Detail from a discarded 1900s children’s book I bought from the recycling center yesterday: ‘CAMEL’
update: A 150-dpi scan of the full page can be viewed here.
Archive for October, 2005
This post has been removed
The original blog entry that appeared on this page, and all follow-up comments posted by the public, have been removed under threat of lawsuit. In May-July 2008, the World Scientific and Engineering Academy and Society (”WSEAS”), represented by the law office of Charles Lee Mudd Jr. in Chicago, threatened to bring suit for defamation, trade libel, and commercial disparagement because of my public complaints on their marketing practices and institutional culture in 2004–2005.
I disagree with all their assessments of the situation, and am disappointed to consider the chilling effect this decision may have on others who have made the same complaints. But as a writer running a small business I am unable to afford the expense and stress of a legal case on such a trivial matter.
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Detail from a discarded 1900s children’s book I bought from the recycling center today: ‘DEER’
update: A somewhat reduced (150dpi) version of the whole page may be viewed here.
The Memory Hole [rescuing knowledge, freeing information]
The Memory Hole [rescuing knowledge, freeing information] contains material and reports generally unavailable elsewhere. (Via TeleRead.)
What I’m reading
Somebody famous — one of the most influential authors of the 20th Century, in fact — being reprinted via DIstributed Proofreaders. The page I just read:
…lished, inhabitants of a host of other worlds have–dropped here, hopped here, wafted, sailed, flown, motored–walked here, for all I know–been pulled here, been pushed; have come singly, have come in enormous numbers; have visited occasionally, have visited periodically for hunting, trading, replenishing harems, mining: have been unable to stay here, have established colonies here, have been lost here; far-advanced peoples, or things, and primitive peoples or whatever they were: white ones, black ones, yellow ones–
I have a very convincing datum that the ancient Britons were blue ones.
Of course we are told by conventional anthropologists that they only painted themselves blue, but in our own advanced anthropology, they were veritable blue ones–
Annals of Philosophy, 14-51:
Note of a blue child born in England.That’s atavism.
Giants and fairies. We accept them, of course. Or, if we pride ourselves upon being awfully far-advanced, I don’t know how to sustain our conceit except by very largely going far back. Science of today–the superstition of tomorrow. Science of tomorrow–the superstition of today.
Notice of a stone ax, 17 inches long: 9 inches across broad end. (Proc. Soc. of Ants. of Scotland, I-9-184.)
Amer. Antiquarian, 18-60:
Copper ax from an Ohio mound: 22 inches long; weight 38 pounds.Amer. Anthropologist, n.s., 8-229:
Stone ax found at Birchwood, Wisconsin–exhibited in the collection of the Missouri Historical Society–found with “the pointed end embedded in the soil”–for all I know, may have dropped there–28 inches long, 14 wide, 11 thick–weight 300 pounds.Or the footprints, in sandstone, near Carson, Nevada–each print 18 to 20 inches long. (Amer. Jour. Sci., 3-26-139.)
These footprints are very clear and well-defined: reproduction of them in the Journal–but they assimilate with the System, like sour apples to other systems: so Prof. Marsh, a loyal and unscrupulous systematist, argues:
…
“Science of today—the superstition of tomorrow. Science of tomorrow—the superstition of today.” Whether one is a skeptic or gullible fool, that cynical appraisal seems valid. Here’s to Charlie.
Left as an exercise for the student: How about a nice slice of Buffon pie?
It is a centuries-old tradition that when one presents a mathematical recreation or exercise, there must be a humorous or fanciful framing story about a farmer and some animals crossing a river, or a mysterious alien visitor from the fourth dimension, or a lady and a tiger. Maybe there’s just some implicit drunken old tweed-wearing fart fiddling with matchsticks and odd-sized coins in a mythic pub somewhere.
There shall be none of that here today. No Chinamen, no chess boards, no bridges, no salesmen, no pie slicing, no needles, no seating arrangements, no Islands of Liars. No. Not today.
Do this thing: Draw a circle of radius 1, centered at (0,0). Generate a large list of N random pairs of (radius, angle) uniformly from the ranges (0,2) and [0,2π), respectively. For each such pair, draw a circle of radius 1, centered at the point denoted by the pair (radius, angle).
Now look at all the little teeny crescenty shapes into which the N overlapping circles cut the original centered circle. Think of these as "polygons" with curved sides, and vertices wherever two circles intersect. Notice that in this system with curves, there can be nonempty "polygons" with two sides: two intersecting circles always create three "polygons" with two sides each.
Here is an example of what it might look like:
Do this thing: Determine the expected distribution of the number of sides of all the pieces the original circle has been broken into, for N in {1,2,4,8,16,32,44,97,111}. I don't care what happens outside the circumference of that first circle, the one shown in red in the image. I just care about the little pieces inside it. Does the distribution of the number of "polygon" sides approach a Normal distribution as N gets large?
Consider this thing: What if the circle was dissected with straight lines, arranged using the same sort of random points (radius ∈ [0,1), angle ∈ (0,2π]) to denote the points of closest approach of the line to the origin (0,0)? In other words, the point chosen at random is taken to be the position where a line segment extending (radius) distance in direction (angle) from the origin would just touch and be perpendicular to the cutting line you draw. In this case, would the distribution of polygon side counts change significantly?
Do these things: In the first case — the one with the circles — color each “polygon” that has two sides fuligin, three sides chatoyant, four sides ultraviolet, five sides megayellow, six sides octarine, seven sides opaline, and eight or more sides viridian. What proportion of the “polygons” of the same color are adjacent (share at least one edge segment)?
What proportion of all adjacent pairs of “polygons” differ by no more than one step?
What proportion of the area of the original circle will disappear as you remove the two-sided, three-sided and other “polygon” classes, in turn?
Suppose you throw away every piece of the cut circle that is not a 2-sided “polygon”: how much of the area of the circle remains as a function of N? Do it for the 3-sided “polygons”, and the others too. Which class contains the largest area of the original circle? Which the least?
Which class, when sorted out in this way by number of “polygon” sides, contains the largest contiguous chunk of the circle, counting “polygons” as contiguous only if they share edges, but not if they touch only at corners?
Networks gallery
visualcomplexity.com | A visual exploration on mapping complex networks.
(Via information aesthetics.)
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