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Science & Math

Nobrow Cartoons by Mark Heath

nobrow klein bottles

After Hours


When the Cavendish Laboratory at Cambridge University instituted an annual dinner in 1897, it began a tradition of “postprandial proceedings” — typically songs sung around a piano. This air, “Ions Mine,” was sung to the tune of “Clementine”:

In the dusty lab’ratory,
‘Mid the coils and wax and twine,
There the atoms in their glory
Ionize and recombine.

(chorus) Oh my darlings! Oh my darlings!
Oh my darling ions mine!
You are lost and gone forever
When just once you recombine!

In a tube quite electrodeless,
They discharge around a line,
And the glow they leave behind them
Is quite corking for a time.

(repeat chorus)

And with quite a small expansion,
1.8 or 1.9,
You can get a cloud delightful,
Which explains both snow and rain.

(repeat chorus)

In the weird magnetic circuit
See how lovingly they twine,
As each ion describes a spiral
Round its own magnetic line.

(repeat chorus)

Ultra-violet radiation
From the arc of glowing lime,
Soon discharges a conductor
If it’s charged with minus sign.

(repeat chorus)

Alpha rays from radium bromide
Cause a zinc-blende screen to shine,
Set it glowing, clearly showing
Scintillations all the time.

(repeat chorus)

Radium bromide emanation,
Rutherford did first divine,
Turns to helium, then Sir William
Got the spectrum, every line.

(repeat chorus)

The fourth verse was contributed by J.J. Thomson himself.

In a Word

n. a visible manifestation of Satan

Potassium chlorate brings out the worst in gummy bears.

In their 1996 manual Chemical Curiosities, H.W. Roesky and K. Möckel introduce this demonstration with an invocation from the Talmud: “He who ponders long over four things were better never to have been born: that which is above, that which is below, that which came before, and that which comes hereafter.”

(Please don’t try this yourself.)

Command Performance

J.B.S. Haldane’s father was a physiologist who would sometimes take his son along while investigating mines in order to teach him the rudiments of science. At one point they were lowered by a bucket into a pit in North Staffordshire, where a tunnel’s low roof forced their party to crawl:

“After a while, we got to a place where the roof was about eight feet high and a man could stand up. One of the party lifted his safety lamp. It filled with blue flame and went out with a pop. If it had been a candle this would have started an explosion, and we should probably have been killed. But of course the flame of the explosion inside the safety lamp was kept in by the wire gauze. The air near the roof was full of methane, or firedamp, which is a gas lighter than air, so the air on the floor was not dangerous.

“To demonstrate the effects of breathing firedamp, my father told me to stand up and recite Mark Anthony’s speech from Shakespeare’s Julius Caesar, beginning ‘Friends, Romans, countrymen.’ I soon began to pant, and somewhere about ‘the noble Brutus’ my legs gave way and I collapsed on to the floor, where, of course, the air was all right. In this way I learnt that firedamp is lighter than air and not dangerous to breathe.”

So It Goes

The Man who thought about Proteids sat by the roadside, writing with an indelible pencil in a little notebook. And Spring, all in pink and white, came tripping by, and cried to him: ‘I will dance for you! Watch me dance!’ She danced very prettily, but the Man went on writing, and never looked at her once. So Spring, being young, burst into tears, and told her sister, Summer.

Summer said to herself: ‘Spring is very foolish to cry. Probably he does not like dancing. I will sing to him.’ She sang a beautiful sleepy song to him, but he never listened, being busy writing in his little notebook. Summer was indignant, and told her sister, Autumn.

Autumn said: ‘There are many good men who do not like dancing. I will give him some of my wine.’ So she went to the Man and offered him her purple wine, but he merely said, ‘I do not drink wine,’ and resumed his writing. Then Autumn was very angry indeed, and told her big brother, Winter, all that had passed.

Winter was an enormous fellow, with a dreadful roar and howl, and every time he moved, snowflakes came whirling from his flowing robes. ‘Show me the fellow,’ he bellowed, puffing out his cheeks. Then he saw the Man who thought about Proteids, still sitting by the roadside.

‘Do you know me?’ roared Winter, and the Man looked and his teeth chattered like dead men’s bones.

Then Winter seized him by the neck and whirled him round and round, and finally flung him over his left shoulder into space.

And the Man who thought about Proteids has not been seen since, but, the other day, a boy found the little note-book lying by the roadside.

– J.B. Priestley, Brief Diversions, 1922

That’s Logic


“If it is feared by a schizophrenic that nothing feared by a schizophrenic is the case, then there must be at least one other schizophrenic fear besides this one.”

– P.T. Geach, quoted in A.N. Prior, “On a Family of Paradoxes,” Notre Dame Journal of Formal Logic, 1961

Sicherman Dice


What’s unusual about these dice is obvious. But what’s normal about them?

When thrown together, they produce the same probability distribution as a pair of ordinary dice. There are six ways to throw a 7, five ways to throw an 8, etc. This the only possible alternate arrangement in which all the face values are positive.

They were discovered/invented by George Sicherman of Buffalo, N.Y.

A Chemical Traffic Light

A solution of glucose, sodium hydroxide, and indigo carmine, when shaken, will change from yellow to red to green. Left to sit, it will revert to red again, then yellow, and the process can be repeated.

The indigo carmine is green when oxidized, yellow when reduced, and red in the intermediate semiquinone state.


  • Holmes and Watson never address one another by their first names.
  • Until 1990, the banknote factory at Debden, England, was heated by burning old banknotes.
  • The vowels AEIOUY can be arranged to spell the synonyms AYE and OUI.
  • 741602 + 437762 = 7416043776
  • “In all matters of opinion our adversaries are insane.” — Mark Twain

Two trick questions:

Who played the title role in Bride of Frankenstein? Valerie Hobson — not Elsa Lanchester.

Did Adlai Stevenson ever win national office? Yes — Adlai Stevenson I served as vice president under Grover Cleveland in 1893.


gedanken tank puzzle 1

A tank of water has two holes of equal area, one at top and one at bottom. The top one leads to a downspout, so that both holes discharge their water at the same level. Ignoring friction, which hole produces the faster flow of water?

You actually don’t need to know the physics in order to solve this — it yields to an insight.

Click for Answer

Order and Chaos


Arrange a deck of cards in alternating colors, black and red. Now cut the deck so that the bottom card of one pile is black and the other is red. Riffle-shuffle the two piles together again. Now remove cards from the top of the pack in pairs. How many of these pairs should we expect to contain cards of differing colors?

Surprisingly, all of them will. During the shuffle, suppose a black card falls first. It must be followed by either the next card in its own pile, which is red, or the first card from the other pile, which is also red. Either way, this first pair will contain one black card and one red card, and by the same principle so will each of the other 25 pairs produced by the shuffle. This effect was first identified by mathematician Norman Gilbreath in 1958.

Related: Arrange the deck in a repeating cycle of suits, such as spade-heart-club-diamond, spade-heart-club-diamond, etc. Ranks don’t matter. Now deal about half of this deck onto the table and riffle-shuffle the two halves back together. If you draw cards from the top in groups of four, you’ll find that each quartet contains one card of each suit.

See So Much for Entropy.

Blind Dates

stover calendar trick

A calendar curiosity by Canadian magician Mel Stover:

Offer any month’s calendar to a friend and have him outline a 4×4 square of dates. Ask him to circle any date in that square and cross out the other numbers in its row and column. Have him do this three more times and then add the circled numbers.

You can predict his answer by totaling the numbers in either pair of diagonally opposite corners in the square and doubling that number. Why does this work?

Near Thing

‘Well, do you know the one,’ I began, ‘in which two geologists converse in a cafe? One of them says: ‘Yes, unfortunately fifteen billion years from now the Sun will cool, and then all life on Earth will perish.’ A card-player nearby has been half listening to the joke, and turns in terror to the geologist: ‘What did you say? In how many years will the Sun cool?’ ‘Fifteen billion years,’ the scientist replies. The card-player lets out a sigh of relief: ‘Oh, I was afraid you said fifteen million!’

– László Feleki in Impact of Science on Society, 1969



“Even if I could be Shakespeare, I think I should still choose to be Faraday.” — Aldous Huxley

“The High Standard of Education in Scotland”

We were staying in Ballater, a small town on Deeside in Scotland. In the town was a tiny shop which sold tourist attractions and picture postcards, and in its minute window was a very fine specimen of smoky quartz material. Buying a postcard, I said to the proprietor, ‘That’s a fine group of smoky quartz in your window’ and had this reply in very broad Scotch:

‘That’s no smoky quartz, that’s topaz. It’s a crystal. You can tell crystals by the angles between their faces. If you’re interested I’ll lend you a book on the subject.’

I knew enough (crystals being rather in my line) to be sure it was smoky quartz, and on return to base looked up a book on Mineralogy which said ‘Smoky Quartz, also known as Cairngorm, is called Topaz in Scotland.’

– Sir W.L. Bragg, quoted in R.L. Weber, A Random Walk in Science, 1973

In a Word


n. ignorance; lack of knowledge

n. the study of ignorance

In 1927, Hungarian physiologist Albert Szent-Györgyi isolated a substance in lemons and oranges that seemed to prevent scurvy.

He couldn’t identify it chemically, so he called it “ignose,” meaning “I do not know.”

When the editors of the Biochemical Journal asked for a different name, Szent-Györgyi suggested “godnose.” Finally they settled on “hexuronic acid.”

It turned out to be vitamin C.


From Royal V. Heath, Scripta Mathematica, June 1952:

heath magic square

In the square above, all rows, columns, and diagonals produce the same sum. And:

16 + 11 + 13 + 10 = 9 + 14 + 12 + 15
16 + 17 + 14 + 3 = 11 + 22 + 9 + 8
2 + 15 + 20 + 13 = 5 + 12 + 23 + 10
16 + 5 + 17 + 12 = 20 + 9 + 13 + 8
2 + 11 + 15 + 22 = 14 + 23 + 3 + 10
10 + 16 + 17 + 23 = 11 + 13 + 20 + 22
2 + 8 + 9 + 15 + 11 + 13 + 20 + 22 = 3 + 5 + 12 + 14 + 10 + 16 + 17 + 23

Most remarkably, everything above holds true if you square each term.

A Balanced Diet


In studying metabolism in the early 1600s, Santorio Santorio undertook a unique study: He conducted his daily activities on a platform attached to a steelyard scale. After years of readings, he learned that his food always weighed more than his excretions, and concluded that the rest was lost through “invisible perspiration,” the loss of matter through the pores and breath.

Santorio’s conclusions remained the state of the art for more than a century. When Ben Franklin wrote in 1742, “If thou art dull and heavy after Meat it is a sign that thou hast exceeded due measure,” he was essentially repeating Santorio’s aphorism of 150 years earlier, “Meats which promote Perspiration bring Joy, but those which obstruct it Sorrow.”



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.”

Topsy Turvy


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.

Fish Scales


While a student at Cambridge, Paul Dirac attended a mathematical congress that posed the following problem:

After a big day’s catch, three fisherman go to sleep next to their pile of fish. During the night, one fisherman decides to go home. He divides the fish in three and finds that this leaves one extra fish. He throws this into the water, takes one third of the remaining fish, and departs.

The second fisherman awakes. Not knowing that the first has left, he too divides the fish into three piles, finds one fish left over, discards it, and takes a third of the remainder. The third fisherman does the same. What is the least number of fish that the fishermen could have started with?

Dirac proposed that they had begun with -2 fish. The first fisherman threw one into the water, leaving -3, and took a third of this, leaving -2. The second and third fisherman followed suit.

This story was recalled by “a well-meaning experimenter” in the Russian miscellany Physicists Continue to Laugh (1968). “I could tell many other stories about theoreticians and their work,” he wrote, “but they have told me that one theoretician is writing a story under the title ‘How Experimental Physicists Work.’ That, of course, will be presented upside down.”

All Greek

In 1948, George Washington University doctoral student Ralph Alpher was working on a cosmology thesis under physicist George Gamow. As the paper took shape, “Gamow, with the usual twinkle in his eye, suggested that we add the name of Hans Bethe to an Alpher-Gamow letter to the editor of the Physical Review,” listing the authors as Alpher-Bethe-Gamow.

Bethe agreed to join, and the result, now known as the αβγ paper, was published on April 1, 1948 (“believe it or not, a date not of our asking”). “The response was fascinating,” Alpher later recalled, “ranging from feature articles, Sunday supplement stories, newspaper cartoons and voluminous mail from religious fundamentalists, to a packed audience of over 200, including members of the press, at the traditionally public (though usually not in this sense) ‘defence’ of the thesis.”

Gamow added, “There was, however, a rumor that later, when the alpha, beta, gamma theory went temporarily on the rocks, Dr. Bethe seriously considered changing his name to Zacharias.”