Necktie Mathematics

About a week ago, I realized that I didn't know how to tie a tie. I mean, I did something to the tie when I put it on, but I'm not sure what. It ended up looking alright though. Anyhow, I decided enough was enough, so I went online to learn for myself the full range of tie knots, expecting maybe three or four. I soon discovered that two physicists, Yong Mao and Thomas Fink, had set out in 2001 to unravel a mathematical model for understanding tie knots. Based on the supposition that there are three different moves one can make with a tie (cross to the left, right or go down through the top) and the two possible directions a tie can face, they figured out that there are exactly 85 different ways to tie a tie, about a dozen of which are really aesthetically pleasing.

I take a weird delight in seeing an element of fashion reduced down to mathematical principles to be dissected. By denoting each move by a pair of letters (Li, for instance, means go to the Left, facing In) Mao and Fink are able to set out the instructions for a tie knot simply and concisely. For instance, the Windsor knot is Li Co Ri Lo Ci Ro Li Co T, which translates to:

For a full explanation, plus how to tie all 85 knots, go to Fink's homepage, or buy his book The 85 Ways to Tie a Tie (not cheap; I recommend looking for it used). If you are further intrigued, read his summary Designing Tie Knots by Random Walks, or the full paper that inspired the book, Tie Knots, Random Walks, and Topology.

(I do not endorse the ad at top in any way, other than that I think it's funny.)

Makerbot

For less than a thousand dollars, you can now buy a 3D printer. That's about 124,000 dollars less than they used to cost. Makerbot started putting its DIY printers up for sale last year, and have gotten so many orders that they can no longer keep up with production. So they hired out a bunch of the Makerbots they'd already sold, and had them make more Makerbots. Creepy, and awesome. They send you the kit, you put it together, feed it some plastic, load a 3D file, and the machine will make it while you watch. The makerbot phenomenon has spawned a site, Thingiverse, dedicated to open source 3D files, and a large community who are only beginning to unravel what having a machine like this will mean for the future of manufacturing. Want a new toy for your kids? Print it. Need a new lathe for your workshop? Print it. Want a sculpture of Walt Disney's head for your living room? Print it.

Cory Doctorow is, of course, all over this, and put out a new book last year titled Makers, that takes as its very premise a near future where devices like this are omnipresent. As with all Doctorow books, you can buy it on Amazon, or download the ebook for free from the link above.

Read more on this and the DIY revolution at Wired Magazine.

Christopher Alexander

Christopher Alexander is someone I discovered this fall, and whose books I cannot stop reading. The one I've read the most of, "A Pattern Language," is remarkable, revolutionary and entirely beautiful. It deals with, as most of Alexander's books do, the forming of living human environments, from the regional level, to the city, neighborhood, building, house, and room levels. It forced me to rethink how buildings ought to be made, and expressed in clear, methodical language why it is that certain houses and urban environments feel so "right," human, or whole.

His philosophy is deeply refreshing in its careful and disciplined insistence that the flourishing of human life and community ought to be at the very heart of architecture and urban planning. This might seem like a truism, but it is very much contested among modern architects and planners, as can easily be seen from modern architecture. In fact, I was startled at how closely related the ideals set out in A Pattern Language corresponded to the distributive ideal in Catholic circles. Government at a local level, an emphasis on small communities with strong cultures, the necessity of the integration of all ages of life together, the preservation of sacred places, the notion that families ought to grow food and not become alienated from their labor...it's all there, not as a utopian dream, but an ideal that can be gradually worked towards. The book is a wonder; almost every chapter (there are some 250 of them) makes one exclaim "Yes! Exactly!" as well as providing insights I'd never heard of.

Perhaps the best way to get a handle on Alexander is to read this debate between himself and Peter Eisenman, a modernist-deconstrictivist, who openly admits that Alexander's theory of architecture infuriates him. Keep in mind, that for the most part it is people like Eisenman who are in charge of providing the theory that underlies most "relevant" architecture done in the western world today.

Alexander: I don't fully follow what you're saying. It never occurred to me that someone could so explicitly reject the core experience of something like Chartres [Cathedral]. It's very interesting to have this conversation. If this weren't a public situation, I'd be tempted to get into this on a psychiatric level. I'm actually quite serious about this. What I'm saying is that I understand how one could be very panicked by these kinds of feelings. Actually, it's been my impression that a large part of the history of modern architecture has been a kind of panicked withdrawal from these kinds of feelings, which have governed the formation of buildings over the last 2000 years or so.

Why that panicked withdrawal occurred, I'm still trying to find out. It's not clear to me. But I've never heard somebody say, until a few moments ago, someone say explicitly: "Yes, I find that stuff freaky. I don't like to deal with feelings. I like to deal with ideas." Then, of course, what follows is very clear. You would like the Palladio building; you would not be particularly happy with Chartres, and so forth. And Mies ... 

Eisenman: The panicked withdrawal of the alienated self was dealt with in Modernism -- which was concerned with the alienation of the self from the collective.

Eisenman repeats several times that architecture's purpose is to express the state of modern man: his alienation, fragmentation, etc. He finds it inappropriate to make architecture that serves man's basic nature, needs, and feelings, because, I suppose, that's just not where the world spirit is right now. It's like listening to Lucifer calmly describing the building code in Hell.

Read the full debate here

Read samples from Alexander's books below

A Pattern Language

The Nature of Order: The Phenomenon of Life

The Nature of Order: The Process of Creating Life 

The Nature of Order: The Vision of a Living World

The Nature of Order: The Luminous Ground