if (next == NULL) read(other_blogs);

I‘m officially admitting to myself and the world that this is the final post to Discreet Math. I do, however, have this twitter feed, and this ripular blog that I run with tumblr. Both have rss feeds, as well as built-in "following" functionality if you are a twitterer or a tumblrr.

If you start reading my tumblog, please let me know. I'm curious if I'm the only one who sees what I put up there.

The effect of emacs on the Ctrl key

Kalil Azad's Mathematical Mindset

Thanks to the increasingly hive-like mind of 43 folders, I landed on this essay about how to think about math on Kalil Azad's excellent BetterExplained. (As we are now in the midst of the era of humees and wudzups, domain names composed of good ol' real words are such a breath of fresh air.)

I honestly wonder how I never came across this guy before. I really like his style, keeping each point short enough to swallow and emboldening the high phrases.

In the above-linked essay he conveys the tricky business of mathematical meaning and how it simultaneously lives in and transcends real-world examples. One skill that makes good mathematicians good at mathematics is the ability to jump between the specific and the general, the concrete and abstract, with tremendous agility. It allows one to see the pathological edge cases without drowning in multiplicity.

In case of power outage

In the EECS building on the Berkeley campus...

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.

Continuous and discrete

This photo is more than two years old. You can tell because in spite of the huge grin on my face, the crow's feet near my eyes are still relatively small.



Thanks to C. Dewey for finally getting around to making these public.



And in case you were wondering: Yes. Yes we do.

Let T be a shirt...

I used to think I needed this shirt.



Now I realize that I need this one.



LOL rights reserved the respective creators, images used with their respective (implicit) permissions.

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!

Delinquency

For those distraught by the dearth of mathematically themed writings in this space, may I suggest my shared items in Google Reader, easily accessed either by the first of the above links, or in the sidebar of this page, entitled "And what have I been reading?"

My distractions from these posts have not been all work. I've written before about the great strides being made in human-computer interaction, especially regarding tools for musical creation. Last Saturday night I had the extreme pleasure of seeing Björk (or B. Guðmundsdóttir, for the sake of nomenclatural purity) perform at the Shoreline amphitheater, with M. Bell at the helm of a reactable. This instrument, first pointed out to me by J. Hopper (who is inexplicably nigh invisible to Google), is similar to the audiopad from MIT's media lab, but with a crucial difference: it is out of the prototype stage, and in front of a mainstream audience. Hopefully commercialization is not too far off.

Since when is 'B' a number?

It is finished

My adviser, A. Schilling, has just finished a paper extending my first result, proving my conjecture on the matter and thereby tying up the last loose end left by my thesis.

E8, AIM, and PR

I was very happy to hear the voice of M. Vazirani, who served on my dissertation committee (see the evidence below) on last week's episode of KQED's California Report. It's a great little piece, accessible to all. You can download it, or stream it from the page linked above.

In some sense it seems perfectly natural for a radio station whose call letters are a common mathematical initialism (or is it a physical one?) to report on mathematical news. As I mentioned before, this story in particular is catching a lot of attention. At a conference I attended last week, the topic of E₈ and its broad media exposure arose; I attributed this phenomenon to the fact that this is one of the first major milestones to be reached by an AIM-sponsored project, and that AIM puts a much greater (and much needed) emphasis on public relations than do other mathematical research institutions.

In the meantime, I found another connection between my own work and the E₈ project. The big character table calculation was carried out on SAGE, a multi-processor AMD Opteron machine built by Western Scientific, who also built my multi-processor AMD Opteron machine, frost. Hopefully some adaptation of the adage on great minds thinking alike can be applied to these systems.

I've received a variety of junk messages ...

which is not ideal.

I recently found a message labeled as spam with "On nullstellensatz" as its subject. This isn't the only time a math term has turned up in this context–earlier today I was treated to "so mcclain go matroid"–but it is the most sophisticated language I've seen in the Pynchon-esque maelstrom of unsolicited commercial email.

If they really want to reach the algebraic geometry crowd, they should go beyond the relatively pedestrian terms nullstellensatz and matroid. Imagine eye-catching phrases such as "Resolve your too small singularity NOW!" or "Satisfy infinite polynomials with finite basis".

I'm a bad geek

Unlike last year, I did absolutely nothing to celebrate π day this year. I can at least send out a post facto link to the (boing)²-ing of Stanford's L. E. O'Neal.

I still prefer my proposed finger-play. It's also the binary representation of 503 (i.e., 111110111), making it especially appropriate for PDX'ers.

Build character!

A few research institutions and news outlets, as well as some blogs have reported on what is generally being termed the "mapping" of E₈. This is about as good a layman's description of this result as can be given, although for those who know a smattering of group theory, it would be better to say that the fruit of these labors is a table relating the conjugacy classes of E₈ to each other. Seeing as there are 453,060 such classes, this requires "writing down" 205,263,363,600 numbers; these are enough to cover Manhattan, and they require 60 times more storage than the human genome, as the researchers and the reporters to whom they've spoken are fond of pointing out.

I can't help but notice the striking resemblance between some of the pictures from the atlas project and the output of one of my projects. Granted, you can't use it to generate E₈ crystals, but then again, it's just running on a simple webserver.

And by the way, if you or anyone you know would like to take over the development of this software, please contact me. This was the start of something really good, but other concerns have taken center stage since then.

Would it help if I drew a flow chart?

Such great things come out of MIT's media lab: one of their visitors has built a water-based computer.

This could come in handy in the event of a massive electromagnetic pulse. However, I suspect most people would have other matters on their mind at that point.

In all seriousness, this is a wonderful project. Like other mechanical algorithm devices, it allows the fundamental procedures of computation to be animated in space, relieving the burden of mental modeling from the executor.

But remember, if you're seated in the first six rows, you may get wet during this subroutine.

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.

Over my head

I looked up, stretching my neck, and saw this lovely ornament hanging above my cubicle.