God Plays Dice

A few days ago I posted about the Porter Square snowdecahedron. Here are more pictures of it and pictures of some smaller ones. The project is due to Dan Beyer. He previously made a dodecahedron out of a tree stump (apparently the trick is to make a wedge corresponding to the dihedral angle of the dodecahedron beforehand) and has proposed dodecahedra built of traffic cones as public art for construction sites.

(I found Dan Beyer's site via metafilter; I don't recall how I found the original picture on flickr linked to in the previous post.)

Not only does God throw dice, but Einstein does too, or at least a stencil of him on a wall in the Upper Haight in San Francisco does. This post suggests that it may have been by the graffiti artist Banksy. It's been painted over.

More pictures here and here.

It's been painted over, apparently. That's probably for the best, because that means I won't try to find it when I move to the Bay Area.

(Oh, yeah, I'm moving! I got a job at Berkeley.)

The Fibonacci cutting board is being sold by 1337motif at etsy. (Note: that's pronounced "leetmotif"; it took me a while to figure it out.) It's basically this tiling, where a rectangle of size F_n by F_n+1 is repeatedly decomposed into a square of size F_n by F_n and a rectangle of size F_n-1 by F_n, but made of wood instead of pixels.

There's also the double Fibonacci cutting board made in a similar pattern.

1337motif is Cameron Oehler's work. Nost of his other work is inspired by video games; you can see it here. I wonder how often the cutting boards get used as cutting boards; at 125,ドル if I had one I'd hang it on the wall and not get food on it. Personally, I'd like a Sierpinski triangle cutting board.

Apparently in France they have an interesting solution to cake-cutting problems -- a plate with markings on the rim for the proper place to cut into 3, 5, 6, 7, or 9 slices, called the plat diviseur. See also here. You can buy them here; the site is in French. Some especially ornate examples are due to Paul Urfer, who appears to be the original inventor.

I found out about these from The Number Warrior, Jason Dyer. Unfortunately I have no use for one of these, because I live alone, in a small apartment where I couldn't reasonably have enough people over to need a whole cake, and so I do not buy a whole cake at once.

I suspect I have some French readers. Have you seen these before?

From Steele this morning, a metaphor for mathematics I hadn't heard before: mathematics is like an oil painting. Basically, people doing oil paintings start by making a very rough sketch of the painting and then progressively build up the details of the figures. (I've never painted in oil, so correct me if I'm wrong.)

Mathematics is similar. In research one only starts out with a vague idea of the result and then progressively refines it; in teaching one first gives a sketch of an argument and then comes back and fills in the details. Teaching was the context here; often in classes which depend on measure-theoretic probability, which this is, we first give a semi-formal proof of a result and only later come back and fill in the σ-fields, justify the magic words like "dominated convergence", and so on.

Compare perhaps Hackers and Painters by Paul Graham, which compares the two title groups.

Within spitting distance of my apartment (okay, maybe not literally), tonight, will be the Artclash Collective's Fun-a-Day show. Basically, for the entire month of January, a bunch of people each do some creative thing each day, and then these are exhibited. (The exhibit takes place tonight, at Studio 34 Yoga, 4522 Baltimore Avenue, Philadelphia.)

Some friends of mine, this year, did Breakfast Pastry a Day (I helped -- by eating some pastry), SEPTA Haiku a Day (which is still ongoing -- the person in question commutes by SEPTA and I guess once you start making haiku it's a tough habit to break), Scrabble a Day (no link -- although I actually took part in this one by being an opponent), Internet Troll a Day (or so I've heard), and so on. (More conventional "art" like drawings, comic strips, songs, etc. also is pretty well represented.)

Unfortunately most of my creativity lies in mathematics... and theorem-a-day would just be too hard. I googled "theorem a day" and most of what comes up are variations on Erdös' quote "A theorem a day means promotion and pay; a theorem a year and you're out on your ear." (What does a theorem a week bring? Or a theorem a month? And does anything rhyme with month? The best I can do is "n-plus-oneth", which isn't a word in ordinary English -- but it is in mathematical English!) Although something like "proof-without-words-a-day" seems feasible. And a project involving pretty pictures, of course, has the advantage that the non-mathematical people in the audience (which, in a general audience, is most of them) could enjoy it too. But I tend to be the sort of mathematician who has much better pictures in my head than I can put on paper. Making a good mathematical picture is hard.

Then again, maybe it's precisely for this reason that I should be making more pictures that really do reflect what's going on in some mathematical problem. So come to Fun-a-Day in 2009... my work might be there! (We'll see how I feel next January.)

• Hello, India? I Need Help With My Math, by Steve Lohr, today's New York Times. The article's really about how consumer services, like business services before them, are being offshored; tutoring is just an example.


• Pollock or Not? Can Fractals Spot a Fake Masterpiece?, from Scientific American. The verdict seems to be mixed. Pollock's paintings often contain certain fractal patterns, and certain simple images look "the same" as a Pollock painting in a certain sense. The researchers argue that their work is still valid, though:
  

  "There's an image out there of fractal analysis where you send the image through a computer and if a red light comes on it means it isn't a Pollock and if a green light comes on it is. We have never supported or encouraged such a mindless view."

  
  I'd agree with them, so long as it's more likely for the metaphorical "green light" to turn on when it sees a Pollock than when it sees a non-Pollock; there's no single way to test whether a creative work is by a particular person, other than going back in time and watching them create it.


• On the cruelty of really teaching computing science, by the late Edsger Dijkstra. (I've had this one in the queue of "things I want to talk about" for a while, but I don't remember what I wanted to say, so here it is. There are a bunch of similar things which should dribble out in the near future.) But I can't resist commenting on this:
  

  My next linguistical suggestion is more rigorous. It is to fight the "if-this-guy-wants-to-talk-to-that-guy" syndrome: never refer to parts of programs or pieces of equipment in an anthropomorphic terminology, nor allow your students to do so. This linguistical improvement is much harder to implement than you might think, and your department might consider the introduction of fines for violations, say a quarter for undergraduates, two quarters for graduate students, and five dollars for faculty members: by the end of the first semester of the new regime, you will have collected enough money for two scholarships.

  
  I've long felt the same way about mathematical objects. There are exceptions, but for me these are mostly exceptions in which the mathematics describes some algorithm that has input which is actually coming from somewhere. Here it's not so much the program that is getting anthropomorphized as the user.
  
  And why are they always "guys"? How is it that scribbles of chalk on a blackboard, or pixels on a screen, can have gender? Note that I am not suggesting that mathematical objects should be female, or that some of them should be male and some of them should be female, with the choice being made, say, by the flipping of a coin. (Incidentally, the description of mathematical objects as "guys" seems to be much more common at my current institution than at my previous one.)
  
  By the way, Dijkstra is saying here that he thinks computer science should be taught in a formal manner -- proving the correctness of programs alongside actually writing them -- and that to de-emphasize the pragmatic aspect, students shouldn't execute their programs on a computer, since doing so enables them to not think about what the program is doing. I'm not sure if I agree with this.
  

A three-part blog post on how a theoretical physics paper gets made: inspiration, calculation, culmination. This tells the story through the example of a particular paper on cosmological inflation. (From Cocktail Party Physics.) The comments are probably worth reading, too.

Somewhat relatedly, although more about the mechanics of writing, Terence Tao on rapid prototyping of papers -- basically, sketch out the outline of the paper first, making the statements of the key intermediate results, and then fill in the gaps, rather than writing from beginning to end. I can't vouch for this working on the level of writing research papers for the simple reason that I have written none. (I hope this changes soon.) But it seems to work reasonably well for writing, say, solutions to rather involved homework problems that can take a few pages, and have three or four major intermediate results.

Also, Can Scientists be Great Communicators?, from The Accidental Scientist. I would say that regardless of whether or not we are (and I'm including mathematicians in this "we"), we have to be. This is true both in terms of communication among scientists (which is tremendously useful for driving along the whole scientific enterprise, because otherwise we'd all be reinventing the wheel) and in communication with the non-scientific public, which I think is quite important. For one thing, ultimately a lot of the money that funds science comes from taxes; if these people are in the end paying our salaries, don't we owe them some explanation what we're doing? But also, communicating complicated ideas in non-technical terms forces us to actually understand them. Feynman, when he was preparing his famous freshman physics lectures at Caltech, said that if he couldn't reduce something to the level where he could explain it to freshmen, it meant that he didn't really understand it. When you can't fall back on technical terms and convoluted equations you have to understand what you're doing. So communicating with the hypothetical "educated layman" perhaps pays dividends within science as well. I just wish that people didn't automatically glaze over when they heard I'm a mathematician, though...

Communicating with this person is becoming more and more feasible thanks to the web 2.0-ification of science. Write something. Google will find it. You'd be surprised to see how many hits I get from what looks like people trying to buy used furniture, for example. And although I offer no advice there on how much used furniture should cost, I feel like I'm doing something by just exposing them to the idea that perhaps mathematics can be used to figure out such things. It's a subtle propaganda campaign.

Another subtle propaganda campaign might be the sculptures at Bathsheba Sculpture (by Bathsheba Grossman), which are for the most part models of various mathematical objects, done via 3D printing in metal; she has both mathematical and artistic training. What other sorts of training might be useful for mathematicians?