An optical illusion. Squares A and B are the same color.
Science & Math
Richard’s Paradox
Clearly there are integers so huge they can’t be described in fewer than 22 syllables. Put them all in a big pile and consider the smallest one. It’s “the smallest integer that can’t be described in fewer than 22 syllables.”
That phrase has 21 syllables.
Math Notes
84 + 24 + 04 + 84 = 8208
Buffon’s Needle
Remarkably, you can estimate π by dropping needles onto a flat surface. If the surface is ruled with lines that are separated by the length of a needle, then:
drops is the number of needles dropped. hits is the number of needles that touch a line. The method combines probability with trigonometry; a needle’s chance of touching a line is related to the angle at which it comes to rest. It was discovered by the French naturalist Georges-Louis Leclerc in 1777.
Clarke’s Law
Clarke’s Third Law: Any sufficiently advanced technology is indistinguishable from magic.
Benford’s Corollary: Any technology distinguishable from magic is insufficiently advanced.
Raymond’s Second Law: Any sufficiently advanced system of magic would be indistinguishable from a technology.
Sterling’s Corollary: Any sufficiently advanced garbage is indistinguishable from magic.
Langford’s application to science fiction: Any sufficiently advanced technology is indistinguishable from a completely ad-hoc plot device.
Math Notes
13 + 33 + 63 = 244
23 + 43 + 43 = 136
The Necktie Paradox
You and I are having an argument. Our wives have given us new neckties, and we’re arguing over which is more expensive.
Finally we agree to a wager. We’ll ask our wives for the prices, and whoever is wearing the more expensive tie has to give it to the other.
You think, “The odds are in my favor. If I lose the wager, I lose only the value of my tie. If I win the wager, I gain more than the value of my tie. On balance I come out ahead.”
The trouble is, I’m thinking the same thing. Are we both right?
Unquote
“Why are numbers beautiful? It’s like asking why is Beethoven’s Ninth Symphony beautiful. If you don’t see why, someone can’t tell you. I know numbers are beautiful. If they aren’t beautiful, nothing is.” — Paul Erdös
Math Notes
73939133
7393913
739391
73939
7393
739
73
7
… are all prime. So are:
357686312646216567629137
57686312646216567629137
7686312646216567629137
686312646216567629137
86312646216567629137
6312646216567629137
312646216567629137
12646216567629137
2646216567629137
646216567629137
46216567629137
6216567629137
216567629137
16567629137
6567629137
567629137
67629137
7629137
629137
29137
9137
137
37
7
But see Not So Fast.
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