I’ve been designing printable models of the Lawson-Klein surfacew = cos(u) cos(2v)
x = cos(u) sin(2v)
y = sin(u) cos(v)
z = sin(u) sin(v)
As you can plainly see, this figure lives in S3 (positively curved 3-space), so stereographic projection can bring it into E3 (Euclidean 3-space) without adding more self-intersections. (It crosses itself at u=nπ.)
To minimize the distortion of the projection, I want the projection center to be as far as possible from the surface. One thing I tried was pursuit: starting with an arbitrary point P in S3 and an arbitrary point L(u,v) in the surface, move (u,v) to bring L closer to P while simultaneously moving P away from L. This gets me nowhere so far: it either fails to converge or P converges to the antipodes of L, which is also in the surface (change u by π).
A recent comment on this blog from someone named ‘air jordan 1 ebay’:
Hello, i read your blog occasionally and i own a similar one and i was just wondering if you get a lot of spam responses? […]
Yes. Yes, I do.
need a pun here about music and cryptography
Given a piece of music written for just intonation, clearly you could derive another piece by replacing all factors of 3 with factors of 5 and vice versa (or pick some other pair of primes). Sometimes the result might even be good.
For years I’ve occasionally had a mysterious itch at my lowest left rib, nothing showing on the skin. Now it has spread rightward at the same altitude, making me think: could this be mild shingles?
The Curious Case of the Catchy but Inappropriate Title
In Mamet’s The Spanish Prisoner (1997), Joe, for a genius, is a bit stupid:
Jimmy tells Joe to “bring the Process” to their meeting in the park. Joe never mentioned that word to Jimmy. Though Joe is already suspicious of Jimmy, he does not notice. (Well, maybe he’s too angry to notice.)
The fake FBI agents tell Joe that Jimmy is working a classic Spanish Prisoner scam, though Jimmy has done almost nothing to set up such a story. If he says the “princess” is in trouble, will Joe hand over the Process to help her? Hardly. So why doesn’t Joe remark that it doesn’t fit?
When the police ask for something with Jimmy’s fingerprints, the plot requires Joe to take a day or so to remember the switched book.
Susan is the obvious suspect for the theft of Joe’s knife; this does not occur to Joe.
theories of magic
All comics have to have a setting. Very often, almost all of that setting can be implied, especially if the comic is set in the quote-unquote “real world”. If you’re using magic or hypertechnology to drive your plots, however, it’s important to define how that magic or that hypertechnology works.
Much as some of us would like it to be important, no, it isn’t. Think of fairy tales; think of Tolkien, who never expounded a theory of magic and probably never thought of needing one. The scientific approach to magic was, I think, invented by such writers as Fletcher Pratt and Randall Garrett; it is the novel feature of their works.
I’ve noticed some changes in jumping from MacOS 10.6.x to 10.9:
The keystroke Command Option Eject no longer puts the computer to sleep.
On the Dock, the active app indicator is much less visible.
Scroll bars no longer have arrow buttons, so I can’t click to scroll slowly.
When I charge my telephone on USB, it’s no longer recognized as a volume.