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~ (n): An office or position that provides its occupant with an outstanding opportunity to speak out on any issue.

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Tag Archives: mathematics

Turning Coffee into Theorems

30 Tuesday Jul 2013

Posted by jrbenjamin in Science

≈ 2 Comments

Tags

Daily Rituals, Daily Rituals: How Artists Work, Mason Currey, math, mathematics, Paul Erdős, science

Paul Erdős

“Paul Erdős was one of the most brilliant and prolific mathematicians of the twentieth century. He was also, as Paul Hoffman documents in his book The Man Who Loved Only Numbers, a true eccentric—a ‘mathematical monk’ who lived out of a pair of suitcases, dressed in tattered suits, and gave away almost all the money he earned, keeping just enough to sustain his meager lifestyle; a hopeless bachelor who was extremely (perhaps abnormally) devoted to his mother and never learned to cook or even boil his own water for tea; and a fanatic workaholic who routinely put in nineteen-hour days, sleeping only a few hours a night.

Erdős liked to work in short, intense collaborations with other mathematicians, and he crisscrossed the globe seeking fresh talent, often camping out in colleagues’ homes while they worked on a problem together. One such colleague remembered an Erdos visit from the 1970s:

… he only needed three hours of sleep. He’d get up early and write letters, mathematical letters. He’d sleep downstairs. The first time he stayed, the clock was set wrong. It said 7:00, but it was really 4:30 A.M. He thought we should be up working, so he turned on the TV full blast. Later, when he knew me better, he’d come up at some early hour and tap on the bedroom door. ‘Ralph, do you exist?’ The pace was grueling. He’d want to work from 8:00 A.M. until 1:30 A.M. Sure we’d break for short meals but we’d write on napkins and talk math the whole time. He’d stay a week or two and you’d collapse at the end.

Erdős owed his phenomenal stamina to amphetamines—he took ten to twenty milligrams of Benzedrine or Ritalin daily. Worried about his drug use, a friend once bet Erdős that he wouldn’t be able to give up amphetamines for a month. Erdős took the bet and succeeded in going cold turkey for thirty days. When he came to collect his money, he told his friend, ‘You’ve showed me I’m not an addict. But I didn’t get any work done. I’d get up in the morning and stare at a blank piece of paper. I’d have no ideas, just like an ordinary person. You’ve set mathematics back a month.’ After the bet, Erdős promptly resumed his amphetamine habit, which he supplemented with shots of strong espresso and caffeine tablets. ‘A mathematician,’ he liked to say, ‘is a machine for turning coffee into theorems.'”

__________

From the section on Paul Erdős in Mason Currey’s book Daily Rituals: How Artists Work.

Erdős also had a distinctive lexicon which he used regardless if his audience understood its terms or not. For instance, although he was an atheist, Erdős spoke of “The Book” — a hypothetical volume into which God had poured his most nebulous mathematical proofs. He would frequently declare, “You don’t have to believe in God, but you should believe in The Book.”

Moreover, while he doubted the existence of God, he referred to the divine as the “Supreme Fascist,” or SF, which he accused of hiding his socks and Hungarian passports, and of concealing the most exquisite mathematical concepts and proofs from man. Often Erdős would declare, after discovering an especially beautiful mathematical proof, “This one’s from The Book!”.

Some other terms from Erdős’s dictionary:

– Children were referred to as “epsilons” (because in mathematics, particularly calculus, an arbitrarily small positive quantity is commonly denoted by the Greek letter (ε))
– Women were “bosses”
– Men were “slaves”
– People who stopped doing mathematics had “died”
– People who physically died had “left”
– Music was “noise”
– To give a mathematical lecture was “to preach”
– To give an oral exam to a student was “to torture” him/her.

Erdős’s affirmative mantra was, “Problems worthy of attack prove their worth by fighting back.”

He also declared, “Why are numbers beautiful? It’s like asking why is Beethoven’s Ninth Symphony beautiful. If you don’t see why, someone can’t tell you. I know numbers are beautiful. If they aren’t beautiful, nothing is.”

For his epitaph, he suggested, “Végre nem butulok tovább,” which is Hungarian for “I’ve finally stopped getting dumber.”

Erdős is also the only person to have an Erdős number of 0.

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Isaac Newton

26 Tuesday Mar 2013

Posted by jrbenjamin in Interview, Science

≈ 22 Comments

Tags

Alexander Pope, Astronomy, calculus, Gravity, history, Isaac Newton, Laws of Gravity, mathematics, Neil deGrasse Tyson, Optics, physics, Planetary Motion, science, scientists, Smartest Person Ever, Time Magazine

Isaac Newton

If you could meet and talk with any scientist who had ever lived, who would it be, and why?

“Isaac Newton. Isaac Newton. No question about it: Isaac Newton. The smartest person ever — ever to walk the face of this earth. You read his writings, the man was connected to the universe in spooky ways. The most successful scientists in the history of the world are those who pose the right questions… Newton, his questions reached into the soul of the universe, and he pulled out insights and wisdom that transformed our understanding of our place in the cosmos.

Someone said to him, ‘Isaac, why is it that planets orbit in these shapes you call ellipses, rather than circles? Why that shape?’ Newton said, ‘You know, I’ll get back to you on that.’ He goes away for a few months, comes back, and says, ‘Here’s the answer. Here’s why gravity produces ellipses for orbits.’

His friend asks, ‘Well how’d you figure that out?’

He says, ‘Well I had to invent this new kind of mathematics to do it.’ He invented calculus. Most of us sweat through it — for multiple years in school — just to learn it. He invented it practically on a dare.

He discovered the laws of motion. The laws of gravity. The laws of optics. Then he turned twenty-six.”

__________

Neil deGrasse Tyson’s response to the question, “If you could meet and talk with any scientist who had ever lived, who would it be, and why?”

Nature and Nature’s laws lay hid in night;
God said Let Newton be! and all was light.
– Alexander Pope’s intended epitaph for Newton’s tomb in Westminster Abbey.

Pick up the James Gaelic’s much praised biography Isaac Newton, then watch the Time Magazine interview below:

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The Arithmetic of Nothingness

06 Wednesday Mar 2013

Posted by jrbenjamin in Philosophy

≈ 4 Comments

Tags

Arithmetic, Jim Holt, mathematics, numbers, Why Does the World Exist?, zero

Raindrops on a Car

“As for the origin of the numeral ‘0,’ that has eluded historians of antiquity. On one theory, now discredited by scholars, the numeral comes from the first letter of the Greek word for ‘nothing,’ ouden. On another theory, admittedly fanciful, its form derives from the circular impression left by a counting chip in the sand–the presence of an absence.

Suppose we let 0 stand for Nothing and 1 stand for Something. Then we get a sort of toy version of the mystery of existence: How can you get from 0 to 1?

In higher mathematics, there is a simple sense in which the transition from 0 to 1 is impossible. Mathematicians say that a number is ‘regular’ if it can’t be reached via the numerical resources lying below it. More precisely, the number n is regular if it cannot be reached by adding up fewer than n numbers that are themselves smaller than n.

It is easy to see that 1 is a regular number. It cannot be reached from below, where all there is to work with is 0. The sum of zero 0’s is 0, and that’s that. So you can’t get from Nothing to Something.

Curiously, 1 is not the only number that is unreachable in this way. The number 2 also turns out to be regular, since it can’t be reached by adding up fewer than two numbers that are less than 2. (Try it and see.) So you can’t get from Unity to Plurality.

The rest of the finite numbers lack this interesting property of regularity. They can be reached from below. (The number 3, for example, can be reached by adding up two numbers, 1 and 2, each of which is itself less than 3.) But the first infinite number, denoted by the Greek letter omega, does turn out to be regular. It can’t be reached by summing up any finite collection of finite numbers. So you can’t get from Finite to Infinite.”

__________

From the chapter “The Arithmetic of Nothingness” in Jim Holt’s new book Why Does the World Exist?: An Existential Detective Story.

The photograph: Rain on the hood of a car. Houston, Texas.

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