135 = 1 + 3^{2} + 5^{3}

175 = 1 + 7^{2} + 5^{3}

518 = 5 + 1^{2} + 8^{3}

598 = 5 + 9^{2} + 8^{3}

# Science & Math

# Guess

Once upon a time, there lived a rich farmer who had 30 children, 15 by his first wife who was dead, and 15 by his second wife. The latter woman was eager that her eldest son should inherit the property. Accordingly one day she said to him, “Dear Husband, you are getting old. We ought to settle who shall be your heir. Let us arrange our 30 children in circle, and counting from one of them, remove every tenth child until there remains but one, who shall succeed to your estate.”

The proposal seemed reasonable. As the process of selection went on, the farmer grew more and more astonished as he noticed that the first 14 to disappear were children by his first wife, and he observed that the next to go would be the last remaining member of that family. So he suggested that they should see what would happen if they began to count backwards from this lad. She, forced to make an immediate decision, and reflecting that the odds were now 15 to 1 in favour of her family, readily assented. Who became the heir?

— W.W. Rouse Ball, *Mathematical Recreations & Essays*, 1892

# Shades of Gray

An optical illusion. Squares A and B are the same color.

# 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

8^{4} + 2^{4} + 0^{4} + 8^{4} = 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

1^{3} + 3^{3} + 6^{3} = 244

2^{3} + 4^{3} + 4^{3} = 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