12 = 1
112 = 121
1112 = 12321
11112 = 1234321
111112 = 123454321
1111112 = 12345654321
11111112 = 1234567654321
111111112 = 123456787654321
1111111112 = 12345678987654321
Science & Math
Seeing Double
More proof (if any were needed) that 2 equals 1:
s = 1 – 1/2 + 1/3 – 1/4 + 1/5 – 1/6 + 1/7 – 1/8 + 1/9 – 1/10 + 1/11 – 1/12 …
2s = 2 – 2/2 + 2/3 – 2/4 + 2/5 – 2/6 + 2/7 – 2/8 + 2/9 – 2/10 + 2/11 – 2/12 …
Rearrange terms:
2s = (2 – 2/2) – (2/4) + (2/3 – 2/6) – (2/8) + (2/5 – 2/10) – (2/12) …
2s = 1 – 1/2 + 1/3 – 1/4 + 1/5 – 1/6 …
But that’s just s again. So 2s = s, and therefore 2 = 1.
(Thanks, Gonzalo!)
Hive Mind
A colony of harvester ants contains the same total number of neurons as a human brain.
Space Ghost
In September 2002, astronomers noticed something odd: An object about 60 feet long was orbiting Earth. It must have arrived recently, but it didn’t resemble any recently launched spacecraft. It might have been an asteroid … but it appeared, spookily, to bear titanium dioxide paint. Was it an alien ship?
The object disappeared again in June 2003, so officially we’re still baffled. But the best guess is that it’s an old stage of Apollo 12 that somehow wandered away from Earth in 1971, circled the sun about 30 times, and came home to visit. If that’s true then it might come back again in 2032—we can visit it on our rocket scooters.
MacFarlane’s Bear
In 1864, the Inuit gave the skin and skull of an “enormous” yellow-furred bear to naturalist Robert MacFarlane. He packed them up and shipped them to the Smithsonian Institution, where they were placed in storage and forgotten.
Fifty-four years later, zoologist Clinton Hart Merriam unpacked the remains and realized they represented an entirely new species, and MacFarlane’s specimen was apparently the last of its kind. No one has ever seen a living “MacFarlane’s bear,” except for those Inuit — and now their story is lost.
Proof That Five Equals Four
-20 = -20
25 – 45 = 16 – 36
52 – 45 = 42 – 36
52 – 45 + 81/4 = 42 – 36 + 81/4
(5 – 9/2)2 = (4 – 9/2)2
5 – 9/2 = 4 – 9/2
5 = 4
We already know that 1 = 0, that 2 = 1 and that one dollar equals one cent. Does this mean that money has no value?
“Interest of Money”
Dr. Price, in the second edition of his “Observations on Reversionary Payments,” says: “It is well known to what prodigious sums money improved for some time at compound interest will increase. A penny so improved from our Saviour’s birth, as to double itself every fourteen years — or, what is nearly the same, put out at five per cent. compound interest at our Saviour’s birth — would by this time have increased to more money than could be contained in 150 millions of globes, each equal to the earth in magnitude, and all solid gold. A shilling, put out at six per cent. compound interest would, in the same time, have increased to a greater sum in gold than the whole solar system could hold, supposing it a sphere equal in diameter to the diameter of Saturn’s orbit. And the earth is to such a sphere as half a square foot, or a quarto page, to the whole surface of the earth.”
— Barkham Burroughs’ Encyclopaedia of Astounding Facts and Useful Information, 1889
Proof That 1 Equals 0
More proof that math is broken:
0 = 0 + 0 + 0 + …
0 = (1 – 1) + (1 – 1) + (1 – 1) + …
Okay so far? Now shift the parentheses:
0 = 1 + (-1 + 1) + (-1 + 1) + (-1 + 1) + …
0 = 1 + 0 + 0 + 0 + …
0 = 1
Now we’ll have to scrap the whole discipline.
Dudeney Numbers
Only six numbers have this curious property:
1 = 1; 13 = 1
8 = 5 + 1 + 2; 83 = 512
17 = 4 + 9 + 1 + 3; 173 = 4913
18 = 5 + 8 + 3 + 2; 183 = 5832
26 = 1 + 7 + 5 + 7 + 6; 263 = 17576
27 = 1 + 9 + 6 + 8 + 3; 273 = 19683
They’re called Dudeney numbers, after the English author and mathematician who discovered them. (Regular readers know I’m something of a fan.)
Shibboleth
Isaac Asimov proposed a simple way to distinguish chemists from non-chemists: Ask them to read aloud the word unionized.
Non-chemists will pronounce it “union-ized”, he said — and chemists will pronounce it “un-ionized.”