Posts Tagged ‘Möbius Strip’
“Reality is merely an illusion, albeit a very persistent one”*…
To look for the strange wave-like properties of quantum particles, physicists hurtle them through a long tunnel-like instrument known as an interferometer
Magnify a speck of dirt a thousand times, and suddenly it no longer seems to play by the same rules. Its outline, for example, won’t look well-defined most of the time and will resemble a diffuse, sprawling cloud. That’s the bizarre realm of quantum mechanics. “In some books, you’ll find they say a particle is in various places at once,” says physicist Markus Arndt of the University of Vienna in Austria. “Whether that really happens is a matter of interpretation.”
Another way of putting it: Quantum particles sometimes act like waves, spread out in space. They can slosh into each other and even back onto themselves. But if you poke at this wave-like object with certain instruments, or if the object interacts in specific ways with nearby particles, it loses its wavelike properties and starts acting like a discrete point—a particle. Physicists have observed atoms, electrons, and other minutiae transitioning between wave-like and particle-like states for decades.
But at what size do quantum effects no longer apply? How big can something be and still behave like both a particle and a wave? Physicists have struggled to answer that question because the experiments have been nearly impossible to design.
Now, Arndt and his team have circumvented those challenges and observed quantum wave-like properties in the largest objects to date—molecules composed of 2,000 atoms, the size of some proteins. The size of these molecules beats the previous record by two and a half times. To see this, they injected the molecules into a 5-meter-long tube. When the particles hit a target at the end, they didn’t just land as randomly scattered points. Instead, they formed an interference pattern, a striped pattern of dark and light stripes that suggests waves colliding and combining with each other…
One possibility physicists are exploring is that quantum mechanics might in fact apply at all scales. “You and I, while we sit and talk, do not feel quantum,” says Arndt. We seem to have distinct outlines and do not crash and combine with each other like waves in a pond. “The question is, why does the world look so normal when quantum mechanics is so weird?”…
A record-breaking experiment shows an enormous molecule is also both a particle and a wave—and that quantum effects don’t only apply at tiny scales: “Even Huge Molecules Follow the Quantum World’s Bizarre Rules.”
Read the paper published in Nature Physics by Arndt and his team here.
* Albert Einstein
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As we dwell on duality, we might spare a thought for August Ferdinand Möbius; he died on this date in 1868. 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).
“The cyclical rebirth of caste in America is a recurring racial nightmare”*…
Dorothy and Lillian Gish and D.W. Griffith at the White House, 1922. Library of Congress
The year 1915 marked the fiftieth anniversary of the end of the Civil War. Monuments to Confederate and Union heroes were being dedicated all over the country. Woodrow Wilson, a fan of Jim Crow laws, was president. He had allowed federal workplaces to segregate again.
Enter Thomas Dixon Jr., Wilson’s classmate from Johns Hopkins. A film had just been made of Dixon’s second novel, “the true story” of the South under Reconstruction. Would the president, he wondered, be interested in viewing it? (He would.)
“History written with lightning,” Wilson declared of The Clansman, the second film ever to be screened in the White House. It was an endorsement guaranteed to head off resistance from town censor boards charged with shutting down entertainment deemed unsuitable or incendiary to the public…
The Clansman was a silent movie with title cards. It depicted whites as victims and blacks as villains. Benevolent former masters were denied votes and subjugated by newly freed blacks taking over the country. In an early scene, black legislators sit at desks, shoeless and drunk, too busy stuffing their faces with fried chicken to work. The title card read: “An historical facsimile of the State House of Representatives of South Carolina in 1870.” South Carolina had been the first state to elect a majority-black legislature and that the card implied that the apish behavior depicted was historically accurate, too.
In a later scene, the white heroine (played by Lillian Gish) is threatened by a black man unable to contain his urge to “mongrelize” the white race. Before she is ravaged, a savior army rides in: The Ku Klux Klan. The title-card copy comes straight from the president’s five-volume History of the American People, published in 1902:
More of this sad story, and its aftermath, at “Hatred Endorsed by a President.”
The New Jim Crow: Mass Incarceration in the Age of Colorblindness
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As we ruminate on recurrence, 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). See ““It might help to think of the universe as a rubber sheet, or perhaps not.”
“It might help to think of the universe as a rubber sheet, or perhaps not”*…
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.”
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.
“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).
“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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