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Science & Math

Perspective

http://commons.wikimedia.org/wiki/File:PaleBlueDot.jpg

Earth seen from 4 billion miles away, photographed by Voyager 1 on June 6, 1990.

Of the “pale blue dot,” astronomer Carl Sagan said, “That’s here. That’s home. That’s us. On it everyone you love, everyone you know, everyone you ever heard of, every human being who ever was, lived out their lives. The aggregate of our joy and suffering, thousands of confident religions, ideologies, and economic doctrines, every hunter and forager, every hero and coward, every creator and destroyer of civilization, every king and peasant, every young couple in love, every mother and father, hopeful child, inventor and explorer, every teacher of morals, every corrupt politician, every ‘superstar,’ every ‘supreme leader,’ every saint and sinner in the history of our species lived there — on a mote of dust suspended in a sunbeam.”

Exception Paradox

If every rule has an exception, then there must be an exception to the rule that every rule has an exception.

Purple Rain

http://www.sxc.hu/photo/327153

The sky isn’t blue. It’s actually violet, but a quirk of human vision makes us less sensitive to those wavelengths.

Nevermore

http://www.sxc.hu/photo/86239

Seeing a red apple should increase your confidence that all ravens are black.

Why? Because the statement “All ravens are black” is logically equivalent to “All non-black things are non-ravens.” And seeing a red apple (or green grass) confirms this belief.

This is logically inescapable, even if it’s counterintuitive. It’s known as Hempel’s paradox.

Oral Exam

http://books.google.com/books?vid=OCLC03824720&id=phdTZ03tJB8C&pg=PA1&lpg=PA1&dq=%22Wonderful+and+Scientific+Museum%22&as_brr=1#PPA1,M1

Math prodigy George Bidder was born to a Devonshire stonemason in 1806. In a public appearance at age 11, he answered each of these questions in less than a minute:

  • What is the cube root of 673,373,097,125? “Answer, 8,765.”
  • If a mouse can draw one ounce and a half, how many mice can draw 50,000 tons? “Answer, 1,194,666,666, and one ounce over.”
  • If a coach travels from Exeter to Plymouth, 44 miles, every day in a year, how often does a wheel turn round that is 2 feet 9 inches? “Answer, 30,835,200.”
  • If a fan of a windmill goes round 15 times in a minute, how many times will it go round in 7 years, 4 months, 1 week, 2 hours, 3 minutes — 365 days 6 hours to the year, and 28 days to the month? “Answer, 57,897,245.”
  • If the ministers have taken of the income tax 12 millions of money in 1-pound notes, how many miles would they cover a road 30 feet wide, each note being 8 inches by 4 and a half? “He directly answered, 18 miles, 1,653 yards, and one foot.”
  • Suppose the earth to consist of 971 million of inhabitants, and suppose they die in 33 years and four months, how many have returned to dust since the time of Adam, computing it to be 5,850 years? “Answer, 170,410,500,000.” Multiply it again by 99. “Answer, 16,870,639,500,000.”

(Reported in Kirby’s Wonderful and Scientific Museum, 1820)

Attaboy

http://en.wikipedia.org/wiki/Image:Experiment1940.jpg

Sorry about the photo. It’s a dog’s head, kept alive in the 1940s by an experimental Soviet device called an autojector, which pumped oxygenated blood through it. Reportedly this kept the head alive for hours — it would cock its ears at sounds and lick its chops when citric acid was smeared on them.

That ain’t all. If you believe the 1940 film Experiments in the Revival of Organisms, Soviet scientist Sergei S. Bryukhonenko drained the blood from a dog until it reached clinical death, left it in that state for 15 minutes, then connected it to the autojector. In the film, the heart and lungs resume functioning, and 12 hours later the dog is reported to be on its feet, barking and wagging its tail.

Is all this for real? The film’s authenticity is debated — some say it may show re-enactments rather than authentic experiments — but the research itself was well documented, leading eventually to modern heart-lung machines and a posthumous Lenin Prize for Bryukhonenko.

A Pyramid of Palindromes

12 = 1
112 = 121
1112 = 12321
11112 = 1234321
111112 = 123454321
1111112 = 12345654321
11111112 = 1234567654321
111111112 = 123456787654321
1111111112 = 12345678987654321

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

http://commons.wikimedia.org/wiki/File:Earth6391.jpg

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.”

“Lamps Lighted by Currents Passed Through the Human Body”

http://en.wikipedia.org/wiki/Image:Twain_in_Tesla%27s_Lab.jpg

Mark Twain in the laboratory of his friend, inventor Nikola Tesla, where in 1894 Twain briefly became a human light bulb:

In Fig. 13 a most curious and weird phenomenon is illustrated. A few years ago electricians would have considered it quite remarkable, if indeed they do not now. The observer holds a loop of bare wire in his hands. The currents induced in the loop by means of the “resonating” coil over which it is held, traverse the body of the observer, and at the same time, as they pass between his bare hands, they bring two or three lamps held there to bright incandescence. Strange as it may seem, these currents, of a voltage one or two hundred times as high as that employed in electrocution, do not inconvenience the experimenter in the slightest. The extremely high tension of the currents which Mr. Clemens is seen receiving prevents them from doing any harm to him.

– T.C. Martin, “Tesla’s Oscillator and Other Inventions,” Century Magazine, April 1895

Doomsday Clock

Every issue of the Bulletin of the Atomic Scientists since 1947 has displayed a clock face on its cover, symbolizing the world’s proximity to nuclear war (in the judgment of the bulletin’s board of directors).

At its most dire, the clock stood at two minutes to midnight in 1953, when the United States and the Soviet Union tested thermonuclear devices within nine months of one another. Thirty-eight years later, when the superpowers signed the START treaty in 1991, the clock reached 17 minutes to midnight, its most hopeful position to date.

That doesn’t mean we’re making progress. Today it stands at 7 minutes to midnight — which is just where it started 59 years ago.

Bullseye

0.999… is the same as 1. Not just very close, but precisely identical:

a = 0.999…
10a = 9.999…
10aa = 9.999… – 0.999…
9a = 9
a = 1

There’s no trick here. It’s just a mathematical fact that most people find deeply counterintuitive.

One, Three, Five …

In English, every odd number contains the letter e.

The Feynman Point

Between the 762nd and 767th decimal places of pi there are six 9s in a row.

It’s called the Feynman point, because physicist Richard Feynman said he’d like to recite 761 digits and end with “… nine, nine, nine, nine, nine, nine, and so on.”

More Mathematical Coincidences

32 + 42 = 52

And:

33 + 43 + 53 = 63

A Mathematical Coincidence

2646798 = 21 + 62 + 43 + 64 + 75 + 96 + 87

Don’t Blink

The world’s slowest science experiment is the “pitch drop experiment” at the University of Queensland. In 1927, physics professor Thomas Parnell poured some pitch into a funnel to see how long it would take to drip out. Pitch is pretty viscous: When Parnell died in 1948, only two drops had fallen.

The experiment is still going on. The eighth drop fell on Nov. 28, 2000, allowing experimenters to calculate that the pitch has a viscosity about 100 billion times that of water.