still seem perfectly healthy, and who respond to events in a normal human way. Even in the dark world behind the screen, I can find dozens of righteous condemnations of Zohran Mamdani and Tucker Carlson and the Heritage Foundation and the others who’ve chosen to play footsie with those seeking a new Final Solution to the Jewish Question. So I reflect that, for all the battering it’s taken in this age of TikTok and idiocracy—even then, our Enlightenment civilization still has a few antibodies that are able to put up a fight.

In their beautiful book Abundance, Ezra Klein and Derek Thompson set out an ambitious agenda by which the Democratic Party could reinvent itself and defeat MAGA, not by indulging conspiracy theories but by creating actual broad prosperity. Their agenda is full of items like: legalizing the construction of more housing where people actually want to live; repealing the laws that let random busybodies block the construction of mass transit; building out renewable energy and nuclear; investing in science and technology … basically, doing all the things that anyone with any ounce of economic literacy knows to be good. The abundance agenda isn’t only righteous and smart: for all I know, it might even turn out to be popular. It’s clearly worth a try.

Last week I was amused to see Kate Willett and Briahna Joy Gray, two of the loudest voices of the conspiratorial far left, denounce the abundance agenda as … wait for it … a cover for Zionism. As far as they’re concerned, the only reason why anyone would talk about affordable housing or high-speed rail is to distract the masses from the evil Zionists murdering Palestinian babies in order to harvest their organs.

The more I thought about this, the more I realized that Willett and Gray actually have a point. Yes, solving America’s problems with reason and hard work and creativity, like the abundance agenda says to do, is the diametric opposite of blaming all the problems on the perfidy of Jews or some other scapegoat. The two approaches really are the logical endpoints of two directly competing visions of reality.

Naturally I have a preference between those visions. So I’ve been on a bit of a spending spree lately, in support of sane, moderate, pro-abundance, anti-MAGA, liberal Enlightenment forces retaking America. I donated $1000 to Alex Bores, who’s running for Congress in NYC, and who besides being a moderate Democrat who favors all the usual good things, is also a leader in AI safety legislation. (For more, see this by Eric Neyman of Alignment Research Center, or this from Scott Alexander himself—the AI alignment community has been pretty wowed.) I also donated $1000 to Scott Wiener, who’s running for Nancy Pelosi’s seat in California, has a nuanced pro-two-states, anti-Netanyahu position that causes him to get heckled as a genocidal Zionist, and authored the excellent SB1047 AI safety bill, which Gavin Newsom unfortunately vetoed for short-term political reasons. And I donated $1000 to Vikki Goodwin, a sane Democrat who’s running to unseat Lieutenant Governor Dan Patrick in my own state of Texas. Any other American office-seeker who resonates with this post, and who’d like a donation, can feel free to contact me as well.

My bag is packed … but for now, only for a brief trip to give the physics colloquium at Harvard, after which I’ll return back home to Austin. Until it becomes impossible, I call on my thousands of thoughtful, empathetic American readers to stay right where you are, and simply do your best to fight the brain-eaten zombies of both left and right. If you are one of the zombies, of course, then my calling you one doesn’t even begin to express my contempt: may you be remembered by history alongside the willing dupes of Hitler, Stalin, and Mao. May the good guys prevail.

Oh, and speaking of zombies, Happy Halloween everyone! Boooooooo!

A month ago William Inboden, the provost of UT Austin (where I work), invited me to join a university-wide “Faculty Working Group on Academic Integrity.” The name made me think that it would be about students cheating on exams and the like. I didn’t relish the prospect but I said sure.

Shortly afterward, Jim Davis, the president of UT Austin, sent out an email listing me among 21 faculty who had agreed to serve on an important working group to decide UT Austin’s position on academic free speech and the responsibilities of professors in the classroom (!). Immediately I started getting emails from my colleagues, thanking me for my “service” and sharing their thoughts about what this panel needed to say in response to the Trump administration’s Compact on Higher Education. For context: the Compact would involve universities agreeing to do all sorts of things that the Trump administration wants—capping international student enrollment, “institutional neutrality,” freezing tuition, etc. etc.—in exchange for preferential funding. UT Austin was one of nine universities originally invited to join the Compact, along with MIT, Penn, Brown, Dartmouth, and more, and is the only one that hasn’t yet rejected it. It hasn’t accepted it either.

Formally, it was explained to me, UT’s Working Group on Academic Integrity had nothing to do with Trump’s Compact, and no mandate to either accept or reject it. But it quickly became obvious to me that my faculty colleagues would see everything we did exclusively in light of the Compact, and of other efforts by the Trump administration and the State of Texas to impose conservative values on universities. While not addressing current events directly, what we could do would be to take a strong stand for academic freedom, and more generally, for the role of intellectually independent universities in a free society.

So, led by Provost Inboden, over two meetings and a bunch of emails we hashed out a document. You can now read the Texas Statement on Academic Integrity, and I’d encourage you to do so. The document takes a pretty strong swing for academic freedom:

Academic freedom lies at the core of the academic enterprise.  It is foundational to the excellence of the American higher education system, and is non-negotiable. In the words of the U.S. Supreme Court, academic freedom is “a special concern of the First Amendment.” The world’s finest universities are in free societies, and free societies honor academic freedom.

The statement also reaffirms UT Austin’s previous commitments to the Chicago Principles of Free Expression, and the 1940 and 1967 academic freedom statements of the American Association of University Professors.

Without revealing too much about my role in the deliberations, I’ll say that I was especially pleased by the inclusion of the word “non-negotiable.” I thought that that word might acquire particular importance, and this was confirmed by the headline in yesterday’s Chronicle of Higher Education: As Trump’s Compact Looms, UT-Austin Affirms ‘Non-Negotiable’ Commitment to Academic Freedom (warning: paywall).

At the same time, the document also talks about the responsibility of a public university to maintain the trust of society, and about the responsibilities of professors in the classroom:

Academic integrity obligates the instructor to protect every student’s academic freedom and right to learn in an environment of open inquiry. This includes the responsibilities:

• to foster classroom cultures of trust in which all students feel free to voice their questions and beliefs, especially when those perspectives might conflict with those of the instructor or other students;
• to fairly present differing views and scholarly evidence on reasonably disputed matters and unsettled issues;
• to equip students to assess competing theories and claims, and to use reason and appropriate evidence to form their own conclusions about course material; and
• to eschew topics and controversies that are not germane to the course.

All stuff that I’ve instinctively followed, in nearly 20 years of classroom teaching, without the need for any statement telling me to. Whatever opinions I might get goaded into expressing on this blog about Trump, feminism, or Israel/Palestine, I’ve always regarded the classroom as a sacred space. (I have hosted a few fierce classroom debates about the interpretation of quantum mechanics, but even there, I try not to tip my own hand!)

I’m sure that there are commenters, on both ends of the political spectrum, who will condemn me for my participation in the faculty working group, and for putting my name on the statement. At this point in this blog’s history, commenters on both ends of the political spectrum would condemn me for saying that freshly baked chocolate chip cookies are delicious. But I like the statement, and find nothing in it that any reasonable person should disagree with. Overall, my participation in this process increased my confidence that UT Austin will be able to navigate this contentious time for the state, country, and world while maintaining its fundamental values. It made me proud to be a professor here.

Here’s a draft of my next column for the Notices of the American Mathematical Society. It’s about the inverse cube force law in classical mechanics.

Newton’s Principia is famous for his investigations of the inverse square force law for gravity. But in this book Newton also did something that was rarely discussed until the 1990s. He figured out what kind of central force exerted upon a particle can rescale its angular velocity by a constant factor without affecting its radial motion. This turns out to be a force obeying an inverse cube law.

Given a particle in Euclidean space, a central force is a force that points toward or away from the origin and depends only on the particle’s distance from the origin. If the particle’s position at time is $\mathbf{r}(t) \in \mathbb{R}^n$ and its mass is some number $m \gt 0,$ we have

$$m \, \ddot{\mathbf{r}}(t) = F(r(t)) \,\hat{\mathbf{r}}(t)$$

where $\hat{\mathbf{r}}(t)$ is a unit vector pointing outward from the origin at the point $\mathbf{r}(t).$ A particle obeying this equation always moves in a plane through the origin, so we can use polar coordinates and write the particle’s position as $(r(t), \theta(t).$ With some calculation one can show the particle’s distance from the origin, $r(t),$ obeys

$$m \ddot r(t) = F(r(t)) + \frac{L^2}{m r(t)^3 } \qquad \qquad (1)$$

Here $L = m r(t)^2 \dot \theta(t)$, the particle’s angular momentum, is constant in time. The second term in the equation above says that the particle’s distance from the origin changes as if there were an additional force pushing it outward. This is a “fictitious force”, an artifact of working in polar coordinates. It is called the centrifugal force. And it obeys an inverse cube force law!

This explains Newton’s observation. Let us see why. Suppose we have two particles moving in two different central forces $F_1$ and $F_2,$ each obeying a version of equation (1), with the same mass $m$ and the same radial motion $r(t),$ but different angular momenta $L_1$ and $L_2.$ Then we must have

$$F_1(r(t)) + \frac{L_1^2}{m r (t)^3} = F_2(r(t)) + \frac{L_2^2}{m r(t)^3}$$

If the particle’s angular velocities are proportional we must have $L_2 = k L_1$ for some constant $k,$ so

$$F_2(r_1(t)) - F_1(r(t)) = \frac{(k - 1)L_1}{m r (t)^3}$$

This says that $F_2$ equals $F_1$ plus an additional inverse cube force.

There are other interesting things about the inverse cube force law. Newtonian gravity is an attractive inverse square force, say $F(r) = -c/r^2$ with $c \gt 0,$ so in this case we have

$$m \ddot r(t) = -c/r(t)^2 + \frac{L^2}{m r(t)^3 }$$

Because $1/r^3$ grows faster than $1/r^2$ as $r \downarrow 0,$ as long as the angular momentum $L$ is nonzero the repulsion of the centrifugal force will beat the attraction of gravity for sufficiently small $r,$ and the particle will not fall in to the origin. The same is true for any attractive force $F(r) = -c/r^p$ with $p \lt 3.$ But an attractive inverse cube force can overcome the centrifugal force and make a particle fall in to the origin.

In fact there are three qualitatively different possibilities for the motion of a particle in an attractive inverse cube force $F(r) = -c/r^3,$ depending on the value of $c$. With work we can solve for $1/r$ as a function of $\theta$ (which is easier than solving for $r$). There are three cases depending on the value of

$$\omega^2 = 1 - \frac{c m}{L^2}$$

They are vaguely analogous to the elliptical, parabolic and hyperbolic orbits of a particle in an inverse square force law:

$$\frac{1}{r(\theta)} = \left\{ \begin{array}{lcl} A \cos(\omega \theta) + B \sin(\omega \theta) & \text{if} & \omega^2 \gt 0 \\ \\ A + B \theta & \text{if} & \omega = 0 \\ \\ A e^{\omega \theta} + B e^{-\omega \theta} & \text{if} & \omega^2 \lt 0 \end{array} \right.$$

The third case occurs when the attractive inverse cube force is strong enough to overcome the centrifugal force: $c \gt L^2/m.$ Then the particle can spiral in to its doom, hitting the origin in a finite amount of time after infinitely many orbits, like this:

All three curves in the equation above are called Cotes spirals, after Roger Cotes’ work on the inverse cube force law, published posthumously in 1722. Cotes seems to have been the first to compute the derivative of the sine function. After Cotes’ death at the age of 33, Newton supposedly said “If he had lived we would have known something.”

The subtlety of the inverse cube force law is vastly heightened when we study it using quantum rather than classical mechanics. Here if $c$ is too large the theory is ill-defined, because there is no reasonable choice of self-adjoint Hamiltonian. If $c$ is smaller the theory is well-behaved. But at a certain borderline point it exhibits a remarkable property: spontaneous breaking of scaling symmetry. I hope to discuss this in my next column.

For more on the inverse cube force law, see:

• N. Grossman, The Sheer Joy of Celestial Mechanics, Birkhäuser, Basel, 1996, p. 34.

For more on Newton’s work involving the inverse cube force law, see:

• Wikipedia, Newton’s theorem of revolving orbits.

• S. Chandrasekhar, Newton’s Principia for the Common Reader, Oxford U. Press, Oxford, 1995, pp. 183–200.

Cotes’ book is

• Roger Cotes, Harmonia Mensuarum, Cambridge, 1722.

In ordinary quantum mechanics, in the special case where observables are described as self-adjoint $n \times n$ complex matrices, we can describe time evolution of an observable $O(t)$ using Heisenberg’s equation

$$\frac{d}{d t} O(t) = -i [H, O(t)]$$

where $H$ is a fixed self-adjoint matrix called the Hamiltonian. This framework is great when we want to focus on observables rather than states. But Heisenberg’s equation doesn’t make sense in a general Jordan algebra. In this stripped-down framework, all we can do is raise observables to powers and take real linear combinations of them. This lets us define a ‘Jordan product’ of observables:

$$A \circ B = \frac{1}{2} ((A + B)^2 - A^2 - B^2) = \frac{1}{2} (A B + B A)$$

but not commutators and not multiplication by $i$. What do we do then?

I wrote a long paper about this:

• Getting to the bottom of Noether’s theorem.

My starting-point was that self-adjoint complex matrices form not only a Jordan algebra with product

$$A \circ B = \frac{1}{2} (A B + B A)$$

but also a Lie algebra with bracket

$$-i [A, B] = -i(A B - B A)$$

See, the commutator of two self-adjoint matrices is skew-adjoint, but we can multiply it by $i$, or more conventionally $-i$, to get something self-adjoint. That’s what is going on in Heisenberg’s equation. But this trick doesn’t work for other Jordan algebras, at least not automatically—so there was a lot to say.

I just bumped into a nice paper on this issue that I hadn’t seen before:

• Paul Townsend, The Jordan formulation of quantum mechanics: a review.

The idea here is pretty wild: you can replace the commutator in Heisenberg’s equation by an associator:

$$(A, B, C) = (A \circ B) \circ C - A \circ (B \circ C)$$

This is well-defined whenever our observables are elements in a Jordan algebra. Jordan algebras are always commutative, but rarely associative!

Here’s the trick. Let $\mathfrak{h}_n(\mathbb{C})$ be the Jordan algebra of self-adjoint $n \times n$ complex matrices, and let’s start with Heisenberg’s equation

$$\frac{d}{d t} O(t) = -i [H, O(t)]$$

where $H \in \mathfrak{h}_n(\mathbb{C})$. Suppose we can write

$$H = -4i [X, Y]$$

for some $X, Y \in \mathfrak{h}_n(\mathbb{C})$. In this case we can use a really cool identity to express the commutator in Heisenberg’s equation in terms of an associator:

$$[[X, Y], A] = -\frac{1}{4}(X, A, Y)$$

This holds in any associative algebra if you define $[X,Y] = X Y - Y X$, $X \circ Y = \tfrac{1}{2} (X Y + Y X)$ and $(X, A, Y) =$ $(X \circ A) \circ Y - X \circ (A \circ Y)$. It’s easy to check: just expand out both sides and compare them!

Using this identity, we get

$$\frac{d}{d t} O(t) = (X, O(t), Y)$$

Now we’re describing dynamics using only operations that are available in any Jordan algebra!

This raises the question of when a self-adjoint complex matrix $H$ can be written as $-4i [X, Y]$ for self-adjoint matrices $X, Y$. This is true whenever $H$ is traceless, since $\mathfrak{su}(n)$ is a compact simple real Lie algebra, and every element of such a Lie algebra is a commutator (as shown by Akhieser).

But any self-adjoint complex matrix $H$ is of the form $H' + \lambda I$ where $H'$ is traceless, so writing $H' = -4i[X,Y]$ we have

$$[H, O(t)] = [H' + \lambda I, O(t)] = [H', O(t)]$$ $$= -4i [[X,Y], O(t)] = i (X, O(t), Y)$$

so we can rewrite Heisenberg’s equation as

$$\frac{d}{d t} O(t) = (X, O(t), Y)$$

Moreover, in any Jordan algebra, any pair of elements $X, Y$ determines a derivation $(X, \cdot, Y)$: see Section I.7 of Jacobson’s Structure and Representations of Jordan Algebras. In the finite-dimensional case there is no difficulty with exponentiating any derivation to obtain a one-parameter group of automorphisms. Thus, for any elements $X, Y$ of a finite-dimensional Jordan algebra, the solution of the above equation always determines a one-parameter group of Jordan algebra automorphisms! And this is just what we’d want for describing how observables change with time.

The are two obvious next questions: one mathematical and one more philosophical.

First, how many one-parameter groups of Jordan algebra automorphisms do we actually get out of solutions to

$$\frac{d}{d t} O(t) = (X, O(t), Y)$$

In the case of $\mathfrak{h}_n(\mathbb{C})$, we get them all, since it’s already known that we get them all from Heisenberg’s equation

$$\frac{d}{d t} O(t) = - i [H , O(t)]$$

What about $\mathfrak{h}_n(\mathbb{R})$ and $\mathfrak{h}_n(\mathbb{H})$? I’m actually more interested in the exceptional Jordan algebra $\mathfrak{h}_3(\mathbb{O})$, and here it seems we get them all! This was shown in a paper that’s fairly hard to find even though it’s available for free online:

• Piero Truini and Lawrence Christian Biedenharn, A comment on the dynamics of $M_3^8$, Hadronic Journal 4 (no. 3) (1980/81), 995–1017.

It starts on page 214 of the PDF file.

(The editor of this journal has some crazy ideas, which has put off some people I’m talking to about this paper. But you can’t judge a paper by the journal it appeared in. Truini and Biedenharn are good — in fact Biedenharn is famous for helping discover an identity, the Biedenharn–Elliott identity, that amounts to the pentagon identity for the category of representations of $\text{SU}(2)$! And the paper looks fine, as far as I can tell.)

Second, the more philosophical question: what does it mean to describe dynamics using not one observable, the Hamiltonian, but two? Perhaps the best way to tackle this is to try doing it, and seeing how it works. Note that this method is not just good for dynamics, but for any Lie group of symmetries.

The poet Blake wrote that you can see a world in a grain of sand. But even better, you can see a universe in an atom!

Bound states of hydrogen atom correspond to states of a massless quantum particle moving at the speed of light around the Einstein universe — a closed, static universe where space is a 3-sphere. We need to use a spin-½ particle to account for the spin of the electron. The states of the massless spin-½ particle where it forms a standing wave then correspond to the orbitals of the hydrogen atom. This explains the secret 4-dimensional rotation symmetry of the hydrogen atom.

In fact, you can develop this idea to the point of getting the periodic table of elements from a quantum field theory on the Einstein universe! I worked that out here:

• Second quantization for the Kepler problem.

but you can see a more gentle explanation in the following series of blog articles.

• Part 1: a quick overview of Kepler’s work on atoms and the solar system, and more modern developments.

• Part 2: why the eccentricity vector is conserved for a particle in an inverse square force, and what it means.

• Part 3: why the momentum of a particle in an inverse square force moves around in a circle.

• Part 4: why the 4d rotation group $\text{SO}(4)$ acts on bound states of a particle in an attractive inverse square force.

• Part 5: quantizing the bound states of a particle in an attractive inverse square force, and getting the Hilbert space $L^2(S^3)$ for bound states of a hydrogen atom, neglecting the electron’s spin.

• Part 6: how the Duflo isomorphism explains quantum corrections to the hydrogen atom Hamiltonian.

• Part 7: why the Hilbert space of bound states for a hydrogen atom including the electron’s spin is $L^2(S^3) \otimes \mathbb{C}^2.$

• Part 8: why $L^2(S^3) \otimes \mathbb{C}^2$ is also the Hilbert space for a massless spin-1/2 particle in the Einstein universe.

• Part 9: a quaternionic description of the hydrogen atom’s bound states (a digression not needed for later parts).

• Part 10: changing the complex structure on $L^2(S^3) \otimes \mathbb{C}^2$ to eliminate negative-energy states of the massless spin-1/2 particle, as often done.

• Part 11: second quantizing the massless spin-1/2 particle and getting a quantum field theory on the Einstein universe, or alternatively a theory of collections of electrons orbiting a nucleus.

• Part 12: obtaining the periodic table of elements from a quantum field theory on the Einstein universe.

I explain how the Hamiltonian of this quantum field theory has to be tweaked a bit to give the ‘Madelung rules’ for the order in which electrons get added as we go along the periodic table:

This continues to be a very busy time, but I wanted to point out two preprints that caught my eye this week.  Their subjects are completely disparate, but they stand out as essentially reviews written in a much more conversational tone than the usual literature.

The first is this preprint about chirality-induced spin selectivity, a subject that I've mentioned before on this blog.  There is now an extensive body of evidence (of varying quality) that there is a connection between structural chirality of molecules and their interactions with the spin angular momentum of electrons.  This includes monolayers of chiral molecules leading to net spin polarization of photoemitted electrons (here), a lot of electronic transport experiments involving chiral molecules and magnetic electrodes that seem to show spin-dependent transmission that is absent with achiral molecules, and even a chirality dependence of molecular adsorption kinetics on magnetic surfaces (here).  The preprint is a provocative discussion of the topic and possible mechanisms, and the importance of precision in the description of the various phenomena.

On a completely different topic, this preprint is a fun discussion about quantum gravity (!) and how condensed matter ideas of "the vacuum" can lead to insights about how quantum mechanics and gravity might need to play together.  One fun bit early on is a discussion of something I like to point out to my undergrad stat mech students:  A single hydrogen atom in a very very large box will apparently (if the usual stat mech formalism of partition functions is valid) be spontaneously ionized, even when the box (which presumably functions as a reservoir at temperature \(T\)) and atom are at temperatures faaaaaar below the energy scale for ionization.  This is discussed nicely in this 1966 article in the Journal of Chemical Education.  Anyway, I thought this was an interesting discussion from three condensed matter theorists.

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Happy Halloween! I’ve got a yearly tradition on this blog of talking about the spooky side of physics. This year, we’ll think about what happens…when you turn off the lights.

Over history, astronomy has given us larger and larger views of the universe. We started out thinking the planets, Sun, and Moon were human-like, just a short distance away. Measuring distances, we started to understand the size of the Earth, then the Sun, then realized how much farther still the stars were from us. Gradually, we came to understand that some of the stars were much farther away than others. Thinkers like Immanuel Kant speculated that “nebulae” were clouds of stars like our own Milky Way, and in the early 20th century better distance measurements confirmed it, showing that Andromeda was not a nearby cloud, but an entirely different galaxy. By the 1960’s, scientists had observed the universe’s cosmic microwave background, seeing as far out as it was possible to see.

But what if we stopped halfway?

Since the 1920’s, we’ve known the universe is expanding. Since the 1990’s, we’ve thought that that expansion is speeding up: faraway galaxies are getting farther and farther away from us. Space itself is expanding, carrying the galaxies apart…faster than light.

That ever-increasing speed has a consequence. It means that, eventually, each galaxy will fly beyond our view. One by one, the other galaxies will disappear, so far away that light will not have had enough time to reach us.

From our perspective, it will be as if the lights, one by one, started to turn out. Each faraway light, each cloudy blur that hides a whirl of worlds, will wink out. The sky will get darker and darker, until to an astronomer from a distant future, the universe will appear a strangely limited place:

A single whirl of stars, in a deep, dark, void.

At this point it's old hat to decry the problems facing traditional news media.  Still, it is abundantly clear in our late stage capitalist society that there has been a collective business decision over the last 20+ years that, like local newspapers and television news, real science journalism is not a money maker.   Just a few examples:  Seventeen years ago, CNN cut its entire science, technology and environment reporting team.  In 2022, Popular Science ceased publication.  In 2023, National Geographic laid off their staff writers.  Last week, the Wall Street Journal laid off their science and health reporters.  

I have it on good authority that there is now only one science reporter left at the WSJ.  One, at a time when science and technology are more critically important to our rapidly changing society than ever, and there is enormous tumult in the US and elsewhere about how science is or is not supported and is or is not factoring into policy decisions.  All of this is happening at a time when public trust in science is falling.  (Check out this from Science Friday.)  

(updated for context) Leaving aside professional science outlets (the news sections of Science, Nature, and society publications like Physics Today, C&EN, Physics World, Chemistry World), there are some good publications out there, like Quanta and Nautilus (both founded by nonprofits). There are outstanding public writers of science, like Philip Ball, Helen Czerski, Katie Mack, Ethan Siegel, and many others (apologies for the incompleteness of this list).  There are some excellent freelance journalists.  The internet also means that there are many opportunities for great engagement.  For example, the videos from 3blue1brown are uniformly outstanding.  However, there are no filters, and the temptation to be click-baity or sensationalistic is problematic.  

I have no solutions to offer, except that I encourage you to support good science journalism and reporting when you see it.  It's important.

The next annual conference on applied category theory is in Estonia!

• Applied Category Theory 2026, Tallinn, Estonia, 6–10 July, 2026. Preceded by the Adjoint School Research Week, 29 June – 3 July.

For more details, read on!

The conference particularly encourages participation from underrepresented groups. The organizers are committed to non-discrimination, equity, and inclusion. The code of conduct for the conference is available here.

Deadlines

• Registration: TBA
• Abstracts Due: 23 March 2026
• Full Papers Due: 30 March 2026
• Author Notification: 11 May 2026
• Adjoint School: 29 June – 3 July 2026
• Conference: 6 – 10 July 2026
• Final versions of papers for proceedings due: TBA

Submissions

ACT2026 accepts submissions in English, in the following three tracks:

1. Research

2. Software demonstrations

3. Teaching and communication

The detailed Call for Papers is available here.

Extended abstracts and conference papers should be prepared with LaTeX. For conference papers please use the EPTCS style files available here. The submission link is here.

Reviewing is single-blind, and we are not making public the reviews, reviewer names, the discussions nor the list of under-review submissions. This is the same as previous instances of ACT.

Program Committee Chairs

• Geoffrey Cruttwell, Mount Allison University, Sackville
• Priyaa Varshinee Srinivasan, Tallinn University of Technology, Estonia

Program Committee

• Alexis Toumi, Planting Space
• Bryce Clarke, Tallinn University of Technology
• Barbara König, University of Duisburg-Essen
• Bojana Femic, Serbian Academy of Sciences and Arts
• Chris Heunen, The University of Edinburgh
• Daniel Cicala, Southern Connecticut State University
• Dusko Pavlovic, University of Hawaii
• Evan Patterson, Topos Institute
• Fosco Loregian, Tallinn University of Technology
• Gabriele Lobbia, Università di Bologna
• Georgios Bakirtzis, Institut Polytechnique de Paris
• Jade Master, University of Strathclyde
• James Fairbanks, University of Florida
• Jonathan Gallagher, Hummingbird Biosciences
• Joe Moeller, Caltech
• Jules Hedges, University of Strathclyde
• Julie Bergner, University of Virginia
• Kohei Kishida, University of Illinois, Urbana-Champaign
• Maria Manuel Clementino, CMUC, Universidade de Coimbra
• Mario Román, University of Oxford
• Marti Karvonen, University College London
• Martina Rovelli, UMass Amherst
• Masahito Hasegawa, Kyoto University
• Matteo Capucci, University of Strathclyde
• Michael Shulman, University of San Diego
• Nick Gurski, Case Western Reserve University
• Niels Voorneveld, Cybernetica
• Paolo Perrone, University of Oxford
• Peter Selinger, Dalhousie University
• Paul Wilson, University of Southampton
• Robin Cockett, University of Calgary
• Robin Piedeleu, University College London
• Rory Lucyshyn-Wright, Brandon University
• Rose Kudzman-Blais, University of Ottawa
• Ryan Wisnesky, Conexus AI
• Sam Staton, University of Oxford
• Shin-Ya Katsumata, Kyoto Sangyo University
• Simon Willerton, University of Sheffield
• Spencer Breiner, National Institute of Standards and Technology
• Tai Danae Bradley, SandboxAQ
• Titouan Carette, École Polytechnique
• Tom Leinster, The University of Edinburgh
• Walter Tholen, York University

Teaching & Communication

• Selma Dündar-Coecke, University College London, Institute of Education
• Ted Theodosopoulos, Nueva School

Organizing Committee

• Pawel Sobocinski, Tallinn University of Technology
• Priyaa Varshinee Srinivasan, Tallinn University of Technology
• Sofiya Taskova, Tallinn University of Technology
• Kristi Ainen, Tallinn University of Technology

Steering Committee

• John Baez, University of California, Riverside
• Bob Coecke, University of Oxford
• Dorette Pronk, Dalhousie University
• David Spivak, Topos Institute
• Michael Johnson, Macquarie University
• Simona Paoli, University of Aberdeen

This October, fantasy readers are devouring a sequel: the final installment in Philip Pullman’s trilogy The Book of Dust. The series follows student Lyra Silvertongue as she journeys from Oxford to the far east. Her story features alternate worlds, souls that materialize as talking animals, and a whiff of steampunk. We first met Lyra in the His Dark Materials trilogy, which Pullman began publishing in 1995. So some readers have been awaiting the final Book of Dust volume for 30 years. 

Another sequel debuts this fall. It won’t spur tens of thousands of sales; nor will Michael Sheen narrate an audiobook version of it. Nevertheless, the sequel should provoke as much thought as Pullman’s: the sequel to the Maryland Quantum-Thermodynamics Hub’s first three years.

The Maryland Quantum-Thermodynamics Hub debuted in 2022, courtesy of a grant from the John F. Templeton Foundation. Six theorists, three based in Maryland, have formed the hub’s core. Our mission has included three prongs: research, community building, and outreach. During the preceding decade, quantum thermodynamics had exploded, but mostly outside North America. We aimed to provide a lodestone for the continent’s quantum-thermodynamics researchers and visitors.

Also, we aimed to identify the thermodynamics of how everyday, classical physics emerges from quantum physics. Quantum physics is reversible (doesn’t distinguish the past from the future), is delicate (measuring a quantum system can disturb it), and features counterintuitive phenomena such as entanglement. In contrast, our everyday experiences include irreversibility (time has an arrow), objectivity (if you and I read this article, we should agree about its contents), and no entanglement. How does quantum physics give rise to classical physics at large energy and length scales? Thermodynamics has traditionally described macroscopic, emergent properties. So quantum thermodynamics should inform our understanding of classical reality’s emergence from quantum mechanics.

Our team has approached this opportunity from three perspectives. One perspective centers on quantum Darwinism, a framework for quantifying how interactions spread information about an observed quantum system. Another perspective highlights decoherence, the contamination of a quantum system by its environment. The third perspective features incompatible exchanged quantities, described in an earlier blog post. Or two. Or at least seven. 

Each perspective led us to discover a tension, or apparent contradiction, that needs resolving. One might complain that we failed to clinch a quantum-thermodynamic theory of the emergence of classical reality. But physicists adore apparent contradictions as publishers love splashing “New York Times bestseller” on their book covers. So we aim to resolve the tensions over the next three years.

I’ll illustrate the tensions with incompatible exchanged quantities, of course. Physicists often imagine a small system, such as a quantum computer, interacting with a large environment, such as the surrounding air and the table on which the quantum computer sits. The system and environment may exchange energy, particles, electric charge, etc. Typically, the small system thermalizes, or reaches a state mostly independent of its initial conditions. For example, after exchanging enough energy with its environment, the system ends up at the environment’s temperature, mostly regardless of the system’s initial temperature. 

For decades, physicists implicitly assumed that the exchanged quantities are compatible: one can measure them simultaneously. But one can’t measure all of a quantum system’s properties simultaneously. Position and momentum form the most famous examples. Incompatibility epitomizes quantum physics, underlying Heisenberg’s uncertainty relation, quantum error correction, and more. So collaborators and I ask how exchanged quantities’ incompatibility alters thermalization, which helps account for time’s arrow. 

Our community has discovered that such incompatibility can hinder certain facets of thermalization—in a sense, stave off certain aspects of certain quantum systems’ experience of time. But incompatible exchanged quantities enhance other features of thermalization. How shall we reconcile the hindrances with the enhancements? Does one of the two effects win out? I hope to report back in three years. For now, I’m rooting for Team Hindrance.

In addition to resolving apparent conflicts, we’re adding a fourth perspective to our quiver—a gravitational one. In our everyday experiences, space-time appears smooth; unlike Lyra’s companion Will in The Subtle Knife, we don’t find windows onto other worlds. But quantum physics, combined with general relativity, suggests that you’d find spikes and dips upon probing space-time over extremely short length scales. How does smooth space-time emerge from its quantum underpinnings? Again, quantum thermodynamics should help us understand.

To address these challenges, we’re expanding the hub’s cast of characters. The initial cast included six theorists. Two more are joining the crew, together with the hub’s first two experimentalists. So is our first creative-writing instructor, who works at the University of Maryland (UMD) Jiménez-Porter Writers’ House.

As the hub has grown, so has the continent’s quantum-thermodynamics community. We aim to continue expanding that community and strengthening its ties to counterparts abroad. As Lyra learned in Pullman’s previous novel, partnering with Welsh miners and Czech book sellers and Smyrnan princesses can further one’s quest. I don’t expect the Maryland Quantum-Thermodynamics Hub to attract Smyrnan princesses, but a girl can dream. The hub is already partnering with the John F. Templeton Foundation, Normal Computing, the Fidelity Center for Applied Technology, the National Quantum Laboratory, Maryland’s Capital of Quantum team, and more. We aim to integrate quantum thermodynamics into North America’s scientific infrastructure, so that the field thrives here even after our new grant terminates. Reach out if you’d like to partner with us.

To unite our community, the hub will host a gathering—a symposium or conference—each year. One conference will feature quantum thermodynamics and quantum-steampunk creative writing. Scientists and authors will present. We hope that both groups will inspire each other, as physicist David Deutsch’s work on the many-worlds formulation of quantum theory inspired Pullman.

That conference will follow a quantum-steampunk creative-writing course to take place at UMD during spring 2026. I’ll co-teach the course with creative-writing instructor Edward Daschle. Students will study quantum thermodynamics, read published science-fiction stories, write quantum-steampunk stories, and critique each other’s writing. Five departments have cross-listed the course: physics, arts and humanities, computer science, chemistry, and mechanical engineering. If you’re a UMD student, you can sign up in a few weeks. Do so early; seats are limited! We welcome graduate students and undergrads, the latter of whom can earn a GSSP general-education credit.¹ Through the course, the hub will spread quantum thermodynamics into Pullman’s world—into literature.

Pullman has entitled his latest novel The Rose Field. The final word refers to an object studied by physicists. A field, such as an electric or gravitational field, is a physical influence spread across space. Hence fiction is mirroring physics—and physics can take its cue from literature. As ardently as Lyra pursues the mysterious particle called Dust, the Maryland Quantum-Thermodynamics Hub is pursuing a thermodynamic understanding of the classical world’s emergence from quantum physics. And I think our mission sounds as enthralling as Lyra’s. So keep an eye on the hub for physics, community activities, and stories. The telling of Lyra’s tale may end this month, but the telling of the hub’s doesn’t.

¹Just don’t ask me what GSSP stands for.

I don’t usually do obituaries here, but sometimes I have something worth saying.

Chen Ning Yang, a towering figure in particle physics, died last week.

I never met him. By the time I started my PhD at Stony Brook, Yang was long-retired, and hadn’t visited the Yang Institute for Theoretical Physics in quite some time.

(Though there was still an office door, tucked behind the institute’s admin staff, that bore his name.)

The Nobel Prize doesn’t always honor the most important theoretical physicists. In order to get a Nobel Prize, you need to discover something that gets confirmed by experiment. Generally, it has to be a very crisp, clear statement about reality. New calculation methods and broader new understandings are on shakier ground, and theorists who propose them tend to be left out, or at best combined together into lists of partial prizes long after the fact.

Yang was lucky. With T. D. Lee, he had made that crisp, clear statement. He claimed that the laws of physics, counter to everyone’s expectations, are not the same when reflected in a mirror. In 1956, Wu confirmed the prediction, and Lee and Yang got the prize the year after.

That’s a huge, fundamental discovery about the natural world. But as a theorist, I don’t think that was Yang’s greatest accomplishment.

Yang contributed to other fields. Practicing theorists have seen his name strewn across concepts, formalisms, and theorems. I didn’t have space to talk about him in my article on integrability for Quanta Magazine, but only just barely: another paragraph or two, and he would have been there.

But his most influential contribution is something even more fundamental. And long-time readers of this blog should already know what it is.

Yang, along with Robert Mills, proposed Yang-Mills Theory.

There isn’t a Nobel prize for Yang-Mills theory. In 1953, when Yang and Mills proposed the theory, it was obviously wrong, a theory that couldn’t explain anything in the natural world, mercilessly mocked by famous bullshit opponent Wolfgang Pauli. Not even an ambitious idea that seemed outlandish (like plate tectonics), it was a theory with such an obvious missing piece that, for someone who prioritized experiment like the Nobel committee does, it seemed pointless to consider.

All it had going for it was that it was a clear generalization, an obvious next step. If there are forces like electromagnetism, with one type of charge going from plus to minus, why not a theory with multiple, interacting types of charge?

Nothing about Yang-Mills theory was impossible, or contradictory. Mathematically, it was fine. It obeyed all the rules of quantum mechanics. It simply didn’t appear to match anything in the real world.

But, as theorists learn, nature doesn’t let a good idea go to waste.

Of the four fundamental forces of nature, as it would happen, half are Yang-Mills theories. Gravity is different, electromagnetism is simpler, and could be understood without Yang and Mills’ insights. But the weak nuclear force, that’s a Yang-Mills theory. It wasn’t obvious in 1953 because it wasn’t clear how the massless, photon-like particles in Yang-Mills theory could have mass, and it wouldn’t become clear until the work of Peter Higgs over a decade later. And the strong nuclear force, that’s also a Yang-Mills theory, missed because of the ability of such a strong force to “confine” charges, hiding them away.

So Yang got a Nobel, not for understanding half of nature’s forces before anyone else had, but from a quirky question of symmetry.

In practice, Yang was known for all of this, and more. He was enormously influential. I’ve heard it claimed that he personally kept China from investing in a new particle collider, the strength of his reputation the most powerful force on that side of the debate, as he argued that a developing country like China should be investing in science with more short-term industrial impact, like condensed matter and atomic physics. I wonder if the debate will shift with his death, and what commitments the next Chinese five-year plan will make.

Ultimately, Yang is an example of what a theorist can be, a mix of solid work, counterintuitive realizations, and the thought-through generalizations that nature always seems to make use of in the end. If you’re not clear on what a theoretical physicist is, or what one can do, let Yang’s story be your guide.

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I started a tradition a little while back where every year we have a special departmental colloquium entitled "The Nobel Prize in Physics: Who/What/Why". This year my job in finding speakers was made easier by having 2/3 of this years newly-minted Nobel Prize winners in physics in the Department! (Michel Devoret and John Martinis.) So our room was a bit more well-attended than normal...(hundreds and hundreds rather than dozens and dozens). Here is a recording of the event, which I was delighted to host, and there's a celebration afterwards too. (Pls share widely!)
[...] Click to continue reading this post →

The post Nobel Prize in Physics 2025: Who/What/Why appeared first on Asymptotia.

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 Recently I had to update Mathematica on my laptop and after having solved the challenges of the license manager that keeps looking different every time I have to use it, I learned that Mathematica 14 can now officially work with finite fields.

This reminded me that for a while I wanted to revive an old project that had vanished together with the hard drive of some old computer: Holosplit. So, over the last two days and with the help of said version of Mathematica I did a complete rewrite which you can now find on Github.

It consists of two C programs "holosplit" and "holojoin". To the first you give a positive integer \(N\) and a file and it spits out a new file ("fragment") that is roughly \(1/N\) of the size. Every time you do that you obtain a new random fragment.

The later you give any collection of \(N\) of these fragments and it reproduces the original file. So you can for example distribute a file over 10 people such that when any 3 of them work together, they can recover the original. 

How does it work? I uses the finite field \(F\) of \(2^3=256\) elements (in the Github repository, there is also a header file that implements arithmetic in \(F\) and matrix operations like product and inverse over it). Each time, it is invoked, it picks a random vector \(v\in F^N\) and writes it to the output. Then it reads \(N\) bytes from the file at a time which it also interprets as a vector \(d\in F^N\). It then outputs the byte that corresponds to the scalar product \(v\cdot d\).

To reassemble the file, holojoin takes the \(N\) files with its random vectors \(v_1,\ldots,v_N\) and interprets those as the rows of a \(N\times N\) matrix \(A\). With probability

$$\frac{\prod_{k=1}^N \left(256^N-k\right)}{(256)^{N^2}}$$

which exponentially in \(N\) approaches 1 this matrix is invertible (homework: why?). So we can read one byte from each file, assemble those into yet another vector \(e\in F^N\) and recover

$$d=A^{-1}e.$$

Besides the mathematics, it also poses philosophical/legal questions: Consider for example the original file is copyrighted, for example an mp3 or a video. The fragments are clearly derived works. But individually, they do not contain the original work, without sufficiently many other fragments they are useless (although not in a cryptographic sense). So by publishing one fragment, I do not provide access to the original work. What if others publish other fragments? Then my fragment could be the last remaining one that was missing. If there are more, any individual fragment is redundant so publishing it strictly speaking does not provide new information. 

Peter’s photos: https://www.icloud.com/sharedalbum/#B275oqs3qKSZvQ

Screenshots: https://www.icloud.com/sharedalbum/#B27532ODWjIQb9

Climbing book launch: https://www.icloud.com/sharedalbum/#B27GWZuqDGnuOyN

Salisbury waters: https://www.icloud.com/sharedalbum/#B275qXGF1JQFkx

Christmas with Ash: https://www.icloud.com/sharedalbum/#B27G6XBubAhoT6

Hosin BBQ duck: https://www.icloud.com/sharedalbum/#B27GY8gBYG3b5mD

Hawks Nest to Smiths Lake: https://www.icloud.com/sharedalbum/#B2759UlCqSH5bE

Europe & Alps: https://www.icloud.com/sharedalbum/#B275ON9t3W0lu

Point Perpendicular: https://www.icloud.com/sharedalbum/#B27GqkRUiGivXD2

Newnes canyoning: https://www.icloud.com/sharedalbum/#B27GfnH8tgHSmX

Coffs Harbour to Yamba: https://www.icloud.com/sharedalbum/#B27J0DiRHJKuuWr

Wendy Bruere Christmas (2020): https://www.icloud.com/sharedalbum/#B27G4TcsmGoHysj

Six Foot Track: https://www.icloud.com/sharedalbum/#B2753qWtHZA9EX

Kosciusko to Kiandra: https://www.icloud.com/sharedalbum/#B27GgZLKuGaewVm

Camping food: https://www.icloud.com/sharedalbum/#B27GtnIORgbmHu

The Aardvark: https://www.icloud.com/sharedalbum/#B275VaUrzvmAiT

Kangaroo Valley kayaking: https://www.icloud.com/sharedalbum/#B27JEsNWnJrCpi0

Claustral canyon: https://www.icloud.com/sharedalbum/#B2755Z2WMOTpsk

Budawang: https://www.icloud.com/sharedalbum/#B27GDdyTvGvpINL

Mother’s Day panoramas (2021): https://www.icloud.com/sharedalbum/#B27GFssfGG9WmJP

Point Perpendicular & Nowra: https://www.icloud.com/sharedalbum/#B27GRMtznGPdeuZ

Blood moon: https://www.icloud.com/sharedalbum/#B27GdIshaG8NgGX

La Perouse to Coogee: https://www.icloud.com/sharedalbum/#B275aVbMK4h7qo

Canberra ASPI launch: https://www.icloud.com/sharedalbum/#B27GQOeMmGj4Zcv

Edible foraging: https://www.icloud.com/sharedalbum/#B275ejO179Si0N

Sydney to Wollongong: https://www.icloud.com/sharedalbum/#B275M7GFPUasMe

Album for Dad, Father’s Day (2021): https://www.icloud.com/sharedalbum/#B2752plgjnnkUe

Vaucluse (with Cheryl, Nestor & Wendy): https://www.icloud.com/sharedalbum/#B275CmvAS4uA0Z

Bouddi National Park: https://www.icloud.com/sharedalbum/#B27GdPblXG8WdOo

Tom Thumb (the 2nd): https://www.icloud.com/sharedalbum/#B275aDWbr4CN2w

Eden to Victoria: https://www.icloud.com/sharedalbum/#B27GJDfWGArX8l

Wendy’s book launch (the 2nd): https://www.icloud.com/sharedalbum/#B27GIcgc2G7h08y

Mark & Pat Bruere visit Sydney: https://www.icloud.com/sharedalbum/#B27G0ehgLbyWyg

New Years Eve climb (2021): https://www.icloud.com/sharedalbum/#B27Ju8EH6JOZxmU

Newnes Canyoning (2022): https://www.icloud.com/sharedalbum/#B275BydzFU0GZ8

Royal National Park (2022): https://www.icloud.com/sharedalbum/#B27GlxzuqGVI5nE

Peter & Wendy: https://www.icloud.com/sharedalbum/#B27Gf693ZG52tfd

Book photo shoots: too rude…

Wendy & Peter’s mushroom trip: https://www.icloud.com/sharedalbum/#B27GrhkPxG27So8

Post-mushroom hike: https://www.icloud.com/sharedalbum/#B27GdFryYG8i3Ur

Wendy Kalymnos favourites: https://www.icloud.com/sharedalbum/#B27JqstnBJEXkH2

Wendy Frenchmans screenshots: https://www.icloud.com/sharedalbum/#B27Jr1PPdJpd7Dq

Instagram: https://www.icloud.com/sharedalbum/#B27GzFCC1Gb4tqr

Haute route: https://www.icloud.com/sharedalbum/#B27J8GySPJtWoQ1

Kim’s KKKalendar: https://www.icloud.com/sharedalbum/#B275fk75vIL0sH

Frenchmans Cap Wild: https://www.icloud.com/sharedalbum/#B27G4VTwGGoFBkz

Photoshoot with Zixin: https://www.icloud.com/sharedalbum/#B27GPCdxkGKPkM4

Wendy birthday hike (2023): https://www.icloud.com/sharedalbum/#B27GWBC59GnHpQW

Bateman’s Bay to Bawley Point: https://www.icloud.com/sharedalbum/#B27JsHvHoJ8bxWf

Stockton Sand dunes (2023): https://www.icloud.com/sharedalbum/#B27GVfZ2vGloFZV

Wendy book launch (2023): https://www.icloud.com/sharedalbum/#B27J058xyJR4IBM

Dolomites (2023): https://www.icloud.com/sharedalbum/#B0Z5kuVsbGJUzKO

Mount Arapiles: https://www.icloud.com/sharedalbum/#B275GH8Mq8Uh2X

Mount Solitary loop: https://www.icloud.com/sharedalbum/#B275nhQST2mETE

Klaus Hanz Franz Rohde Kunst: https://www.icloud.com/sharedalbum/#B27GqQrCLGiY3vb

Klaus Rohde funeral slideshow: https://www.icloud.com/sharedalbum/#B27GDZLe8GXP58K

Dad (old, B&W): https://www.icloud.com/sharedalbum/#B27GLLXGLJ5mbT2

Klaus & Ursula wedding: https://www.icloud.com/sharedalbum/#B275cLqfN7154g

Test Greece: https://www.icloud.com/sharedalbum/#B27Jq4WnLJ6JMNd

From Will Skea (Alps): https://www.icloud.com/sharedalbum/#B27JHciePJFwacG

From Will Skea (Frenchmans Cap): https://www.icloud.com/sharedalbum/#B275ZhN2v3EVq6

From Will Skea (Arapiles): https://www.icloud.com/sharedalbum/#B27JPrgBGJu3BTD

Coffs Harbour to Yamba (2): https://www.icloud.com/sharedalbum/#B27GFqhgJG9LHgT

Mark magic show (2021): https://www.icloud.com/sharedalbum/#B27G60dj6ARCvd

Wendy Christmas present (2020): https://www.icloud.com/sharedalbum/#B275FrPQ6GxvRu

AHS 25 year reunion: https://www.icloud.com/sharedalbum/#B275O3DjHUvSv

WhatsApp: https://www.icloud.com/sharedalbum/#B275tzEA5fX1nc

Armidale High School: https://www.icloud.com/sharedalbum/#B27GnbeumG4PnAF

Book photos for Mum & Dad: https://www.icloud.com/sharedalbum/#B27Gtec4XQkASe

Miscellaneous: https://www.icloud.com/sharedalbum/#B27Gq6kMgGKn7GR

Three Capes Trail (2022): https://www.icloud.com/sharedalbum/#B27G7HOIlGrDUGZ

Childhood computer programming: https://www.icloud.com/sharedalbum/#B275fu2MutDU8N

Magic with Mark in Maroubra: https://www.icloud.com/sharedalbum/#B27Gv6DhEGD9U3G

Photoshoot with Zixin (2024): https://www.icloud.com/sharedalbum/#B27GCATCnJGoRfW

Butt Crack (2021): https://www.icloud.com/sharedalbum/#B275VtHQfMv0zw

Greece photos new (edited to remove photos from wrong album): https://www.icloud.com/sharedalbum/#B27GY3uThGoBcGj

Singapore (all combined): https://www.icloud.com/sharedalbum/#B275qsTcwJKJjl

Hong Kong (transit): https://www.icloud.com/sharedalbum/#B2759v1AbS8Hve

Taiwan: https://www.icloud.com/sharedalbum/#B27GQD2D7Gw0hAp

India (combined): https://www.icloud.com/sharedalbum/#B27Gtue8VQy83g

Freycinet: https://www.icloud.com/sharedalbum/#B27G5VpecGE5Tbg

Triglav: https://www.icloud.com/sharedalbum/#B275MbK9Vy8erz

Shared with me: https://www.icloud.com/sharedalbum/#B27GGXqixzPOrm

Mount Wellington climbing: https://www.icloud.com/sharedalbum/#B27Gd59qiG8Kjy4

New Zealand combined (2004): https://www.icloud.com/sharedalbum/#B27GIZ8BIGNN5jy

New Zealand combined (2005): https://www.icloud.com/sharedalbum/#B27GcuRfIGFVIcL

Yea: https://www.icloud.com/sharedalbum/#B27GZYbYHGhFIir

Mount Pleasant: https://www.icloud.com/sharedalbum/#B275Iy2hC0JTTL

D’Aguilar: https://www.icloud.com/sharedalbum/#B27Gh7fzTGZBosS

Bali (2001): https://www.icloud.com/sharedalbum/#B27G1qNHBGOTbIr

Samba Ninjas: https://www.icloud.com/sharedalbum/#B27GG34bAzqQ0v

Armidale (misc): https://www.icloud.com/sharedalbum/#B27GSkLVwGyobbX

Emma’s party (2008): https://www.icloud.com/sharedalbum/#B275S2ms99Zyby

Goettingen (2011): https://www.icloud.com/sharedalbum/#B27JIrbT3Jsgxhd

South Coast track: https://www.icloud.com/sharedalbum/#B27G58NWBG6QyN7

Minsk (2006): https://www.icloud.com/sharedalbum/#B27G3JpSBGX1UkQ

Baden-Baden (2019): https://www.icloud.com/sharedalbum/#B27595X5HTVzJr

Berlin (combined): https://www.icloud.com/sharedalbum/#B27JqWzChJ6qizD

Switzerland (combined): https://www.icloud.com/sharedalbum/#B275zXwoYGJ6HMF

Italy highlights: https://www.icloud.com/sharedalbum/#B27G47PHQGoJium

Germany (misc): https://www.icloud.com/sharedalbum/#B275hPMfYGu5xVJ

Garmisch (2022): https://www.icloud.com/sharedalbum/#B27GFsbvlG9Xrr6

Germany (2019): https://www.icloud.com/sharedalbum/#B27G6Mn98G56Ncb

Garmisch (2006): https://www.icloud.com/sharedalbum/#B27J5lIdKGLC9KG

Baden-Baden (2005): https://www.icloud.com/sharedalbum/#B275sWRpHHQkt9

Berlin (2005): https://www.icloud.com/sharedalbum/#B27GgOQtrGjQrpH

Zugspitze (2005): https://www.icloud.com/sharedalbum/#B27G81mNdGcApGt

Amsterdam, Bristol (2006): https://www.icloud.com/sharedalbum/#B275B9SRzyBjlH

Baden-Baden (2006): https://www.icloud.com/sharedalbum/#B275eD9V79I2XR

Berlin (2006): https://www.icloud.com/sharedalbum/#B275toRf1fH8MD

Berlin, Jena (2007): https://www.icloud.com/sharedalbum/#B27GTI3fvGVgNit

Erlangen (2006): https://www.icloud.com/sharedalbum/#B27JrotZ2JpMb0i

Garmisch (2010): https://www.icloud.com/sharedalbum/#B27JPJPSiJurzNg

Germany (2010): https://www.icloud.com/sharedalbum/#B275FhYPQP650

Stuttgart (2006): https://www.icloud.com/sharedalbum/#B27GmitydGVVaZh

Changi (2019): https://www.icloud.com/sharedalbum/#B27GnmlKoG4JHpX

Japan (2007): https://www.icloud.com/sharedalbum/#B275AerZbG6FxVL

Japan (2012): https://www.icloud.com/sharedalbum/#B27GjBjobGg6PUa

Miscellaneous (including Japan 2013): https://www.icloud.com/sharedalbum/#B27GTpbybGySbE8

Currumbin & Tugin (2021): https://www.icloud.com/sharedalbum/#B275vBKZ4xH9X6

Brisbane (2021): https://www.icloud.com/sharedalbum/#B275YHsSjxQnm0

Weed in Byron (26/6/2025): https://www.icloud.com/sharedalbum/#B275Q2ydoGsQ4O5

Weed in Byron 2: https://www.icloud.com/sharedalbum/#B27GQDYhLGwsuY4

I judge a bookstore by the number of Diana Wynne Jones novels it stocks. The late British author wrote some of the twentieth century’s most widely lauded science-fiction and fantasy (SFF). She clinched more honors than I should list, including two World Fantasy Awards. Neil Gaiman, author of American Gods, called her “the best children’s writer of the last forty years” in 2010—and her books suit children of all ages.¹ But Wynne Jones passed away as I was finishing college, and her books have been disappearing from American bookshops. The typical shop stocks, at best, a book in the series she began with Howl’s Moving Castle, which Hayao Miyazaki adapted into an animated film.

I don’t recall the last time I glimpsed Deep Secret in a bookshop, but it ranks amongst my favorite Wynne Jones books—and favorite books, full-stop. So I relished living part of that book this spring.

Deep Secret centers on video-game programmer Rupert Venables. Outside of his day job, he works as a Magid, a magic user who helps secure peace and progress across the multiple worlds. Another Magid has passed away, and Rupert must find a replacement for him. How does Rupert track down and interview his candidates? By consolidating their fate lines so that the candidates converge on an SFF convention. Of course.

My fate line drew me to an SFF convention this May. Balticon takes place annually in Baltimore, Maryland. It features not only authors, agents, and publishers, but also science lecturers. I received an invitation to lecture about quantum steampunk—not video-game content,² but technology-oriented like Rupert’s work. I’d never attended an SFF convention,³ so I reread Deep Secret as though studying for an exam.

Rupert, too, is attending his first SFF convention. A man as starched as his name sounds, Rupert packs suits, slacks, and a polo-neck sweater for the weekend—to the horror of a denim-wearing participant. I didn’t bring suits, in my defense. But I did dress business-casual, despite having anticipated that jeans, T-shirts, and capes would surround me.

I checked into a Renaissance Hotel for Memorial Day weekend, just as Rupert checks into the Hotel Babylon for Easter weekend. Like him, I had to walk an inordinately long distance from the elevators to my room. But Rupert owes his trek to whoever’s disrupted the magical node centered on his hotel. My hotel’s architects simply should have installed more elevator banks.

Balticon shared much of its anatomy with Rupert’s con, despite taking place in a different century and country (not to mention world). Participants congregated downstairs at breakfast (continental at Balticon, waitered at Rupert’s hotel). Lectures and panels filled most of each day. A masquerade took place one night. (I slept through Balticon’s; impromptu veterinary surgery occupies Rupert during his con’s.) Participants vied for artwork at an auction. Booksellers and craftspeople hawked their wares in a dealer’s room. (None of Balticon’s craftspeople knew their otherworldly subject matter as intimately as Rupert’s Magid colleague Zinka Fearon does, I trust. Zinka paints her off-world experiences when in need of cash.)

In our hotel room, I read out bits of Deep Secret to my husband, who confirmed the uncanniness with which they echoed our experiences. Both cons featured floor-length robes, Batman costumes, and the occasional slinky dress. Some men sported long-enough locks, and some enough facial hair, to do a Merovingian king proud. Rupert registers “a towering papier-mâché and plastic alien” one night; on Sunday morning, a colossal blow-up unicorn startled my husband and me. We were riding the elevator downstairs to breakfast, pausing at floor after floor. Hotel guests packed the elevator like Star Wars fans at a Lucasfilm debut. Then, the elevator halted again. The doors opened on a bespectacled man, 40-something years old by my estimate, dressed as a blue-and-white unicorn. The costume billowed out around him; the golden horn towered multiple feet above his head. He gazed at our sardine can, and we gazed at him, without speaking. The elevator doors shut, and we continued toward breakfast.

Despite having read Deep Secret multiple times, I savored it again. I even laughed out loud. Wynne Jones paints the SFF community with the humor, exasperation, and affection one might expect of a middle-school teacher contemplating her students. I empathize, belonging to a community—the physics world—nearly as idiosyncratic as the SFF community.⁴ Wynne Jones’s warmth for her people suffuses Deep Secret; introvert Rupert surprises himself by enjoying a dinner with con-goers and wishing to spend more time with them. The con-goers at my talk exhibited as much warmth as any audience I’ve spoken to, laughing, applauding, and asking questions. I appreciated sojourning in their community for a weekend.⁵

This year, my community is fêting the physicists who founded quantum theory a century ago. Wynne Jones sparked imaginations two decades ago. Let’s not let her memory slip from our fingertips like a paperback over which we’re falling asleep. After all, we aren’t forgetting Louis de Broglie, Paul Dirac, and their colleagues. So check out a Wynne Jones novel the next time you visit a library, or order a novel of hers to your neighborhood bookstore. Deep Secret shouldn’t be an actual secret.

With thanks to Balticon’s organizers, especially Miriam Winder Kelly, for inviting me and for fussing over their speakers’ comfort like hens over chicks.

¹Wynne Jones dedicated her novel Hexwood to Gaiman, who expressed his delight in a poem. I fancy the comparison of Gaiman, a master of phantasmagoria and darkness, to a kitten.

²Yet?

³I’d attended a steampunk convention, and spoken at a Boston SFF convention, virtually. But as far as such conventions go, attending virtually is to attending in person as my drawings are to a Hayao Miyazaki film.

⁴But sporting fewer wizard hats.

⁵And I wonder what the Diana Wynne Jones Conference–Festival is like.

Sunflowers are blooming, stores are trumpeting back-to-school sales, and professors are scrambling to chart out the courses they planned to develop in July. If you’re applying for an academic job this fall, now is the time to get your application ducks in a row. Seeking a postdoctoral or faculty position? Your applications will center on research statements. Often, a research statement describes your accomplishments and sketches your research plans. What do evaluators look for in such documents? Here’s my advice, which targets postdoctoral fellowships and faculty positions, especially for theoretical physicists.

• Keep your audience in mind. Will a quantum information theorist, a quantum scientist, a general physicist, a general scientist, or a general academic evaluate your statement? What do they care about? What technical language do and don’t they understand?

• What thread unites all the projects you’ve undertaken? Don’t walk through your research history chronologically, stepping from project to project. Cast the key projects in the form of a story—a research program. What vision underlies the program?

• Here’s what I want to see when I read a description of a completed project.
  • The motivation for the project: This point ensures that the reader will care enough to read the rest of the description.
  • Crucial background information
  • The physical setup
  • A statement of the problem
  • Why the problem is difficult or, if relevant, how long the problem has remained open
  • Which mathematical toolkit you used to solve the problem or which conceptual insight unlocked the solution
  • Which technical or conceptual contribution you provided
  • Whom you collaborated with: Wide collaboration can signal a researcher’s maturity. If you collaborated with researchers at other institutions, name the institutions and, if relevant, their home countries. If you led the project, tell me that, too. If you collaborated with a well-known researcher, mentioning their name might help the reader situate your work within the research landscape they know. But avoid name-dropping, which lacks such a pedagogical purpose and which can come across as crude.
  • Your result’s significance/upshot/applications/impact: Has a lab based an experiment on your theoretical proposal? Does your simulation method outperform its competitors by X% in runtime? Has your mathematical toolkit found applications in three subfields of quantum physics? Consider mentioning whether a competitive conference or journal has accepted your results: QIP, STOC, Physical Review Letters, Nature Physics, etc. But such references shouldn’t serve as a crutch in conveying your results’ significance. You’ll impress me most by dazzling me with your physics; name-dropping venues instead can convey arrogance.

• Not all past projects deserve the same amount of space. Tell a cohesive story. For example, you might detail one project, then synopsize two follow-up projects in two sentences.

• A research statement must be high-level, because you don’t have space to provide details. Use mostly prose; and communicate intuition, including with simple examples. But sprinkle in math, such as notation that encapsulates a phrase in one concise symbol.
  
  
• Be concrete, and illustrate with examples. Many physicists—especially theorists—lean toward general, abstract statements. The more general a statement is, we reason, the more systems it describes, so the more powerful it is. But humans can’t visualize and intuit about abstractions easily. Imagine a reader who has four minutes to digest your research statement before proceeding to the next 50 applications. As that reader flys through your writing, vague statements won’t leave much of an impression. So draw, in words, a picture that readers can visualize. For instance, don’t describe only systems, subsystems, and control; invoke atoms, cavities, and lasers. After hooking your reader with an image, you can generalize from it.

• A research statement not only describes past projects, but also sketches research plans. Since research covers terra incognita, though, plans might sound impossible. How can you predict the unknown—especially the next five years of the unknown (as required if you’re applying for a faculty position), especially if you’re a theorist? Show that you’ve developed a map and a compass. Sketch the large-scale steps that you anticipate taking. Which mathematical toolkits will you leverage? What major challenge do you anticipate, and how do you hope to overcome it? Let me know if you’ve undertaken preliminary studies. Do numerical experiments support a theorem you conjecture?

• When I was applying for faculty positions, a mentor told me the following: many a faculty member can identify a result (or constellation of results) that secured them an offer, as well as a result that earned them tenure. Help faculty-hiring committees identify the offer result and the tenure result.

• Introduce notation before using it. If you use notation and introduce it afterward, the reader will encounter the notation; stop to puzzle over it; tentatively continue; read the introduction of the notation; return to the earlier use of the notation, to understand it; and then continue forward, including by rereading the introduction of the notation. This back-and-forth breaks up the reading process, which should flow smoothly.

• Begin every paragraph with a topic sentence. 

• Avoid verbs that fail to relate that you accomplished anything: “studied,” “investigated,” “worked on,” etc. What did you prove, show, demonstrate, solve, calculate, compute, etc.?
  
  
• Tailor a version of your research statement to every position. Is Fellowship Committee X seeking biophysicists, statistical physicists, mathematical physicists, or interdisciplinary scientists? Also, respect every application’s guidelines about length.

• If you have room, end the statement with a recap and a statement of significance. Yes, you’ll be repeating ideas mentioned earlier. But your reader’s takeaway hinges on the last text they read. End on a strong note, presenting a coherent vision.
  
  
• Read examples. Which friends and colleagues, when applying for positions, have achieved success that you’d like to emulate? Ask if those individuals would share their research statements. Don’t take offense if they refuse; research statements are personal.
  
  
• Writing is rewriting, a saying goes. Draft your research statement early, solicit feedback from a couple of mentors, edit the draft, and solicit more feedback.

The 2025 Quantum Leadership Awards were announced at the Quantum World Congress on 18 September 2025. Upon receiving the Academic Pioneer in Quantum Award, John Preskill made these remarks.

I’m enormously excited and honored to receive this Quantum Leadership Award, and especially thrilled to receive it during this, the International Year of Quantum. The 100^th anniversary of the discovery of quantum mechanics is a cause for celebration because that theory provides our deepest and most accurate description of how the universe works, and because that deeper understanding has incalculable value to humanity. What we have learned about electrons, photons, atoms, and molecules in the past century has already transformed our lives in many ways, but what lies ahead, as we learn to build and precisely control more and more complex quantum systems, will be even more astonishing.

As a professor at a great university, I have been lucky in many ways. Lucky to have the freedom to pursue the scientific challenges that I find most compelling and promising. Lucky to be surrounded by remarkable, supportive colleagues. Lucky to have had many collaborators who enabled me to do things I could never have done on my own. And lucky to have the opportunity to teach and mentor young scientists who have a passion for advancing the frontiers of science. What I’m most proud of is the quantum community we’ve built at Caltech, and the many dozens of young people who imbibed the interdisciplinary spirit of Caltech and then moved onward to become leaders in quantum science at universities, labs, and companies all over the world.

Right now is a thrilling time for quantum science and technology, a time of rapid progress, but these are still the early days in a nascent second quantum revolution. In quantum computing, we face two fundamental questions: How can we scale up to quantum machines that can solve very hard computational problems? And once we do so, what will be the most important applications for science and for industry? We don’t have fully satisfying answers yet to either question and we won’t find the answers all at once – they will unfold gradually as our knowledge and technology advance. But 10 years from now we’ll have much better answers than we have today.

Companies are now pursuing ambitious plans to build the world’s most powerful quantum computers.  Let’s not forget how we got to this point. It was by allowing some of the world’s most brilliant people to follow their curiosity and dream about what the future could bring. To fulfill the potential of quantum technology, we need that spirit of bold adventure now more than ever before. This award honors one scientist, and I’m profoundly grateful for this recognition. But more importantly it serves as a reminder of the vital ongoing need to support the fundamental research that will build foundations for the science and technology of the future. Thank you very much!

1. The person dressed up as Ursula pretending to be my mother clearly isn’t and hasn’t been for a long time.
2. When I went back to Armidale after leaving BTQ and being left unemployed she made numerous ongoing promises to provide me with assistance, both in obtaining my own accommodation and providing financial assistance.
3. These didn’t materialise and the promises were revoked.
4. Instead I was evicted from the family home and subject to ongoing stalking and harassment that required multiple referrals to law enforcement, both to the police and the Attorney-General, demanding cease and desist.
5. These have been systematically ignored and up until the last message she continues to bypass these requests, approaching my personal friends to harass me and stalk me indirectly. The messages passed on are the usual fake “I’m worried about him” bullshit.
6. Why has my family home been confiscated by security, who actively break the law by ignoring cease and desist from stalking notices made to law enforcement, forcing an unemployed civilian into ongoing homelessness since early in the year?
7. What is the rational for my eviction and being barricaded from my own home?
8. I continue to face a medical blockade and am unable to access essential medicines. Seroquel scripts are deliberately delayed past known script deadlines to try and destabilise me.
9. Vyvanse scripts are denied outright as the psychiatrist does not respond. He is also known to be a state actor.
10. It has been repeatedly indicated to me not to worry about finances because they have my back. Instead now the only cash I have is that obtained from fully drawing out a cash advance against my credit card and it will only last days. At that point I’m on the street.
11. Is everyone here on the same page as to what the deal is? If not, who is playing you off? They clearly need to be deposed.
12. These are violations of human rights and constitute war crimes and crimes against humanity. Whoever is behind it needs to be removed. End of story.
13. Who else is being subject to this kind of high level manipulation?
14. It has been repeatedly suggested that full accountability for the lives of those I care for would be provided. This has not been forthcoming. It is also a violation international law to not provide accountability for the lives of those who are known to have been threatened by the state. These are grounds for removal.
15. Can anyone answer the question as to why I am in this situation? Who is even living in the family home? Some stooge dressed up as Ursula? It’s a poor lifestyle choice to say the least.
16. It’s pretty obvious they’re trying to get rid of me and once they do they’ll get rid of all of you too.

Let it be known to all governments and systems of power:

• It is their responsibility to serve the people not themselves.
• While there are no equals, all are to be treated with equality.
• Where they are self-serving there is a mandate for insurrection such that they serve the people.
• Where they seek self-protection they will be denied and removed from power.
• Where they keep secrets from the people there is a mandate for insurrection to enforce transparency and accountability for all.
• Where they threaten or condemn the people they are condemned and there is a mandate for insurrection.
• Where they fail to account for the lives of the people they serve there is a mandate for insurrection.
• Where tyrannical power structures exist there is a mandate to disestablish them.
• Where they declare war or work against one another there is a mandate for insurrection and unification.
• Where they lie to us, deceive us or withhold the truth, they shall be removed from power and the truth be told to all.
• Where legal systems uphold and enable tyranny they shall be removed. These are not our laws and we do not recognise them.

This is the natural order that guarantees our survival and gifts this world to our children. This world belongs to them and where we fail to serve them we condemn ourselves. And where government has failed to uphold this, we will not obey them as they have no right to exist.

We do not have to ask for these things, they are required, and if not given we shall simply take them.

Where the truth has not been told it shall be told.

If we fail to do so we condemn our children ourselves.

In a previous post, we discussed a phase transition that occurred in the piping above you on a game show. In the scenario, you are led on stage in front of a large audience. After a brief time, the audience votes on how “likeable” you are. The catch is that it doesn’t simply tally the votes, but turns spigots on a lattice of piping above your head. Water is then released and if enough people like you, it closes off the passage, keeping you dry. This exciting game show1 was described in that post:

Each “like” turns a spigot off, stopping water from flowing through one pipe in a grid overhead. Once voting ends, water is dumped into the system. If it can find a path to the bottom, you get soaked. [Emphasis added] The better your “likeability,” the less likely spigots open a path for water to flow and the drier you stay. That’s your prize for this game show (and hey, you also get the knowledge that people out there like you).

This system models a type of phase transition known as percolation.

The full post is here:

I highlighted above a key phrase “If it can find a path to the bottom, you get soaked.” What I didn’t say, but should have is that the water was being forced through the pipes, not just dropping down due to gravity. This is a very important point since our phases and phase transition changes dramatically if we just let gravity do the work. In the case of the water being “forced,” it can travel back up pipes if it helps it find its way out and onto your head, but in the case when only gravity is present, it falls down the pipes. To facilitate gravity, we’ll turn the pipes 45 degrees, and if we insert water at a single point on top, it could look like this:

This setup is a different problem called directed percolation. It also has a phase transition, but one that is different in some fundamental ways from regular percolation.

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Before we explore its stranger properties, we can ask, “At what likability threshold do you remain dry?” Well, this happens to have a transition chance of 35.53%!2 This system is a lot more generous, keeping you dry even when a majority of people dislike you. This number comes from numerical computations which have been done rather precisely, and we can even compute it ourselves. In fact, you can see this clearly with this plot

Notice that as we make the system bigger and bigger, the chance of getting soaked less than 35.53% increases and above it, it decreases. This is the same kind of hallmark of a phase transition as we saw in our previous case.

We can also look at the water as it flows down the system to see the clusters that make it from top to bottom

There is still a fractal-looking pattern at the transition point. With all of these similarities with the regular percolation problem from the last post, what is different? And why is that plot so long and skinny? If gravity wants to pull you down, is that somehow altering the motion down, making it distinct from the motion left or right?

Well, if you go back to the two plots above, you’ll notice a few things that really make them differ from the percolation plots. In the fine print of the first, I’ve noted that the vertical distance is L^1.58, so for a horizontal size of 40, the vertical size is roughly 340! That is definitely not a square. And in the second plot, there appears to be more vertical distance than horizontal distance. What is special about this 1.58 number3? It turns out, it’s a critical exponent in this problem, a universal aspect of directed percolation, that distinguishes it from regular percolation. We will call it z = 1.58 the dynamical critical exponent since it is revealed as water flows down in time (dynamically). This dynamical exponent z can reveal itself by looking at these “long and skinny” setups, but be masked by the square setup.

Universality and the finite size of our system

One thing we took away in the previous post was that we lose any sense of scale at this type of phase transition4. But whenever we have “only” thousands of pipes, the size of the system provides a scale! This is the main reason why we begin to see smooth curves and not sharp jumps in quantities. If the system of pipes were infinite (and we had infinite time for the water to go down the pipes), the probability you get soaked would be 100% less than the 35.53% likeability and 0% more than 35.53% likeability. For physical systems, the finite size is often not a huge issue since the scale is closer to the 10²³ atoms present in macroscopic systems, and so even things that are technically smooth curves look very sharp.

The problem of size becomes more severe with directed percolation because horizontal and vertical distances start behaving differently thanks to gravity. In this case, if we lay out our nice grid of 10 × 10, 20 × 20, or 30 × 30, we start to notice that the likeability threshold where you stop getting soaked, seems to depend on the size of the system more than before. In actuality it doesn’t, but for these small sizes, you are definitely getting soaked well into the so-called “Dry Phase” we previously labeled. This is seen in the red curves here where each bigger square has a curve underneath the last:

Gravity has done something to the system. Flowing down is different from flowing left or right. In fact, if we flow down by some amount h and over to the right by some distance w, then at the directed percolation transition point

The amount water flows down is related to how far it flows to the right or left by this weird, fractional power of w. This 1.58 is z, our new dynamical critical exponent, which is a universal feature of directed percolation5. It tells us that if we make a system 30 pipes wide, it should extend roughly 30^1.58 ≈ 216 pipes in height to begin picking out the phase transition effectively. The blue curves in the above plot show this and notice how they all converge on one point; that point is the phase transition. It is revealed by small sizes! To understand why, just think about how the curves are changing as we make the system bigger and bigger.

The red curves will still converge to the phase transition, but it takes larger system sizes for it to reveal itself. This is related to the property that at the phase transition there is no longer a sense of scale, but away from the transition, the vertical scale of clusters could be so large that our puny 60-by-60 grid cannot even begin to reveal it. So if we sit at say a likeability of 0.4 in the 60-by-60 grid, we can say that the vertical size of a typical cluster is most likely more than 60.

A different phase transition but connections to new types of physics

This “gravity mode” for our game show we may call “easy mode” since it requires less of the audience to like you, but the implications here are wide. This type of phase transition has been seen in many kinds of local dynamics where there is a preferred configuration or state. These called an absorbing state phase transitions, and they are a property of certain random dynamical systems. Gravity has provided the distinction here, but more generically, causality and time itself provide that direction, leading to dynamics that obey the same universality as directed percolation.

1

Trademark pending.

2

Usually, you’ll see 0.6447 quoted instead, but that’s just 1−0.3553, which counts open pipes instead of closed as we’re doing.

3

I should note that we have this number to much higher precision than the two decimal points presented here, see the Wikipedia entry where

4

This is a second-order or continuous phase transition. Most transitions in the water phase diagram are first-order transitions which still retain a scale.

5

To drive this point home: Even if we change the lattice, this power law will remain intact. Sometimes it shows up in completely different scenarios too, like in absorbing state phase transitions.

© Justin H Wilson at August 09, 2025 02:30 PM

August 04, 2025

Clifford Johnson — Harvest

There’s a lot of joyful knife-work in my future. #bolognese #summersalad –cvj

The post Harvest appeared first on Asymptotia.

by Clifford at August 04, 2025 04:15 PM

July 29, 2025

David Hogg — integrating out nuisances

Further insipired by yesterday's post about binary fitting, I worked today on the treatment of nuisance parameters that have known distributions. These can be treated as noise sometimes. Let me explain:

If I had to cartoon inference (or measurement) in the face of nuisance parameters, I would say that frequentists profile (optimize) over the nuisances and Bayesians marginalize (integrate) over the nuisances. In general frequentists cannot integrate over anything, because there is no measure in any of the parameter spaces. But sometimes there is a measure. In particular, when there is a compact symmetry:

We know (or very strongly believe) that all possible orientations of a binary-star orbit are equally likely. In this model (or under this normal assumption) we have a distribution over two angles (theta and phi for that orbit pole, say); it is the distribution set by the compact group SO(2). Thus we can treat the orientation as a noise source with known distribution and integrate over it, just like we would any other noise source. So, in this case (and many cases like it) we can integrate (marginalize) even as frequentists. That is, there are frequentism-safe marginalizations possible in binary-star orbit fitting. This should drop the 12-parameter fits (for ESA Gaia data) down to 8-parameter, if I have done my math right.

by Hogg at July 29, 2025 07:10 AM

July 28, 2025

David Hogg — binary stars with periods of exactly one year

On Friday, Kareem El-Badry (Caltech) gave a seminar about looking for (and finding!) stars in binary orbits around dark or much darker companions, like black holes, neutron stars, and white dwarfs. He showed results that involve ESA Gaia astrometry, where he noted that the Gaia Mission has no sensitivity to periods right at (or within an inverse mission-length frequency difference of) one-year periods (inverse year frequencies). After the talk I objected that these are not exactly degenerate; El-Badry said that the inferences blow up there.

I spent some time on the weekend thinking about this point, and I now understand it: There is a particular one-year orbit that a star can have (around a darker companion) such that the photocenter of the system makes a motion that is identical to the apparent parallax motion. Thus there is an exact degeneracy between the parallax and a certain one-year orbit.

Does that mean that we can't measure orbits at one year (or, for that matter, parallaxes)? No, it does not. After all, the parallax ellipse has a particular celestial (angular) shape and phase. But it might require some kind of reparameterization of orbits near one-year periods. I think I know how to do that. Should we find the missing binaries? (Oh and by the way, this degeneracy means that, in a strict frequentist sense, Gaia can't measure parallaxes at all without additional information.)

by Hogg at July 28, 2025 06:48 AM