Gnarly Gnews

(The free, humorous bi-monthly math newsletter.) The Gnarly Gnews ™
Published by the SMP Company, PO Box 1563, Santa Fe, NM 87504
Copyright 2010 by Montgomery Phister, Jr.
www.gnarlymath.com
Vol. 11, No. 3, January/February 1879
New York City
Page 1

Albert Abraham Michelson
Measures the Speed of Light
Does Light Really have a Speed? And Here's Another Question. How do we See, Anyway? We heard that a young officer at the Naval Academy had measured the speed of light, of all things. So we went down to Annapolis and looked him up. Found him in a laboratory at the Academy, introduced ourselves, and told him we didn't know that light traveled. He laughed. "There have been all sorts of ideas about light," he said, "and about how we see things. Euclid thought light came out of our eyes and hit the thing we were looking at. How do suppose he explained why we couldn't see things in the dark? "But Aristotle believed that something came into the eyes from the object we were looking at. And a very accomplished Muslim scholar, Alhazen, wrote a book on optics in the 11th century where he proved that we see objects because light is reflected from them. That of course explains why we can't see things when it's dark, and why things look red if they're illuminated by a red light." We told him that made sense, and asked why anyone would think light has a speed. It must travel infinitely fast. For example, when we see lightning strike, it takes seconds for the sound to reach us. The light reached us right away. "Your observation is correct," Michelson replied. "Sound travels at about 1090 feet per second. So if you hear the thunder 5 seconds after the strike, you figure it struck 5 times 1090 or 5450 feet away. That just shows light is faster than sound, not that it's infinitely fast. "The ancient Greeks, including Aristotle, thought light was infinitely fast. Alhazen again had the right idea. He felt that light moved, and couldn't be in two places at once. "Galileo actually tried to measure the speed of light. He and a friend measured the time it took for light to travel between two points a mile apart. It seemed the time was zero, so they concluded light must travel very fast indeed. "It was a Danish astronomer named Ole Roemer who made the first real measurement of light's speed. in 1676. Galileo had seen that Jupiter had several moons, and Roemer, like many other astronomers, was studying them. He concentrated on one of them, named Io, and measured the time it took for Io to revolve around Jupiter -- he'd note when Io first went out of sight, and then he'd note when it went out of sight again -- about two days later. Repeating that measurement over and over during the year, he noticed the time for Io to go around kept changing. When the earth was most distant from Jupiter, it took 22 minutes longer for Io to go around Jupiter than it did when the earth was closest to Jupiter. "Roemer figured this difference in time was caused by the fact that light had to travel further when the earth was far away than it did when the earth was close to Jupiter. So the speed of light would be the extra distance light had to travel divided by the extra time it took -- 22 minutes. The extra distance, as you can see from the figure above, was twice the distance from the Earth to the Sun, so Speed of light = c = 2 x 93,000,000 miles / (22 minutes) = 8,454,545 miles per minute = 8,454,545 miles per minute x 1 minute / (60 seconds) = 141,000 miles per second. And that was not bad. Pretty close to the actual speed." We figured he had found a better answer. "I did," he replied. "I had read about how two Frenchmen had contrived to measure light's speed. A scientist named Fizeau did it in 1849, and Foucault in 1862. They both used gadgets which rotated, and I tried the same idea." He showed us a diagram "I built a mirror which rotated, shown here in red. I sent a beam of sunlight through a slit in a metal plate. It hit the mirror and was reflected to another mirror almost 2000 feet away. By the time the beam returned, the mirror had rotated slightly (as show in pink), and so the beam would hit the plate slightly away from the slit. "To find how fast the beam traveled, I measured the angle between the light beam going through the slit and its returning when the mirror had rotated. Call that angle y. If the mirror is rotating at R turns per second, then the time for the light to go through the slit and return is Time = (1 / R) x (y / 360). 1/R is the time for one revolution, and y/360 is the fraction of a revolution corresponding to y degrees. In one of hundreds of measurements, my mirror went around 256.03 times per second and the angle y was 0.37 degrees. The exact distance was 3972.46 feet, or 0.75236 miles. "So for that measurement, time was (1/R) x (y/360) = y / 360R = 0.37 / (360 x 256.03) = .000004014 seconds "So the speed of light c = 0.75236 / .000004014 = 187,434 miles/second "I ran the experiment many, many times. Averaging all the results, I concluded the speed of light is pretty close to 186,359 miles/second." Sounded like a lot of work for one number. We changed the subject and asked how he came to the Naval Academy. "You might find it surprising," he replied, "but I was born in Prussia, and when I was two years old my folks moved to the United States. We first went to Murphy's Camp, in California, where my father set up shop selling stuff to gold miners. When the gold ran out we moved to a silver mining town in Nevada, and finally to San Francisco. I graduated from high school there and tried go get an appointment to go to Annapolis. But the Congressman appointed a guy who was the son of a Civil War soldier. I knew that President Grant appointed boys to the Academy, so I went to Washington and he got me in. I graduated five years ago, doing very well in science but not so well in seamanship and such things. I was sent on a two-year cruise in the West Indies, and then became an instructor here, teaching physics and chemistry." We thanked him for educating us, and went home wishing we had measured the speed of light, or something A Double-Dactyl Diller a Doller a Albert A. Michelson Hoped he could measure the Quickness of light. Built him a mirror that Whirlaboutationally Gave him an angle that Caused him delight. Today's Gnarly Weather We will have snow today in New York, and with the telegraph everyone in the world will know about it in a few minutes	Who Ever Heard of a Telephone? Mr. Bell Not Only Heard of it. He Invented it The past couple of years we've been hearing of a keen new invention called the "Telephone" which lets people talk to one another even if they're not in the same room. The inventor was a chap named Alexander Graham Bell, and we figured we ought to talk to him. We found him in his office in New Haven. He had a strong Scot accent (which we won't try to reproduce here), and we asked where it had come from. "Well, I was born in Scotland, wasn't I?" he replied. "In Edinburgh. I became interested in speech because my mother started losing her hearing when I was about 12. That was bad enough, but then my elder brother Melville died of tuberculosis. Mother and Father decided we should move to Canada. They bought a farm in Brantford, Ontario, and continue to live there. "I was still interested in the human voice, and was intrigued by the Mohawk Indians. I learned their language and put together a book that used Visible Speech Symbols to pronounce their words." He laughed. "They made me an Honorary Chief, and I danced in a ceremony with a feathered hat." We wondered what "Visible Speech Symbols" were. "It's a system my father invented. He made up some symbols which stood for sounds. With them, you could translate any language into these symbols, which could be read by anyone. Of course, you could pronounce words in a foreign language, but you couldn't understand what you're saying unless you knew the language." We asked whether he could give us an example. "Sure enough," he said. "Here are the sounds BILSV, and here they're put together to say Visible. A German, for example, could pronounce this as "visible", though he wouldn't know what it meant." Fascinating. Then we asked when it was he came to the U.S.? "I first came to Boston eight years ago teaching deaf children, and then was a professor at Boston University. I kept moving back and forth between Brantford and Boston, usually spending summers in Canada." We wondered how he thought of the telephone. "I was always inventing things," he said. "When I was twelve, a friend and I invented and built a gadget for taking the husks off of wheat. Then when I was sixteen my brother and I built a talking head. The neighbors came by to see it and were delighted. "Next I got interested in the telegraph, which Samuel Morse invented in 1837. Marvelous idea. Before its invention, news had to travel by horse or ship, so it took days or weeks for important news, like Napoleon's surrender, to reach Moscow or New York. In 1866 the first telegraph line crossed the Atlantic Ocean, and three years later the East and West coasts of the U.S. were connected together. Today there are telegraphs in almost every town. "The whole thing started with an experiment by Joseph Henry, who taught math and science at the Albany Academy in New York. In 1830, in his classroom, he hung a bell from a string, mounted an iron bar on a pivot, and put an electromagnet near the bar." We didn't know what an electromagnet was. "If you wind a wire 'round and 'round a piece of iron," he replied, "and run an electric current through the wire, the iron becomes a magnet. So when he connected a battery to the electromagnet and threw the switch, the electromagnet attracted the iron bar, which swung around and hit the bell. His wire was strung all around the classroom several times (as indicated by the dotted line), so he was showing that you could send a message -- a bell ring -- some distance through wires. "Samuel Morse adapted the idea to create (and patent) the telegraph. In the figure above, the telegraph key on the left is sending to the key on the right, many miles away. When the left key is pressed down, current from the red battery goes through the gray electromagnet on the left, through the telegraph wires, through the magnet on the right, and then through the key on the right (which must be pressed down to receive). Each of the magnets attracts the yellow bar above the magnet, causing a 'click'. Notice that the return line goes through the ground -- the wires are connected to a metal stake that's pounded into the earth -- so you only need to run one wire over the lines between stations. "I saw that the same scheme, with some changes, could be used to send voices over wires. After much experiment, I patented the system shown above. You speak into the blue cone on the left. That causes a thin pad called a diaphragm, at the end of the cone, to vibrate, which moves the arm attached to it (at point c). Movement of this arm creates a current in the gray electromagnet. That current is carried through telephone lines to the electromagnet on the right, and its changing current causes the arm on the right to vibrate, creating a sound which comes out of the blue cone on the right. "Another inventor, Elisha Gray, had the same idea at almost the same time so he challenged my patent. It took a long time to get things straightened out, but finally my patent was declared good. "Two years ago the Bell Telephone Company was created to build telephone systems, and today already hundreds of people have telephones. I expect in the future almost everyone in the United States will have one. But we'll see." We thanked Mr. Bell for telling us his story, and went back to the office to order a telephone. This Month's Riddle Q. How did Alexander Graham Bell differ from Albert Abrahamson Michelson? (Answer on the next page)

The Gnarly Gnews ™
Vol. 11, No. 3, January/February 1879
New York City
Page 2

School Days

Horace, you can't measure the speed of light with a flashlight and a stopwatch.

Answer to this Month's Riddle
Q. How did Alexander Graham Bell differ from Albert Abrahamson Michelson?

A. One was preoccupied with light, the other with sound..
(Back to top of page)

Notice

      We looked up Chloe, our favorite math helper. "I have some bad news," we told her.
      "That's not cool," she replied. "What's gone down?"
      It was difficult for me to say. "Last September my wife of 35 years, Melinda Miles Phister, passed away. Since then life has been difficult."
      Chloe was sympathetic at once. "Oh, Monty," she said. "That's so bad! What happened?"
      "She got sick," I replied. "But it made me think. The Gnarly Gnews is in its eleventh year, has treated all of the more-or-less simple topics in mathematics and some of the more complicated ones. So I've decided that this will be the last issue."
      "Eleven years! Wow! Didn't realize," Chloe said. "So what'll you do? Like, retire?"
      "Well," I said, "my granddaughter Sarah had an idea. She suggested a new topic, one as important as math. So starting in March I will have a new newsletter whose general topic will be English and writing, including writing poetry. The letter will be posted here on www.gnarlymath.com, and all subscribers to the Gnarly Gnews will get a zip file of the new issue every other month. I think I'll call it Gnarly Gnenglish.
      "Of course, most subscribers are interested in math, and may want to unsubscribe. But anyone wanting to find out more about the English language is welcome. If they don't unsubscribe, they'll get Gnenglish every other month.
      "English!" said Chloe. "Then I'm, like, done for. Out of here. Maybe you've noticed? My English? It's not all that gnarly"
      We agreed. "No, Chloe, your English could be improved. Maybe you should subscribe to Gnarly Gnenglish.
      "But It's been great fun writing the Gnews all this time, and I'm grateful to all readers who enjoyed it. Anyhow, the e-book containing past issues will of course always be available. Have you bought a copy, Chloe?"
      But she was gone, muttering to herself.

Sam'll Answer
DEAR SAM:
We've heard all about measurements of the speed of light. Who first measured the speed of sound?
A SOUND PERSON

DEAR SOUND PERSON,
      A Frenchman named Marin Mersenne was the first person to measure the speed of sound, in about 1640. He used two different methods. In one, he shot off a gun while standing some distance from a wall, and moved back and forth until he heard the echo of the shot in one second. Then the speed of light in feet per second was twice his distance from the wall.
      He also used a gun in his second method, measuring the time between when he saw the flash from the gun's muzzle and the time he heard the sound. Knowing his distance from the gun, he could calculate the speed of sound. His measurements indicated that sound traveled at 1480 feet per second. He also discovered the speed was the same for different tones and for different volumes. Today we know the speed of sound is near 1090 ft/sec.
      But Mersenne is most famous for his interest in prime numbers. He was unsuccessful in finding a formula for primes (we still don't have one), but he did find that a number one less than a prime power of two often gave him a prime number. These numbers are called Mersenne numbers.
      The formula for a Mersenne number is M = (2 to the power of p) - 1, where p is prime. Here are the first few Mersenne numbers. Note they are not all prime.
      p=2, M = 2^2 - 1 = 4 - 1 = 3
      p=3, M = 2^3 - 1 = 8 - 1 = 7
      p=5, M = 2^5 - 1 = 32 - 1 = 31
      p=7, M = 2^7 - 1 = 128 - 1 = 127
      p=11, M = 2^11 - 1 = 2048 - 1 = 2047
       = 23 x 89 not prime
      p=13, M = 2^13 - 1 = 8192 - 1 = 8191
      p=17, M = 2^17 - 1 = 131,072 - 1 = 131,071

Limerick      Now Bell is a mighty fine name,
     And Michelson's clearly the same
        But sadly these Als
        Had never been pals
     Though both were accustomed to fame.

Answer to last month's puzzle      We were told that light travels at a speed of 300,000 km/sec, and were asked how many feet per second, and miles per hour that is.
     It's easy, using canceling:
     300,000 km/sec x 1 mile / 1.609 km = 186,451 miles/sec x 3600 sec/1 hour = 671,223,600 miles/hour
     = 671,223,600 miles/hour x 5280 feet/1 mile x 1 hour/3600 seconds = 984,461,280 feet/second

A Clerihew
      Alexander Graham Bell
      In inventing was known to excel.
      He thought the telegraph was a fine idea
      But he knew his telephone would turn out to be
            the communication panacea.

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