08
Jan 10

Poincaré Conjecture: Controversy and Eccentricity

Evidently there’s a newish biography out about Grigori Perelman, the man primarily responsible for solving the Poincaré Conjecture. Masha Gessen, a Russian journalist and author, has released “Perfect Rigor: A Genius + the Mathematical Breakthrough of the Century”, a work about the life of the curious mathematician who has vanished from the professional math community. She explains her work in an interview with failuremag.com, in which she describes the rationale behind the work, and gives some insights into both the Poincaré Conjecture and the life of Perelman.

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.


08
Jan 10

Crossword Puzzle Copies?

Matt Gaffney, a 15 year veteran of professional crossword puzzle writing, wrote an article in late November for Slate about the likeliness of two crossword puzzle creators replicating the same, or approximately the same, puzzle. Crosswords exhibit 180-degree rotational symmetry, meaning that “if you turn the grid upside down, the pattern of black squares will look the same as it does right-side up.” Couple that with a specifically themed puzzle (e.g. Halloween and Edgar Allen Poe), a certain number of long word entries, and general crossword rules (e.g. no two letter words are allowed), the probability may be higher than you think.

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!

(Photo by jessie.whittle)


07
Jan 10

Self-Interacting Machines

As I look through articles that I’ve bookmarked over the last many months, I realized that I had saved two that concerned machines that were built to interact with themselves in novel ways. I find this self-interaction quite entertaining for a reason I can’t quite pinpoint. Perhaps it’s because I generally think of a machine as a black box that takes an input and produces an output. I tend to segregate the input and the output entirely from the black box. But these machines are built only with the purpose of performing an action on themselves. They are input, output, and black box. And I find that extremely entertaining.

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.


07
Jan 10

Alice, Wonderland, and Math

Having just completed both of Lewis Carol’s books concerning Alice and her adventures in Wonderland, the recent Boing Boing post about Melanie Bayley and her research into the idea that scenes were added into the narrative after the initial draft in order to mock new math of the day, namely symbolic algebra. As one example, Bayley likens the Mad Hatter tea party scene to the concept of the quaternion introduced by William Rowan Hamilton. Without giving away the punchline, Bayley paints an interesting picture of why the three guests at the tea party are stuck at their table, constantly swapping seats. Read the full article at New Scientist here, which gives many more examples of how Carol lampooned the so-called “new math”. Who likes imaginary numbers, anyway?


07
Jan 10

Babbage’s Difference Engine

My mother-in-law made me privy to a story that aired on NPR about a group of people who built a copy of Charles Babbage’s Difference Engine using only materials available from the Victorian age, which is a feat which alluded the mathematician during his lifetime. This machine is the second of two that has been built, and is on display at the Computer History Museum in Mountain View, Calif. through the end of 2010. Concerning the physical dimensions of the machine:

“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.