Am I fascinated by scale because I'm a Libra?

One of the greatest gifts given us by mathematics is a language for scale. It's how we know that 1,000 is different from 1, which is in turn different from 0.1.

One of my earlier memories is of attending this captivating exhibit on the limits of scale as understood thirty years ago. Those extremities have not been pushed back much further since then. Amusingly, it was only last year that I found out that it was produced by one of the most significant design houses of post-WWII America.

Someone (sadly uncredited, working for Nikon) has created an interactive work with the same lessons. Everyone should learn what's out there, what's up there, what's in there, and where we live in it all.

On the rise

As a counterpoint to his miserable formula from a year ago, R. Stevens gives a metric for quality of life.

I'm very happy to have had both input variables move in the right direction recently. More sleep, less time in a car!

Gang sines

R. Stevens models his forthcoming design, featuring both a transcendental number and an earthly delight:



With right thumb and left ring finger extended, he'd be repping the circle with proper digits.

Hyperbolic frolic

I had the tremendous pleasure today to attend an exhibit of works by M. C. Escher in my hometown. It was an incredible treat to see so many familiar images, a few of which have adorned my walls, in one place. There were a number of surprises, too: lovingly crafted scenes of Italian buildings and staircases, and a series of early woodcuts with biblical subjects. One of these even had the reversed initials so common to an artist's early ink prints.

I was most struck by the technical prowess that went into his prints. Take "Circle Limit IV", which not only illustrates the peculiar geometry of the hyperbolic plane, but does so with a thought-provoking two-color woodcut. Few in history had the exacting vision required to create interlocking patterns with such precision, while at the same time communicating so much personality. The exhibit includes two "segment proofs", prints of one third of the work. Taken out of the context of its two triplet siblings, the details that Escher chose to omit as he moves toward infinity are brought into sharper relief, making his genius all the more apparent.

Also consider the hauntingly evocative "Rippled Surface", the studies for which include perspective drawings of concentric red and black circles to indicate the local maxima and minima of the wave as it propagates across the water.

Rhythm of Illusion remains at the San Jose Museum of Art through Sunday, April 22, 2007. If you are anywhere near the south bay before then, I urge you to attend.

I thought this one goes up to eleven

One of the more intelligent sorts of mathematical questions I've been asked are those on the nature of higher dimensions. Somewhere in our pop history it was decided that since we lived in the third dimension, there should be others, like so many arrondissement. These are usually just three-dimensional spaces where things are wacky, not the fundamentally larger spaces they ought to be. In fact, some authors believed they could exchange dimensions for vowels.

It's at once refreshing and disappointing to see an exposition such as this. The animation and sound are lovely, and a rather decent volley is made at the concepts of "splits" and "folds", even if the subtle beauty in the relationship and differences between these is largely ignored. However, the narrator suggests that each "dimension" has some inherent parameters defining it, such as "the seventh dimension" being the space of all possible outcomes from the origin of the universe, and similarly pinning the notion of "split" and "fold" only to certain dimensions.

Do you want to see ten-dimensional space? Here it is:

Anyway, isn't supersymmetry supposed to be eleven-dimensional? Or does 11-D SUSY refer to a women named Susan with an impossibly small ribcage?

Non-orientable garments

Every mathematician worth their salt knows of The Acme Klein Bottle Company, although I'm one of the few I know who has made a purchase there; specifically, a question mark as a wedding gift to the former proprietors of a Seattle restaurant. (Some are more familiar with the proprietor as the narrator of one of the world's first cyber-espionage stories.) The business has diversified since my order five years ago, having extended to include knit wool hats with zero volume. Now absent from the site (although I swear they were there the last time I looked) are matching Möbius band scarves; fortunately, this need is filled by other resources on the web.

A new foray into the realm of one-sided wearables (brought to my attention by the pillar of hipster science) is the Möbius shoe, pictured below. Of course, to make the outfit work, one would need a matching Fortunatus' Purse.

Synchronicity

The other day, I took the time to read S. Yegge's latest essay on software, complex systems, and consciousness; the thesis of the work, an idea that Steve has been refining for some time now, is that "the most important principle in all of software design is this: Systems should never reboot." He gives numerous examples of software products that fail to incorporate this principle, and a few that provide a weak, half-hearted attempt at it. He then goes on to explain that given his (quite reasonable) definition of software, the best systems have this idea built into their core:

So my first argument against rebooting is that in nature it doesn't happen. Or, more accurately, when it does happen it's pretty catastrophic. If you don't like the way a person works, you don't kill them, fix their DNA, and then regrow them. If you don't like the way a government works, you don't shut it down, figure out what's wrong, and start it back up again. Why, then, do we almost always develop software that way?

To celebrate turning 30, R. Stevens created a new t-shirt design (which is now available). Imagine my surprise to find this in his official announcement:

We all have pretty much the same personalities we were born with, just earlier versions. Our software never really gets rewritten, it just evolves.

Rich, Steve, allow me to introduce you to each other.

Part of an RC graph

Also known as a pipe dream. While clearly not what the original designers had in mind for these tiles, this arrangement creates a beautiful rhythm, and could even be used in Schubert geometry.

SECANTS RATE highly in my book

Longtime readers already know that I'm a regular visitor to dieselsweeties.com to get the daily comic by R. Stevens (or rstevens, as he prefers) featuring the inimitable Clango Cyclotron. He really should visit LBL at some point and see some of the ARCANE TESTS they carry out with the 88". You know, Clango could get in touch with his roots; after all, that first 'L' stands for Lawrence, the inventor of the cyclotron.

I'm enough of a fan of DS that I got my lovely wife a t-shirt featuring a punchline from the comic for Christmas last year. Being a mammalogist, this is far and away the most appropriate of the DS shirts for her to wear, although our CAT RESENTS A message so positive about another species.


I get the impression that R. Stevens is a cat person (and Mac user) like me; given the opportunity, I would CARESS TEN, AT least.

A wish of mine has been granted, and some recent Diesel Sweeties strips have featured mathematically-themed humor. It's good to see that R. Stevens RECASTS A NET from time to time to trawl for these sorts of jokes. The second, in addition to referencing one of the great integer sequences, is concerned with puns, which mathematicians inexplicably enjoy more than most other people. Some mathematicians also enjoy anagrams, although that's more easily explained by the fact that they are a special case of permutations.

To celebrate cope with the commerce season, Stevens is running an anagrammatically named contest. He's a rather good sport about it, even suggesting that writers might describe his pants as a one-ACRE ASS TENT. If I were to open myself up to such public conversation, I'd feel like an ANT AT RECESS, leaving myself completely at the whim of schoolkids. I like his output too much to be so cruel; I especially enjoy Maura's antics (A TART'S SCENE if ever there was one) and the strips in which A SCAT ENTERS. I usually detest "bio-humor", but somehow Stevens treats it so absurdly that it has a certain appeal.

Here's wishing R. Stevens, Clango, and the whole Diesel Sweeties crew a Merry Present Season and a Happy New Year!

Get your hands on some games

One of the most common expository metaphors of discrete mathematics is "playing a game". Sometimes this is taken quite literally, as with the algebro-geometric algorithm jeu de taquin, the enumerative object named for an 8-bit Nintendo game, and the patience sorting algorithm, which American audiences might prefer to call the Klondike sorting algorithm. It shouldn't be surprising that some discrete games have been a rich source of interesting mathematical questions, and that a certain game with a long history still poses academic challenges.

And speaking of games, an excellent source of casual games is J. Bibby's site Jay is Games. I discussed one of their recommended games earlier, although I came across it independently of JiG.

In Planarity, I often have planarized a subset of the vertices and want to move them all at once. If only the interface would let me manipulate more than one vertex at a time! J. Han has put together a device implementing a multi-touch interface in his lab at the Courant Institute; in addition to running silly graph-theoretic games, it augurs what may very well be the next paradigm in human-computer interaction. In case the video on that page isn't enough to make you covet the tenth-generation iMac, take a look at this live demo. He mentions while illustrating the "puppet" application that cutting-edge mathematics and computational science make those dancing drawings possible. We are finally reaching the stage where the massive computational power sitting on the desktop can be harnessed to make computers behave in a way that is convenient to us, rather than the other way around. This is true innovation.

Discrete topology

Of all the things that the title could mean, such as defining every singleton subset to be open, or discretizing the continuous as A. V. Evako does, this is by far the best I've ever seen.

Limited options precipitate creativity

All mathematicians (and many others) immediately recognize the sequence 1, 1, 2, 3, 5, 8 as the first few Fibonacci numbers. In this article, G. K. Pincus proposes a new poetic form, the fib, whose line lengths (measured in syllables) are given by these numbers.

At first, I suspected that most such verses would simply be twenty syllables of English prose broken up to fit the "design parameters". After all, history is full of awkward attempts to use mathematical toys such as the Fibonacci senquence as a basis for art. However, after reading some contributions from the comments to the original post, as well as those featured in a follow-up article, I've found that this form has a real character to it. The first four lines are short and punchy, almost primal; the last two lines seem locquacious by comparison, allowing an outpour of articulate expression. It seems that Pincus struck that delicate balance of constraint; both sufficient to focus creative drive while relaxed enough to prevent the output from being artificial and bland.

Good?
Bad?
Great? Poor?
I'm no judge
Of this kind of thing,
But I know I like what I see.

Human Experience Engineering

Last December C. Wetherell, a Google software engineer, told me that his next twenty-percent project would be an algorithm for love. It seems to have entered beta.

Complimentarily, Red Robot of Diesel Sweeties has been honing an algorithm for hate. While I would not take on such a research program myself, I commend him for this endeavor, as it progresses our overall understanding of emotional algorithms. Perhaps Google should recruit Red Robot to be their new Director of Human Experience Engineering.

Perhaps a more practical approach would be for Google to acquire an anti-social networking site, such as Snubster, or perhaps adapt Orkut to this end.

A formula for misery

R. Stevens does it again; this time, he illustrates why Math is Life.

Non, c'est pas une Weezer logo

As part of a run of strips on superheroes, R. Stevens produced a comic in which a character points out that "... Justice League is not a reputable science journal." Buzzwords from mathematical physics puncuate the retort that follows.

I know what the golden "W" in the comic's header stands for, but I can't help but wish it was meant to recognize E. Witten as the strongest driving force in string theory.

Many scientifically concerned individuals bemoan the lack of public interest in science and mathematics. Perhaps what we need is better personal brand management, beginning with a broad campaign of brand identification.

Here, I'll start.

Fossil fuel lovers

Diesel Sweeties by R. Stevens has featured math humor on two occasions. I hope Stevens includes such gags again.