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.
It feels like a good time to enumerate the science things I’ve written or co-written over this past year. In reverse chronological order:
Continue reading My 2016 in Official Physics Writing
An image burbled up in my social-media feed the other day, purporting to be a list of “17 Equations that Changed the World.” It’s actually been circulating for a while (since early 2014), and purports to summarize the book by that name written by Ian Stewart. This list is typo-ridden, historically inaccurate and generally indicative of a lousy knowledge-distribution process that lets us down at every stage, from background research to fact-checking to copy-editing.
Continue reading 17 Equations that Clogged My Social-Media Timeline
I’ve had a few scholarly items come out in the past several weeks—new stuff, and updated versions of old stuff. Here are their coordinates:
Continue reading New(-ish) Publications
Here is physicist John Archibald Wheeler, interviewed in the documentary The Creation of the Universe (1985):
There’s nothing deader than an equation. You write that down in a square on a tile floor. And on another tile on the floor you write down another equation, which you think might be a better description of the Universe. And you keep on writing down equations hoping to get a better and better equation for what the Universe is and does.
And then, when you’ve worked your way out to the end of the room and have to step out, you wave your wand and tell the equations to fly.
And not one of them will put on wings and fly.
Yet the Universe flies!
It has a life to it that no equation has, and that life to it is a life with which we are also tied up.
I saw that documentary as a kid, and that little speech was one part that stuck with me ever after. For the story of how Wheeler made this point to his physics classes, see arXiv:1405.2390, page 292.
I finally have my thesis in a shape that I feel like sharing. Yes, this took over three months after my committee gave their approval. Blame my desire to explain the background material, and the background to the background….
In a complex system, the individual components are neither so tightly coupled or correlated that they can all be treated as a single unit, nor so uncorrelated that they can be approximated as independent entities. Instead, patterns of interdependency lead to structure at multiple scales of organization. Evolution excels at producing such complex structures. In turn, the existence of these complex interrelationships within a biological system affects the evolutionary dynamics of that system. I present a mathematical formalism for multiscale structure, grounded in information theory, which makes these intuitions quantitative, and I show how dynamics defined in terms of population genetics or evolutionary game theory can lead to multiscale organization. For complex systems, “more is different,” and I address this from several perspectives. Spatial host–consumer models demonstrate the importance of the structures which can arise due to dynamical pattern formation. Evolutionary game theory reveals the novel effects which can result from multiplayer games, nonlinear payoffs and ecological stochasticity. Replicator dynamics in an environment with mesoscale structure relates to generalized conditionalization rules in probability theory.
The idea of natural selection “acting at multiple levels” has been mathematized in a variety of ways, not all of which are equivalent. We will face down the confusion, using the experience developed over the course of this thesis to clarify the situation.
A certain mindset sees the movie Aliens and thinks it would be awesome to be a Space Marine. Because it’s like being a Marine, but in space.
A certain mindset skims a bit of cyberpunk fiction and thinks the future will be amazing, because Ruby-coding skills will clearly translate to proficiency with katanas. You know, katanas.
A certain mindset learns a little about the Victorian era and is instantly off in a fantasy of brass-goggled Gentlemen Aviators, at once dapper and wind-swept, tending the Tesla apparatus on their rigid airship. All art in the genre carries the tacit disclaimer in its caption, “(Not pictured: cholera.)” In the designation steampunk, the -punk has nothing to do with anarchy (in the UK or elsewhere), the suffix having been conventionalized into a mere signifier of anachronism. A steampunk condo development promises units for the reasonable price of 2 to 7.5 million dollars apiece.
[To be fair, Gibson and Sterling’s The Difference Engine (1990), which is in some part responsible for the whole wibbly-wobbly steamery-punkery, did spend some of its time with the run-down and the passed-over. It also, I’m guessing unintentionally, underscored the incoherence of the premise, when in its final pages, Ada Lovelace describes a fanciful notion of the late Charles Babbage, whose fictional version dreamed of doing computation with electricity. The fictional Babbage’s never-implemented plan relied on such hypothetical devices as resistors and capacitors. The book’s plot begins in 1855; the Leyden jar was invented 110 years earlier. Carl Friedrich Gauss built a working telegraph years before the historical Babbage even designed his Analytical Engine. But our aesthetic can’t allow that, of course.]
It is against this background that we should read “Silicon Valley is a Science Fictional Utopia,” a recent piece in Model View Culture. I have enjoyed and appreciated MVC quite a bit in the past few months, which is why I was rather flummoxed to find a statement in that essay that just refused to parse. The overall thesis sounds roughly right to me, but not all the examples seem to fit as written. Here’s the part that jumped out at me:
Continue reading Those Who Aspire to Solaria
A few weeks ago, I found an old physics book on a colleague’s “miscellaneous” shelf: University of Chicago Graduate Problems in Physics, by Cronin, Greenberg and Telegdi (Addison-Wesley, 1967). It looked like fun, so I started working through some of it.
Physics problems age irregularly. Topics fall out of vogue as the frontier of knowledge moves on, and sometimes, the cultural milieu of the time when the problem was written pokes through. Take the first problem in the “statistical physics” chapter. It begins, “A young man, who lives at location $A$ of the city street plan shown in the figure, walks daily to the home of his fiancee…”
No, no, no, that just won’t do any more. Let us set up the problem properly:
Asami is meeting Korra for lunch downtown. Korra is $E$ blocks east and $N$ blocks north of Asami, on the rectangular street grid of downtown Republic City. Because Asami is eager to meet Korra, her path never doubles back. That is, each move Asami takes must bring her closer to Korra on the street grid. How many different routes can Asami take to meet Korra?
Solution below the fold.
Continue reading Less Heteronormative Homework
This is, apparently, a time for reflection. What have I been up to?
And so this is Korrasmas
Things have been Done
Kuvira is fallen
A new ‘ship just begun
We all knew it
Well, other than watching cartoons?
At the very beginning of 2014, I posted a substantial revision of “Eco-Evolutionary Feedback in Host–Pathogen Spatial Dynamics,” which we first put online in 2011 (late in the lonesome October of my most immemorial year, etc.).
In January, Chris Fuchs and I finished up an edited lecture transcript, “Some Negative Remarks on Operational Approaches to Quantum Theory.” My next posting was a solo effort, “SIC-POVMs and Compatibility among Quantum States,” which made for a pretty good follow-on, and picked up a pleasantly decent number of scites.
Then, we stress-tested the arXiv.
By mid-September, Ben Allen, Yaneer Bar-Yam and I had completed “An Information-Theoretic Formalism for Multiscale Structure in Complex Systems,” a work very long in the cooking.
Finally, I rang in December with “Von Neumann was Not a Quantum Bayesian,” which demonstrates conclusively that I can write 24 pages with 107 references in response to one sentence on Wikipedia.
Shimer College: the worst school in America?
Subhead: This tiny, eccentric institution in Chicago was just voted the worst place to study in America. But does Shimer, which shuns lectures and has no societies or clubs, deserve such an accolade? Jon Ronson went there to investigate.
In the body, we have a bit more detail:
This is a ‘great books’ college. The great books of the western tradition, not the professors, are the teachers: Da Vinci’s Notebooks and Aristotle’s Poetics and Homer’s Odyssey and de Beauvoir’s Ethics of Ambiguity and Kafka and Derrida and Nietzsche and Freud and Marx and Machiavelli and Shakespeare and the Bible.
Continue reading Concerning “Great Books”
Here is Paul Dirac in October 1927:
If we are honest — and scientists have to be — we must admit that religion is a jumble of false assertions, with no basis in reality. The very idea of God is a product of the human imagination. It is quite understandable why primitive people, who were so much more exposed to the overpowering forces of nature than we are today, should have personified these forces in fear and trembling. But nowadays, when we understand so many natural processes, we have no need for such solutions. I can’t for the life of me see how the postulate of an Almighty God helps us in any way. What I do see is that this assumption leads to such unproductive questions as why God allows so much misery and injustice, the exploitation of the poor by the rich and all the other horrors He might have prevented. If religion is still being taught, it is by no means because its ideas still convince us, but simply because some of us want to keep the lower classes quiet. Quiet people are much easier to govern than clamorous and dissatisfied ones. They are also much easier to exploit. Religion is a kind of opium that allows a nation to lull itself into wishful dreams and so forget the injustices that are being perpetrated against the people. Hence the close alliance between those two great political forces, the State and the Church. Both need the illusion that a kindly God rewards — in heaven if not on earth — all those who have not risen up against injustice, who have done their duty quietly and uncomplainingly. That is precisely why the honest assertion that God is a mere product of the human imagination is branded as the worst of all mortal sins.
To which Wolfgang Pauli is said to have replied,
Continue reading Dirac, Pauli and You
For your edutainment:
Continue reading Links
One day, I’ll be able to explain the story behind how I got into this, but looking back on all the oddities of it, I’m not sure that a medium other than manga could do it justice.
My Struggles with the Block Universe [arXiv:1405.2390]
Christopher A. Fuchs, Maximilian Schlosshauer (foreword), Blake C. Stacey (editor)
This document is the second installment of three in the Cerro Grande Fire Series. Like its predecessor arXiv:quant-ph/0105039, “Notes on a Paulian Idea,” it is a collection of letters written to various friends and colleagues, most of whom regularly circuit this archive. The unifying theme of all the letters is that each has something to do with the quantum. Particularly, the collection chronicles the emergence of Quantum Bayesianism as a robust view of quantum theory, eventually evolving into the still-more-radical “QBism” (with the B standing for no particular designation anymore), as it took its most distinctive turn away from various Copenhagen Interpretations. Included are many anecdotes from the history of quantum information theory: for instance, the story of the origin of the terms “qubit” and “quantum information” from their originator’s own mouth, a copy of a rejection letter written by E. T. Jaynes for one of Rolf Landauer’s original erasure-cost principle papers, and much more. Specialized indices are devoted to historical, technical, and philosophical matters. More roundly, the document is an attempt to provide an essential ingredient, unavailable anywhere else, for turning QBism into a live option within the vast spectrum of quantum foundational thought.
As the comment field says, “CAUTION, do not unthinkingly print from a printer: 2,348 pages, 4 indices, 6 figures, with extensive hyperlinking.”
MSwtBU was originally submitted to the arXiv on 10 May 2014, the anniversary of the predecessor volume and before that of the Cerro Grande Fire, which started the whole business. To my knowledge, it is the longest item currently on the arXiv.
omg 2000+ pages. There goes my free time.
— Dave Bacon, via Twitter
It is not possible that what is common to several classes should have any quality which is excluded from one of them. If, for example, no bankers are poor and no lawyers are honest, it is impossible that lawyers who are bankers should be either poor or honest.
From “On the Algebra of Logic” in Studies in Logic, Charles Sanders Peirce, editor, pp. 17–71 (1883).
Betcha people at Science and PLOS are giggling fit to burst right about now.
While looking through old physics books for alternate takes on my quals problems, I found a copy of Sir James Jeans’ Electricity and Magnetism (5th edition, 1925). It’s a fascinating time capsule of early views on relativity and what we know call the “old quantum theory,” that is, the attempt to understand atomic and molecular phenomena by adding some constraints to fundamentally classical physics. Jeans builds up Maxwellian electromagnetism starting from the assumption of the aether. Then, in chapter 20, which was added in the fourth edition (1919), he goes into special relativity, beginning with the Michelson–Morley experiment. Only after discussing many examples in detail does he, near the end of the chapter, say
If, then, we continue to believe in the existence of an ether we are compelled to believe not only that all electromagnetic phenomena are in a conspiracy to conceal from us the speed of our motion through the ether, but also that gravitational phenomena, which so far as is known have nothing to do with the ether, are parties to the same conspiracy. The simpler view seems to be that there is no ether. If we accept this view, there is no conspiracy of concealment for the simple reason that there is no longer anything to conceal.
Continue reading Time Capsule