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.)

Maillardet’s Automaton

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Martin Scorsese’s film Hugo was inspired by a real event. In 1928 Philadelphia’s Franklin Institute received the remains of an 18th-century brass automaton that had been damaged in a fire. It had been donated by the descendants of wealthy manufacturer John Penn Brock; they knew it had been acquired in France and supposed it to be the work of the German inventor Johann Nepomuk Maelzel, famed for his metronome.

The institute’s machinist set about restoring the machine and discovered that its mechanism used an ingenious system of cams to store almost 300 kilobits of information. When he had finished his work, he placed a pen in its hand and watched it draw four strikingly elaborate illustrations and write three poems (click to enlarge):

The final poem contained a surprise — in its border the machine wrote Ecrit par L’Automate de Maillardet, “written by the automaton of Maillardet.” The automaton’s creator was not Johann Maelzel but the Swiss mechanician Henri Maillardet — and this fact had been remembered only because he had taught the machine to write his name.

Subsequent research showed that Maillardet had created the automaton in the 1700s and exhibited it throughout Europe and Russia. How it came to America is not known. It’s on display today at the Franklin Institute, which demonstrates its talents publicly several times a year.

Podcast Episode 36: The Great Moon Hoax

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In 1835 the New York Sun announced that astronomers had discovered bat-winged humanoids on the moon, as well as reindeer, unicorns, bipedal beavers and temples made of sapphire. The fake news was reprinted around the world, impressing even P.T. Barnum; Edgar Allan Poe said that “not one person in ten” doubted the story. In this episode of the Futility Closet podcast we’ll review the Great Moon Hoax, the first great sensation of the modern media age.

We’ll also learn why Montana police needed a rabbi and puzzle over how a woman’s new shoes end up killing her.

Sources for our segment on the Great Moon Hoax:

Matthew Goodman, The Sun and the Moon, 2008.

The Museum of Hoaxes has an excellent summary of the hoax and its significance in media history, including the text of all six articles.

Listener mail:

Lauren May, “Terrified Banstead Family Confronted by ‘Dark Figure’ on Bypass,” Epsom Guardian, Feb. 23, 2012.

Michael Munro, “‘The Springer’ Leaps From WW2 Urban Legend to Anti-Fascist Superhero,” io9, Sept. 3, 2014 (accessed Nov. 30, 2014).

Eric A. Stern, “Yes, Miky, There Are Rabbis in Montana,” New York Times, Dec. 4, 2009.

“Body of Boy Found as Snow Melts,” The Hour, March 1, 1978.

You can listen using the player above, download this episode directly, or subscribe on iTunes or via the RSS feed at http://feedpress.me/futilitycloset.

Many thanks to Doug Ross for the music in this episode.

If you have any questions or comments you can reach us at podcast@futilitycloset.com. Thanks for listening!

The Pythagoras Tree

Draw a square and perch two smaller squares above it, forming a right triangle:

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Now perch still smaller squares upon these, and continue the pattern recursively:

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Charmingly, if you keep this up you’ll grow a tree:

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Image: Wikimedia Commons

It was dubbed the Pythagoras tree by Albert Bosman, the Dutch mathematics teacher who discovered the figure in 1942. (Each trio of squares demonstrates the Pythagorean theorem.)

At first it looks as though the tree must grow without bound, but in fact it’s admirably tidy: Because the squares eventually begin to overlap one another, a tree sprouted from a unit square will confine itself to a rectangle measuring 6 by 4.

Bygones

The epilogue of The Time Machine contains this strange passage:

One cannot choose but wonder. Will he ever return? It may be that he swept back into the past, and fell among the blood-drinking, hairy savages of the Age of Unpolished Stone; into the abysses of the Cretaceous Sea; or among the grotesque saurians, the huge reptilian brutes of the Jurassic times. He may even now — if I may use the phrase — be wandering on some plesiosaurus-haunted Oolitic coral reef, or beside the lonely saline lakes of the Triassic Age.

What indeed can “now” mean in this context? If the Time Traveller’s life ended on a prehistoric beach, argues philosopher Donald C. Williams, then surely this became an established fact on the day that it happened. If the concept of time is to have any coherence, then history is a tapestry that is eternal and unchanging; to say that it can be changed “at” some future moment seems to be a flat contradiction. “At” where?

“Time travel,” Williams writes, “is analyzable either as the banality that at each different moment we occupy a different moment from the one we occupied before, or the contradiction that at each different moment we occupy a different moment from the one which we are then occupying — that five minutes from now, for example, I may be a hundred years from now.”

(Donald C. Williams, “The Myth of Passage,” Journal of Philosophy, July 1951.)

Punchup

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In order to restore Shakespeare to popularity in the 1930s, the theater critic and satirist A.E. Wilson suggested getting Noël Coward to rewrite Romeo and Juliet:

Julia (sweetly): O, Ro, must you be going? It isn’t four o’clock yet. Another cocktail, darling?
Romeo: Thanks.
Julia: And anyway, don’t be stupid, darling. That wasn’t the lark, silly. It was the thingummyjig, believe me.
Romeo: Rot; it was the lark. The beastly thing’s always singing at this devastating hour of the morning. And it’s getting light and I’d rather leave and live than be caught by your beastly husband and kicked out.
Julia (yawning): Oh, very well, then. Have it your own way, darling.
Romeo: Beastly fag getting up. I’ll stay. Give me another cocktail.
Julia: Sweetest.
Romeo (drinking cocktail): Angel face. (A pause.) But it wasn’t a nightingale.
Julia: It was.
Romeo: Oh, do shut up talking about it. You make me sick.
Julia (sweetly insistent): But dearest, it was the nightingale.
Romeo: Oh, what does it matter, you ass. Let’s get back to bed and forget it. (They go.)

(From Gordon Snell, The Book of Theatre Quotes, 1982.)

Dueling Pennies

A certain strange casino offers only one game. The casino posts a positive integer n on the wall, and the customer flips a fair coin repeatedly until it falls tails. If he has tossed n – 1 times, he pays the house 8n – 1 dollars; if he’s tossed n + 1 times, the house pays him 8n dollars; and in all other cases the payoff is zero.

The probability of tossing the coin exactly n times is 1/2n, so the customer’s expected winnings are 8n/2n + 1 – 8n – 1/2n – 1 = 4n – 1 for n > 1, and 2 for n = 1. So his expected gain is positive.

But suppose it turns out that the casino arrived at the number n by tossing the same fair coin and counting the tosses, up to and including the first tails. This presents a puzzle: “You and the house are behaving in a completely symmetric manner,” writes David Gale in Tracking the Automatic ANT (1998). “Each of you tosses the coin, and if the number of tosses happens to be the consecutive integers n and n + 1, then the n-tosser pays the (n + 1)-tosser 8n dollars. But we have just seen that the game is to your advantage as measured by expectation no matter what number the house announces. How can there be this asymmetry in a completely symmetric game?”