## Posts Tagged ‘**Mathematics**’

## “The endless repetition of an ordinary miracle”*…

In 1611 Johannes Kepler wrote a scientific essay entitled

De Nive Sexangula;commonly translated as “On the Six-Cornered Snowflake.” It was the first investigation into the nature of snowflakes and what we’d now call crystallography. Since he was a gentleman and a scholar back when you could be such a thing without being ironic or a hipster, Kepler gave the essay as a New Year’s gift. As Kepler wrote on the title page:

To the honorable Counselor at the Court of his Imperial Majesty, Lord Matthaus Wacker von Wackenfels, a Decorated Knight and Patron of Writers and Philosophers, my Lord and Benefactor.As the title suggests, Kepler’s main concern was the question of why snowflakes are almost always six-pointed…

Follow the train of thought from the stacking of spheres to the intricacies of tiling at “Snowflakes and Cannonball Stacks.”

* Orhan Pamuk, *Snow*

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**As we pause to ponder patterns,** we might recall that it was on this date in 1891, about 20 miles outside of Midland, Texas, that the first rainmaking experiment in the U.S. was conducted. Robert St. George Dyrenforth, a Washington patent attorney and retired Army officer, led a team that used “mortars, casks, barometers, electrical conductors, seven tons of cast-iron borings, six kegs of blasting powder, eight tons of sulfuric acid, one ton of potash, 500 pounds of manganese oxide, an apparatus for making oxygen and another for hydrogen, 10- and 20-foot-tall muslin balloons and supplies for building enormous kites” to create enormous explosions meant to help clouds form. Their efforts– which were based more on Dyrenforth’s instinct than on anything resembling scientific evidence– were entirely unsuccessful. Still, at a time of extreme drought, it’s likely that almost anything seemed worth trying. (The full– and very entertaining– story, here.)

## “The past is never dead. It’s not even past”*…

Science has a habit of asking stupid questions. Stupid, that is, by the standards of common sense. But time and time again we have found that common sense is a poor guide to what really goes on in the world.

So if your response to the question “Why does time always go forwards, not backwards?” is that this is a daft thing to ask, just be patient…

In our experience the past is the past and the future is the future, but sometimes the two can cross over; and while the past seems set in stone, some scientists believe that the future can change it: “The quantum origin of time.”

* William Faulkner, *Requiem for a Nun*

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**As we head down the rabbit hole,** we might spare a thought for Jules Henri Poincaré; he died on this date in 1912. A mathematician, theoretical physicist, engineer, and a philosopher of science, Poincaré is considered the “last Universalist” in math– the last mathematician to excel in all fields of the discipline as it existed during his lifetime.

Poincaré was a co-discoverer (with Einstein and Lorentz) of the special theory of relativity; he laid the foundations for the fields of topology and chaos theory; and he had a huge impact on cosmogony. His famous “Conjecture” held that if any loop in a given three-dimensional space can be shrunk to a point, the space is equivalent to a sphere; it remained unsolved until Grigori Perelman completed a proof in 2003.

## “We’re supposed to keep evolving. Evolution did not end with us growing opposable thumbs”*…

The CEO of Enron – now in prison – happily applied ‘selfish gene’ logic to his human capital, thus creating a self-fulfilling prophecy. Assuming that the human species is driven purely by greed and fear, Jeffrey Skilling produced employees driven by the same motives. Enron imploded under the mean-spirited weight of his policies, offering a preview of what was in store for the world economy as a whole…

Frans de Waal on the flaws in the “competition-is-good-for-you” logic: “How Bad Biology is Killing the Economy.”

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**As we concentrate on cooperation,** we might spare a thought for Martin Gardner; he died on this date in 2010. Though not an academic, nor ever a formal student of math or science, he wrote widely and prolifically on both subjects in such popular books as *The Ambidextrous Universe* and *The Relativity Explosion *and as the “Mathematical Games” columnist for *Scientific American*. * *Indeed, his elegant– and understandable– puzzles delighted professional and amateur readers alike, and helped inspire a generation of young mathematicians.

Gardner’s interests were wide; in addition to the math and science that were his power alley, he studied and wrote on topics that included magic, philosophy, religion, and literature (c.f., especially his work on Lewis Carroll– including the delightful* Annotated Alice*— and on G.K. Chesterton). And he was a fierce debunker of pseudoscience: a founding member of CSICOP, and contributor of a monthly column (“Notes of a Fringe Watcher,” from 1983 to 2002) in *Skeptical Inquirer*, that organization’s monthly magazine.

## “There are three types of lies — lies, damn lies, and statistics”*…

In today’s world, we are constantly bombarded with averages and medians: the

averagetemperature in New York in April is 52 degrees; Stephen Curryaverages30 points per game; themedianhousehold income in the United States is $51,939.But the concept of taking many different measurements and representing them with one best number is a relatively recent invention. In fact, there are no historical examples of the average or median being used in this manner prior to the 17th Century.

So how did the concept of averages and medians develop? And how did the average triumph as the measurement of our times? The supremacy of the average over the median has had profound consequences about how we understand data. In many cases, it has led us astray…

More at “How the Average Triumphed Over the Median.”

* Benjamin Disraeli

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**As we average it out,** we might recall that it was on this date in 1913 that employees of the City of New York held a “Parade of Statistical Graphics,” replete with large graphs on horse-drawn floats, and a photograph with people arranged in a bell-shaped curve. The crowd’s favorite was the float devoted to the decline in death rate due to improvements in sanitation and nursing.

## “In Japanese and Italian, the response to [‘How are you?’] is ‘I’m fine, and you?’ In German it’s answered with a sigh and a slight pause, followed by ‘Not so good’.”*…

If you own a smartphone and are trying to learn a language, you probably have Duolingo. At this very moment the app—which tries to turn language learning into a rewarding game—may be not-so-subtly suggesting that you are overdue for some Spanish vocabulary practice.

How many other people are learning Spanish, and where do they live?Duolingo recently answered such questions by running the numbers on their 120 million users, spanning every country on the planet. The company identified the most popular language for each country, among the 19 it offers…

More at “The languages the world is trying to learn, according to Duolingo.” [Note the absence of Mandarin, Japanese, Arabic and other Asian and Middle Eastern languages– surely a reflection, at least in large part, of the offers available on Duolingo, which teaches *in* more languages than it teaches…]

* David Sedaris, *Let’s Explore Diabetes with Owls*

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**As we prepare to conjugate,** we might send elegantly phrased and eclectic birthday greetings to Persian polymath Omar Khayyam; the philosopher, mathematician, astronomer, epigrammatist, and poet was born on this date in 1048. While he’s probably best known to English-speakers as a poet, via Edward FitzGerald’s famous translation of the quatrains that comprise the *Rubaiyat of Omar Khayyam*, Omar was one of the major mathematicians and astronomers of the medieval period. He is the author of one of the most important treatises on algebra written before modern times, the *Treatise on Demonstration of Problems of Algebra,* which includes a geometric method for solving cubic equations by intersecting a hyperbola with a circle. His astronomical observations contributed to the reform of the Persian calendar. And he made important contributions to mechanics, geography, mineralogy, music, climatology and Islamic theology.

## “Gravity is a habit that is hard to shake off”*…

*click here for zoomable version*

Last week, scientists at The Laser Interferometer Gravitational-Wave Observatory, or LIGO, announced that they had confirmed Einstein’s century-old theoretical prediction of “gravitational waves,” a feature of his theory of general relativity.

Our friends at PhD Comics explain why that matters:

*email readers click here for video*

* Terry Pratchett

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**As we go with the flow,** we might send carefully-calculated birthday greetings to Einstein’s rough contemporary Alfred North Whitehead; he was born on this date in 1861. Whitehead began his career as a mathematician and logician, perhaps most famously co-authoring (with his former student, Bertrand Russell), the three-volume *Principia Mathematica* (1910–13), one of the twentieth century’s most important works in mathematical logic.

But in the late teens and early 20s, Whitehead shifted his focus to philosophy, the central result of which was a new field called process philosophy, which has found application in a wide variety of disciplines (e.g., ecology, theology, education, physics, biology, economics, and psychology).

“There is urgency in coming to see the world as a web of interrelated processes of which we are integral parts, so that all of our choices and actions have consequences for the world around us.”

## “I’m gonna put a curse on you and all your kids will be born completely naked”*…

More at “Rejected Titles for *Kids Say the Darnedest Things*.” (Younger readers click here for explanatory background.)

* Jimi Hendrix

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**As we remark that an acorn never falls far from the tree,** we might spare a thought for Christian Goldbach; he died on this date in 1764. A mathematician, lawyer, and historian who studied infinite sums, the theory of curves and the theory of equations, he is best remembered for his correspondence with Leibniz, Euler, and Bernoulli, especially his 1742 letter to Euler containing what is now known as “Goldbach’s conjecture.”

In that letter he outlined his famous proposition:

Every even natural number greater than 2 is equal to the sum of two prime numbers.

It has been checked by computer for vast numbers– up to at least 4 x 1014– but remains unproved.

(Goldbach made another conjecture that every odd number is the sum of three primes; it has been checked by computer for vast numbers, but remains unproved.)

Goldbach’s letter to Euler* (source, and larger view)*