Second Thoughts

Behold the mighty Dinosaur,
Famous in prehistoric lore,
Not only for his weight and strength
But for his intellectual length.
You will observe by these remains
The creature had two sets of brains —
One in his head (the usual place),
The other at his spinal base.
Thus he could reason a priori
As well as a posteriori.
No problem bothered him a bit:
He made both head and tail of it.
So wise he was, so wise and solemn,
Each thought filled just a spinal column.
If one brain found the pressure strong
It passed a few ideas along;
If something slipped his forward mind
‘Twas rescued by the one behind;
And if in error he was caught
He had a saving afterthought.
As he thought twice before he spoke
He had no judgments to revoke;
For he could think, without congestion,
Upon both sides of every question.

Oh, gaze upon this model beast,
Defunct ten million years at least.

— Bert Leston Taylor, A Line-O’-Verse or Two, 1911

Time and Chance

A deck contains 52 cards, 12 court cards, 4 suits, and 13 ranks.

A year contains 52 weeks, 12 months, and 4 seasons of 13 weeks.

If A=1, J=11, Q=12, and K=13, then the values in a deck of cards total 364.

See Apropos.

The Thought That Counts

In 1988 Martine Tischer proposed a novel way to add interest to a gift: wrap it in sheets of uncut U.S. currency:

First of all, currency, particularly U.S. paper currency having the color green, is very attractive and suggests power and wealth … If desired, the package can be framed. Also if desired, the recipient of the package can deposit the whole sheet in a bank or exchange it at a bank for cut bills. The wrapping itself can be used as a medium of exchange, since it is money.

See Gotcha.

Ones in a Million

Of the integers from 1 to 1,000,000, which are more numerous: the numbers that contain a 1 or those that don’t?

Click for Answer


How to clean a 40-foot spectrograph, from R.W. Wood’s Researches in Physical Optics, 1913:

The long tube was made by nailing eight-inch boards together, and was painted black on the inside. Some trouble was given by spiders, which built their webs at intervals along the tube, a difficulty which I surmounted by sending our pussy-cat through it, subsequently destroying the spiders with poisonous fumes.

This was the least of Wood’s exploits. Walter Bruno Gratzer, in Eurekas and Euphorias, writes that the physicist “would alarm the citizens of Baltimore by spitting into puddles on wet days, while surreptitiously dropping in a lump of metallic sodium, which would explode in a jet of yellow flame.”


“Men who are unhappy, like men who sleep badly, are always proud of the fact.” — Bertrand Russell

In a Word

n. seasickness

After an unusually queasy Channel crossing in 1868, Henry Bessemer conceived a steamer whose cabin was mounted on gimbals. In heavy seas the hull could roll beneath the passengers without rippling their cognac.

Work began immediately; in 1872 constructor E.J. Reed promised, “Although she may not fulfil every random prophecy that has been printed respecting her, she will thoroughly fulfil the object which the travelling public desire — namely, that of enabling us to cross to and from the Continent with health, decency, and comfort.”

The 350-foot S.S. Bessemer undertook her first public voyage on May 8, 1875 — and inauspiciously crashed into the pier. She moved too slowly and would not answer the helm. Investors lost confidence and the ship was eventually sold for scrap, but Bessemer insisted to the last that his conception had not been fully realized: “My hydraulic controlling apparatus was never completed, was never tested at sea, and consequently never failed.”

Topsy Turvy,_schematic.svg

The north pole is the south pole. Earth’s north magnetic pole is actually the south pole of its magnetic field — a compass needle points “north” because opposites attract.

(Thanks, Jeremy.)

The Figure 8 Puzzle

figure 8 puzzle

Can this loop of string be freed from its wire? Stewart Coffin, who devised the puzzle in 1974, writes, “I soon became convinced that this was impossible, but being a novice in the field of topology, I was at a loss for any sort of formal proof.” He published the challenge in a newsletter and has been receiving requests for a solution ever since. Adding to the confusion, in 1976 a British puzzle editor mistakenly claimed with that Coffin’s creation was equivalent to another puzzle with a known solution, and Pieter van Delft and Jack Botermans published an amusingly bewildering “solution” of their own in their 1978 book Creative Puzzles of the World.

In the meantime, fans around the world have continued to experiment, and mathematicians Inta Bertuccioni and Paul Melvin have both offered proofs that the puzzle is unsolvable. “Whoever would have guessed that this little bent piece of scrap wire and loop of string would launch itself on an odyssey that would carry it around the world?” Coffin writes. “Will it mischievously rise again, perhaps disguised in another form, as topological puzzles so often do?”

The Grate Beyond

An anonymous proof that heaven is hotter than hell, from Applied Optics, August 1972:

The temperature of Heaven can be rather accurately computed from available data. Our authority is the Bible: Isaiah 30:26 reads, Moreover the light of the Moon shall be as the light of the Sun and the light of the Sun shall be sevenfold, as the light of seven days. Thus Heaven receives from the Moon as much radiation as the Earth does from the Sun and in addition seven times seven (forty-nine) times as much as the Earth does from the Sun, or fifty times in all. The light we receive from the Moon is a ten-thousandth of the light we receive from the Sun, so we can ignore that. With these data we can compute the temperature of Heaven: The radiation falling on Heaven will heat it to the point where the heat lost by radiation is just equal to the heat received by radiation. In other words, Heaven loses fifty times as much heat as the Earth by radiation. Using the Stefan-Boltzmann fourth-power law for radiation

grate beyond power law

where E is the absolute temperature of the Earth — 300K. This gives H as 798K absolute (525°C).

The exact temperature of Hell cannot be computed but it must be less than 444.6°C, the temperature at which brimstone or sulfur changes from a liquid to a gas. Revelations 21:8: But the fearful and unbelieving … shall have their part in the lake which burneth with fire and brimstone. A lake of molten brimstone means that its temperature must be below the boiling point, which is 444.6°C. (Above that point it would be a vapor, not a lake.)

We have then, temperature of Heaven, 525°C. Temperature of Hell, less than 445°C. Therefore, Heaven is hotter than Hell.