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.

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.

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.

Shaken to the (multi) core

Catherine Crawford, chief architect for next-generation systems software at IBM Systems Group's Quasar Design Center, has made a bold statement about the future of software; as is to be expected, some sources make it sound a little more sensationally apocalyptic.

This isn't the first time I've brought up the many-core future of the desktop. You may be wondering who will have the expertise to write the software that will take advantage of this massively parallel paradigm. Well, that will be just one skill that I'll be developing while a postdoctoral fellow at a very fine institution.

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.

A perfect cube

For those born in 1979 (and that includes me and a great many of my friends) last year was a big one. We're 27, or 3×3×3, or 3³, and it's probably the last time we can count our years in the form nⁿ, although let's hope not the last perfect cube.

Speaking of which, it's so easy to forget how low an odometer can read:

It was a major year for me in a number of other ways as well. About a month after adding three letters to my name, I bought my first new car. It has many more cubes to go–in fact, its first scheduled maintenance isn't until after 46³ miles.

But back to the number at hand. Our time spent being 27 is split between the year just past and the year just begun, and as has been the case for the past seven years, our age bears some resemblance to the number at the top of the calendar; just drop the zeros, and there it is. But this year there's another connection, albeit one that is purely numerological and not at all mathematical.

When I took a course in algebra from K. Ribet, he mentioned an algebraist who every year published a list of all the groups with order equal to the year. One of my classmates pointed out that in certain years, this would be a rather short list; for instance, in 1979 only one group qualified. This year isn't as dull as all that, but it is manageable, since 2007=3×3×223. For instance, I know from one of Prof. Ribet's homework assignments (specifically, Problem 28) that all such groups are solvable and have at least one normal Sylow subgroup.

But what I like, even though I know it's nothing but a quirk of our base-10 notation, is the typographical similarity between the prime factorizations of 27 and 2007, 3×3×3 and 3×3×223. That the products differ by two zeros and the factorizations differ by two appearances of the numeral 2 makes the numerological aesthetics all the more appealing. I know it's not math, but it sure is pretty.

In the shadow of Sun

You know you live in Silicon Valley when your employer is on the same exit as campuses for Yahoo! and Sun.

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!

Ph.inally D.one

There's another F-word that I could have used to title this post, but I know that some of my readership prefer more Ph.amily-Ph.riendly language.

It's hard to get a Ph.D., and not just in the sense that a lot of work goes into the coursework, finding a topic, making an original contribution to the field, etc. After it seems that everything is done; after all 130 pages have been edited, re-edited, and verified by three committee members; after it's been printed on at least 20# paper with at least 25% cotton content; after the cover sheet has been signed by all three members (one of whom is in Australia, another of whom is now in Paris); after two additional copies of the abstract (without page numbers) have been printed; the work isn't done. There are two anonymous questionnaires, one from the NSF and one from UC Davis; there is a release form authorizing the powers that be to copy the document that I spent the last four years preparing onto microfilm and bind it in the library; there is an appointment (between the hours of 1:00 and 4:00 on Tuesday) to be made with one of the staff in the office of graduate studies, wherein the above forms are put in order to be passed on the appropriate offices, and every page of my dissertation is examined to ensure that the pages are consecutive, as are the chapters, and the sections, and the subsections, and that my font is suficiently large and uniform throughout, and that the margins are respected (god forbid you disrespect the margins!). Frankly, if this kind of administrative scrutiny was demanded of bachelors recipients, the numbers for that degree would be much lower. But if you can make it through all of that, then you will have satisfied all requirements of the degree of Doctor of Philosophy, and I'm proud to report that I have done precisely that.


I was somewhat surprised by my elation when D. Swindall handed me that certificate. For many months now, when asked how far along I was, I've said something like "It's mostly paperwork at this point," or "I just have some administrative details to take care of," or "I'm down to minor editing." After saying such a white lie so many times I started to believe that the work I had left really was negligible, and that, for all intents and purposes, I was done. I had even walked; how much could that feeling of completion be enhanced by mere paperwork?

A whole lot, as it turns out. After spending those fifteen minutes yesterday witnessing the inspection of my dissertation's pages, I could say, for the first time without qualification, that I am Dr. Philip Max Sternberg. I'm now as educated as my wife, (although the jury's still out as to who's the smarter one). I'm also the second Dr. Sternberg in my family, a tradition that my father would be happy to see me carry on. Of course, in his view, the important aspect of this endeavor is scholarship, not the title; I'm glad to have had him instill me with that sense of values. For this, and many other reasons, I'm extremely grateful to have the opportunity to dedicate my dissertation to his memory.


Yesterday marked the end of this stage of my life in another way, too; my Jetta, my first car, my graduation present, the car that carried me through all of grad school, was sold to a young couple, both of whom just started their graduate studies. It served me well, and was with me for many fond memories. But it was time to let it go. I think it was best to have it pass out of my hands at the same time as my dissertation; the sense of completion and finality is made all the more real because of it.

A big day, in so many ways.

In my office for the last time

(photo credit: Isaiah Lankham)

A big day for crystals

Two papers just went on the arXiv dealing with crystals for generalized Kac-Moody algebras. None other than M. Kashiwara is involved in this project, so it must be big.

Oh, and there's this one, too. I think I know the author from somewhere.

These robes were made for walking

Note the bell-shaped sleeves and velvet; that's what sets us Doctors apart from the mere Masters, or (I'm loath even to say it) the Bachelors.


In all seriousness, it's great to have had the degree conferred upon me, even if my transcript still lacks the Regents' imprimatur.

Thanks to Andy for being there with his camera!

Cubicles have no doors

While I, unlike the heroes of this comic strip, am quite productive at my workplace, I am highly attuned to passersby. My back is to the entry-break in the carpeted wall, so my reactions are as follows:

1. When I do not have headphones on, I turn to look every time someone passes by;
2. When I have headphones on, I am startled by a tap on my shoulder by whoever needs my attention.

The first is less disruptive, but more frequent, so there is clearly an optimization problem buried here. In either case, it is clear why the principles of feng shui dictate that one should always have a clear view of the entrance to their space.

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.

Watershed

The project I mentioned in some previous posts is now on the arXiv.

On the local structure of doubly laced crystals
P. Sternberg

It's good to have publicly visible work.

For future reference

It's always a joy (if a slightly vain one) to see one's work cited, as in this paper which makes an important step in the program to understand the representation theory of quantum affine algebras:

Paths and tableaux descriptions of Jacobi-Trudi determinant associated with quantum affine algebra of type D_n
W. Nakai, T. Nakanishi

I've received a few citations before, but the sense of recognition that comes from seeing my name on the page is still strong. According to researchers who are considerably my senior, this feeling is very slow to fade.

It reminds me of a point of advice made by Gian-Carlo Rota at a 1996 conference in his honor:

8 Give lavish acknowledgments

I have always felt miffed after reading a paper in which I felt I was not being given proper credit, and it is safe to conjecture that the same happens to everyone else. One day, I tried an experiment. After writing a rather long paper, I began to draft a thorough bibliography. On the spur of the moment, I decided to cite a few papers which had nothing whatsoever to do with the content of my paper, to see what might happen.

Somewhat to my surprise, I received letters from two of the authors whose papers I believed were irrelevant to my article. Both letters were written in an emotionally charged tone. Each of the authors warmly congratulated me for being the first to acknowledge their contribution to the field.

One may conclude that the marginal cost of liberal citation is overwhelmed by the potential for improved collegiality.

Revisionism

The first draft of the first paragraph of the paper I've been writing needed a little more depth, so I added a few clauses and then cleaned up the grammar. Once it was printed out and in black and white, though, I saw that the new version was horribly written; repeated words, confusing syntax, and who knows what other barriers to readability. Less can be more, and still not be enough.

Asymptotically approaching truth

Over the past month, I've been writing a paper based on some results that I completed last October. At least, I thought I had completed them. As I type, there are more and more subtle details that I realize I need to consider. What I thought would have been a ten-page note, including an introduction and technical padding, has grown to be twice that length, and I haven't even started adding examples. I really am close to putting it on the arXiv, I swear...

It's a pun, not a spelling error

So, the natural (albeit somewhat narcissistic) thing to do once you start a blog is to do a blog search for the name, right? And what do I find, but a whole lot of individuals who don't know the difference between "discrete" and "discreet".

This leads to two unpleasant situations:

• A reader who doesn't know the difference sees this blog, reinforcing their error (and not seeing the humor in the name);
  
• A reader who does know the difference sees this blog and assumes that I don't know the difference.

Seriously, learn the language and don't rely on spell-check to clean up your act.