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Posts Tagged ‘calculus

“All practical jokes, friendly, harmless or malevolent, involve deception, but not all deceptions are practical jokes”*…

 

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When you think of the ancient Greeks, practical jokes might not be the first thing that comes to mind. But along with art, architecture, and philosophy, you can add trick cups to their list of accomplishments.

The Pythagorean cup is so-named because it was allegedly invented by Pythagoras of Samos (yes, the same guy who gave us theories about right triangles). It’s a small cup with a column in its center. It doesn’t look like much, but when an unsuspecting drinker fills it past a designated level, the liquid mysteriously drains out. Legend has it that Pythagoras used it as a way to punish greedy drinkers who poured themselves too much wine…

A timeless practical joke, brought to you by the ancient Greeks: more merriment at “Pythagorean Cup.”

* W. H. Auden, The Dyer’s Hand

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As we ponders pranks, we might send a “Alles Gute zum Geburtstag” to the polymathic Gottfried Wilhelm Leibniz, the philosopher, mathematician, and political adviser, who was important both as a metaphysician and as a logician, but who is probably best remembered for his independent invention of the calculus; he was born on this date in 1646.  Leibniz independently discovered and developed differential and integral calculus, which he published in 1684;  but he became involved in a bitter priority dispute with Isaac Newton, whose ideas on the calculus were developed earlier (1665), but published later (1687).

As it happens, Leibnitz was no mean humorist.  Consider, e.g…

If geometry conflicted with our passions and our present concerns as much as morality does, we would dispute it and transgress it almost as much–in spite of all Euclid’s and Archimedes’ demonstrations, which would be treated as fantasies and deemed to be full of fallacies. [Leibniz, New Essays, p. 95]

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Written by LW

July 1, 2018 at 1:01 am

“I go to seek a Great Perhaps”*…

 

As we’ve noted before, 2016 seemed a bumper year for the Grim Reaper.  Jason Crease tested that perception against the data…

It’s become cliché that unusually many prominent people died in 2016. Is this true?…

Find out at “Was 2016 especially dangerous for celebrities? An empirical analysis.

[Image above: source]

* François Rabelais

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As we usher in the new, we might spare a thought for the first woman in the Western world considered to be a mathematician: Maria Gaetana Agnesi, she died this date in 1799.  While she thought and wrote broadly about natural science and philosophy, she is best remembered for her work in differential calculus– perhaps most particularly for her work on the cubic curve now know as the “witch of Agnesi.”

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Written by LW

January 9, 2017 at 1:01 am

“All opinions are not equal. Some are a very great deal more robust, sophisticated and well supported in logic and argument than others”*…

 

Now more than ever:  Get a free logical fallacy poster.

* Douglas Adams, The Salmon of Doubt

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As we dedicate ourselves to discipline, we might send carefully-calculated birthday greetings to John Wallis; he was born on this date in 1616.  An English mathematician who served as chief cryptographer for Parliament and, later, the royal court, he helped develop infinitesimal calculus and is credited with introducing the symbol ∞ for infinity.

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Written by LW

December 3, 2016 at 1:01 am

“There is not a discovery in science, however revolutionary, however sparkling with insight, that does not arise out of what went before”*…

 

Analysis of an ancient codebreaking tablet has revealed that Babylonian astronomers had calculated the movements of Jupiter using an early form of geometric calculus some 1,400 years before we thought the technique was invented by the Europeans.

This means that these ancient Mesopotamian astronomers had not only figured out how to predict Jupiter’s paths more than 1,000 years before the first telescopes existed, but they were using mathematical techniques that would form the foundations of modern calculus as we now know it…

Look more closely at the foundations of modern calculus at “This ancient Babylonian map of Jupiter just changed history as we know it.”  And read the Science article reporting the findings here.

* Isaac Asimov

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As we calculate the differential, we might send radiant birthday greetings to James Alfred Van Allen; he was born on this date in 1914.   A space scientist who learned to miniaturize electronics during World War II, he was instrumental in establishing the field of magnetospheric research in space, and led the scientific community for the inclusion of scientific research instruments on space satellites.  The Van Allen radiation belts were named after him, following their discovery by his Geiger–Müller tube instruments in 1958 on the Explorer 1, Explorer 3, and Pioneer 3 satellites during the International Geophysical Year.

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Written by LW

September 7, 2016 at 1:01 am

“What is the difference between a taxidermist and a tax collector? The taxidermist takes only your skin”*…

 

A Ferris wheel of chipmunks, formerly part of the Dead Pals of Sam Sanfillippo

 

Last October, Atlas Obscura co-presented a Rogue Taxidermy Fair with its fellow Brooklyn-based (and former Roughly Daily subject) Morbid Anatomy in celebration of a new book on “rogue taxidermy.”

The Crucified Sheep

 

Read more about– and see more of– the Fair at “The Crucified Sheep, Tattooed Frogs, and Crocheted Skeletons of a Rogue Taxidermy Fair in Brooklyn,” and revisit (R)Ds earlier look at rogue taxidermy here.

* Mark Twain

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As we strike a pose, we might recall that it was on this date in 1697 that Isaac Newton received and solved Jean Bernoulli’s brachistochrone problem.  The Swiss mathematician Bernoulli had challenged his colleagues to solve it within six months.  Newton not only solved the problem before going to bed that same night, but in doing so, invented a new branch of mathematics called the calculus of variations.  He had resolved the issue of specifying the curve connecting two points displayed from each other laterally, along which a body, acted upon only by gravity, would fall in the shortest time.  Newton, age 55, sent the solution to be published, at his request, anonymously.  But the brilliant originality of the work betrayed his identity, for when Bernoulli saw the solution he commented, “We recognize the lion by his claw.”

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Written by LW

January 26, 2015 at 1:01 am

Caveat discipulus…

 

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As we lick our pencils, we might send thoughtful birthday greetings to Immanuel Kant; he was born on this date in 1724.  One of the central figures of modern philosophy, Kant is remembered primarily for his efforts to unite reason with experience (e.g., Critique of Pure Reason [Kritik der reinen Vernunft], 1781), and for his work on ethics (e.g., Metaphysics of Morals [Die Metaphysik der Sitten], 1797) and aesthetics (e.g., Critique of Judgment [Kritik der Urteilskraft], 1790).  But he made important contributions to mathematics as well:  Kant’s argument that mathematical truths are a form of synthetic a priori knowledge was cited by Einstein as an important early influence on his work.

There is … only a single categorical imperative and it is this: Act only on that maxim through which you can at the same time will that it should become a universal law.

– Chapter 11, Metaphysics of Morals

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Written by LW

April 22, 2013 at 1:01 am

Next to nothing…

Neutinos are so small and so nearly without mass that 50 trillion of them pass unimpeded through a person’s body every second.  Ironically, this nearly nonexistent particle seems poised to start a revolution…

One of the two detectors in the MINOS neutrino experiment sits in the Soudan Underground Laboratory in Minnesota. A recent analysis of MINOS data hints that neutrinos and antineutrinos might not weigh the same-- a challenge to Einstein’s theory of special relativity.

Current theories of particle physics are based on two assumptions: All known forces arise from interactions with neighboring particles and they all obey Einstein’s special relativity theory, which holds that the speed of light and the laws of physics are always the same regardless of a particle’s speed or rotation. For that to hold true, particles and antiparticles—-including neutrinos and their antipartners — must have the same mass.

But new measurements from an experiment called MINOS (for Main Injector Neutrino Oscillation Search) seem to contradict that notion. The three known types of neutrinos —electron, muon and tau — act like chameleons, transforming from one type into another as they travel.

MINOS found that during a 735-kilometer journey from Fermilab to the Soudan Underground Laboratory in Minnesota, about 37 percent of muon antineutrinos disappeared — presumably morphing into one of the other neutrino types — compared with just 19 percent of muon neutrinos, reports MINOS spokesman Robert Plunkett of Fermilab.

That difference in transformation rates suggests a difference in mass between antineutrinos and neutrinos… “One thing is clear — if the masses are different for neutrinos and antineutrinos, then the most sacred symmetry of quantum field theory, CPT (for charge, parity and time), is broken in the neutrino sector,” says Tom Weiler of Vanderbilt University in Nashville.

Read the full story in Science News.

As we wax nostalgic for symmetry, we might send a “Alles Gute zum Geburtstag” to the remarkable Gottfried Wilhelm Leibniz, the philosopher, mathematician, and political adviser, who was important both as a metaphysician and as a logician, but who is probably best remembered for his independent invention of the calculus; he was born on this date in 1646.  Leibniz independently discovered and developed differential and integral calculus, which he published in 1684;  but he became involved in a bitter priority dispute with Isaac Newton, whose ideas on the calculus were developed earlier (1665), but published later (1687).

Leibnitz

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