Discreet Math

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

2008-05-25T10:22:00.000-07:00

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

The effect of emacs on the Ctrl key

2008-01-15T13:20:00.000-08:00

Kalil Azad's Mathematical Mindset

2007-12-21T15:35:00.000-08:00

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

2007-12-04T21:04:00.001-08:00

In case of power outage

2007-07-27T16:42:00.001-07:00

In the EECS building on the Berkeley campus...

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

2007-07-23T20:21:00.000-07:00

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

Continuous and discrete

2007-07-14T20:33:00.000-07:00

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...

2007-06-02T09:06:00.000-07:00

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

2007-05-22T23:03:00.000-07:00

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

2007-05-21T20:36:00.000-07:00

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

Since when is 'B' a number?

2007-05-06T14:49:00.000-07:00

It is finished

2007-04-17T09:34:00.000-07:00

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

2007-04-05T20:25:00.000-07:00

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

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

2007-03-28T21:20:00.000-07:00

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

I'm a bad geek

2007-03-27T19:42:00.000-07:00

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!

2007-03-20T12:57:00.000-07:00

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.

Would it help if I drew a flow chart?

2007-02-27T17:31:00.000-08:00

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

Gang sines

2007-02-20T22:19:00.000-08:00

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

2007-02-18T17:13:00.000-08:00

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

Over my head

2007-02-12T12:09:00.000-08:00

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

I thought this one goes up to eleven

2007-02-02T21:20:00.000-08:00

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,

Shaken to the (multi) core

2007-01-31T23:07:00.000-08:00

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

Let the CHI flow

2007-01-24T19:15:00.000-08:00

For the purposes of this post, that's Computer-Human Interaction, not the Chinese concept of life force.I made my way to PARC again last Thursday to hear a great talk about how the landscape of electronic entertainment is changing thanks to developments in HCI. It really says something about my interests that so many of the topics that T. Blaine covered were already familiar to me. Off the top

Non-orientable garments

2007-01-22T10:43:00.000-08:00

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

Synchronicity

2007-01-19T08:04:00.000-08:00

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

...should you choose to accept it...

2007-01-18T23:31:00.000-08:00

If you've ever been bored while sitting at a computer, you've probably killed a few hours flipping over square tiles, hoping not to upturn a land mine. This polytopal variant pulls the old stand-by out of the plane and pushes it into the world of combinatorial spheres.I especially like the dramatic "mission failed TRY AGAIN!!" and "mission completion!!" messages that close each level.

Touch you I

2007-01-11T20:31:00.000-08:00

If you're reading this, you must have heard Tuesday's big news. Even if you weren't following it on twitter or the web, you found out soon enough, either from a major news outlet or by reading any of the thousands of blogs discussing it.That number is no exaggeration: as of this writing, technorati lists 83,622 posts, and Google Blog Search returns about 86,006 results from the past three

Oh do I now, Bert? Or should I say "Guntar"?

2007-01-07T20:00:00.000-08:00

Ever since I completed my Ph.D., this family of spam has become all the more amusing. Even if I did, wouldn't I want it from someone who can spell "degree"?Fwd: You Need a Better Dergee,{} and we can Help! From: (270) 818-XXXX Bert <293guntar@xxxxxxx.net>In jus tas little as 2 *weeks* you can have a masters degree from a national university.A better job, more income and a better life can all be

A perfect cube

2007-01-01T20:06:00.000-08:00

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

Howdy, neighbor

2006-12-29T23:28:00.000-08:00

Constructing phylogenetic trees from distances is crucial to computational genomics. That's why this paper is such a comfort; R. Mihaescu, D. Levy, and L. Pachter have shown that the neighbor-joining algorithm accomplishes this task very quickly, at least in an asymptotic and probabilistic sense.I once overheard the third author wish to see his website at the top of the list of Liors. Back then

In the shadow of Sun

2006-12-22T13:27:00.000-08:00

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

Familiar territory

2006-12-20T21:55:00.000-08:00

See, set theory is easy!

Recursion is child's play

2006-12-15T13:23:00.000-08:00

Every mathematician (and almost everyone, in fact) is familiar with the "Tower of Hanoi" problem. Not only is it a great way to occupy a patient child for a while, it provides a wonderful illustration of the twin concepts of recursion and induction in the description of the solution to the n-disk problem and the expression of the minimum number of steps in the optimal solution, respectively.But

0-0-0-...-0

2006-12-13T21:47:00.000-08:00

The three authors I mentioned recently for completing my work on doubly-laced crystals have put another paper on the arXiv, this time using their framework to unravel some fascinating properties of An-crystals. A special prize awaits the first to explain the title of this post in a comment!

Part of an RC graph

2006-12-09T15:06:00.000-08:00

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.

Divide and be conquered

2006-12-08T09:47:00.000-08:00

When I first read about J. Anderson's new theory of diving by zero, I was skeptical. There are numerous algebraic tricks one can play to make zero-division work out, and I would be surprised to see a novel approach to this problem so late in the game. After seeing the details of the "theory", I knew it was garbage, and suspected that it had already been dissected by M. Chu-Carroll at Good Math,

Another shot at the travelling salesman problem

2006-12-06T13:53:00.000-08:00

H. Kleiman has written a (very short) paper in which he claims to have proven that P=NP. Many of the usual red flags are up; e.g., his article is only available as a pdf (i.e., he provides no LaTeX source) and the references are light. On the other hand, he withholds the usual bluster with which such claims are made, instead using language like "we (hopefully) can always obtain an optimal tour

SECANTS RATE highly in my book

2006-12-05T09:32:00.000-08:00

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

Elucidating low technology

2006-11-30T11:51:00.000-08:00

All manner of news outlets are reporting on the just announced unraveling of the heretofore mysterious Antikythera mechanism, rediscovered over 100 years ago after falling to the bottom of the Sea of Crete nearly 2000 years before that. Network World has a few photos of the X-ray and tomographic technicians at work, and Wired has put up some beautiful pictures of the device produced from

The other half

2006-11-27T18:34:00.000-08:00

Appropriately enough, on the day that I filed my dissertation, a paper went up completing my work on characterizing B2-crystals by local criteria. It's great to see this, since my article proved only half of the desired result. As I said before, it's good to have publicly visible work; if I didn't, I would not have been given due acknowledgment both in the references and the introduction.

Ph.inally D.one

2006-11-22T23:08:00.000-08:00

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,

In my office for the last time

2006-11-21T13:45:00.000-08:00

(photo credit: Isaiah Lankham)

Return fire!

2006-11-17T16:56:00.000-08:00

M. Diaby claims to have invalidated R. Hofman's refutation of his purported proof of P=NP that was discussed earlier. It's not so much an article as an invitation to a public shouting match, seeing as it lacks an abstract, or references, or even self-contained expository prose. I hope Hofman responds again; this could get interesting.

What's a four-letter word starting with "R" for "Computer technology developed by D. Patterson"?

2006-11-16T10:39:00.000-08:00

It all depends on your interests: if data storage is your thing, the answer is RAID; if you like compilers and microprocessor architecture, you're probably looking for RISC. If, on the other hand, you're taken by what the future might hold for parallel computing, the correct acronym is RAMP; Research Accelerator for Multiple Processors. If you want to continue to be impressed, look over the

Get your hands on some games

2006-11-08T09:02:00.000-08:00

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

Bucking the trend

2006-11-06T09:59:00.000-08:00

As the title of my dissertation indicates, I've done research on crystals. Most non-mathematicians think that crystals refer to three-dimensional polytopes with evident symmetries; I've had to tell many a suddenly eager listener that what they call polyhedra are not the topic of my work. There is a path between crystals and polytopes, but it makes a lengthy journey through Lie theory and

num·ber: a musical selection

2006-11-02T12:04:00.000-08:00

A. Gelfand (any relation to I. Gelfand or S. Gelfand?) has written a pair of stories for Seed and Wired concerning R. Mahanthappa and his new cryptologically inspired album, Codebook. I highly recommend that you give it a listen; between Gelfand's articles, the label's site for the recording, and the artist's myspace page you can listen to most of the numbers on the CD.I really appreciate his

Symptoms of withdrawal

2006-11-01T09:08:00.000-08:00

When I first saw mention of a proof of the existence of a solution to the Navier-Stokes equations, I assumed that it had more in common with "proofs" of P=NP or the Riemann hypothesis. In fact, P. Smith had some keen original insights, even if the paper ultimately needed to be withdrawn. There is no shame in this, of course. As G. Kuperberg has illustrated with many examples posted next to his

Rather, it's been a big week for crystals

2006-10-31T14:23:00.000-08:00

I mentioned some new results on crystals a short while ago; and today, there are two more. These are are of even greater interest to me, as they naturally follow my contribution to the program on perfect crystals. The next step in M. Okado's research is to obtain an explicit description of type $D_n^{(1)}$-crystals. Since I have more experience dealing with such objects than just about anyone

IP $\neq$ LP

2006-10-26T13:30:00.000-07:00

And in case you might have heard otherwise, we still don't know about P and NP. There are some recently submitted papers (all of which are rather light on references) in the Computational Complexity section of the CS arXiv claiming that P and NP are the same thing, based on formulating the traveling salesman problem as a linear program. Of course, they all make the classic mistake of

A big day for crystals

2006-10-25T11:16:00.000-07:00

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.

Entropy always increases

2006-10-18T19:03:00.000-07:00

And that goes for information too, of course. We all should be used to this phenomenon by now; whenever a scientific opinion or study is released, the press mangles it terribly, especially with its attention-grabbing, copy-selling headlines. It should come as no surprise that when a news source simply relays stories of interest to a niche group, there may be an additional loss of fidelity.For

Discrete topology

2006-10-16T13:43:00.000-07:00

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.

Simply irresistible

2006-09-25T17:32:00.000-07:00

I hope no one at this conference chooses to speak about acyclic graphs; the audience might not see the forest for the trees.

Art, technically

2006-09-19T08:22:00.000-07:00

Seed magazine interviewed Matmos, ostensibly about their use of an enigma machine in their forthcoming album, although their conversation turned more generally to their use of "scientific" sources in their music. Who knew that one of the fringe benefits of getting Ph.D. in English would turn out to be access to the vaults of a cryptography research company?Matmos, as well as their more

Russian reveals result, refuses reward

2006-08-22T12:12:00.000-07:00

The previously mentioned G. Perelman has surprised the world by insisting that he not be seen as a "figurehead".But, hey, someone's got to win the prizes, and A. Okounkov, W. Werner and T. Tao seem happy to oblige.

Stacks!

2006-08-18T12:52:00.000-07:00

Stacks are one of the most fundamental abstract data structures in computer science, providing most with their first exposure to dynamic memory allocation. And as E. LaForest explains, they can also serve in place of registers in a processor core, potentially with a dramatic performance benefit. I'm curious to see how far this technology can go; will we have stack-based handhelds in ten years?

How many mathematicians does it take to prove the Poincaré conjecture?

2006-08-16T10:30:00.000-07:00

Perhaps a better question would be "How many math-months does it take to prove it?"* It's been three years since the Perelman program was announced, about 30 since Thurston's geometrization conjecture, and 102 since Poincaré first declared that the 3-sphere was unique among 3-manifolds for having trivial fundamental group; there were, of course, many more stops along the way. The answers to

Sometimes all you need is three pages

2006-08-01T23:14:00.000-07:00

Do you know how to increase the volume of a cardboard box by crushing it? I. Pak does. And he shows the world how to do it inInflating the cube without stretchingI. PakThat's definitely the most enjoyable paper I 've read in a while.

High Performance

2006-07-21T11:36:00.000-07:00

I now have an account on Jacquard for the purpose of parallel programming, which I'll be getting into later this summer. I would imagine it's not unlike sitting in the driver's seat of a Lotus.Those who are concerned about how I might use all this power can rest easy; I've agreed not to use it to develop weapons of mass destruction, and I am forbidden from using it on behalf of citizens of

These robes were made for walking

2006-07-07T01:07:00.000-07:00

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!

Irrationally effective

2006-06-30T09:01:00.000-07:00

Everyone knows that e has some nice combinatorial properties, but occasionally a counting result comes along that transcends the well-known mundanity of cute factorials.Counting and Computing by eM. Hassani

The problem that just won't go away

2006-06-29T17:55:00.000-07:00

Do you like maps? Do you like colors? Do you like coloring maps? Do you like signed permutations? I like signed permutations because they describe genetic mutations. I also like the fact that maybe, just maybe, there's a connection between mutations and how many colors are necessary for map-making.Signed permutations and the four color theoremS. Eliahou, C. Lecouvey

Cubicles have no doors

2006-06-07T21:32:00.000-07:00

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:When I do not have headphones on, I turn to look every time someone passes by;When I have headphones on, I am startled by a tap on my shoulder by whoever needs my attention.The first is less

When does a hiatus become a leave of absence?

2006-06-05T23:10:00.000-07:00

Abject apologies to those who would like to have read more frequent musings in this space. You have witnessed the effect of finishing a doctoral dissertation. After a decent run of at-least-weekly posts, I realized that I wasn't going to be able to keep it up during my home stretch. Having recently begun a transition to a new phase of my career, I expect to be able to devote an appropriate

I guess you can write a paper about just about anything these days

2006-06-05T21:47:00.000-07:00

But I really shouldn't be so harsh. The authors suggest that their work "rediscovers" a lost proof of a very interesting set theoretic result. And attention-grabbing titles can only help to spice up the literature-scape.Division by threePeter G. Doyle, John Horton Conway

The new generation of audio ransom note

2006-04-17T19:45:00.000-07:00

Wired's music guy, E. Van Buskirk, interviewed S. König about his software project cum musical mash-up collage tool cum political statement on intellectual property, sCrAmBlEd?HaCkZ!. It's not only an interesting idea, but there are also numerous computational challenges to making it work, and work so well. I want to know how he does all that! I suppose I'll find out when it gets

Limited options precipitate creativity

2006-04-12T16:24:00.000-07:00

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".

Pants are one thing, but this is ridiculous

2006-04-11T17:25:00.000-07:00

Pants to the power of two? And how did they get a a tree, anyway? Perhaps they were assisted by monkeys?Squarepants in a Tree: Sum of Subtree Clustering and Hyperbolic Pants DecompositionDavid Eppstein

Pachterian geometry

2006-04-10T11:25:00.000-07:00

The hardest midterm I ever took was a Numerical Analysis take-home exam. One problem asked for a definition of "the circle that best approximates four co-planar points" and apply our definition to given data. This problem has clear applications to transceiver placement optimization; e.g., where to put a cell phone tower. The model discussed in this preprint describes not only multiple

But what about $K_5$ and $K_3,3$?

2006-04-07T12:50:00.000-07:00

As a dear friend once told me, everyone should take time to play games. Here's one that I think my reader(s) will enjoy. In fact, I think (t)he(y) may have already. I'd really love to see it played on a 2-torus.

Human Experience Engineering

2006-04-06T20:01:00.000-07:00

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

The high TeX arXiv

2006-04-05T09:12:00.000-07:00

Numerous posts of mine point to the arXiv, the famous "e-print" server managed by Cornell University. Those at the helm of this marvelous resource have always ridden the leading edge of internet usage. For instance, consider this decade-old page, in which they point out that "... large databases such as this one (which has millions of distinct URL's that lead to gigabytes of data) are likely

Mathematics reaps the benefits of physical insight

2006-03-29T12:11:00.000-08:00

A few days ago, slashdot linked to this essay by M. du Sautoy in Seed on the relationship between the Riemann Hypothesis and quantum physics. I've been consistently impressed by Seed's provision of scientific reporting that neither glosses over significant concepts nor drowns the non-specialist in technical details. I think it answers the scientist's perpetual complaint against journalists'

A formula for misery

2006-03-28T12:31:00.000-08:00

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

The other side of the arXiv

2006-03-27T21:48:00.000-08:00

It turns out that some decent papers are posted to arXiv:cs, where authors are not listed alphabetically.Convex Separation from Optimization via HeuristicsL. M. Ioannou, B. C. Travaglione, D. CheungIt's good to see convex geometry presented in a decidedly algorithmic setting, since it really thrives there.

No opportunity for subtle wordplay

2006-03-27T10:53:00.000-08:00

The fourth Abel prize has been awarded to L. Carleson of the Royal Institute of Technology, Sweden "for his profound and seminal contributions to harmonic analysis and the theory of smooth dynamical systems." The Slashdot story mentions that "[h]is theorems have been helpful in creating [the] iPod," and includes a decent layman's explanation of Prof. Carleson's contributions to analysis.

Watershed

2006-03-24T13:08:00.000-08:00

The project I mentioned in some previous posts is now on the arXiv.On the local structure of doubly laced crystalsP. SternbergIt's good to have publicly visible work.

Non, c'est pas une Weezer logo

2006-03-23T09:26:00.000-08:00

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

What's a five-letter word for "Surfaces of genus zero with three boundary cycles"?

2006-03-22T10:07:00.000-08:00

Any situation can be made humorous (or more so, if it's already funny) by the addition or subtraction of pants or monkeys. At least, so said a dear friend of mine several years ago. I'm inclined to believe him.As far as I know, there is no mathematical object known as a monkey; until last night, I thought the same was true of pants. As this nomenclature is due to W. Thurston, it has been

A nice round number

2006-03-14T13:59:00.000-08:00

If you write dates with the month before the day, today is 3/14, or more affectionately, π day. Those who are especially meticulous celebrate at a moment about half a minute past 1:59. Yesterday, the Independent ran an article celebrating the wonderful properties and history of this number. Unfortunately, the following sentence appeared near the end of the story:Pi, you see, is always going to

Physics and Sociology, helping each other

2006-03-13T13:40:00.000-08:00

The history of Mathematical Physics includes many examples of both of its constituent disciplines providing insight to the other. The mathematical tools of differential equations, linear algebra, and manifolds have allowed for precise descriptions of physical models; at the same time, formulas such as the Riemann-Roch Theorem and the ongoing X=M Conjecture could never have been discovered

Look, biological imaging is actually useful

2006-03-08T17:36:00.000-08:00

A group led by David Shapiro of SUNY Stony Brook has developed a new algorithm for image reconstruction from X-ray diffraction microscopy. And as has been reported on Cornell's news site, it is easily adapted to quickly solve sudoku puzzles.So, will a sizable number of young Americans realize that combinatorialists solve puzzles like sudoku, and decide that they want to pursue discrete math as a

For future reference

2006-03-08T00:31:00.000-08:00

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 DnW. Nakai, T. NakanishiI've received a few citations before, but the sense of recognition

We don't need no (constructivist) education!

2006-03-01T12:23:00.000-08:00

In the world of mathematical research, the word "constructivism" refers to a debate addressing the existence of objects that cannot be explicitly constructed. If such assumptions are disallowed, some aspects of the infinite become very difficult to deal with. However, in the field of mathematics education (which is simultaneously close to and distant from mathematical research), constructivism

A matter of preference

2006-02-28T17:01:00.000-08:00

From Incomplete Preferences to Ranking via OptimizationP. Chebotarev, E. ShamisThis fascinating problem deals with how to determine a full ranking of a finite list of candidates given only partial preference data. For instance, if I prefer cola to coffee and green tea to black tea, and you prefer coffee to black tea, the following are compatible rankings for these preference data:

Wrapped in a riddle

2006-02-26T13:45:00.000-08:00

Slashdot has reported on a project to decode three original Enigma messages intercepted in 1942. The method employed is, of course, brute force distributed computing, combined with statistical methods and some clever optimization tricks.I had thought that the Enigma had been completely unraveled; as it turns out, even with today's computers, very sophisticated computational tools are required

Revisionism

2006-02-23T18:03:00.000-08:00

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

2006-02-17T14:23:00.000-08:00

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

Return to roots

2006-02-14T08:35:00.000-08:00

A curious identity and the volume of the root spherical simplex C. De Concini, C. ProcesiTake a maximal parabolic subgroup of an affine Weyl group. Take the product of its exponents, and divide by the product of its degrees. Now, sum that over all maximal parabolic subgroups; you get 1. Now that's an elegant equation.And further, acconding to E. Vinberg, this also tells us about the ratio of

Fusion coefficients

2006-02-11T10:21:00.000-08:00

Fusion products of Kirillov-Reshetikhin modules and fermionic multiplicity formulasE. Ardonne, R. KedemThe second author is my "academic aunt", having been advised by B. McCoy.I love combinatorics in mathematical physics.

Fossil fuel lovers

2006-02-10T10:29:00.000-08:00

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

In 2006 we use the technology of 1958 to recreate the technology of 1849

2006-02-09T11:14:00.000-08:00

A. Carol has built a difference engine No. 2 from LEGO.* Not only does this evoke fond childhood memories of building trucks and castles, but it also calls me to consider the role of mechanically assisted computation in mathematics.The difference engine sits at a fascinating point in the history of the relationship between mathematicians and machines. Because the mechanism by which its atomic

On the lighter side

2006-02-08T16:00:00.000-08:00

A New Upper Bound on Rubik's Cube GroupSilviu RaduThe Rubik Cube has had more success inhabiting pop consciousness than any other big discrete object. I never got really good at it myself; I could solve one side perfectly well, but that's no big achievement. I suppose my ability to hold parallel data in my head has improved in the past 15 years, but I doubt that would be the best use of my time

From the arXiv

2006-02-08T10:56:00.000-08:00

Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection A. Kuniba, M. Okado, R. Sakamoto, T. Takagi, Y. YamadaThis paper elucidates the relationship between rigged configurations and Young tableaux. Being able to pass back and forth between them is essential to the application of my first result.Alcove walks, Hecke algebras, spherical functions, crystals and column strict

Just apply yourself!

2006-02-06T10:48:00.000-08:00

I'm very fortunate to be in a math department where little to no distinction is made between pure and applied mathematics. In D. Zeilberger's opinion, one who sees such a distinction as impacting the value of their work deserves a rather harsh qualitative evaluation as a mathematician.Consider the areas of computer science, theoretical physics, and theoretical ecology. Most of the questions

It's a pun, not a spelling error

2006-02-03T13:36:00.000-08:00

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

Let $n\in\mathbb{Z}_{\geq 0}$.

2006-02-03T13:24:00.000-08:00

This is a repository for my thoughts, observations, and reactions to goings-on in the world of mathematics. If you notice a slant towards discrete math/combinatorics, it's because that's the kind of math I do.If you can't understand the title of this post, you really should learn TeX.