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Fun Facts 76-100!

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A few posts ago, I challenged myself to post 100 facts I found interesting, to celebrate the 100th post of my blog. It was rather hard to do this all for one blog post, so I stretched them across a couple posts. So here they are, the last 25! You can find the first 50 here, and facts 51-75 here.

It was a lot harder goal than I thought it would be, but it was also fun too. Probably it was extra challenging because in the mean time, I was preparing for a huge exam, finishing a novel draft, and on vacation. Now I’m through those, so no more excuses! 25 more facts!

 

76. Iodine is the heaviest element commonly needed by organisms with an atomic weight of 127. Iodine is added to table salt to help people get their daily amount of iodine. Consuming too little iodine can affect the thyroid gland; pregnant women who don’t consume enough iodine can give birth to less-intelligent babies.

77. Baseball player Hack Wilson holds the single season record for RBIs, with 160. His odd physique was considered notable; he had a barrel chest and tiny legs and odd facial features. Scientists now believe he had fetal alcohol syndrome, which results in distinctive facial features.

78. Water is an unusual compound in a number of ways. For one, its most common solid phase is less dense than its liquid phase, thus why ice floats in water. There are actually 15 phases of solid ice. The chart here shows a number of them.

79. Ice XI is found in some Antarctic ice. It’s actually thought to be more stable than regular ice, but it takes millennia to form.

80. A diamond isn’t forever. Solid carbon also comes in several structures, such as diamond, coal, and buckyballs. Diamond isn’t the most stable state at room temperature and pressure, and very, very slowly converts back to coal.

81. There are 109 species of tulips.

82. In the 1630s in Europe, speculation on tulips led to a bubble and then a collapse called the “tulip mania“. It is considered the first speculative bubble.

83. The Sognefjord in Norway is one of the longest and deepest fjords in the world (127 miles long, 4300 ft deep). This is deeper than the adjacent sea.

84. There are coral reefs at the bottom of some fjords, discovered as recently as the year 2000. This is why there is often rich fishing in the fjords.

85. The number of Norwegian descendants living in the United States is roughly equal to the current population of Norway.

86. There are fewer people living permanently in the fjord country of Norway today than there were in the mid 1800’s.

87. To some extent, you can tell when a person’s family emigrated from Norway based upon where they settled. The earliest settlements were in Illinois and Pennsylvania. Settlements then moved west to Wisconsin, Minnesota, Iowa and North Dakota. (This will irrelevant to most readers, but interested me: Westby, WI is the second most Norwegian speaking town in the US, and Vernon county, WI is the 6th most Norwegian speaking county in the country.)

88. The earliest chemical evidence for the existence of beer dates back to 3500 BC, though it may have been produced as early as 9500 BC when the grains were first grown.

89. The first addition of hops (the agent which adds bitterness and also acts as a preservative) to beer was mentioned in the year 822. The India Pale Ale is known as a bitter beer because many hops were added for its journey from Britain to India. They preserved the beer and helped to conceal bad flavors too.

90. Lagers are produced by bottom-fermenting yeasts, while ales are produced by top-fermenting yeasts. Lagers also are fermented at lower temperatures. Bottom-fermenting yeasts are a relatively recent innovation, and lagers weren’t mass-produced until the mid 1800s. The world’s top-selling beers are now all lagers.

91. Hops are being investigated as possibly useful in hormone replacement treatments. They are currently used in preparations for treating menstrual cramps.

92. The Czech Republic drinks the most beer per capita of any country in the world. Beer in CZ can be bought for 28 Kr at a restaurant. The exchange rate today is 19.6 Kr to the US dollar, or $1.43 for a pint. The US is 12th per capita.

93. Cashews are a relative to poison ivy and poison sumac. The irritant is contained in the skin of the fruit. This is why they aren’t sold in their shells. People who are sensitive to poison ivy can react to contact with cashews or mangos, which are also related.

94. Coffee first arrived in Europe in the 1500s. In 1600, the pope declared it a “christian drink”, settling concerns of its Muslim origins. Some have speculated that the arrival of coffee in Europe brought about the Renaissance.

95. Finland drinks the most coffee per year, at over 12 kg of beans per person. Most of the top of the list is dominated by Scandinavian countries, doubtless to fight off the long winter nights. The US is way down at #26, with 4.2 kg per person per year.

96. The earliest recording of tea drinking was in China in 1000 BC. Tea first reached England in 1660, but it took awhile before it was an everyday drink.

97. The greatest per capita consumer of tea is Paraguay, at 11 kg per year per person. The US is way down at #70, consuming half a kilogram a year. I am doing my part to bring our average up.

98. Chocolate was cultivated at least as early as 1100 BC in central america. Most of it is produced now in West Africa, specifically Côte d’Ivoire.

99. White chocolate does in fact contain derivatives of the cocoa plant. In the US, it is required to have at least 20% cocoa butter by weight. Since it does not contain cocoa solids, it doesn’t contain caffeine.

100. There is a strong correlation between a country’s chocolate consumption and the number of Nobel prize winners it has. This result was published in the New England journal of medicine.

Thanks for reading! I hope you found the facts as interesting as I did to find them, but boy and I glad I’m done with them. =)

Interesting facts: 50-75

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Today I post interesting facts 51-75. These last weeks have been incredibly intense, and it’s been tough meeting my 100 fact challenge celebrating reaching 100 posts. I will follow with the last 25 later this week or next Monday. The blog has had to take a backseat to work and to my book writing efforts; I will hit 70,000 words tomorrow and I am closing in on the finish. And without further ado, more facts!

 

51. Earth’s magnetic poles switch every few hundred thousand years, as a result of natural movements in iron in the crust. I wondered how this might affect migratory species using magnetic senses, but there isn’t enough evidence from the last switch 41,000 years ago to tell.

52. The creator of Kellogg’s cornflakes was at war with sexuality. The cornflakes were a part of this, as an unstimulating food. He was a strong advocate against masturbation– advocating circumcision and application of acid to the genitals.

53. Left-handed people are at a higher risk for numerous ailments, including schizophrenia, ADHD, and depression. I am what they call mixed-handed– I do some tasks with my right hand (writing), and some with the other (sports).

54. Eta Carinae is sometimes one of the brightest stars in the sky, and sometimes not. It is a system including a luminous blue variable, which grows a coat of obscuring gas, and then periodically blasts it off. In 1843, it was the second brightest object in the sky. It currently cannot be seen with the naked eye.

55. George Washington did not have wooden teeth. His dentures were made of gold, hippopotamus ivory, lead, and human and animal teeth (including horse and donkey teeth).

56. Goldfish actually have memories of about three months. As anyone who ever owned a goldfish should know.

57. Alfred Tennyson was troubled and interested by the science of his time. Themes about evolution and references to the contemporary phrase “ontogeny recapitulates phylogeny” (a since debunked scientific concept which claims an organism develops in vitro according to its phylum order) can be found in his poetry, specially In Memoriam.

58. Water-induced wrinkles are not caused by the skin absorbing water and swelling. They are caused by the autonomic nervous system, which triggers localized vasoconstriction in response to wet skin, yielding a wrinkled appearance. This may have evolved because it gives ancestral primates a better grip in slippery, wet environments.

59. Eating nuts, popcorn, or seeds does not increase the risk of diverticulitis.These foods may actually have a protective effect.

60. The Coriolis effect does not determine the direction that water rotates in a bathtub drain or a flushing toilet. The Coriolis effect induced by the Earth’s daily rotation is too small to affect the direction of water in a typical bathtub drain. The effect becomes significant and noticeable only at large scales, such as in weather systems or oceanic currents. Other forces dominate the dynamics of water in drains.

61. Abner Doubleday did not invent baseball.

62. Nikola Tesla was a badass scientist. Thomas Edison isn’t as great as you thought. Tesla pioneered AC current distribution and the lightbulb. Edison stole ideas from Tesla and attempted to undermine him to increase his own profits.

63. Paul Erdös wrote over 1500 math papers. If you’ve heard of six degrees of Kevin Bacon, this was originally known as the Erdös number, the number of degrees of separation from publishing a paper with Erdös. He was very eccentric. For years, he lived out of his suitcase, traveling across the world and collaborating on papers. He didn’t know how to open juice containers and used amphetamines to give him energy. His epitaph was “I’ve finally stopped getting dumber.”

64. Catherine the Great was the longest-ruling female monarch in Russian history. She was actually prussian, and married Peter the Great’s grandson. She probably conspired in his assassination, and took the throne. Her son changed Peter the Great’s succession laws to exclude women from rule.

65. Marie Curie was the first woman to win a nobel prize, and the only person to win in multiple sciences. She discovered polonium and radium and x-rays. She used x-rays to help diagnose injuries in WW1. She eventually died due to radiation-related illness.

66. Ramanujan was an indian-born mathematical genius. With little formal instruction, he devised many theorems that are still being incorporated into mathematical theory. He died at 32.

67. Michael Faraday was a pioneering scientist in electromagnetism, although he also received little formal education. He discovered benzene, and discovered the relationship between light and magnetism. He knew little math beyond trigonometry. The unit of capacitance, Farad, is named after him, as well as numerous constants and devices.

68. the symbol pi, π, originally referred to the perimeter of a circle. only in 1706 was it used to mean the ratio of perimeter to diameter.

69. James Tiptree Jr., a prominent science fiction writer, was actually a woman. She wrote under the pseudonym for two decades until she killed her husband and then herself.

70. In the early years of the Soviet Union, a type of genetics besides Mendelian genetics became accepted as correct, known as Lysenkoism. In Lysenkoism, the way you raised a crop determined its outcome, not the type of seed. Widespread starvation occurred in the Soviet five-year plans, partially due to Lysenkoism.

71. There are over 20,000 species of orchids, or four times the number of mammalian species. Many of them are epiphytes, meaning they grow above the ground in tree-borne habitats.

72. East germans could only buy Trabant cars. Used Trabants were more expensive than new ones, because the waiting line was shorter.

73. A girl in Sweden survived her body temperature dropping to 55 F (13 C) in 2010.

74. Hypothermia is highly correlated to age. Older people suffer hypothermia at a much higher rate.

75. The Cape Hatteras lighthouse is the tallest base to tip lighthouse in the United States. Due to shore encroachment, it was moved in 1999. Its light can be seen 20 miles out to sea.

100 posts, 100 fun facts

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This list making business is slow stuff, and too interesting, so I decided to split it into two 50-fact posts. Happy memorial day, and happy 100 posts to me! Here are your first 50 factoids!

1. People from different cultures differ in what colors they perceive. As a simple example, english speakers deem pink as a different color than red. Russian speakers don’t, but they have a fundamentally different word for dark and light blue. In chinese, red and pink are red and pastel red, and likewise with blue.

2. Corrosion occurs preferentially where you can’t see it, such as under the head of a bolt or a foot or two under sea water. This is due to small concentration differences which cause a charge differential, which leads to corrosion. This is one reason trying to detect corrosion is very hard.

3. The biggest silicon wafers made are 45 cm or 17.7″, though they aren’t yet in production. The silicon is 99.9999999% pure, and monocrystaline.

4. Glass doesn’t have a set crystal structure; this is why it can cut so badly, because shards can be arbitrarily sharp. Auto glass is laminated with plastic to help hold it in place.

5. Many of the scenes in engineering in “Star Trek” and “Star Trek: Into Darkness” are filmed at the Anheuser-Busch brewery in Los Angeles. Look for the green labels reading “VF##”– these are vertical fermenters. In another part of the movie, Chekhov slides past some really shiny tanks on a red floor– these are horizontal fermenters. I used to work at an AB brewery, so I got really excited when I first noticed this.

6. A neutron star is so-called because all the electrons and protons are forced by immense gravitational pressure to combine. The whole star is nearly as dense as a nucleus, or 5.9×10^14 times denser than water. This is equivalent to the weight of a 747 in the space of a grain of sand.

7. Have you ever tried dividing by zero on a calculator? A black hole is remarkably similar to dividing by zero in space.

8. Near a black hole, forces called “tidal forces” (which are felt everywhere, but are crazy strong near a black hole) can be very strong over short distances, ripping anything apart. This is called “spaghettification” (no joke).

9.  After the death of Ivan the Terrible in Russia, three men claimed to be his lost son, Dimitri. They are collectively referred to as the false Dimitris. The first successfully became Czar for ten months, after which his was killed and cremated. His ashes were loaded into a cannon and shot towards Poland, as he was believed to be a Polish spy.

10. The word “defenestration” means “the act of being thrown from a window”. The need for such a word was precipitated by two such events in Prague.

11. The 1904 World’s Fair and Olympics were held in St. Louis. In the marathon, the man who finished first hitched a ride in a car, one favorite made himself sick eating apples, and another favorite was run off course by an angry dog.

12. Toasted ravioli, or breaded deep-fried ravioli, are a culinary delight in St. Louis. Also popular is provel, a cheese used almost exclusively in St. Louis (giving a hilarious Wikipedia by someone who seems unimpressed).

13. The Cahokia mounds are a set of artificial hills in Southern Illinois. They may look unimpressive, but they are about a thousand years old, built by a native culture which later abandoned them. An old nickname of nearby St. Louis is “mound city”, because similar mounds used to be found in the city.

14. Peter the Great of Russia was 6′ 7″. In his early adulthood, he traveled to Europe to learn about shipbuilding, a passion of his. He tried to pass off as a member of the company, but his great height continuously gave him away. The little shack where he lived in Holland still stands near Amsterdam.

15. Over 100,000 serfs died building St. Petersburg, Russia. Peter the Great commissioned the city because the only Russian port at the time, Archangel, was occluded by ice 6 months of the year.

16. 5 people died building the Empire State Building.

17.  The first electric light bulb and dynamo west of the Mississippi was on the campus of the University of Missouri at Academic Hall. The building caught fire and burned to the ground, leaving only the front columns of the building. They remain standing today.

18. Thomas Jefferson has two tombstones: one at his home of Monticello, and one at the University of Missouri. The University of the Missouri is the first land-grant university in the Louisiana Purchase, and many aspects of the university were modeled after Jefferson’s University of Virginia.

19. Cape Hatteras on the Outer Banks has had over 600 recorded shipwrecks. The most recent occurred during Hurricane Sandy in 2012.

20. In November 1956, the USSR invaded Hungary. The Hungarian water polo team fled the country after watching the invasion from nearby mountains. On December 4, the Russian and Hungarian teams met in the gold medal qualifying game of the 1956 Olympics. The game is called the “Blood in the Water” game, due to its violence. The story is told in a documentary called “Freedom’s Fury.”

21. The shortest player in the history of baseball was Eddie Gaedel, who batted for the St. Louis Browns on August 19, 1951. He stood 3’7″ tall, and wore the number”1/8″. Because he had such a small strike zone, he was walked. His contract was voided by baseball the next day.

22. Mercury is a toxic metal that used to be used in thermometers due to its consistent thermal expansion. The mad hatter concept owes to mercury poisoning in old hat makers. A researcher at Duke died in 1997 after a few drops of methyl mercury fell on her glove; organic mercury is incredibly toxic.

23. Humans now have 46 chromosomes in 23 pairs, but at some point in history, they had 48 chromosomes, the same as chimpanzees. Scientists theorize that the number changed when the human population dwindled at one point in history.

24. Splenda is chemically identical to sugar, but it is the mirror image “left-handed” sugar. The left-handed sugar tastes the same as sugar, but it can’t be digested, because the human body only handles right-handed molecules. However, brain scans of people eating sugar or splenda show that the brain registers more reward sensation with sugar. The body can be clever! (I tried to find this study; unfortunately, searching about splenda turns up a lot of nonsense to wade through.)

25. Cuttlefish can change the color of their skin for communication or for camouflage. They can make complex, varying patterns, or they can match a stationary one. Check out this video of a cuttlefish matching a chessboard.

26. Women generally have a better sense of smell than men. in particular, they are better at smelling something they’ve smelled before, where men show less improvement.

27. The Marianas Trench, the deepest ocean trench, is 6.8 miles deep at its deepest point. We still know very little about our deep oceans.

28. Giant squids have been written about since ancient times, but we took our first picture of one in 2004.

29. Only two elements are liquid at standard room temperature: mercury and bromine.

30. The world’s deepest hand dug well in is Greensburg, Kansas. Greensburg was decimated by an EF5 tornado in 2007. It has since started rebuilding, and aims to be the first LEEDS certified green city in the US.

31. Hurricane Camille came over land in Louisiana in 1969 as a category 5 hurricane. Of the 259 deaths caused, 123 were in the mountains of Virginia, in Nelson County (over 1% of the population). The storm dropped 27 inches of rain in a few hours. 133 bridges were washed out, and birds drowned in the trees.

32. Many of Thomas Jefferson’s inventions still reside at Monticello in Charlottesville, VA. There is a clock that tells the day of the week, a dumb-waiter, and a device for writing on two pieces of paper at once.

33. Blue eyes are caused by the presence of less pigment in the eye, resulting in a different light scattering pattern. Blue-eyed baseball players sometimes have much lower daytime hitting averages, because blue eyes filter out less glare.

34. Albinism is principally defined by eye defects caused by the lack of pigment during the formation of the eye. Without pigment in the iris, the eye doesn’t properly focus light, leading to numerous vision problems. It is possible to be albino while still having normally pigmented skin.

35. Catgut is prepared from animal intestine, and was used historically to make strings for instruments. Its name is probably a shortening from cattle gut, for those of us who like kitties.

36. Paper didn’t make its way to Europe until after the year 1000. It was made from old fabric and clothes. Old paper doesn’t yellow and age the same way as 1900’s paperbacks because it tended to be acid-free. Books can last centuries if the paper and ink are acid free.

37. Organisms around deep sea vents metabolize hydrogen sulfide from the vents to survive. 300 new species have been discovered around such vents; because exploration there is so hard, there are likely many more.

38. Hydrogen Fluoride is considered a weak acid, because hydrogen and fluoride bond strongly as resist dissociation. However, HF will go after just about anything including glass. HF is very dangerous to work with, because it does not hurt immediately. It seeps through the skin and begins to dissolve the bone.

39. Phosgene was used in chemical warfare in World War 1. The Japanese also used it extensively in World War 2. It smells like freshly cut grass.

40. The kite buggy was invented in China in the 1300s. It is a cart drawn by wind power. It seems hard.

41. Capillary action in trees helps fluid rise in trees. This is how tree several hundred feet tall supply water to the leaves.

42. The Negro Leagues baseball museum is in Kansas City, Missouri. Many of the negro leagues teams were fairly successful, and drew enthusiastic crowds. The exclusion of blacks from baseball was shameful, but they made something great in spite of it. You can learn about Satchel Paige or Buck O’Neal, as well as the various negro leagues teams.

43. The Eads bridge in St. Louis was the longest of its kind when it was built, over a mile wide. The supports are some of the deepest ever sunk, and 15 workers died due to decompression sickness.

44. The Anheuser-Busch brewery in St. Louis is the biggest brewery in the world. It outputs 25 million barrels per year. You can visit for free and get some complimentary beer.

45. The international rose test garden in is Portland, Oregon. It is free to visit and they have over 550 varieties.

47. The male paradise whydah grows out a foot-long feather during mating time to impress the female paradise whydah. The paradise whydah is a parasitic species that uses the nest of the melba finch.The male whydah imitates the melba finches song. In captivity, the whydah cannot reproduce without the melba finch also present.

48. The carrion flower is an enormous bloom that stinks of rotting flesh. It can be up to nine feet tall.

49. Blue is a rare color for organic molecules. This may be because the color is associated with alkaline conditions, which are relatively rare in organisms.

50. Monarch butterflies can sense the earth’s magnetic field. They use it to complete their 2000 mile migration.

Come back Thursday for 50 more interesting factoids! Happy 100 posts!

Website changes and Zish!

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As you may see, I have been doing some house-keeping on the blog. Most especially this includes a new banner. I’ve been doing so many posts about science and artists that a banner about book-binding seemed awfully limiting. So now the tagline is “sci-fi, art, and science”. I have also updated the about page and streamlined the pages bar at the top of the screen.

I hope this makes the blog easier to view. Plus, I think the new banner is super cute, which is tough for a picture that includes a rocket ship, a robot and a squid. Any feedback is very welcome.

In other progress news, I am making headway on Zish & Argo book II. In book II, Zish and Argo travel to a planet where the native species has a very unusual kind of pet. More to come!

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I got snowquestered

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I normally post on Monday, Wednesday, and Friday, but yesterday we got about a foot of very wet snow. (To those who are saying this storm was overhyped: it delivered, just not in DC. Proof below!) Branches everywhere are down. My house has been out of power for 36 hours now. This morning it was 49 F in the house; cold but totally manageable. The cats have been hunting us for our warmth. They are stuck at home now while we get respite at the university.

So I’m going to skip yesterday’s post, and just show some pics of the snow. Here’s hoping I have power by tomorrow!

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Cute therapy

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Already the week is on a tough vector, so I thought I’d post some kitty pictures from the years. I have one 4 1/2-year-old muted calico named Lobelia who is built like a teddy bear but isn’t much for cuddling. My other is a 2-year-old all black male named Erg who weighs 14 lbs and craves contact. Erg tries to cuddle Lobelia and is often rebuffed, so he chases her instead. Erg is an amazing hunter, and although he is an indoor cat, he has caught many roaches, spiders, crickets, 2 mice and a snake. (We have a door with a high gap in an unfinished area where the bugs tend to come in.) So, some pictures! SONY DSC

Lobelia sometimes scratches her ears too much, so she gets the cone. When the cone is on, she is so dejected that many things can be stacked on her. It’s hard to resist.

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Lobelia poofs her tail and points it down when she is trying to start play.

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Erg’s first bird.

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Lobelia and her hated enemy, the CD tray.

Valentine’s Thoughts

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I never understood the fuss about Valentine’s Day. In elementary school, it was a day that ostracizing the odd kid was officially approved of in the form of who didn’t get valentines. As the kid who claimed to be a cat (and later an alien), that kid was me. It didn’t get me down. It instilled a sense that I was in charge of my own happiness every day of the year. Just as every day, I’d try to bear the knocks and celebrate the compliments. I try to do my best every day of the year. Some times I’m going to have a bad day. Perhaps as a practical pessimist, I don’t have use for a day that is awful unless it’s wonderful.

But let me celebrate what I do like about Valentine’s:

  • Chocolate: Seasonal candy makes every holiday better. Cadbury eggs and candy corn and Valentine’s truffle boxes on sale after the holidays are awesome. As a kid I used to go to the chocolate shop the day after every major holiday and score some 75% off candy. 
  • Flowers: Not so much purchasing them, because they get kind of ragged and expensive this time of year. More that they are popping out of the ground. Here the crocuses are erupting by the hundreds now. The daffodil greens are up. The lenten roses are blooming. The little spring snowflakes are out. The world is at last offering up its bouquets after the winter.
  • Hand-made valentines: I feel like a genius when I make valentines out of doilies and construction paper. I always think they look awesome, and they definitely look more awesome than the pre made ones. Years ago a good friend made me one and I think it made my decade.

Also, it’s finally February! Today the sun sets at 5:50 PM. Every day has an extra hour of better sunshine than this day last month. The world teases with little flowers. Soon the sun will come out and all the trees will bloom. Baseball returns! Soon we shall be wearing short sleeves again. 

Cheer to your Monday and Valentine’s Week!SONY DSC   SONY DSC SONY DSC SONY DSC

Soviet Comedy Movies

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Soviet comedy movies are surprisingly awesome and funny. They also provide a window into a culture that was otherwise pretty cut-off from the west. A rather groomed and cultivated window, but still a window. And you can watch them on youtube, since they have no formal distribution in the west. This link contains a whole list of them; I will discuss a couple specific ones in this post.

The Diamond Arm (Russian: Бриллиантовая рука, Transliteration: brilliantovaya ruka) (number 6 on the playlist): A slapstick style comedy. Criminals conspire to smuggle jewels into Russia. The protagonist wins a vacation abroad, and due to a mix-up, unwittingly becomes a mule for the jewels.

The Irony of Fate, or Enjoy Your Bath! (Russian: Ирония судьбы, или С лёгким паром!, Transliteration: Ironiya sudby, ili S lyogkim parom!) (Number 9 on the playlist): This is the “it’s a wonderful life” of Russia. They apparently play it all the time for New Year’s. A group of men go get very drunk at a bath house, before one of them flies out in the morning. They are still drunk in the morning, and accidentally put the wrong man on the plane. The man, who has been passed out, does not realize he is in the wrong city. He takes a cab to his street and building, and his key even opens the door, even though he is now in Leningrad, not Moscow. This is a spoof of the homogeneity of the Russian building style at the time. All the same street names, all the same buildings, even the same locks. The man gets a glimpse at how his life could be different.

The video below is a charming song from the movie called “esli u vas”. It’s an interesting study in Russian optimism. Basically, the lyrics of the song are about the things that can’t happen to you if you don’t expose yourself to them, but then you will have never experienced life. If you don’t have a dog, your neighbor can’t poison it (!), if you don’t have a house, you won’t fear house fires, if you don’t have friends, you won’t fight with them, etc. I couldn’t find a link with a nice translation.

 

Fun Science: Chaos

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The common concept of chaos as the disordered unknown is a concept thousands of years old. Chaos as a branch of mathematics refers to an extremely ordered but complex behavior. In some lights, mathematical chaos might seem utterly random; different inspections reveal order. The first model of chaos emerged in the 1950s to model the movement of air in the atmosphere– the Lorenz model.

Defining Chaos in Mathematics

First, let’s discuss what chaos is in a mathematical sense (chaos on scholarpedia). In daily language, we would assume that something chaotic is not at all predictable. Chaos is deterministic, which means that if we know the position or value of a chaotic element exactly, then we know every value that it will ever have for all times. Many non chaotic systems are deterministic also; if we measure the position and velocity of a pendulum and its frictional loss, we can predict its path for all time.

If we are measuring some value, there is a limit to our possible accuracy. If you measure your weight, you are measuring your weight plus or minus some error associated with the instrument. We know some scales are more accurate, and some are less accurate. When we measure the position and velocity of the pendulum, there is some error, but the behavior at position x plus a little bit (or x+ε) is essentially identical to the behavior at position x. In a chaotic system, the paths following positions x+ε and x will be entirely different after some window of time. The paths will be similar for some window of time; the length of this window is determined by how chaotic the system is. This behavior is known as sensitive dependence upon initial conditions (or more famously, the butterfly effect).

The lower half of the image below shows the difference between two paths starting at x+ε and x in the Lorenz attractor. The paths are nearly the same, until they quickly become very different. You can look at the Lorenz attractor in more detail and play with it here. The link goes to a Java applet hosted by Caltech where you can change the parameters and see what happens in a time series and in a different representation called the state space.

The above image also shows the third of the three most common criteria for chaos: periodicity. This means that the system oscillates in some kind of way. The top half the picture above shows the time series of z variable (see link above for the full model if you are interested). If we plot the data in a different way, we get the image below. This image is called the Lorenz attractor. We see it loops around, but that it is bounded in space. That is, there are places we can say the path will not go. Intriguingly, the Lorenz attractor has a fractal dimension of 2.06. For more on fractals, you can read my posts on fractals and fractal dimensions.

Simple example of chaos: the double pendulum

Many pretty simple systems can exhibit chaos. The easiest example is the double pendulum, which is just a pendulum whose bottom is the top for a second pendulum.  The video below shows the complexity of behavior achieved by the double pendulum. Chaos has also been demonstrated in electrical circuits, biological systems, electrochemical reactions and planetary orbits. In another post, I will write about the amazingly universality of chaos, which shows how all of the diverse systems I listed are in fact very similar.