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dinnner.  also, I like the shadows on the building in the background. click for larger version There was a praying mantis on this window screen earlier. I think the lizard had it for brunch. §§§§ Today's topic is the section sign. It would deserve a blog posting for no other reason than to celebrate its appearance. I wish it came up more often in topics I blog about, just because it looks so good on a page. It's one of the characters I make a point of checking out when a new font comes my way.

English language Wikipedia tells us its "likely origin" is a combination of two capital esses for the Latin signum sectiōnis and leaves it at that. German language Wikipedia on the other hand offers a plethora of alternate proposed origins, including signum separandi, Senatus Sententia, gothic C (ℭ) for caput, or the Egyptian hieroglyph Unicode hex 130A2 written at the close of a section and denoting a pause. That last one seems like a stretch, but hey, it's got a book citation—just the ticket to confer legitimacy in the land of Wikipedia.

§ inspires the logo of Section Sign Records, somewhat of a graphic double entendre given the similarity to dal segno in music notation.

§ appears in the logo of Austria's Federal Ministry for Justice.

Last but not least: a stock photo house offers a pic of a grass snake (Natrix natrix) roughly assuming a § shape. 1/140 second Echinopsis subdenudata What could be better than one cactus flower, if not three?

This species won't self-pollinate so it relies on nearby plants flowering concurrently. I've seen flowers sync up and open on the same morning even when the flowers were on different plants in separate pots. I don't know for sure but I suspect the synchronization in separated plants is mediated by airborne chemicals.

Last week, when I said I was skeptical about there being a collective unconscious (in people, not cacti), a friend disagreed and said it was plausible in light of experiments by Grinberg-Zylberbaum—who I'd never heard of before and have since read up on. To summarize: in the 1990s, Professor Jacobo Grinberg-Zylberbaum at the National University of Mexico observed similar EEG waveforms in pairs of people separated and placed in carefully isolated rooms, which he attributed to (what else?) quantum mechanical effects. Professor Grinberg-Zylberbaum mysteriously disappeared in 1994 and hasn't been heard from since.

A carefully collected and analyzed body of such evidence could impress me, but Grinberg-Zylberbaum's work alone doesn't. The papers of his I've read don't go into enough detail, at least one of the people working in his lab didn't draw the same conclusions he did from the measurements, the results haven't been consistently replicated by others, and Grinberg-Zylberbaum's attempts to base the claimed correlations on quantum mechanics are grasping at straws. I can explain further if anyone cares.

Meanwhile, I don't expect to get any seeds this time. I used to have a few of these cacti but now I've just got the one.
I came across this diagram on a techie blog today.

Then I noticed that Google ran a John Venn doodle tomorrow.

The diagram may be a somewhat inexact guide to definitions. But it illustrates why, of these monosyllabic epithets, geek is the most likely to be worn with pride.

The blog I found the diagram on didn't know who to credit for it. I found several instances on the web but I don't know who originated it nor who rendered this version—but my thanks to both.
I'll start with what I liked about the movie Boyhood. It's not overdone, it was a risky project to undertake, and it has some poignant, thoughtful moments.

And yet I was nowhere near as taken with it as was pretty much every critic. It's a movie about the plainness of life, and I'm a tough customer for such stories. That's not to say I can't appreciate them, just that the style and tone are going to have to carry the day. And indeed a lot of people are delighted with the tone of Boyhood; I just wasn't one of them.

IMDB quotes director/writer Richard Linklater as having said, Most of us are losers most of the time, if you think about it. To the extent I get his point, it doesn't necessarily translate into my wanting to watch losers on screen.

I find Linklater an OK director but not much of a writer. There's a scene in Boyhood where the father picks a less-than-optimal time and place to talk to his teenage kids about contraception. The daughter cringes. I found that one of the stronger scenes in the movie, but even so it's still quite plain. I've witnessed awkward parent-child interaction that put it to shame and I'll quote it here now. The setting was a bunch of us out climbing, including a married couple and their 16-year-old son.

<son's name>, are you having sex?
If you were having sex, you'd tell me, right?
Why not?

Boyhood has no dialogue that perfect. Pituophis catenifer annectens ♂ On September 1, 1983, the Soviet Union shot down Korean Air Flight 007 which had violated its airspace.

The USA was quick to insist that the Soviets had fired on the plane with full knowledge that it was a civilian airliner. But we didn't know that. From the introduction to Seymour Hersh's book on KE007, The Target is Destroyed:
Those [intelligence agents] who chose to talk to me did so out of a conviction that political abuse of communications intelligence has become a reality in the Reagan administration, and a belief that to protest to their superiors about it would be futile and damaging to their careers. Some of those interviewed did retire from intelligence service shortly after the events described in this book. In a few cases, the mishandling of Flight 007 played a role in their decision to get out.
The USSR in turn claimed the flight had been deliberately sent into Soviet airspace at the request of the USA. That assertion was also ahead of any available evidence.

Five years later, the USS Vincennes shot down Iran Air Flight 655. Statements by US officials featured numerous untruths, e.g.:
  • the Vincennes was in international waters at the time (it was in Iranian waters)
  • Flight 655 was outside of a commercial air corridor (it wasn't)
  • Flight 655 was descending (it was climbing)
So yeah I'm skeptical about everything I hear in these early days after Malaysia Airlines Flight 17 went down. Today, math (but nothing scarier than matrix multiplication and a whiff of complex arithmetic).

When I first did photography, scaling an image was done by moving an enlarger head up and down and mirroring an image was a matter of turning the negative over. In computer graphics, scaling and mirroring are mathematical transformations: (x,y) coördinates of image elements are replaced by linear combinations of the original x and y.

Matrix multiplication is a concise way to express linear combinations:
the values of  a b c d  control the type of transformation Sample transformation matrices and their effects on text:

original scale mirror rotate shear
identity matrix both x and y scaled by 150% reflected about the x axis counterclockwise rotation a.k.a. oblique or skew
dog 150%qogtheta = 106°x = x + 0.3y

A key feature of using matrices is that multiple transformations in sequence can be folded together by matrix multiplication.

Sometimes a sequence of transformations turns out to be equivalent to a single familiar transformation. A carefully-chosen sequence of three shears is equivalent to rotation, good to know if for some reason you must do arbitrary rotations with a feeble program like Micros‑‑t Paint (which only rotates by multiples of 90° but which does know how to shear).

But matrices aren't just for graphics.

The Fibonacci sequence (0, 1, 1, 2, 3, 5, 8, ...) has the recurrence relation Fn = Fn‑1 + Fn‑2, concisely expressible by powers of a 2×2 matrix:
0 1 1 1 (That this is correct for whole values of n is easily shown by induction.)

Raising a matrix to a power by repeated matrix multiplication is a slow process, but in this case there's a trick loosely akin to the rotation-by-three-shears maneuver. There's an advantageous way to decompose this 0 1 1 1 matrix into three factors. In the language of graphical transformations, the three components are a rotation (by about 211.7°), then a scale-with-reflection, then the inverse of the original rotation. Denoting the appropriate rotation matrix by R:
eigendecomposition Pairs of inverses R‑1 and R cancel out when raising the 0 1 1 1 matrix to powers, and raising a diagonal matrix to a power is as simple as raising each element to the desired power. (See here if that wasn't clear.) That is,
diagonalizable matrix to the nth power which gives the basis for a closed‑form expression for the nth Fibonacci number.

And because raising a matrix to non‑integral powers is even more fun than doing arbitrary rotations in Paint, why not calculate Fn for continuous real values of n? The negative number ‑0.618... in the diagonal matrix means the results are complex, but that just adds to the flavor.

Here's Fn plotted on the complex plane as n varies from [0,7]. The curve intersects the real axis at Fibonacci numbers 0, 1, 1, 2, 3, 5, 8, 13. complex axis scale exaggerated (kind of like elevation on 3D topo maps)

Thanks to everyone whose pages are linked to above and to Ron Knott, on whose page I first saw Fn evaluated for continuous values of n. Caesalpinia gilliesi flower + bee
Philosophy is to science as pornography is to sex: it is cheaper, easier, and some people prefer it.