the British succession

Posted on Saturday, 2014 April 26 by Anton

A change to the law of royal succession has been enacted by some of the 16 Commonwealth Realms, to become effective when all of them have done so. Its most conspicuous feature is removing the preference for male heirs, but only from those sons born after 28 October 2011 (the date of the conference where the terms were decided).

Rather than the date cutoff, it would be simpler in my humble opinion to make explicit exceptions for past cases where sex trumped seniority. There are only two since the last change (1702) in succession law; thus: The descendants of King George III shall precede those of his elder sister Augusta, Duchess of Brunswick; and the descendants of King Edward VII shall precede those of his elder sister Victoria, German Empress.

Augusta’s heir by sex-neutral primogeniture appears to be Prince Alexander of Wied, born 1960, unless her first great-granddaughter Marie of Württemberg (1807–1865), countess of Neipperg, had issue not mentioned in Wikipedia.
Victoria(jr)’s heir by the same rule is Dr Friederike von der Osten, born 1959.

Posted in heraldry | Leave a comment

relax

Posted on Tuesday, 2014 April 01 by Anton

This curve-fitting thingy is one of several projects on which I’ve made progress in rare fits over several years. It ran into two big snags. I haven’t found how to determine which gridpoints are within the pen-width of a blending arc; two methods that ought to work don’t. (What would help: tutoring in drawing pictures in a MacOS display, so that I might have a better idea where they go wrong. And a pony.)

The other snag is this: For each pair of arcs, there is an infinite family of blending arcs; how to choose the osculation points to minimize rapid changes in curvature, while meeting the gridpoint constraints? Continue reading →

Posted in curve-fitting | 2 Comments

love or nothing

Posted on Sunday, 2014 March 23 by Anton

In Watch on the Rhine (1943; screenplay by Dashiell Hammett from a play by Lillian Hellman) the penniless Count remarks,

Blecher, we do not like each other.

The Nazi to whom he hopes to sell information replies,

But that will not stand in the way of our doing business.

To link such a sentiment to fascism implies a remarkable kind of snobbery.

Posted in cinema, ethics | Leave a comment

dream geography

Posted on Sunday, 2014 March 09 by Anton

In a dream, while strolling among bookshops and the like, I chance to meet someone who hates me but is constrained to be polite. With a venomous smile that person asks, the better to avoid them, on what streets one is most likely to meet me. I name two streets in Oakland, one in Berkeley and one in San Francisco.

On waking, I remember that none of those streets exists.

Posted in psychology | Leave a comment

models of the 35 smallest fullerenes

Posted on Monday, 2014 February 24 by Anton

I noticed that Shapeways had 13 models of the roundest of the fullerenes (one of the 1812 forms of C60), but none of the less regular forms; so I made some.

Each of the white pieces has mirror symmetry; the red pieces are chiral. Not shown (because it hasn’t been printed yet): the blue set, which is a reflection of the red set. The idea is that you buy both red and blue if and only if you count reflected chiral forms separately.

These figures have 12 pentagons and up to 8 hexagons. They include the two smallest forms with no nontrivial symmetries, and the two smallest with no ‘peaks’ where three pentagons meet.

Posted in merch, sciences | 4 Comments

FCC cube generator

Posted on Saturday, 2014 February 01 by Anton

I could have used this a week ago.

def fccstack():
	newlimit = 0
	while True:
		oldlimit = newlimit
		newlimit += 1
		# extend z
		for x in xrange(oldlimit):
			for y in xrange((x+oldlimit)&1, oldlimit, 2):
				yield (x,y,oldlimit)

		# extend y
		for x in xrange(oldlimit):
			for z in xrange((x+oldlimit)&1, newlimit, 2):
				yield (x,oldlimit,z)

		# extend x
		for y in xrange(newlimit):
			for z in xrange((y+oldlimit)&1, newlimit, 2):
				yield (oldlimit,y,z)

g = fccstack()
for dummy in xrange(512):
	p,q,r = g.next()
	print "%d %d %d\t%d" % (p,q,r, p+q+r)

This lists coordinates of sites in a face-centred cubic lattice, filling the smallest cube that contains the number of sites required.

Posted in mathematics, neep-neep | Leave a comment

some thoughts about packing

Posted on Monday, 2014 January 27 by Anton

My bundle of 19 fullerenes is arranged in a face-centred cubic lattice, each ball occupying one of the 24 even-numbered cells of a 4×4×3 array (and parts of the adjacent cells). The spacing of the grid planes is determined by the sums of the radii of the circumspheres of nearest-neighbor balls.

There appears to be much more ‘daylight’ between balls than necessary. That’s not a problem here, as the size of the bounding box is not near the limits of the process; but still it got me thinking about how to tighten the packing. Continue reading →

Posted in mathematics | 3 Comments