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Posts Tagged ‘Leibnitz

That which hath made them drunk hath made me bold*…

From Jesse Gaynor in The Paris Review, “Drunk Texts from Famous Authors.”

[TotH to EWW]

* Macbeth, Act2, Scene 2

***

As we get dressed for the party celebrating the births on this date of both Gottfried Wilhelm Leibniz (1646) and Alan Turing (1912), we might spare a moment to wish a Feliz Cumpleaños to Joseph Hill “Joss” Whedon; he was born on this date in 1964.  An award winning writer, producer, director, composer, and comic creator, Whedon is probably best known as the director of this Summer’s smash, The Avengers, and as the creator-writer-director of such critically-acclaimed television series as Firefly, Buffy the Vampire Slayer, and Dollhouse.  It’s less well remembered that he was nominated for an Academy Award for his screenplay for Toy Story, the film that launched Pixar’s feature animation juggernaut.

 source

Written by LW

June 23, 2012 at 1:01 am

Slicing the pi…

 

source

Calculating the value of pi, the mathematical constant that is the ratio of a circle’s circumference to its diameter, is a Sisyphean task– it goes on forever. And from a practical point of view, it’s silly:  resolution to just 39 digits is enough to calculate the circumference of a circle the size of the observable universe with an error no larger than the radius of a hydrogen atom.

Still, the quest continues.  As i09 reports

A pair of pi enthusiasts have calculated the largest chunk of the mathematical constant yet, reaching just over 10 trillion digits. Alexander Yee and Shigeru Kondo, respectively a computer scientist in the US and a systems engineer in Japan, fought hard-drive failures and narrowly missed widespread technical disruptions due to the Japan earthquake to break their previous Guinness world record of 5 trillion digits…

Read the whole story (well, the story-to-date) at “Epic pi quest sets 10 trillion digit record.”

 

As we remember that “pi aren’t square, pie are round,” we might recall that it was on this date in 1675 that Gottfried Wilhelm von Leibniz first used the “long S” as the symbol of the integral in calculus.  Leibnitz’s first such uses were in in private manuscripts; the first public appearance was in his paper “De Geometria,” published in (the appropriately-titled) Acta Eruditorum in June 1686.

The integral of a function of x over the interval [a,b]  (source)

 

Written by LW

October 29, 2011 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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