# What Would I Buy With $3 Million for Math[s]? Leading off the topic of my previous post, I think it’s a good time to ask what we can do with resources that are already allocated. How can we fine-tune the application of resources already set aside for a certain purpose, and so achieve the best outcome in the current Situation? This post will be a gentle fantasy, because sometimes, in the Situation, we need that, or because that’s all I can do today. Last month, Evelyn Lamb asked, how should we revamp the Breakthrough Prize for mathematics? This is an award with$3 million attached, supported by tech billionaires. A common sentiment about such awards, a feeling that I happen to share, is that they go to people who have indeed accomplished good things, but on the whole it isn’t a good way to spend money. Picking one person out of a pool of roughly comparable candidates and elevating them above their peers doesn’t really advance the cause of mathematics, particularly when the winner already has a stable position. Lamb comments,

$\$3$million a year could generously fund 30 postdoc years (or provide 10 3-year postdocs). I still think that wouldn’t be a terrible idea, especially as jobs in math are hard to come by for fresh PhD graduates. But […] more postdoc funding could just postpone the inevitable. Tenure track jobs are hard to come by in mathematics, and without more of them, the job crunch will still exist. Helping to create permanent tenured or tenure-track positions in math would ease up on the job crisis in math and, ideally, make more space for the many deserving people who want to do math in academia. […] from going to the websites of a few major public universities, it looks like it’s around$2.5 million to permanently endow a chair at that kind of institution.

I like the sound of this, but let’s not forget: If we have $3 million per year, then we don’t have to do the same thing every year! My own first thought was that if you can fund 10 postdocs for three years apiece, you can easily pay for 10 new open-source math textbooks. In rough figures, let us say that it takes about a year to write a textbook on material you know well. Then, the book has to be field-tested for at least a semester. To find errors in technical prose, you need to find people who don’t already know what it’s supposed to say, and have them work through the whole thing. If we look at, say, what MIT expects of undergrad math majors, we can work up a list of courses: Continue reading What Would I Buy With$3 Million for Math[s]?

# When Things Get Fractally Bad

So.

My country is now an onrushing catastrophe.

One remarkable thing about the disaster unfolding around us is that it has something of a fractal character. Zoom in on a small part of it, and you find the themes of the whole: Endemic sexism and racism; mass media so institutionally rotten they whiff anything important; contempt for science, expertise and basic adulthood maturity… Systemic failures playing out on the grand scale, but also leaving their signatures in the little moment-to-moment moves. Little eddies amid the maelstrom.

A crisis on all scales demands responses at all scales. Here is one action to support, in the small-to-medium range: Don’t let science go down the memory hole!

The safety of US government climate data is at risk. Trump plans to have climate change deniers running every agency concerned with climate change. So, scientists are rushing to back up the many climate databases held by US government agencies before he takes office.

We hope he won’t be rash enough to delete these precious records. But: better safe than sorry!

The Azimuth Climate Data Backup Project is part of this effort. So far our volunteers have backed up nearly 1 terabyte of climate data from NASA and other agencies. We’ll do a lot more! We just need some funds to pay for storage space and a server until larger institutions take over this task.

The project has already met its first funding goal, but more can’t hurt, and it’s open for contributions until 31 January. With more cash on hand, they can “back up more data, create a better interface for getting it, and put more work into making sure it’s error-free and authenticated.”

Just a few weeks ago, we saw a state government try to cover up the science of climate change, and there’s no reason to think that our new federal government will do anything less.

After the 31st, to support helping at larger scales, there’s the American Civil Liberties Union and Planned Parenthood.

# Reaction GIFs are Useful

It’s pretty darn remarkable, really. Every time—every! smegging! time!—that Steven Pinker opens his yap and opines on something I know about, he comes across as a transparent buffoon. The topic could be modern research on evolutionary dynamics, or it could be fanfiction. Today, thanks to his participation in the annual Edge essay shindig, it’s the Second Law of Thermodynamics. Pinker’s essay is of the kind that starts semi-competently before going off the rails. He takes a valid and important scientific principle, oversimplifies painfully, discards all the actual content and ends up with a vacuous statement that shades into ethical irresponsibility.
Continue reading Reaction GIFs are Useful

# 17 Equations that Clogged My Social-Media Timeline

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

# 3, 8, 24, 28, Eureka!

The news has been so unrelentingly bad these past few weeks that I’m taking momentary refuge in good old numerology. I happened to re-read this blog post by John Baez about the free modular lattice on 3 generators. This is a nice bit of pure math that features rather prominently the numbers 3, 8, 24 and 28. The numerological part is that I noticed the same numbers popping up in a problem that I had studied for other reasons, so I figured it would be fun to write about, even if my 28 isn’t exactly equal to Baez’s 28, so to speak.
Continue reading 3, 8, 24, 28, Eureka!

# New Paper Dance

M. Appleby, C. A. Fuchs, B. C. Stacey and H. Zhu, “Introducing the Qplex: A Novel Arena for Quantum Theory,” arXiv:1612.03234 [quant-ph] (2016).

Abstract:

We reconstruct quantum theory starting from the premise that, as Asher Peres remarked, “Unperformed experiments have no results.” The tools of modern quantum information theory, and in particular the symmetric informationally complete (SIC) measurements, provide a concise expression of how exactly Peres’s dictum holds true. That expression is a constraint on how the probability distributions for outcomes of different, mutually exclusive experiments mesh together, a type of constraint not foreseen in classical thinking. Taking this as our foundational principle, we show how to reconstruct the formalism of quantum theory in finite-dimensional Hilbert spaces. Along the way, we derive a condition for the existence of a $d$-dimensional SIC.

Also available through SciRate, where I have a whole profile.

# New Vita

I get my CV caught up to date, in order to procrastinate on the tasks that will make it obsolete again.

# Profiles in Procrastination

In ages past, biographers read the correspondence of their subjects to gain information. There was something pleasing about finding a new morsel about an old life, a letter turning up in an unexpected place. Now… Hey, I have a page on YouTube that I forgot about until today!

Insofar as the subject of any biography is a singular self, this is the same Blake Stacey as the

Someone or something else created the

page, on which I have twice as many editions as ratings. But I am not the Blake, Stacey who wrote the Boy’s Own Adventure story “The Derelict Hunters: A Thrilling Story of the Dread Sargasso Sea” (more’s the pity).

# New Paper Dance

B. C. Stacey, “Geometric and Information-Theoretic Properties of the Hoggar Lines” (2016), arXiv:1609.03075 [quant-ph].

We take a tour of a set of equiangular lines in eight-dimensional Hilbert space. This structure defines an informationally complete measurement, that is, a way to represent all quantum states of three-qubit systems as probability distributions. Investigating the shape of this representation of state space yields a pattern of connections among a remarkable spread of mathematical constructions. In particular, studying the Shannon entropy of probabilistic representations of quantum states leads to an intriguing link between the questions of real and of complex equiangular lines. Furthermore, we will find relations between quantum information theory and mathematical topics like octonionic integers and the 28 bitangents to a quartic curve.

All things told, SIC-POVMs are just about the damnedest things I’ve ever studied in mathematics.

(Also listed on SciRate.)

# A Frabjous, Albeit Delayed, Day

David Mermin thanked me for finding a glitch in one of his papers. I can retire now, right?

The matter concerns “Hidden variables and the two theorems of John Bell” [Reviews of Modern Physics 65, 3 (1993), pp. 803–15]. Specifically, we turn our attention to Figure 4, the famous “Mermin pentagram,” reproduced below for convenience.

The caption to this figure reads as follows:

Ten observables leading to a very economical proof of the Bell–KS theorem in a state space of eight or more dimensions. The observables are arranged in five groups of four, lying along the legs of a five-pointed star. Each observable is associated with two such groups. The observables within each of the five groups are mutually commuting, and the product of the three observables in each of the six groups is $+1$ except for the group of four along the horizontal line of the star, where the product is $-1$.

In that last sentence, “three observables in each of the six groups” should instead read “four observables in each of the five groups” (in order to agree with the diagram, and to make sense).

Glitches and goofs can happen to anybody. I’m embarrassingly prone to them myself. I also have the pesky kind of personality that is inclined to write in when I find them. This has led to a journal-article erratum once before, and now that I think about it, it provided the seeds for two papers of my own. As they say about Wolverine, being per-SNIKT-ety pays off!

(Incidentally, it took two months for this latest erratum to appear. A sensible system could have done it in as many days, but that’s scientific publishing for you.)

# Daria Makes A Deal, Chapter Eight

Now and then, I see someone mocking the idea of fanfiction—typically, “Tumblr fanfic” in particular. And it’s understandable. I mean, when the canonical material rises to such heights as, um, Batman V Superman, and Tumblr can only offer Martha Kent fighting off time-travelers who come back to kill young Clark, well, is there even really a choice to make? With the “Captain America is Hydra” story arc, Marvel provides readers with the innovative and unprecedented story of Bad Guys Use Space Thing To Make Big Good Guy Bad. Seriously, for sheer inventiveness and entertainment value, how could Tumblr or AO3 even compete?

*snerk*

Yes, fanfiction did give the world Christian Grey. But it also gave us Will Graham and Hannibal Lecter having Christian Grey for dinner, which has to count for something.

For previous installments of Daria Makes A Deal, see the chapter index. (For my research in quantum information theory, see my recap of recent publications.)

Fair warning: I got the Granada TV Sherlock Holmes series for Christmas and have been watching a lot of that lately.

CHAPTER EIGHT

Daria noticed herself climbing a rope up towards a treehouse.

“This is odd,” she said. “I shouldn’t have nearly the upper-body strength to be doing this so easily.” She took a good look at the knotted hemp rope.

Daria tried to work her memory backwards, to see if it offered any clues about her current situation. She recalled the fracas in the hotel lobby, and then Tom and Saavik were looking at her as though she were unwell, and she was telling them that she was just tired. She remembered thinking that she could pass off any odd behavior as due to her recent discovery of her own apparent bisexuality. Which sounded plausible enough. And so she had begged off, pleading the ineffectuality of caffeine, to hide in the room where she had awoken from her dream—

It had been only a dream, but that meant nothing at all.
Continue reading Daria Makes A Deal, Chapter Eight

# New(-ish) Publications

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