There’s no doubt that Perelman’s response to solving one of math’s longest standing problems is part of what is so intriguing to the lay reader. He turned down a Field’s medal and withdrew from professional mathematics. Pieces on him tend to accentuate his eccentricities. Part of what makes the story so very interesting is Perelman’s response, as well as the other cast of characters involved in the solving of the problem. Though it came out in mid-2006, the New Yorker has a fantastic article about the solving of the Poincaré Conjecture and the controversy surrounding it. If you’d like to understand to a greater extent Perelman’s response to his solution, read this article. It’s long, but extremely informative and complete.

In a nutshell, Gaffney found that he had inadvertently used many similar aspects of a puzzle that had been released earlier in the year, and thus traces several reasons why this may have been the case. One interesting twist to the story is what happens when Gaffney asks a third crossword creator to write a similarly themed puzzle. Do you think that this third puzzle turned out to have similar entries to the first two? Read to find out!

First, take this iteration of Claude Shannon’s “Ultimate Machine”, whose sole purpose when turned on is to immediately turn itself back off again:

As the video explains, you can find plans for building your own machine of the same type at Instructables. It should be said that I was introduced to this machine via Boing Boing much earlier when they directed me here. These folks call the machine the “Leave Me Alone Box”, and there are several videos on the site devoted to showing different fan-made machines in action. It looks like this site will also eventually sell a kit which allows you to build your own box. Kevin Kelly also has an article that gives some history about this “Ultimate Machine”.

Secondly, take Michael Kontopoulos’ machines that are built only with the task of nearly knocking themselves over:

Machines that Almost Fall Over from Michael Kontopoulos on Vimeo.

The artist explains his intentions on his website as trying “to capture and sustain the exact moment of impending catastrophe and endlessly repeat it.” I love it! So close to falling, and yet so far away! There are lots of other interesting projects to find on Michael’s website as well.

“The Difference Engine fills half a gallery and stands taller than most men. It’s 5 tons of cast iron, steel and bronze woven together from 8,000 distinct parts. Though it looks like it could be a sculpture, the machine is essentially a giant calculator.”

In other words, it’s gigantic. And it works. It was the best computer that money could buy in 1840, which is probably why it was never actually built. Way too complex and way too much money. It’s worth checking out the NPR story just to see the photos of this monstrous machine. There’s also a video of the machine in action on the Computer History Museum webpage for the Babbage Engine exhibit here.

First, I think it’s appropriate to explain what Logicomix is, and what it is not. First, it is a work of fiction. The authors are clear on this point, and explicitly spell it out in the epilogue. This graphic novel is meant to be a piece of art, not a pristine account of history. But its account of history will definitely give the reader an accurate outline of what happened in mathematics in the 20th century, even if the details aren’t entirely accurate, and even if certain liberties are taken in order to present a story which engages the reader in its narrative format.

Logicomix tells the story of 20th century mathematics by using Bertrand Russell as a narrator. The story is framed as a talk which Russell is giving to an audience directly before Britain’s entrance into World War II. He traces his life’s story from childhood through his work as an activist, and along the way we meet the familiar set of characters from that day, including Frege, Whitehead, Gödel, Wittgenstein, Cantor, etc.

The story is compelling. The authors, Apostolos Doxiadis and Christos Papadimitriou, do an amazing job of following Russell’s career, and of showing the personality and human struggle behind a quest centered around the abstract notion of truth. While most of the characters are obsessed with matters of the brain, the story also focuses on the heart as well. For instance, Logicomix does a good job explaining Russell’s obsession with madness, and his fear associated with it. There is also an aspect of meta-story in Logicomix, whereby the authors themselves appear throughout to drive home points and debate various tidbits of the story. This is an interesting aspect that mirrors to some extent Gödel’s meta-logical statements. I thought this was a good touch.

The art, done by Alecos Papadatos and Annie Di Donna, is stunning. As a material object, this graphic novel is beautiful. I’m a huge proponent of quality, and everything about the novel breathes quality. From the art to the color to the fonts to even the dimensions of the page and panels, Logicomix is extremely well engineered. Kudos to them both!

As a work of historical fiction, this story should appeal both to lovers of logic and mathematics as well as those who enjoy a fantastic story. The authors are using history to drive home what I believe to be an accurate and well-stated point, which I will not divulge here. If there are any flaws, I would point out two. First, Gödel is treated somewhat like a deus ex machina. Rather than providing more exposition into his life, the authors are content to have him come and go quite quickly, though I must admit that I LOVED the first panel in which he appears. It’s probably my favorite panel in the entire work. Secondly, there’s nothing about Turing, other than to mention him in the meta-story toward the end. One cannot truly understand logic without knowing something about computability. Granted, it seems that a sequel may be a possibility which begins with Turing and ends in the 21st century, but only time will tell. Until then, Logicomix comes as highly suggested.

It’s a punchline.  As in “Wouldn’t it be hee-larious if there was a comic about Ada Lovelace and Charles Babbage fighting crime? Thanks, I’ll be here all week!”  The imaginary comic was the punchline to Lovelace: The Origin, drawn because my good buddy Suw Charman got me drunk started a Noble Enterprise called Ada Lovelace Day.

Secondly, Jim Holt wrote a book review last Sunday that introduced me to Logicomix, which the official website describes as follows:

Covering a span of sixty years, the graphic novel Logicomix was inspired by the epic story of the quest for the Foundations of Mathematics.

This was a heroic intellectual adventure most of whose protagonists paid the price of knowledge with extreme personal suffering and even insanity. The book tells its tale in an engaging way, at the same time complex and accessible. It grounds the philosophical struggles on the undercurrent of personal emotional turmoil, as well as the momentous historical events and ideological battles which gave rise to them.

The role of narrator is given to the most eloquent and spirited of the story’s protagonists, the great logician, philosopher and pacifist Bertrand Russell. It is through his eyes that the plights of such great thinkers as Frege, Hilbert, Poincaré, Wittgenstein and Gödel come to life, and through his own passionate involvement in the quest that the various narrative strands come together.

VERY cool. I’ll definitely be picking this up before too long. The art looks fantastic, and I’m sure the story matches up! Check out the review linked to above for a fuller introduction to the story.

Despite his contributions, Turing was convicted under English homophobic laws and sentenced to chemical castration. As PM Brown writes, “In 1952, he was convicted of ‘gross indecency’ – in effect, tried for being gay.” Given the choice between going to prison and undergoing hormone treatments, he chose the latter. Less than three years later Turing was found dead, apparently the result of a cyanide overdose. His death was judged to be a suicide.

While the note obviously cannot change the past, I’m glad to see the British government deliver the note. And I’m extremely proud of those individuals who lobbied the government to acknowledge this terrible mistake. Again, as PM Brown wrote, “So on behalf of the British government, and all those who live freely thanks to Alan’s work I am very proud to say: we’re sorry, you deserved so much better.” So very true.

It appears that Poe did very well with the challenge.

Also, fans of Poe’s writing will know about the short story The Gold Bug, and how this story of a treasure hunt relies on the solving of a cryptogram. Poe’s works are in the public domain, so it’s possible to read this story online through Google Books here, or to download the story (amongst others) from Project Gutenberg here.

I’ve written a few times about using LaTeX in WordPress, but this is certainly an easy way to include typeset equations in a blog. I’m not sure why this hadn’t occurred to me when I first started playing with Wolfram Alpha, but I suppose that’s why people like David write great tips like this!

I must admit that the contents of these carnivals I enjoy the most are ones that take an interesting piece of the math world and make it accessible to a wide reaching audience. Which, I suppose, is generally what I try to do on this blog. The hardcore math is also good, but I like the immediate mystery present in the more accessible posts. I suppose this is because the mystery drew me to math in the first place. Alas.

The basic rules of the Ultimatum Game are simple. One person is given a stack of cash, and told to divide it between themselves and a second party. That second party is then given the chance to accept or reject the offer; if it’s rejected, neither of them get any money. Clearly, any of this free money should be better than nothing, so under assumptions of strictly rational behavior, you might expect all offers to be accepted.

It turns out that tweaking some of the premises of this game leads to some interesting results in terms of human rationality, economic systems, and guilt. I highly recommend reading the article in its entirety. Also, if you’re interested in reading the abstract of actual paper itself, it’s available on the PNAS website here. It also looks like the full paper is available in PDF format if you’d like to read it. Not sure how long it will be available, but it’s there now. Toshio Yamagishi, the lead author, has a website here.

The system derived its playing strength mainly out of brute force computing power. It was a massively parallel, RS/6000 SP Thin P2SC-based system with 30-nodes, with each node containing a 120 MHz P2SC microprocessor for a total of 30, enhanced with 480 special purpose VLSI chess chips. Its chess playing program was written in C and ran under the AIX operating system. It was capable of evaluating 200 million positions per second…In June 1997, Deep Blue was the 259th most powerful supercomputer according to the TOP500 list, achieving 11.38 GFLOPS on the High-Performance LINPACK benchmark.

Brute force. That’s how the computer got the job done. Of course, it’s never that simple. But there is one thing that can be said for certain: If you lose a game of chess, it is because you were outplayed. Plain and simple. And I think it’s for this reason that chess became an apt metaphor for modernist notions of intelligence. Stereotypically speaking, if you ask a person the question of what game smart people play, I would guess that chess would be the most common answer in the western world (perhaps Go in the eastern world). The fate of this game is in the hand of the players entirely. There is no chance involved, with the one exception of which player plays first.

As a child, I had a hard time enjoying games that involved a substantial amount of probability. “What’s the point,” I thought, “of playing a game skillfully if it’s possible for me to lose at the last possible moment due to a bad roll of the dice or a badly dealt card?” But as I’ve grown older, I’ve come to enjoy games like this MORE on average than straightforward skill games like chess. Enter backgammon.

For those of you who don’t know backgammon, I suggest checking out the Wikipedia page here. Backgammon has been played for 5,000 years, and has evolved substantially over that time. For example, of the additions to the game, the doubling cube, drastically changed play and was introduced less than 100 years ago. Backgammon is not like chess. In a single game of backgammon, it’s quite possible for a novice to beat a master due to elements of chance. Said another way, it’s possible to play the best possible game of backgammon you can based on your dice rolls and still lose. And this is the aspect of the game that makes it an apt metaphor for the 21st century. While the 20th century dealt with certainty, the 21st will deal with probability.

And this is not to say that games like backgammon are somehow more subjective than games like chess. There are some amazing machine learning techniques used to study the game (e.g. TD-Gammon), and there are quite a few computer programs, such as GNU Backgammon, that use these techniques to outplay human opponents. Poker games like Texas Hold’em also involve an element of probability, and have grown wildly popular over the last many years. And those of you who know poker know that there are rules that govern “right” playing. Though the cards dictate play, there are strategies that maximize gain and minimize risk. The same is true of backgammon. And with the game popping up in popular culture a bit more, like in the television show Lost, I can only see backgammon growing in popularity.

Klein bottle (procrastination), by Pragmagraphr

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Love & Mathematics, by Lost Archetype

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Vegetable Meets Mathematics, by anroir

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n(n+1), by Jan Tik
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Torus with pairs of Villarceau circles, by Seb Przd

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Railroad Math, by Adamcha

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The Portrait of Conditional Probability, With A Third Ear Maybe, by DerrickT

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One in a billion, by Micah Sittig