# “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

nescience
n. ignorance; lack of knowledge

agnoiology
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.

# Magic

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

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.”

# Overtime

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

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:

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.”