B. C. Stacey, “SIC-POVMs and Compatibility among Quantum States” [arXiv:1404.3774]:

An unexpected connection exists between compatibility criteria for quantum states and symmetric informationally complete POVMs. Beginning with Caves, Fuchs and Schack’s “Conditions for compatibility of quantum state assignments” [Phys. Rev. A 66 (2002), 062111], I show that a qutrit SIC-POVM studied in other contexts enjoys additional interesting properties. Compatibility criteria provide a new way to understand the relationship between SIC-POVMs and mutually unbiased bases, as calculations in the SIC representation of quantum states make clear. Along the way, I correct two mathematical errors in Caves, Fuchs and Schack’s paper. One error is a minor nit to pick, while the other is a missed opportunity.

It was the custom of the ancient Persians to reconsider while sober all Twitter avatar choices made while drunk, and vice versa.

Me encouraging scientists to use Twitter sometimes feels like Bill Hicks saying, “I am available for children’s parties, by the way.”

Or, “Oh, Wikipedia, How I Love Thee. Let me count the ways: one, two, phi…”

From Wikipedia’s page on Duchamp’s Nude Descending a Staircase, No. 2 (today’s version):

It has been noted disquisitively [link] that the number 1001 of Duchamp’s entry at the 1912 Indépendants catalogue also happens to represent an integer based number of the Golden ratio base, related to the golden section, something of much interest to the Duchamps and others of the Puteaux Group. Representing integers as golden ratio base numbers, one obtains the final result 1000.1001φ. This, of course, was by chance—and it is not known whether Duchamp was familiar enough with the mathematics of the golden ratio to have made such a connection—as it was by chance too the relation to Arabic Manuscript of The Thousand and One Nights dating back to the 1300s.

Euhhhhh, non.

As best I can tell, all this is saying is that the catalogue number of Duchamp’s painting contains only 0s and 1s.

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).

From Alex Gabriel:

Chromosomes, as Anne Fausto-Sterling details in Sexing the Body, can’t be relied on as indicators of the other traits here — sets exist beyond XX and XY, as do humans in whom both are found and outwardly ‘female-bodied’ people with the latter. Anatomy comes in endless combinations, such that estimates of ‘ambiguous’ sets’ commonness vary wildly, with some as high as one in twenty-five (John Money, cited in Fausto-Sterling’s work). Bodies with the ‘wrong’ features — height, hair, breast tissue, Adam’s apples — are common. Everyone preadolescent, postmenopausal or otherwise infertile is sexless judging by sperm and ova. Hormones, like most of these attributes, can be altered at will.

When not all these tests are passed, which overrule which? Milinovich describes people with ‘female’ anatomy and XY chromosomes as male, for example — suggesting, confusingly, that she doesn’t think maleness requires physical traits. What reason is there to choose genes rather than body parts when diagnosing sex, and not vice versa? In practice, things tend to go the other way: medics who judge a foetus’s sex via ultrasound, for instance, do so only by identifying outer sex organs, and I know nothing about my chromosomes, interior sex organs, hormones or fertility. The fact (or assumption) I have a penis is seen as enough, most of the time, to classify my sex as male, but why should it outweigh these unknown factors?

It’s common enough for adult cisgender men — deemed male at birth, with bodies read straightforwardly that way — not to grow facial hair. I know two or three who don’t; so probably do you. This isn’t seen to affect their physical sex. Why then, barring blunt intuition, should the absence of a penis? We can argue facial hair is only a secondary sex characteristic, and penises a primary one, but this relies itself on defining sex by reproductive role: the logic is circular. From that standpoint, moreover, why not make testes the sole determinant, so people possessing them and a vulva were ‘males’? Testes have, after all, the more distinct and self-contained function of sperm production. A penis, being a shell for the urethra, is just another pipe among the plumbing — we’ve no grounds except cultural ones to treat it differently from a vas deferens. So why is it more necessary for ‘maleness’?

Milinovich calls sex a static, stubborn fact, then moves inconsistently between ideas (see above) about what it is. If she herself can’t pick a definition, what does this suggest?

Not up to much so far today; just thought I’d leave a note here about PZ Myers’ nice post on Cynthia Gockley.

My “Worked Physics Homework Problems” book now stands at 372 pages. If you ever wonder what I do instead of meeting people.

Take the quiz and find out today: Which mescaline-fuelled Hunter S. Thompson rampage of angry gonzo journalism are you?

Few debunkings of haunted houses, psychic media and so forth and so on rely exclusively, or even primarily, on what we’d call fundamental physics. It is not that the psychic operates in some way which requires a magnetic monopole; it is that the ability of people to do cold reading, plus our tendencies to remember hits and forget misses, plus other aspects of human behaviour, provide an alternative explanation which accounts for our experiences and gives us practical guidance for our future actions.

1996: John Horgan declares THE END OF SCIENCE. 1997: first E. coli genome sequence published. 1998: expansion of Universe found to be accelerating.

“You’ll get so preoccupied with equations that you forget to eat!” #BadWaysToPromoteScienceToYoungWomen

After attending the annual ScienceOnline meetings in North Carolina for many years, this time around, I won’t be going. The primary reason has nothing to do with the upsets in that community of late (oh, yes, I have thoughts, but they’re not for the sharing today). Oh, sure, not seeing the people I’d hoped to see because ongoing problems drove them away—that’s a fine secondary reason. Before and above all that, though, is the fact that I’m mid-PhD. I realized I could no longer justify the time, the stress and, indeed, the carbon footprint of traveling to attend #scio14.

What can one do? I revile air travel more every year. I don’t have time/energy to prepare for the conference beforehand, or to follow up on anything discussed there after. My proposal for the session I was to moderate was, to summarize only slightly, “hey let’s build this website”. Must I travel for that??

A thing which always surprises me: people who can read Kurt Vonnegut’s “Harrison Bergeron” nonparodically. The title character

• is seven feet (2.13 m) tall,
• carries three hundred pounds (136 kg) without effort,
• can easily tear straps meant to withstand 5000 pounds of force (the weight of over 2 tonnes),
• can sing beautifully whilst waving musicians like batons, and
• neutralizes gravity itself through the power of sheer awesomeballs.

But to a certain mindset, which fancies itself much put-upon and misunderstood, Harrison Bergeron could burst through the door waving a BFG9000 and riding a T-rex, all to nary a chuckle.

Every once in a while, a bit of esoteric mathematics drifts into more popular view and leaves poor souls like me wondering, “Why?”

Why is this piece of gee-whizzery being waved about, when the popularized “explanation” of it is so warped as to be misleading? Is the goal of “popularizing mathematics” just to inflate the reader’s ego—the intended result being, “Look what I understand!,” or, worse, “Look at what those [snort] professional mathematicians are saying, and how obviously wrong it is.”

Today’s instalment (noticed by my friend Dr. SkySkull): the glib assertion going around that

$$1 + 2 + 3 + 4 + 5 + \cdots = -\frac{1}{12}.$$

Sigh.

It’s like an Upbuzzdomeworthy headline: These scientists added together all the counting numbers. You’ll never guess what happened next!

“This crazy calculation is actually used in physics,” we are solemnly assured.

Sigh.

The physics side of the story is, roughly, “Sometimes you’re doing a calculation and it looks like you’ll have to add up $$1+2+3+4+\cdots$$  and so on forever. Then you look more carefully and realize that you shouldn’t—something you neglected matters. It turns out that you can swap in $$-1/12$$ for the corrected calculation and get a good first stab at the answer. More specifically, swapping in $$-1/12$$ tells you the part of the answer which doesn’t depend on the particular details of the extra effect you originally neglected.”

For an example of this being done, see David Tong’s notes on quantum field theory, chapter 2, page 27. For the story as explained by a mathematician, see Terry Tao’s “The Euler-Maclaurin formula, Bernoulli numbers, the zeta function, and real-variable analytic continuation.” As that title might hint, these do presume a certain level of background knowledge, but that’s kind of the point. This is an instance where the result itself requires at least moderate expertise to understand, unlike, say, the four-colour theorem, where the premise and the result are pretty easy to set out, and it’s the stuff in between which is much harder to follow.

ADDENDUM (19 January 2014): I’ve heard the argument in favour of this gee-whizzery that it “gets people excited about mathematics.” So what? A large number of people are misinformed; a tiny fraction of that population goes on to learn more and realize that they were, essentially, lied to. Getting people interested in mathematics is a laudable goal, but you need to pick your teaser-trailer examples more carefully.

And I see Terry Tao has weighed in himself with a clear note and some charming terminology.

Zack Kopplin describes an example of crackpot-idea synergy in a recent Slate piece about how “Texas Public Schools Are Teaching Creationism.”

Responsive Ed has a secular veneer and is funded by public money, but it has been connected from its inception to the creationist movement and to far-right fundamentalists who seek to undermine the separation of church and state.

Infiltrating and subverting the charter-school movement has allowed Responsive Ed to carry out its religious agenda—and it is succeeding. Operating more than 65 campuses in Texas, Arkansas, and Indiana, Responsive Ed receives more than \$82 million in taxpayer money annually, and it is expanding, with 20 more Texas campuses opening in 2014.

Along with the usual evolution-denialist drivel, those taxpayer funds are buying a threat to public health:

The only study linking vaccines to autism was exposed as a fraud and has been retracted, and the relationship has been studied exhaustively and found to be nonexistent. But a Responsive Ed workbook teaches, “We do not know for sure whether vaccines increase a child’s chance of getting autism, but we can conclude that more research needs to be done.”

Anti-vax lunacy from the religious right? Who would have thunk it?

Well, other than people who have looked at the data, that is.

Dear Gentlemen,

Betcha people at Science and PLOS are giggling fit to burst right about now.

Yours,
Blake