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.

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

JAME is a Java real-time, multi-threaded fractal graphics platform which supports images and animations. The core of JAME is the graphics engine which supports layers, filters, effects and alpha composition. JAME creates Mandelbrot and Julia fractals and supports zoom, rotation and colours shifting.

The software is entirely free (under GPL3) and is available for Windows, Mac OS X, and Linux as long as you have met some minimum memory requirements and have an up-to-date version of the Java Runtime Environment installed. The website for the project contains some wonderful tutorials to help get you started, and your creations are exportable to various photo and movie extensions. I created the following clip entirely with JAME:

Now, the rendering of this clip took a while on my Macbook Pro, so if you start playing around keep in mind that the rendering of various movie clips could take a significant amount of time, especially if you increase the frame rate, etc. But the clip above took about 5 minutes to create minus the rendering time. That’s pretty awesome for out of the box capability, let alone all of the customizations that are possible once you learn more about the environment.

There’s a gallery of photos on the site to give you an idea of what’s possible to create more a more advanced user, and some awesome photos have been bundled together into a book that can be purchased here. I’ve seen various movies online that show fractal exploration, but it’s a whole other thing entirely to be in control of the exploration. If you have any interest at all in fractals or mathematical art, I highly suggest checking out the software.

I must admit that art museums are often tiresome to me. Large galleries are a sensory overload. Walking through one is an inundation of passive information in a generally sterile environment. In other words, it’s hard for me to actually experience the art. With exceptions, I am merely an observer rather than a participant. Part of what I enjoyed so much about the Chihuly pieces was their experiential nature. I felt that I was part of the art, and that my being present actually mattered.

If I had to summarize my impression of the installation, I would use the phrase “entwinement of the inorganic with the organic”. While walking through the nearly uncountable species of plants in the gardens there are pieces of ornamental glass decorating the landscape. Sometimes it actually appears as if a plant is growing glass branches. In one of my favorite pieces there are tubes of iridescent blue glass standing amongst an army of cool green bamboo. It almost looks as if the two could easily coexist together in nature. Around every corner was a merger of glass and plant. I almost felt like a child on an Easter egg hunt, just waiting for the next treasure to appear unexpectedly. If you’d like to see more examples of what I mean you can see Emily and my pictures here.

While I wouldn’t count Chihuly as my favorite artist (this “honor” is held by James Turrell), I have to thank him for his creative methods. Both Turrell and Chihuly design art which is experiential rather than merely observable. Both use light and color with beautiful effect. Both blur the lines between organic and inorganic. These traits, to me, embody art at its fullest.

I have such a hard time when someone (usually a speaker who knows nothing or relatively nothing about mathematics) uses an analogy that paints the field as the dull black and white objectified reality. First, this is not math. This is some strange twisted view of math that either you learned in second grade or that you have been fed by our culture. This view is pervasive and ugly. Math has so much more to do with elegance and beauty and the greater search of making sense of possibility.

I’d like to see two changes in the popular perception of mathematics. First, I’d like to see a greater effort by the mathematics community to make their material accessible to the popular masses. I believe this can be done by pursuing some of the artistic or philosophical implications and questions brought on by a particular technical result or problem. There are a few people who have done this, and off the top of my head I’d name Ian Stewart as an example. For instance, if one really looks at Euler’s Relation, and digests it like one would a Monet, I believe there’s just as much beauty to behold.

Second, I’d like to see postmodern theologians taking a more mature view of mathematics. Rather than painting it as the personification of the Modern era (and thus mostly an unhelpful and inorganic subject), I’d like each and every one of them to gain a familiarity of the subject and what it means for the twenty-first century. With this aim, I suggest that these readers refer to Godel’s Incompleteness Theorem, with some of the philosophical questions behind it.

Check out the site. And if you have a moment try to engage one of the pieces. Thank you Justin Mullins for taking such a simple idea and running with it.