+ Mathematics! Logic! Philosophy! Comic Book?

other topics: click a “category” or use search box

Graphic novel “Logicomix,” is based on the early life of brilliant philosopher and mathematician Bertrand Russell and his impassioned search for truth.  

Authors Apostolos Doxiadis and Christos Papadimitriou are academic mathematicians and writers who wanted to create an “honest-to-God yarn, simply a story.”  But in this case, the heroes are all logicians.

In Publisher’s Weekly, Calvin Reid says

It’s difficult not to be dazzled by Apostolos Doniadis and Christos Papadimitriou’s Logicomix.  It’s a biography of the mathematician/philosopher Bertrand Russell, a fiercely engaging examination of his elusive attempt to isolate the logical foundations of mathematics, and a rousing historical yarn.

And all of Logicomix’s storytelling and intellectual pyrotechnics are delineated in extraordinarily crisp, cleverly designed and beautifully colored artwork by the team of Alecos Papadatos and Annie Di Donna. 

What a Comic book!  Easily one of the most impressive combinations of popular art and serious history that I’ve encountered in prose or comics.

A dramatic story of madness and reason, love and war, this is a story about the conflict between an ideal rationality and the unchanging, flawed fabric of reality.   In his agonized search for absolute truth, Russell crosses paths with legendary thinkers like Gottlob Frege, David Hilbert, and Kurt Godel.  He finds a passionate student in the great Ludwig Wittgenstein.

But truth eludes him.  According to historian Howard  Zinn

This is an extraordinary graphic novel, wildly ambitious in daring to put into words and drawing the life and thought of one of the great philosophers of the last century…  The book is a rare intellectual and artistic achievement, which will, I am sure, lead its readers to explore realms of knowledge they thought were forbidden to them.

“Logicomix” is at the same time a historical novel and an accessible introduction to some of the biggest ideas of mathematics and modern philosophy. 

Barry Mazur is Gerhard Gade University Professor at Harvard.  He has written that

This magnificent book is about ideas, passions, madness, and the fierce struggle between well-defined principle and the larger good.  It follows the great mathematicians — Russell, Whitehead, Frege, Cantor, Hilbert — as they agonized to make the foundations of mathematics exact, consistent, and complete.  And we see the band of artists and researchers — and the all-seeking dog Manga — creating, and participating in, this glorious narrative.

Writer Apostolos Doxiadis studied mathematics at Columbia.  His international bestseller “Uncle Petros and Goldbach’s Conjecture” was the first novel to make fascinating fiction out of mathematics.  He has awards from his work in film and theater, and is also a pioneer in the study of the interaction of mathematics and narrative.

Co-writer Christos Papadimitriou is the C. Lester Hogan Professor of Computer Science at UCLA Berkeley.  He has won numerous international awards for pathbreaking work in computational complexity and algorithmic game theory.  He is also the author of the novel “Turing: A Novel About Computation.” 

The graphic artists are a husband and wife team, Alecos Papadatos and Annie Di Donna.  Papadatos worked for over twenty years in film animation in France and Greece.  In 1997 he became a cartoonist for the major Athens daily To Vima. 

Annie Di Donna studied graphic arts and painting in France and has worked as an animator on many productions, among them Babar and Tintin cartoons.  The couple have been running an animation studio since 1991.

Michael Harris, professor of mathematics at the Universite Paris 7 and member of the Institut Universitaire de France,

The lives of ideas (and those who think them) can be as dramatic and unpredictable as any superhero fantasy.  Logicomix is witty, engaging, stylish, visually stunning, and full of surprising sound effects, a masterpiece in a genre for which there is as yet no name.

“Logicomix: An Epic Search for Truth,” by Apostolos Doxiadis and Christos H. Papadimitriou, is published by Bloomsbury USA.  ISBN-10 1-59691-452-1; ISBN-13 9978-1-59691-452-0.

tutoring in Columbus OH:   Adrienne Edwards   614-579-6021   or email  aedwardstutor@columbus.rr.com  

+ John R Stallings Partly Solved a Math Puzzle and Cautioned Mathematicians

other topics: click a “category” or use search box

John R Stallings Jr, who found a proof for part of the Poincare Conjecture (one of the longest-standing problems in Mathematics) died at the age of 73 last November.

Dr Stallings, born in Arkansas, graduated from the University of Arkansas and finished his doctorate in mathematics at Princeton in 1959.  After a fellowship at Oxford, he taught at Princeton and then became a professor at Berkeley in 1967.

His work largely involved geometry and topology, the study of fundamental properties of shapes.  He later applied that knowledge to the field of geometric group theory, using geometric and topological concepts to prove theorems in algebra.  

The Poincare Conjecture, proposed by Henri Poincare in 1904, says essentially that any shape that does not have any holes, and that fits within a finite space, can be stretched and deformed into a sphere.

Dr Stallings was far from the first mathematician to tackle the Poincare Conjecture; he wasn’t even the first to find a partial solution. 

Stephen Smale of Berkeley was the first.  In 1960 he proved the conjecture for surfaces of five dimensions and higher.

Dr Stallings, then a postdoctoral fellow at Oxford heard this news, but not the details.  He took a swipe.

In a few days, he had come up with his own proof, which worked for dimensions seven and higher.  Less sweeping than Smale’s, Stallings’s proof applied to a slightly different version of the conjecture.  It employed different mathematical techniques.

Barry Mazur, a Harvard mathematician, says “That tells you more about the nature of the problem.  This is a very, very deep geometric problem and every fact of it is not only interesting, but has ramifications.  Different proofs bring out different aspects of a problem.” 

The four-dimensional case was proved in 1982, and in 2003, a Russian mathematician, Grigori Perelman, completed a proof for the thorniest case, of three dimensions.

“How Not to Prove the Poincare Conjecture”

But in 1965, in a paper titled “How Not to Prove the Poincare Conjecture,” Dr Stallings confessed that he had sought, and failed,  to find a final, complete proof.

The paper — about his non-proof — began humorously: “I have committed — the sin of falsely proving Poincare’s Conjecture.  But that was in another country; and besides, until now no one has known about it.”

He explained his errors in that paper.  Then he offered the reason for his confession: it was “in hope of deterring others from making similar mistakes.”

He ended on this musing note:

I was unable to find flaws in my “proof” for quite a while, even though the error is very obvious.  It was a psychological problem, a blindness, an excitement, an inhibition of reasoning by an underlying fear of being wrong.  Techniques leading to the abandonment of such inhibitions should be cultivated by every honest methematician.

sole source: obituary of John R Stallings, by Kenneth Chang, in the NY Times on 1/20/09.   www.nytimes.com  

tutoring in Columbus OH:   Adrienne Edwards   614-579-6021   or email   aedwardstutor@columbus.rr.com  

+ Debating the Electoral College

other topics: click a “category” or use search box

The Massachusetts Institute of Technology (MIT) plans to apply its engineering and systems know-how to help answer the ongoing question: should we keep or not keep the Electoral College?

The issue is the subject for debate today at a conference which brings together constitutional scholars and mathematics experts, according to a political note in the NY Times.

“Since its creation in 1787, the Electoral College has remained the most mysterious mechanism for electing a president of a country,” says Alexander S Belenky, a visiting scholar at the Center for Engineering Systems Fundamentals at MIT.

“There is no consensus, among mathematicians, systems analysts and political scientists studying the Electoral College, on whether it can satisfactorily serve the United States in the 21st century, especially after two close elections in 2000 and 2004.”

The conference is looking at whether the Electoral College should be retained, eliminated, or modified.

As Election Day draws near, and as people start working the numbers, there is reason to believe that something different might be done, says Arnold I Barnett, MIT management science professor and chairman of the conference.

The Electoral College is often studied from a political angle.  But the MIT professors are looking at it from a mathematical model.  Belenky, author of “How America Chooses Its Presidents,” says it is mathematically possible, for instance, for two candidates to each win 49 percent of the popular vote, and have one of them end up with zero electoral votes and the other with 538.  Or any combination in between. 

Say what?

sole source: political note by Leslie Wayne in the N Y Times on 10/17/08.   www.nytimes.com

tutoring in Columbus OH:   Adrienne Edwards   614-579-6021   or email   aedwardstutor@columbus.rr.com