Sound Reasoning

http://en.wikipedia.org/wiki/File:WiiliamEdwardParry.jpg

Wintering in the Canadian Arctic in 1822, Capt. W.E. Parry made a series of experiments to see whether cold affects the velocity of sound. He marked a line of 5,645 feet on the sea ice, put a six-pounder gun at one end, and stood with a second observer at the other end. The gun fired 15 blank charges, and the observers timed the interval between each flash and its report. Generally they got good results, giving a mean velocity of 1,023 feet per second. But, writes Mr. Fisher:

The Experiments on the 9th February, 1822, were attended with a singular circumstance, which was–the officers’ word of command ‘fire,’ was several times distinctly heard both by Captain Parry and myself, about one beat of the chronometer [half a second] after the report of the gun; from which it would appear, that the velocity of sound depended in some measure upon its intensity.

“The word ‘fire’ was never heard during any of the other experiments; upon this occasion the night was calm and clear, the thermometer 25° below zero, the barometer 28.84 inches, which was lower than it had ever been observed before at Winter Island.” The phenomenon, whatever it was, has never been observed elsewhere, but Parry noted another acoustic oddity on his next voyage.

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A Chemical Compound

What’s unusual about this list of elements?

  • Protactinium
  • Radium
  • Praseodymium
  • Oxygen
  • Iron
  • Sulfur
  • Silicon
  • Oxygen
  • Nitrogen
  • Aluminum
  • Sulfur

Assemble their symbols and you get PaRaPrOFeSSiONAlS.

Other long “chemistry words”: HYPoThAlAmICoHYPoPHYSeAlS and PNEuMoCYSTiS CArInII PNEuMoNiAs.

| Language · Science & Math

Round Numbers

In 1986 The Mathematical Intelligencer published this story about devising a mnemonic for a famous constant:

For a time I stood pondering on circle sizes. The large computer mainframe quietly processed all of its assembly code. Inside my entire hope lay for figuring out an elusive expansion. Value: pi. Decimals expected soon. I nervously entered a format procedure. The mainframe processed the request. Error. I, again entering it, carefully retyped. This iteration gave zero error printouts in all–success. Intently I waited. Soon, roused by thoughts within me, appeared narrative mnemonics relating digits to verbiage! The idea appeared to exist but only in abbreviated fashion–little phrases typically. Pressing on I then resolved, deciding firmly about a sum of decimals to use–likely around four hundred, presuming the computer code soon halted! Pondering these ideas, words appealed to me. But a problem of zeros did exist. Pondering more, solution subsequently appeared. Zero suggests a punctuation element. Very novel! My thoughts were culminated. No periods, I concluded. All residual marks of punctuation = zeros. First digit expansion answer then came before me. On examining some problems unhappily arose. That imbecilic bug! The printout I possessed showed four nine as foremost decimals. Manifestly troubling. Totally every number looked wrong. Repairing the bug took much effort. A pi mnemonic with letters truly seemed good. Counting of all the letters probably should suffice. Reaching for a record would be helpful. Consequently, I continued, expecting a good final answer from computer. First number slowly displayed on the flat screen–3. Good. Trailing digits apparently were right also. Now my memory scheme must probably be implementable. The technique was chosen, elegant in scheme: by self reference a tale mnemonically helpful was ensured. An able title suddenly existed–“Circle Digits”. Taking pen I began. Words emanated uneasily. I desired more synonyms. Speedily I found my (alongside me) Thesaurus. Rogets is probably an essential in doing this, instantly I decided. I wrote and erased more. The Rogets clearly assisted immensely. My story proceeded (how lovely!) faultlessly. The end, above all, would soon joyfully overtake. So, this memory helper story is incontestably complete. Soon I will locate publisher. There a narrative will I trust immediately appear, producing fame. THE END.

The text explains itself: Count the letters in each word (a punctuation mark other than a period counts as a 0, and a digit stands for itself), and you’ll get the first 402 digits of π.

| Science & Math

A Close Shave

Astronomers have the light-year, but nuclear physicists need an analogous unit for measuring tiny distances.

Happily, they have one: The Physics Handbook for Science and Engineering defines the “beard-second” as the length the average physicist’s beard grows in one second, or about 5 nanometers.

Google will even make the conversion for you — type 1 inch in beard-seconds into your search box and see what you get.

| Science & Math

Tempting

The Earl of Yarborough offers you a wager. He’ll shuffle an ordinary deck and deal you 13 cards. If none of your cards ranks above 9, he’ll give you a thousand pounds. Otherwise you must give him one pound.

Should you accept?

Click for Answer
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The Horizontorium

http://books.google.com/books?id=nmQIAAAAQAAJ&pg=RA1-PA57

This clever anamorphic illusion was invented by W. Shires in 1821. Cut out the center piece, make a hole at A, fold it at B, and position it at D. (Here’s a larger version.)

Peer through the hole with one eye, preferably with a light source on your right, and you’ll see the tombstone in three dimensions, surrounded by a low palisade.

Here’s another scene using the same principle; position the eyepiece where the turrets’ lines would converge and “the whole view will appear in its just proportions, representing a castle at a considerable distance, the loftiest part of which appearing scarcely an inch high.”

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“Calculation and Memory”

William Lawson, teacher of mathematics in Edinburgh, who died in 1757, when employed about twenty years before his death as preceptor to the sons of a gentleman, was induced by his employer to undertake an extraordinary piece of mental calculation. Upon a wager laid by his patron, that the numbers from 1 to 40 inclusive could, by memory alone, be multiplied continually–that is, 1 multiplied 2; the product then arising, 2, by 3; the next product, 6, by 4; the next, 24, by 5; and so on, 40 being the last multiplier–Mr. Lawson was, with reluctance, prevailed upon to attempt the task. He began it next morning at seven o’clock, taught his pupils their Latin lessons in the forenoon as usual, had finished the operation by six in the evening, and then told the last product to the gentlemen who had laid the wager; which they took down in writing, making a line of forty-eight figures, and found to be just. … When the operation was over, he could perceive his veins to start, like a man in a nervous fever; the three following nights he dreamed constantly of numbers; and he was often heard to say that no inducement would ever again engage him in a like attempt. A fair copy of the whole operation, attested by the subscriptions of three gentlemen, parties in the wager, was put into a frame with glass, and hung up in the patron’s dining-room.

— Chambers’s Journal, Sept. 27, 1856

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The Great Filter

An advanced civilization passes through eight stages:

  1. A congenial star system
  2. Reproductive molecules
  3. Simple single-cell life
  4. Complex single-cell life
  5. Sexual reproduction
  6. Multicellular life
  7. Tool-using animals with big brains
  8. Colonization explosion

Now, we haven’t observed any intelligent extraterrestrials. That implies that at least one of these steps is very improbable, a “filter” that prevents life from colonizing space.

We’re on step 7. If the filter is among steps 1-6, then we’re not likely to meet any neighbors — something prevents most life forms from getting as far as we have. If the filter is in step 8, then it appears some catastrophe must strike us soon. Our future, it seems, must be either lonely or ruinous.

“The larger the remaining filter we face, the more carefully humanity should try to avoid negative scenarios,” writes George Mason University economist Robin Hanson. “Our main data point, the Great Silence, would be telling us that at least one of these scenarios [e.g., nuclear war, ecological collapse] is much more probable than it otherwise looks.”

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Future Tense

When he wasn’t inventing logarithms, John Napier took a keen interest in military affairs. In 1596 he composed a list of war machines that “by the grace of God and worke of expert craftsmen” he hoped to produce “for defence of this Iland.” These included a piece of artillery that could “clear a field of four miles circumference of all living creatures exceeding a foot of height,” a chariot like “a moving mouth of mettle” that would “scatter destruction on all sides,” and “devises of sayling under water, with divers and other strategems for harming of the enemyes.”

No one knows whether Napier built his machines, but by World War I they were certainly realities — he had foreseen the machine gun, the tank, and the submarine.

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