Draw three circles of equal size and inscribe them with a pentagon, a hexagon, and a decagon.
The sides of these figures form a right triangle — and half of a golden rectangle.
Made to Order
Author: Greg Ross
Artistic License
Artist Donald Evans spent his life painting the postage stamps of nonexistent countries. “The stamps are a kind of diary or journal,” he said. “It’s vicarious traveling for me to a made-up world that I like better than the one that I’m in.”
“On little paper rectangles he painted precise transcriptions of his life,” wrote Willy Eisenhart in The World of Donald Evans (1980). “He commemorated everything that was special to him, disguised in a code of stamps from his own imaginary countries — each detailed with its own history, geography, climate, currency and customs — all of it representative of the real world but, like real stamps, apart from it in calm tranquility.”
He painted them as watercolors the size of actual stamps, handling the paper with tweezers and working always with the same trusty brush. When they were finished he would sometimes cancel them with a fanciful postmark carved from a rubber eraser. He preserved them in a 330-page book modeled on a real stamp catalogue, recording in each case the name of the fictional country, the fictional date, the subject and occasion of the stamp’s issue, and the date on which he had completed the painting. He called this book his Catalogue of the World.
By the time he died in an Amsterdam fire in 1977, Evans had painted nearly 4,000 stamps from 42 imaginary nations, bearing dates from 1852 to 1973. He told the Paris Review, “The more I do, the more crazy and minuscule the detail becomes and the more stamplike they become. And that intrigues me. … One of the things I get excited about in making this work is that I try to make it look real.”
The guiding principle for his work, he said, was “basically that it describes something which I think is interesting and that it looks like a stamp.”
Particulars
We cannot seek or attain health, wealth, learning, justice or kindness in general. Action is always specific, concrete, individualized, unique. And consequently judgments as to acts to be performed must be similarly specific. … A man who aims at health as a distinct end becomes a valetudinarian, or a fanatic, or a mechanical performer of exercises, or an athlete so one-sided that his pursuit of bodily development injures his heart. When the endeavor to realize a so-called end does not temper and color all other activities, life is portioned out into strips and fractions. Certain acts and times are devoted to getting health, others to cultivating religion, others to seeking learning, to being a good citizen, a devotee of fine art and so on. This is the only logical alternative to subordinating all aims to the accomplishment of one alone — fanaticism. This is out of fashion at present, but who can say how much of distraction and dissipation in life, and how much of its hard and narrow rigidity is the outcome of men’s failure to realize that each situation has its own unique end and that the whole personality should be concerned with it?
— John Dewey, Reconstruction in Philosophy, 1920
Straight and Narrow
A.B. Kempe’s provocatively titled How to Draw a Straight Line (1877) addresses a fundamental question. In the Elements, Euclid derives his results by drawing straight lines and circles. We can draw a circle by rotating a rigid body (such as a pair of compasses) around a fixed point. But how can we produce a straight line? “If we are to draw a straight line with a ruler, the ruler must itself have a straight edge; and how are we going to make the edge straight? We come back to our starting-point.”
Kempe’s solution is the Peaucellier–Lipkin linkage, an ingenious mechanism that was invented in 1864 by the French army engineer Charles-Nicolas Peaucellier, forgotten, and rediscovered by a Russian student named Yom Tov Lipman Lipkin. In the figure shown here, the colors denote bars of equal length. The green and red bars form a linkage called a Peaucellier cell, and adding the blue links causes the red rhombus to flex as it moves. A pencil fixed at the outer vertex of the rhombus will draw a straight line.
James Sylvester introduced Peaucellier’s discovery to England in a lecture at the Royal Institution in January 1874, which Kempe says “excited very great interest and was the commencement of the consideration of the subject of linkages in this country.” Sylvester writes that when he showed a model of the linkage to Lord Kelvin, he “nursed it as if it had been his own child, and when a motion was made to relieve him of it, replied ‘No! I have not had nearly enough of it — it is the most beautiful thing I have ever seen in my life.'”
Unquote
“It is true that that may hold in these things, which is the general root of superstition; namely, that men observe when things hit, and not when they miss; and commit to memory the one, and forget and pass over the other.” — Francis Bacon
Désert de Retz
French aristocrat François Racine de Monville added a striking summer house to his estate in 1785 — it was designed to resemble the ruined column of an imaginary gigantic temple:
The “colonne brisée” contained four stories of oval rooms connected by a spiral staircase hung with rare plants under a skylight. It was admired by Benjamin Franklin, and it inspired Thomas Jefferson in his own architectural work. (“How grand the idea excited by the remains of such a column!” he wrote to Maria Cosway.) It had fallen into disrepair by the 1950s, but it was renovated and reopened to the public in 2009.
Fleet Cuts
In 1968, American Hugo Vihlen sailed from Casablanca to Florida in a boat 5 feet 11 inches long.
In 1992, Englishman Tom McNally sailed from Portugal to Fort Lauderdale in a boat 5 feet 4.5 inches long.
In 1993 Vihlen reclaimed the record by sailing from Newfoundland to Falmouth in a boat 5 feet 4 inches long.
“Tom McNally made plans to fight back with a minuscule three-foot, eleven-inch boat, and when Vihlen later heard about that he announced his intention to build a three-foot, eight-inch aluminum boat,” writes William Longyard in A Speck on the Sea (2003). “The battle would continue between these two friends and rivals.”
(Thanks, Dave.)
Light Reading
French writer Paul Fournel’s 1990 novel Suburbia begins conventionally enough:
Table of Contents
A Word from the Publisher vi
Foreword by Marguerite Duras vii
An Introductory Note by the Author viii
Suburbia 9
Afterword by François Caradec 215
Supplement for Use in Schools 217
Index 219
And the “Word from the Publisher” promises that “the quality of this little novel, now that passions have subsided, has emerged ever more forcefully.” But the first page is blank except for four footnotes:
1. In French in the original.
2. Concerning the definition of suburb, see the epigraph et seq.
3. What intention on the author’s part does this brutal opening suggest?
4. Local judge.
The same thing happens on the second page:
1. Notice how Norbert comes crashing onto the scene.
2. This passage is a mixture of backslang and immigrant jargon. Transpose into normal English.
3. Motorcycle.
4. Obscene gesture.
And so on — except for footnotes, all the pages in Suburbia are blank. “In Suburbia Fournel was not attempting to give some postmodernist exploration of the nature of literature,” explains Robert Tubbs in Mathematics in Twentieth-Century Literature and Art (2014). “Suburbia, instead, was written according to the lipogrammatic constraint that it contain no letters or symbols. This constraint force Fournel to write a textless narrative. Because of the footnotes on each page, it has content — it is not an empty text; it is simply a textless text, a text that just happens not to contain any words.”
Liquid Assets
New Zealand engineer Bill Phillips found a unique way to model a national economy in 1949: He used water. Working in his garage, he assembled a conglomeration of tanks, pipes, sluices, and valves into MONIAC, a 7-foot hydraulic computer that modeled the economy of the United Kingdom. Colored water, representing money, is pumped from a bottom reservoir to the top, where it’s distributed among taxes, consumer expenditure, and investment, then finds its way downward through the economy. The user can set “functions” that regulate the effect of national income on tax revenue, government spending on consumption, domestic spending on imports or exports, the interest rate on investment, and the exchange rate on exports and imports.
“To approximate a national economy, a ‘Federal Reserve System’ is added (from a tank through the top U-shaped pump) and bank credit is drawn to expand surplus balances when needed,” noted Fortune in a March 1952 feature. “And, if a Keynesian touch is wanted, the government can engage in ‘deficit financing’ by tapping the surplus balances to increase its own expenditures without additional taxation.”
Phillips unveiled the computer at the London School of Economics in 1949 and impressed his audience so much that he was asked to build copies for Harvard, Cambridge, Oxford, the Ford Motor Company and the Central Bank of Guatemala. Unfortunately his invention was soon outmoded by electronic computers, and today only two working “Phillips machines” remain: one at Cambridge and the other (above) at the Reserve Bank of New Zealand.
UPDATE: Yale economist Irving Fisher proposed a similar system in his Ph.D. dissertation in 1891, described by Paul Samuelson as “the best of all doctoral dissertations in economics.” Fisher used a working model of his machine as a teaching tool for 25 years. (Thanks, Sroyon.)
In a Word
acetarious
adj. used in salads