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Posts Tagged ‘Möbius Strip

“It might help to think of the universe as a rubber sheet, or perhaps not”*…

 

mobius strip

You have most likely encountered one-sided objects hundreds of times in your daily life – like the universal symbol for recycling, found printed on the backs of aluminum cans and plastic bottles.

This mathematical object is called a Mobius strip. It has fascinated environmentalists, artists, engineers, mathematicians and many others ever since its discovery in 1858 by August Möbius, a German mathematician who died 150 years ago, on Sept. 26, 1868.

Möbius discovered the one-sided strip in 1858 while serving as the chair of astronomy and higher mechanics at the University of Leipzig. (Another mathematician named Listing actually described it a few months earlier, but did not publish his work until 1861.)…

The discovery of the Möbius strip in the mid-19th century launched a brand new field of mathematics: topology: “The Mathematical Madness of Möbius Strips and Other One-Sided Objects.”

* Terry Pratchett, Hogfather

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As we return from whence we came, we might wish a Joyeux Anniversaire to Denis Diderot, contributor to and the chief editor of the Encyclopédie (“All things must be examined, debated, investigated without exception and without regard for anyone’s feelings.”)– and thus towering figure in the Enlightenment; he was born on this date in 1713.  Diderot was also a novelist (e.g., Jacques le fataliste et son maître [Jacques the Fatalist and his Master])…  and no mean epigramist:

From fanaticism to barbarism is only one step.

We swallow greedily any lie that flatters us, but we sip only little by little at a truth we find bitter.

Man will never be free until the last king is strangled with the entrails of the last priest.

A thing is not proved just because no one has ever questioned it.

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Written by LW

October 5, 2018 at 1:01 am

“Sounds are quite innoxious, or most distressing, by their sort rather than their quantity”*…

 

More than 20 million people in the U.S. are afraid of flying. Sitting in a chair that’s floating in the air may be technologically stunning to some, but that floating-in-a-tin-can feeling puts some passengers on edge and sends their minds racing: Do the flight attendants look worried? What was that bump? And, oh man, what was that noise?!

 But you don’t have to worry. You’re more likely to drown in your own bathtub than you are to perish in an out-of-control flight. In fact, the last time a U.S.-registered airliner had any fatalities was in 2009.

So unless the sound you hear is the flight attendants telling you to assume a bracing position—which really only means there’s the potential for a problem—everything’s most likely O.K. Still, the unknown can be scary…

A breakdown—by sound—of most things you’ll hear on a flight and what each of those noises means: “A Nervous Flyer’s Guide to Every Ding, Buzz and Whir You Hear on an Airplane.”

* Jane Austen, Persuasion

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As we assume the crash position, we might send never-ending birthday greetings to August Ferdinand Möbius; he was born on this date in 1790.  A German mathematician and theoretical astronomer, he is best remembered as a topologist, more specifically for his discovery of the Möbius strip (a two-dimensional surface with only one side… or more precisely, a non-orientable two-dimensional surface with only one side when embedded in three-dimensional Euclidean space).

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Written by LW

November 17, 2016 at 1:01 am

“The future ain’t what it used to be….”*

Just over a hundred years ago, in 1910, the Cedar Rapids Evening Gazette in Iowa published a list of advances and innovations that they believed would appear during the century, a fascinating list of things scientific/technical and social/political:

  • Cure for cancer.
  • Discovery south pole.
  • Prevent or cure insanity.
  • Influence sex by parental treatment.
  • Create living organisms by artificial means.
  • Phonograph records substitute for letter.
  • Rationing clothing reform, health, comfort, durability only considerations
  • Settle question of communication with Mars. Wonderful astronomical discoveries.
  • Power of mind over matter a practical science devoid of superstitious elements.
  • United States constitution rewritten, providing improved means for conservation of original democratic principles.
  • Marvelous progress in transportation, largely aerial; airships and dirigible balloons crossing oceans and continents in remarkable time. Racing planes make five miles per minute. Inland waterways carry slow freight by improved methods. Monorail supplants two tracks. Electricity replaces steam. Convenient, economical city traffic system broadens city areas, opening suburban lands to householders. Pneumatic tubes for mails and express. Horses curiosities. Automobiles relegated to short distance burden bearing. Ocean steamers for freight, improvement toward speed rather than size.
  • Produce rainfall at will.
  • Temper gold and copper.
  • Roads of nation paved.
  • Conservation of sun’s heat and power.
  • Cure for and elimination of tuberculosis.
  • Development psychic research with fraud eliminated.
  • Movements for universal language, universal religion, universal money.
  • Non-existence of blindness by eliminating causes except accidents.
  • Construction largely of concrete and metal or newly discovered materials.
  • Electricity will move world’s wheels. Later radio-activity may substitute.
  • Terrors of war so multiplied by death dealing inventions, chances of war minimized.
  • Utilization of all energy, reducing consumption of wood and coal. Many fuel substitutes.
  • Population of United States based on present ratio of increased, 1,317,547,000 at opening of twenty-first century.
  • Rational diet with greatly reduced consumption of matter with increased nourishment from proper mastication and choices of foods.
  • Machinery largely substituting manual energy, will promote pursuit of finer arts and sciences; give ample opportunity for relaxation and amusement; emancipate wage slaves. Three-hour work day predicted.
  • Sea water for irrigation.
  • Photographs in natural colors.
  • Women’s political equality.
  • Government control of corporations.
  • Animated pictures in natural colors, transmitted by wireless.
  • Substitution of heavier metals with aluminum, etc.
  • Natural colors reproduced in newspaper pictures.
  • Reduction of elimination all forms of gambling, including stocks.
  • General acceptance of public ownership or control of public utilities.
  • Government operation banking system, elimination of private banks. Postal savings banks.
  • Moral, intellectual and economical awakening in dark sections of Africa, China a world power.
  • Beautiful and healthful cities, offering with homes and work places all forms of free amusement, culture and recreation.
  • Greater premium on brains with corresponding decreased in respect for position not gained by individual achievement.
  • Revision judicial system, deciding causes on improved scientific plan, insuring equal justice. Pathological and psychological treatment for criminals. Crime reduced.
  • Due to universal education, with special reference to hygiene, doctors and drugs be largely eliminated; average age to be near 60 years; men taller, stronger, higher intelligence and morals.

Some of their predictions were spot on (“Natural colors reproduced in newspaper pictures”); some, sadly as yet unrealized (“Cure for cancer”); and some, ironically backwards (“Government control of corporations”). But overall, it’s consoling to be reminded that things that seem wild, even radical at one moment in time– in this case, things like women’s rights and child labor laws– can, with the passage of time, become so obvious as to become human rights that we take for granted.

[TotH to Paleofuture, from whence the illustration above; via the always-excellent Next Draft]

* Yogi Berra

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As we live in the past, we might send twisted birthday greetings to August Ferdinand Möbius; he was born on this date in 1790.  A mathematician and theoretical astronomer, Möbius was so important to the fields of analytic geometry, topology, and number theory that several mathematical concepts are named after him, including the Möbius configuration, the Möbius transformations, the Möbius transform, the Möbius function μ(n), and the Möbius inversion formula

But he is best remembered, of course, as the creator of the Möbius Strip— a two-dimensional surface with only one side…. more specifically: a non-orientable two-dimensional surface with only one side when embedded in three-dimensional Euclidean space… It can be constructed in three dimensions: Take a rectangular strip of paper and join the two ends of the strip together so that it has a 180 degree twist. It is now possible to start at a point A on the surface and trace out a path that passes through the point which is apparently on the other side of the surface from A.

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Written by LW

November 17, 2013 at 1:01 am

Knowing when to hold ’em; knowing when to fold ’em…

 

The documentary Holy Rollers follows the rise of the Church Team, arguably the largest and most well-funded blackjack team in North America. This unlikely group of Christians, pastors, worship leaders and church-planters mastered the art of card counting and marched into traditionally forbidden territory – casinos – to beat the house at it’s own game to the tune of millions of dollars.

It all started as a hobby for two friends, Ben and Colin, who wanted to do something interesting with their math skills and investment money. After making a living off blackjack for a several years, friends and family started asking to be trained as card counters under their professional blackjack expertise. Before long, word spread through church circles and an uncommon fellowship began to form. Led by team managers Ben & Colin, the team quickly grew to include more than 25 players based all over the United States.

In their first year, the Church Team acquired a bankroll of $1.5 million from outside investors, and the team was winning $100,000 a month. In spite of the team’s phenomenal success, many team members remained conflicted, wrestling with how to justify being a Christian and playing blackjack for a living. They found themselves at odds with their own families, congregants, and fellow Christians who feared that they were wandering into morally bankrupt territory.

When the team’s winnings decrease drastically, questions start being raised as to whether someone from the team might be stealing from the bankroll. Where trust is sacred and God sees all, is it even possible? Of course. But do they trust the players on their team? Absolutely. Maybe.

More, on the film’s web site.

 

As we decide to stand, we might wish a twisted Happy Birthday to the theoretical astronomer and mathematician August Ferdinand Möbius; he was born on this date in 1790.  While Möbius made many contributions to geometry (e.g., the Möbius configuration, the Möbius transform, and the Möbius function), he is surely best remembered for his nifty Möbius Strip– a two-dimensional surface with only one side.

A Möbius strip made with a piece of paper and tape. If an ant were to crawl along the length of this strip, it would return to its starting point having traversed every part of the strip (on both sides of the original paper) without ever crossing an edge.

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Written by LW

November 17, 2011 at 1:01 am

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