This week the British government once again refused to pardon Alan Turing. One of the greatest mathematicians of the 20th century, Turing laid the foundations for computer science and played a key role in breaking the Nazi Enigma code during World War II. In 1952 he was convicted of homosexuality. He killed himself two years later, after being chemically castrated by the government.

On Monday, Justice Minister Tom McNally told the House of Lords that the government of Prime Minister David Cameron stood by the decision of earlier governments to deny a pardon, noting that the previous prime minister, Gordon Brown, had already issued an “unequivocal posthumous apology” to Turing. McNally was quoted  in the Guardian:

A posthumous pardon was not considered appropriate as Alan Turing was properly convicted of what at the time was a criminal offense. He would have known that his offense was against the law and that he would be prosecuted. It is tragic that Alan Turing was convicted of an offense which now seems both cruel and absurd–particularly poignant given his outstanding contribution to the war effort. However, the law at the time required a prosecution and, as such, long-standing policy has been to accept that such convictions took place and, rather than trying to alter the historical context and to put right what cannot be put right, ensure instead that we never again return to those times.

The decision came as a disappointment to thousands of people around the world who had petitioned for a formal pardon during the centenary year of Turing’s birth. The Guardian also quoted an email sent by American mathematician Dennis Hejhal to a British colleague:

i see that the House of Lords rejected the pardon Feb 6 on what are formal grounds.

if law is X on date D, and you knowingly break law X on date D, then you cannot be pardoned (no matter how wrong or flawed law X is).

the real reason is OBVIOUS. they do not want thousands of old men saying pardon us too.

Efforts to obtain a pardon for Turing are continuing. British citizens and UK residents can still sign the petition.

To learn more about Turing’s life, you can watch the 1996 BBC film Breaking the Code (above, in its entirety), featuring Derek Jacobi as Turing and Nobel Prize-winning playwright Harold Pinter as the mysterious “Man from the Ministry.” Directed by Herbert Wise, the film is based on a 1986 play by Hugh Whitemore, which in turn was based on Andrew Hodge’s 1983 book Alan Turing: The Enigma.

Breaking the Code moves back and forth between two time frames and two very different codes: one military, the other social. The film runs 91 minutes, and has been added to our collection of Free Movies Online.

Still No Pardon for Alan Turing; Watch the Film Breaking the Code is a post from: Open Culture

“Three passions, simple but overwhelmingly strong, have governed my life,” wrote Bertrand Russell in the prologue to his autobiography: “the longing for love, the search for knowledge, and unbearable pity for the suffering of mankind.”

This five minute video, a preview of a three-part series produced in 2005 for Ontario public television called “The Three Passions of Bertrand Russell,” features a recording of Russell reading passages from the prologue, entitled “What I Have Lived For.” You can read the original text at the Bertrand Russell Society, an excellent online resource, that also makes available free books by Russell, including:

• An Essay on the Foundations of Geometry (1897)
• The Principles of Mathematics (1903)
• Our Knowledge of the External World (1914)
• Introduction to Mathematical Philosophy (1919)
• Mysticism and Logic and Other Essays (1919)
• The Analysis of Mind (1921)
• The Conquest of Happiness (1930)

You can also download the first edition of Russell’s landmark 1910-13 collaboration with Alfred North Whitehead, Principia Mathematica, as well as many of Russell’s essays, including:

• “A Free Man’s Worship” (1903)
• “On Denoting” (1905)
• “The Elements of Ethics” (1910)
• “The Ethics of War” (1915)
• “On Propositions” (1919)
• “Theory of Knowledge” (1926)
• “Why I am Not a Christian” (1927)

To explore the full list of available resources, and to learn how you can support the society’s activities, visit the Bertrand Russell Society website.

Also don’t miss some great Russell material in our own archives, including all six of his 1948 BBC Reith Lectures, a clip from a Canadian television interview featuring his views on God, and his eloquent 1959 message to the future.

Three Passions of Bertrand Russell (and a Collection of Free Texts) is a post from: Open Culture

Countdown is a British TV game show revolving around words and numbers. In the numbers round, contestants select six of twenty-four shuffled tiles with numbers on them. Next, a computer generates a random three-digit target number and the contestants have thirty seconds to get as close to that number as possible by combining the six numbers through addition, subtraction, multiplication and division. This memorable episode of Countdown aired in March 1997 and starred James Martin and his rather unusual way of arriving at the target number of 952.

One YouTube user suggested a different way: 6 x 75 = 450; 450 ÷ 50 = 9; 100 + 3 = 103; 9 x 103 = 927; 927 + 25 = 952

I found yet another way: 100 + 3 = 103; 103 x 6 = 618; 618 x 75 = 46,350; 46,350 ÷ 50 = 927; 927 + 25 = 952

What about you? Any more suggestions?

By profession, Matthias Rascher teaches English and History at a High School in northern Bavaria, Germany. In his free time he scours the web for good links and posts the best finds on Twitter.

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Incredible Mental Math Gymnastics on “Countdown” is a post from: Open Culture

Infinity. It’s a puzzling concept. Is it real, or a mathematical fiction?

Aristotle believed infinity could only be potential, never actual. To speak of an actual infinity, he argued, is to fall into logical contradiction: “The infinite turns out to be the contrary of what it is said to be,” Aristotle wrote in the Physics. “It is not what has nothing outside it that is infinite, but what always has something outside it.”

Aristotle’s logic rested on common sense: the belief that the whole is always greater than the part. But in the late 19th Century, Georg Cantor and Richard Dedekind turned common sense upside down by demonstrating that the part can be equal to the whole. Cantor went on to show that there are many orders of infinity–indeed, an infinity of infinities.

But what relation does the Platonic realm of pure mathematics have to the physical world? Physics is an empirical science, but that hasn’t stopped theorists from imagining the mind-boggling consequences of an infinite universe. To Infinity and Beyond, a one-hour BBC Horizon special featuring interviews with leading mathematicians and physicists, is an entertaining exploration of a subject which, by definition, you won’t be able to wrap your mind around.

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To Infinity and Beyond: A Mind-Bending Documentary from the BBC is a post from: Open Culture

Oliver Knill teaches calculus, linear algebra and differential equations at Harvard, and, several years back, he pulled together a fairly nifty collection of Mathematics Scenes in Movies. Over 150 films are represented here, everything from Good Will Hunting, A Beautiful Mind, Jurassic Park (above) to Alice in Wonderland (1951), The Maltese Falcon and Apocalypse Now. You can watch each scene in flash format on Knill’s site, or download them as a quicktime file.

And, film buffs, don’t miss our collection of 435 Free Movies Online.

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Mathematics in Movies: Harvard Prof Curates 150+ Scenes is a post from: Open Culture

“Music,” Gottfried Leibniz famously said, “is the pleasure the human mind experiences from counting without being aware that it is counting.” Computer artist Alexander Chen makes this pleasure visible with Baroque.Me, his geometric computer animation of the Prelude to Johann Sebastian Bach’s Cello Suite No. 1 in G major.

Chen visualized the piece by imagining a harp with strings that would automatically morph into different lengths according to the principles of Pythagorean tuning. “It’s math based on the fraction 2/3,” writes Chen on his blog. “I started with the longest string, setting it to a symbolic length of pixels. When cut to 2/3 length, it goes up a fifth. Cut its length by 1/2 and it goes up an octave. 3/4 length, one fourth. From these simple numbers I calculated the relative string lengths of all the notes in the piece.” He used eight strings because the Prelude’s phrasing is in groups of eight notes. The strings are “plucked” by two symmetrical pairs of nodes that revolve at a uniform rate, rather like a digital music box.

Chen, 30, lives in Brooklyn, NY, and works in the Google Creative Lab. One of his most popular pieces for Google was the Les Paul Doodle, which allows users to digitally strum the guitar strings. Chen grew up learning music and computer programming in parallel. He plays the classical viola, but with the Bach animation he wanted to remove the performer’s interpretive element from the music. “It’s a piece that I’ve heard a lot since I was a kid,” Chen told the BBC recently. (See the “Mathematical Music” podcast, Nov. 3.) “People always bring different levels of expression to it. People play to different tempos and they add a lot of dynamics, or less dynamics. But what I wanted to let the computer do was just kind of to play in a really neutral way, because what I really wanted to express was how much emotion and intensity is just in the data of the notes themselves. I think that’s really where the beauty of the piece at its core is.”

To hear the Prelude with the interpretive element back in, you can watch this video of Pablo Casals performing it in 1954:

Visualizing Bach: Alexander Chen’s Impossible Harp is a post from: Open Culture

Canadian software developer Matthias Wandel enjoys spending his spare time creating wooden contraptions that combine a childlike sense of wonder with an engineer’s knowledge of mechanics. One of his most popular creations so far is this six-bit binary adding machine, which has tallied nearly one and a half million views on YouTube. As Rick Regan explains at Exploring Binary, the machine functions like a low-tech integrated circuit. “It uses wood instead of silicon, gravity instead of voltage, and marbles instead of current,” he writes. “We don’t need no stinkin’ CMOS!”

The idea came to Wandel after he noticed that one of his earlier marble machines incorporated logic-like elements. “It had occurred to me,” he writes on his woodworking site, “that perhaps with an insane amount of perseverance, it might be possible to build a whole computer that runs on marbles.”  To illustrate the point Wandel built the adding machine, which stores the binary states of six bits and can add numbers from one to 63. The result may be more cool than practical, writes Regan, “but it certainly is educational. It illustrates basic principles of binary numbers, binary arithmetic, and binary logic.”

You can learn more about the machine on Wandel’s Web page, and about the underlying logic and mathematics at Exploring Binary.

The Wonderful, Wooden Marble Adding Machine is a post from: Open Culture

It’s rare that we get to cover math here. So here it goes: Adrian Banner, a lecturer at Princeton, has put together a lecture series (in video) that will help you master calculus, a subject that has traditionally frustrated many students. The 24 lectures (click here) were originally presented as review sessions for Princeton introductory calculus courses offered in 2006, and each session runs about two hours. It’s worth noting that Banner has used the lectures to develop a handy book, The Calculus Lifesaver: All the Tools You Need to Excel at Calculus. To find this course (and many others like it), look in the Math section of our collection of 400 Free Online Courses. Here you will also find Calculus Revisited: Single Variable Calculus, a vintage introductory course filmed by MIT in 1970. Consider it a classic…

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Calculus Lifesaver: A Free Online Course from Princeton is a post from: Open Culture

The Open University strikes again. In June, they released The History of English, a series of witty animated videos that covered 1600 years of linguistic history in ten minutes. Now, they’re back with 60-Second Adventures in Thought, another animated sequence that highlights six famous thought experiments. It all starts with Zeno’s ancient Paradox of the Tortoise and Achilles. (Watch above.) Then we head straight to the 20th century, to five famous thought experiments in physics, math and computer science.

• The Grandfather Paradox (time travel)
• Chinese Room (artificial intelligence)
• Hilbert’s Infinite Hotel (the concept of infinity)
• The Twin Paradox (special relativity)
• Schrödinger’s Cat (quantum mechanics)

You can watch the full series on YouTube and iTunes.

60 Second Adventures in Thought is a post from: Open Culture

Doodling — it’s usually a sign of boredom, an escape from tedium. Vi Hart turns it all upside down, and shows how doodling can be an engaging form of pedagogy. On her web site, you will find other math doodling videos called Stars, Snakes + Graphs, Binary Trees, Sick Number Games and Squiggle Inception. The video above is called Infinity Elephants. Thanks Kim for sending this our way….

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Math Doodling is a post from: Open Culture