New Paper Dance Macabre

C. A. Fuchs, M. C. Hoang and B. C. Stacey, “The SIC Question: History and State of Play,” arXiv:1703.07901 [quant-ph] (2017).

Recent years have seen significant advances in the study of symmetric informationally complete (SIC) quantum measurements, also known as maximal sets of complex equiangular lines. Previously, the published record contained solutions up to dimension 67, and was with high confidence complete up through dimension 50. Computer calculations have now furnished solutions in all dimensions up to 151, and in several cases beyond that, as large as dimension 323. These new solutions exhibit an additional type of symmetry beyond the basic definition of a SIC, and so verify a conjecture of Zauner in many new cases. The solutions in dimensions 68 through 121 were obtained by Andrew Scott, and his catalogue of distinct solutions is, with high confidence, complete up to dimension 90. Additional results in dimensions 122 through 151 were calculated by the authors using Scott’s code. We recap the history of the problem, outline how the numerical searches were done, and pose some conjectures on how the search technique could be improved. In order to facilitate communication across disciplinary boundaries, we also present a comprehensive bibliography of SIC research.

Also available via SciRate.


Maybe I need an “I told you so” category for this blog. Quoting the kicker from The Atlantic‘s portrayal of the State Department:

“This is probably what it felt like to be a British foreign service officer after World War II, when you realize, no, the sun actually does set on your empire,” said the mid-level officer. “America is over. And being part of that, when it’s happening for no reason, is traumatic.”

Reflecting on Confusion

While I was writing Multiscale Structure in Eco-Evolutionary Dynamics, I found myself having a frustrating time reading through big chunks of the relevant literature. The mathematics in the mathematical biology was easier than a lot of what I’d had to deal with in physics, but the arguments were hard to follow. At times, it was even difficult to tell what was being argued about. A blog post by John Baez, on “biology as information dynamics,” called this frustration back to mind—not because it was unclear itself, but rather because it touched on the source of the fog.

I think the basic cause of the trouble is the following:

The application of mathematics to biological evolution is rooted, historically, in statistics rather than in dynamics. Consequently, a lot of model-building starts with tools that belong, essentially, to descriptive statistics (e.g., linear regression). This is fine, but then people turn around and discuss those models in language that implies they have constructed a dynamical system. This makes life quite difficult for the student trying to learn the subject by reading papers! The problem is not the algebra, but the assumptions. And that always makes for a thorny situation.


Last night I thought of a way to summarize why my current big research project appeals to me.

The SIC problem gives us the opportunity to travel all throughout mathematics, because, while the definition looks pretty small, the question is bigger on the inside.

For a taste of why this is so, try here:

The American Physical Society Finally Speaks

The APS, my professional organization, has made some dunderheaded moves of late, but this is more encouraging. An email from the APS president and CEO, broadcast today to the membership at large, begins thusly:

We share the concerns expressed by many APS members about recent U.S. government actions that will harm the open environment that is essential for a successful global scientific enterprise. The recent executive order regarding immigration, and in particular, its implementation, would reduce participation of international scientists and students in U.S. research, industry, education, and conference activities, and sends a chilling message to scientists internationally.

The American Chemical Society had already spoken up:
Continue reading The American Physical Society Finally Speaks

Shorter Pinker

Wasn’t I just kvetching about Steven Pinker? Not that long ago, even? Well, some gifts just won’t stop giving. He’s at it again, this time complaining about the “anti-science PC/identity politics/hard-left rhetoric” of the March for Science. It might have been obvious to some of us ten years or more ago that basic respect for empirical data had become a partisan issue, but not everybody has caught up quite yet.

An academic type like me has a hard time responding to accusations of “identity politics” or “political correctness,” not because the accusations have any intellectual merit, but because the real message isn’t the words on the page. People like me, we see a thing wrapped up in the form of a scholarly argument, and we try to respond with footnotes and appendices. But the clauses and locutions are just dances around the real issue, the fundamental point that was expressed most clearly by the Twitter account @ProBirdRights:

I am feel uncomfortable when we are not about me?

Science Is Now the Enemy

No, let’s be a little more forceful than that. The news warrants that much, and it just keeps coming. For the party now in power, the people who keep rat shit out of your food and stop rivers from catching on fire are now the enemy.

I’m really not feeling that good about our ability to handle the next epidemic that comes our way.

And on a personal note, I’m a queer scientist who has published on biological evolution and the need for financial regulation. So, you can sod off with your cheery hot takes about America becoming Great Again through space exploration, or whatever the Quisling line is this week. Stuff your white dick back in your pants and sit your ass down while the adults work, m’kay?

As Of Today

The United States of America is a failed experiment.

We went out in the way a bad joke would have predicted. We lost against our own racism and sexism, our endemic illnesses whose symptoms were intensified by corrupt law enforcement and institutionally rotten mass media. Undone at the final hour by a bizarre codicil in a slaveowners’ constitution. Undone, pushed over the edge—but the edge was too close all along. When it really mattered, we proved ourselves incompetent: not able to handle our civil responsibilities, indeed, in a sense, not ready for adulthood. In the name of national glory, we have voted ourselves a government of the worst. And now a generation will grow up ignorant, poor and sick, if they get the chance to grow up at all. Many of the things we will lose will be things we can never regain, from international respect to endangered species to the lives of our loved ones.

Many good people will keep up the good fight and stir up, as John Lewis says, the good trouble.

The abyss has opened before us.

Whether the future we make for ourselves will have anything to commend it now depends upon our ability to stare into that abyss and make it blink.

Google Scholar Whisky-Tango-Foxtrottery

Google Scholar is seriously borked today. I heard about the problem when Christopher Fuchs emailed me to say that he had his Google Scholar profile open in a browser and happened to click the refresh button, whereupon his total citation count jumped by 700. After the refresh, his profile was full of things he hadn’t even written. Poking around, I found that a lot of publications in the American Institute of Physics’s AIP Conference Proceedings were being wildly misattributed, almost as if everyone who contributed to an issue was getting credit for everything in that issue.

For example, here’s Jan-Åke Larsson getting credit for work by Giacomo D’Ariano:

screenshot of Google Scholar

And here’s Chris picking up 38 bonus points for research on Mutually Unbiased Bases—a topic not far from my own heart!—research done, that is, by Ingemar Bengtsson:
Continue reading Google Scholar Whisky-Tango-Foxtrottery

Good News if You’re an Evil Prof, Though

This is entertaining:

Let’s say you tell your students that arm folding is a genetic trait, with the allele for right forearm on top (R) being dominant to left forearm on top (L). Results from a large number of studies show that about 11 percent of your students will be R children of two L parents; if they understand the genetics lesson correctly, they will think that either they were secretly adopted, or Mom was fooling around and Dad isn’t their biological father. More of your students will reach this conclusion with each bogus genetic trait that you add to the lesson. I don’t think this is a good way to teach genetics.

Via PZ Myers, who is teaching genetics this semester and has an interest in getting it right.

Potent Quotables

The start of a new semester always brings possibilities to mind. Tom Leinster comments,

A curious thing: in the four classes so far, the number of students attending has been, respectively, 19, 17, 15, 13. Assuming that the arithmetic progression continues, our final class will have $-1$ student. Some of Joachim’s colleagues have expressed an interest in coming along to see what $-1$ student looks like. This presents problems of a philosophical type.

More Google Scholar Irregularities

A few years ago, I noticed a glitch in a paper that colleagues of mine had published back in 2002. A less-than sign in an inequality should have been a less-than-or-equals. This might have been a transcription error during the typing-up of the work, or it could have entered during some other phase of the writing process. Happens to the best of us! Algebraically, it was equivalent to solving an equation
\[ ax^2 + bx + c = 0 \] with the quadratic formula,
\[ x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a},\] and neglecting the fact that if the expression under the square root sign equals zero, you still get a real solution.

This sort of glitch is usually not worth a lot of breath, though I do tend to write in when I notice them, to keep down the overall confusingness of the scientific literature. In this case, however, there’s a surprise bonus. The extra solutions you pick up turn out to have a very interesting structure to them, and they include mathematical objects that were already interesting for other reasons. So, I wrote a little note explaining this. In order to make it self-contained, I had to lay down a bit of background, and with one thing and another, the little note became more substantial. Too substantial, I learned: The journal that published the original paper wouldn’t take it as a Comment on that paper, because it said too many new things! Eventually, after a little more work, it found a home:

The number of citations that Google Scholar lists for this paper (one officially published in a journal, mind) fluctuates between 5 and 6. I think it wavers on whether to include a paper by Szymusiak and Słomczyński (Phys. Rev. A 94, 012122 = arXiv:1512.01735 [quant-ph]). Also, if you compare against the NASA ADS results, it turns out that Google Scholar is missing other citations, too, including a journal-published item by Bellomo et al. (Int. J. Quant. Info. 13, 2 (2015), 1550015 = arXiv:1504.02077 [quant-ph]).

As I said in 2014, this would be a rather petty thing to care about, if people didn’t rely on these metrics to make decisions! And, as it happens, all the problems I noted then are still true now.

A Title Seems Almost Beside the Point

Greta Christina writes:

This round of depression isn’t just worse than my previous episodes: it’s different. My symptoms, the things that help, the things that make it worse — they’re different. I’ve spent the last four years learning how to manage depression, and now, at least to some extent, I need to start all over again.

It’s different because the world is genuinely terrible. That’s not the depression talking: that’s a reasonable, evidence-based assessment of reality. You know the joke, “just because you’re paranoid doesn’t mean they’re not out to get you?” Well, just because you’re depressed doesn’t mean the world’s not terrible. And just because you’re anxious doesn’t mean the world’s not terrifying.

Read the rest.

Greta’s project of blogging once a weekday this month is one of the incentives that’s got me posting more often, though I’m not keeping up with her rate.

Multiscale Structure, Information Theory, Explosions

I’d like to talk a bit about using information theory to quantify the intuition that a complex system exhibits structure at multiple scales of organization. My friend and colleague Ben Allen wrote an introduction to this a while ago:

Ben’s blog post is a capsule introduction to this article that he and I wrote with Yaneer Bar-Yam:

I also cover this topic, as well as a fair bit of background on how to relate probability and information, in my PhD thesis:

In this post, I’ll carry the ideas laid out in these sources a little bit farther in a particular direction.
Continue reading Multiscale Structure, Information Theory, Explosions

"no matter how gifted, you alone cannot change the world"