Archive for the 'mathematics' Category

Categorically Not! - Puzzles!

by
Clifford
on March 6, 2008
in Los Angeles, entertainment, mathematics, science and work
. 2 Comments

The next Categorically Not! is on Sunday March 9th (upcoming). The Categorically Not! series of events that are held at the Santa Monica Art Studios, (with occasional exceptions). It’s a series - started and run by science writer K. C. Cole - of fun and informative conversations deliberately ignoring the traditional boundaries between art, science, humanities, and other subjects. I strongly encourage you to come to them if you’re in the area. Here is the website that describes past ones, and upcoming ones. See also the links at the end of the post for some announcements and descriptions (and even video) of previous events.

The theme this month is Puzzles! Here’s the description from K C Cole:

What isn’t a puzzle? The universe, life and everything are essentially puzzles that, to borrow from Einstein, “beckon like a liberation.” Designing buildings, choreographing dances, cooking meals and getting along with other people all involve solving puzzles (as, of course, does figuring out what’s right in front of your eyes—not to mention putting together a program such as Categorically Not!) A love of puzzles and the challenge of solving them is deeply embedded in human nature.

Categorically Not! - Puzzles! - Speakers

Gwen Roberts, Scott Kim, Gavin Scott.

Our March 9th Categorically Not! features puzzlemaster Scott Kim, who’s Continue reading ‘Categorically Not! - Puzzles!’

Beyond Einstein: Fixing Singularities in Spacetime

by
Clifford
on March 3, 2008
in black holes, cosmology, mathematics, science, string theory and work
. 21 Comments

Not long ago David Morrison (UCSB) came to the mathematics department here at USC to give a colloquium.

David Morrison Colloquium at USC

This was a treat for me for many reasons. Here are three:

  1. It’s always good to see Dave. He’s one of the people I’ve known in the field was since my very first postdoc when I was learning to survive in the big bad world on my own after graduate school. I mostly could not understand a word he or anyone there else said in those days (IAS Princeton, right in the belly of the Continue reading ‘Beyond Einstein: Fixing Singularities in Spacetime’

A Delicious Fractal

by
Clifford
on February 10, 2008
in Los Angeles, food and drink and mathematics
. 8 Comments

romanesque cauliflower

A small Romanesque Cauliflower. (Click for larger view.)

Imagine my delight when I spotted this lovely piece of edible mathematics in the Hollywood Farmer’s Market this morning. The stall has several of them of many sizes (this was a very little one) and of several colours. Wonderful. If you don’t know what I mean when I talk about the mathematics, or use the term fractal, look it up. There are several things of note, among which are the wonderful spiral structures that you can Continue reading ‘A Delicious Fractal’

Möbius Transformations

by
Clifford
on November 28, 2007
in art, mathematics and science
. 12 Comments

This short video is simply lovely. It illustrates (with perfectly chosen music) an important set of mathematical transformations dear to many of us, the Möbius transformations. It is by Douglas Arnold and Jonathan Rogness of the University of Minnesota. It’s a pleasure to watch, whether you work in a mathematically related field or not. Try it:



Also worth looking at (for a host of other reasons) are the comments on the video from Continue reading ‘Möbius Transformations’

Inside Out from the Inside

by
Clifford
on October 29, 2007
in Los Angeles, biology, books, mathematics and science
. 2 Comments

Last night’s Categorically Not! - Inside Out event was just great. The three topics contrasted really nicely, were very well presented as individual topics in their own right, and there were resonances between the different topics through the main umbrella theme - “Inside Out”.

Science writers Sandy Blakeslee and her son Matt Blakeslee did a sort of tag team presentation, taking turns to build up several aspects of the subject (covered in their new book “The Body Has a Mind of Its Own”) of one’s sense of self and that all-so-important division between inside (ourself) and outside (the rest of the universe) that we make with our minds. It’s very dynamic, of course - you extend it a lot when you use tools, from a fork when eating to the car you’re driving in (everyone grunted in recognition when Sandy mentioned how you have the instinct to duck when driving under a low ceiling in a parking garage….). One of the things that I think resonated most with the audience is the description of the work on showing how many celebrated “out of body” experiences that people get have a foundation in Continue reading ‘Inside Out from the Inside’

Inside Out

by
Clifford
on October 27, 2007
in mathematics
. 5 Comments

Part of K C Cole’s teaser for tomorrow’s Categorically Not! - Inside Out said:

Sometimes the results are surprising: circles in the plane can’t be turned inside out, but spheres in 3-dimensional space can be.

This is all the license I need to show you* this wonderful 21 minute video showing exactly that (and explaining some rather beautiful mathematics along the way):



Direct link to the Google Video (for larger viewing) here.

Continue reading ‘Inside Out’

Categorically Not! - Inside Out

by
Clifford
on October 27, 2007
in Los Angeles, art, biology, mathematics, science and theatre
. 2 Comments

Paul Stein of Los Angeles PhilharmonicThe next Categorically Not! is a Blue* one! It’s on Sunday October 28th (tomorrow). The Categorically Not! series of events that are held at the Santa Monica Art Studios, (with occasional exceptions). It’s a series - started and run by science writer K. C. Cole - of fun and informative conversations deliberately ignoring the traditional boundaries between art, science, humanities, and other subjects. I strongly encourage you to come to them if you’re in the area.

Here is the website that describes past ones, and upcoming ones. See also the links at the end of the post for some announcements and descriptions (and even video) of previous events. (Above right: The Los Angeles Philharmonic’s Paul Stein demonstrating “small differences” on the violin, in the event with that theme.)

The theme this month is Inside Out. Here’s the description from K C Cole:

Continue reading ‘Categorically Not! - Inside Out’

…And He Got Einstein’s Office!

by
Clifford
on October 15, 2007
in mathematics and science
. 0 Comments

[Post reconstruction in progress after 25.10.07 hack (comments and images to follow)]:

From the Nobel Prize site, the final one of the year:

The Royal Swedish Academy of Sciences has decided to award The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2007 jointly to Leonid Hurwicz (University of Minnesota, MN, USA), Eric S. Maskin (Institute for Advanced Study, Princeton, NJ, USA), and Roger B. Myerson (University of Chicago, IL, USA), for having laid the foundations of mechanism design theory”.

No, I did not really know what mechanism design theory was either. Some of it sounds rather interesting, in fact. The website has a breakdown of the key contributions and ideas here. Once again, I found that NPR had a really nice radio chat about the prize. You can hear that here. In that audio file, you can learn the origin of this post’s title…. if you cannot already guess.

-cvj

Not Following the Script

by
Clifford
on October 8, 2007
in Los Angeles, academia, mathematics, science and science and society
. 3 Comments

Well, it was a weekend of an unexpected character. Fantastic outside, but I did not see as much of it as I’d have liked. I was working on a script, you see. It needed to be worked on immediately and at the last minute because the work of turning it into the final product that will get seen started this weekend, and so I wanted to make as many comments and suggestions as I could before it was too late. It’s science - don’t worry. Also, it is rare to get to work on something that I know will get made (most things get shelved and never see the light of day), so that was sort of fun. I won’t tell you what it is (sorry) since I’m not actually a writer on the project, but I got the chance to look at the whole thing and make a lot of comments and suggestions, rephrasings, alternative lines, and so forth. All in a good cause. I think it will be out next year.

Yes, I know. “I was working on a script…” Sounds rather like I’ve finally caved in and succumbed to living in Los Angeles completely, working on a script like everyone else Continue reading ‘Not Following the Script’

Reading, Writing, and ’Rithmetic

by
Clifford
on August 7, 2007
in design, mathematics, personal, technology and words
. 5 Comments

Yesterday was (depending upon who’s counting) the 16th anniversary of that thing we call the World Wide Web becoming a public entity. The Web is not to be confused with the Internet, which is much older, of course1. I’m talking about Tim Berners-Lee’s idea and implementation thereof. (I should not neglect to mention that this was done at CERN, the particle physics laboratory in Europe.) His original posting (on the newsgroup alt.hypertext) proposing the structure can be viewed here, and here’s an extract:

The project started with the philosophy that much academic information should be freely available to anyone. It aims to allow information sharing within internationally dispersed teams, and the dissemination of information by support groups.

Reader view

The WWW world consists of documents, and links. Indexes are special documents which, rather than being read, may be searched. The result of such a search is another (”virtual”) document containing links to the documents found. A simple protocol (”HTTP”) is used to allow a browser program to request a keyword search by a remote information server.

The web contains documents in many formats. Those documents which are hypertext, (real or virtual) contain links to other documents, or places within documents. All documents, whether real, virtual or indexes, look similar to the reader and are contained within the same addressing scheme.

To follow a link, a reader clicks with a mouse (or types in a number if he or she has no mouse). To search and index, a reader gives keywords (or other search criteria). These are the only operations necessary to access the entire world of data.

What am I going to do to celebrate?

letter to anonSince everyday I celebrate the WWW by using it a lot, to commemorate the event I think I’m going to pay a visit to the (real, physical) library, then read a good old-fashioned book for a while, and then hand-write a letter. I used to write so many letters, long ago, and from time to time I try to stop everything and pick up a pen and write one. I got in the mood the other day while in Aspen, and went and found some letter-writing paper and envelopes, curled up on a sofa, and wrote for a Continue reading ‘Reading, Writing, and ’Rithmetic’

Showing a Different Way

by
Clifford
on August 1, 2007
in books, cycling, mathematics, minorities in science, science and society, science education, television and women in science
. 55 Comments

danica mckellar Getty imagesDanica McKellar (the actress who played Winnie in that show The Wonder Years that many of you might remember) has been working to try to encourage young girls to go more for “Cute and Smart”, as opposed to “Cute and Dumb”. Bottom line: Less Lindsay Lohan, and Paris Hilton, and more…. well, Danica. (I’m sure there are other Tinseltown examples here… can I have some help?).

Danica sets an excellent example of why the two (being considered attractive on the one hand, and smart on the other) are not mutually exclusive, while not suffering from the “geek” or “nerd” label that is attached by the entertainment industry to certain groups of people who enjoy using their brains a lot. She trained as a mathematician, in fact, doing her undergraduate work at UCLA so well that she did rather good published research work (NPR piece here Update: It is actually more of a theoretical physics problem, it appears.). This is from someone who struggled with the subject in sixth grade. Why is she in the news? She’s written a new book “Math Doesn’t Suck”, the aim being to encourage girls to avoid the (social) barriers to getting into mathematics. Excellent title. (I wonder if they’ll change it to “Maths Doesn’t Suck” if they publish it in Britain? “Suck” British kids have adopted from the USA cultural juggernaut, but “Math”? Not yet.)

danica mckellar math doesn't suckActually, looking at her website, I see that the full title appears to be “Math Doesn’t Suck: How to Survive Middle School Math Without Losing Your Mind or Breaking a Nail”, which is more of a mouthful, a bit less zippy, but oh well. It’s all very Clueless, in a good way. Here’s a link to the book’s site, and it is due out tomorrow.

There’s an article1 on her recent Newsweek quote at CNN, from which I grabbed this:

“When girls see the antics of Paris Hilton and Lindsay Lohan, they think that being fun and glamorous also means being dumb and irresponsible,” the 32-year-old McKellar told Newsweek for editions to hit newsstands Monday.

“But I want to show them that being smart is cool,” she said. “Being good at math is cool. And not only that, it can help them get what they want out of life.”

but you should go and read the whole thing, by clicking here. [Update: Better article here by Corey Binns in Good Magazine. Extract:

“The book hones in on middle school’s trickiest points-––like fractions, ratios, and percentages—and presents them in a style that’s appropriate for the cool kids’ lunch table. Figure out your “type” in boys and you’ll understand greatest common factors. All of those iced lattes celebrities drink make multiplying fractions tasty. Plus, savvy shopping requires killer decimal skills.”

]

Go Danica!

In other news, I learned2 that particle physicist Lisa Randall (author of the popular book with the curious title “Warped Passages”) appears in Vogue this month. Lisa Continue reading ‘Showing a Different Way’

A Bundle of Laughs?

by
Clifford
on July 18, 2007
in film, fun and mathematics
. 19 Comments

To a first approximation, this will not be funny at all to any of you:

gerbes at aspen

I giggled at it, I will confess. I can never get enough insertions of gerbes into a sentence. There’s just something about the total abstractness of the mathematical Continue reading ‘A Bundle of Laughs?’

Mathematics and Strings

by
Clifford
on June 25, 2007
in mathematics, research, science and string theory
. 4 Comments

Not long after I told you about the TASI school and the excellent online lecture resource they were rapidly building, I heard* about a school in Utah that might be of interest, especially if you’re interested in the fruitful interface between mathematics and string theory. The title: “Derived Categories”, and it ran for two weeks with lectures on mathematical aspects and stringy aspects. The main reason I’m telling you Continue reading ‘Mathematics and Strings’

E8

by
Clifford
on March 19, 2007
in mathematics and science
. 20 Comments

E8 and the Gosset polytope 421

No, not another flower from my garden. This is a two dimensional projection (originally hand drawn in the 1960s by Peter McMullen, of a polytope that lives in eight dimensions, known as the Gossett polytope 421. Click here to be taken over to the American Institute for Mathematics (AIM) site for more information about it. (This image was computer generated by John Stembridge, and you can get higher resolution there for use on your T-shirts and so forth.)

What does this all pertain to? A new result from a team of mathematicians. They’ve done what some are calling the mathematician’s equivalent of mapping the genome of a Lie group, the one called E8. Groups pertain to symmetries. Symmetries are Continue reading ‘E8′

Not Improbable

by
Clifford
on January 27, 2007
in academia, mathematics, science, string theory and work
. 13 Comments

elaine chewOn Wednesday night, accompanied by Tameem, a student of mine, I wandered across campus to attend the “Mathematics in Music” event. I blogged about it earlier. I don’t really want to talk about the event itself in this post. It was a nice enough recital of three pieces. I don’t know why, but the promised “mathematics” was disappointingly virtually non-existent. I’m not exaggerating, I’m afraid.

Keep in mind that it may simply just be my misunderstanding of the intent of the event, but there’s simply next to nothing to report in the way of what was said about mathematical aspects of music. There were plenty of opportunities, but (almost) none were taken. I got out my notebook and pen, all excited at what the presenters might say at various points… and the mathematics never showed up. There were a few extremely elementary remarks about tonal ratios in chords, about scales, keys, and time, and that was it, more or less. This was a bit of a shame, since I suspect that Elaine Chew could have talked at length and with some authority on the matter (given the projects she’s involved in - see e.g. here), but mathematics was almost completely missing in the event - despite the title. I imagine there were what seemed like good reasons for this. I was not party to decisions made behind the scenes, so cannot comment further.

More interestingly on that front was what took place in the minutes leading up to the delayed start of the event. First, although it was a free event, they pointed us to the box office where an attendant printed us two tickets from the computer so that we can show them to someone at the door who wasn’t really looking anyway. Fine. We got into the recital hall, but rather than sitting at the obvious available seats, I suggested that we move to the other side of the room where one can get a better view of the piano keyboard. I’m less than happy when I can’t see what a musician is doing, you see, so I always try to sit with the pianist’s view of the piano. So we did that, and found two seats. While we chatted and looked around us at the growing assembly, I spotted a friend and colleague of mine, the composer Veronika Krausas. She was in the company of someone who she introduced as Brian Head, who is a composer, performer (guitar) and music theorist (a “triple threat”, Veronika joked), also in USC’s Thornton school of music. They were looking for seats and there was one on either side of the two we were sitting in, and so they joined us and we chatted some more.

When the event start was about ten or fifteen minutes late -they were trying to get the reassuringly large crown all seated, they announced- Veronika idly looked at her ticket, pointed out that they were numbered, and wondered if we should have been Continue reading ‘Not Improbable’

Mathematics and Music

by
Clifford
on January 22, 2007
in mathematics and music
. 8 Comments

On Wednesday there’ll be an evening event about Mathematics and Music here at USC. If you are nearby and can make it, consider going along. It’s free! It is part of the Visions and Voices programme I’ve talked about before. The presenter/performer will be Elaine Chew, whose research is at the intersection of engineering and music. Read more about the event here. You can find out more about Professor Chew from her website here.

Enjoy!

-cvj

Hooking Up Manifolds

by
Clifford
on January 1, 2007
in Los Angeles, art, design, fun and mathematics
. 9 Comments

lorenz manifold

I love crochet. I spent a huge number of hours doing it when I was young, and only in later years did I realize that the same things that attracted it to me then are the same things that drive and motivate a lot of my research interests. (I many have mentioned this before, but it’s worth saying again).

It’s the love of patterns, plain and simple. If your child -of whetever gender- gets Continue reading ‘Hooking Up Manifolds’

LaTeX Spoken Here!

by
Clifford
on December 12, 2006
in asymptotia, mathematics and science
. 150 Comments

This is a test of LaTeX on the site*.

The first equation I shall try is the following (for more on unpacking this equation and its meaning, see this post and links therein):

u{\cal R}^2-\frac12 {\cal R}{\cal R}^{\prime\prime}+\frac14({\cal R}^\prime)^2=\Gamma^2\ .

Yay! It works. I have implemented it in the comments too. So now we can have a new, sharper tool for our discussions and arguments.

Continue reading ‘LaTeX Spoken Here!’

BBC Publishes Onion Article?

by
Clifford
on December 7, 2006
in mathematics, science and science in the media
. 25 Comments

nullity demoWell, what else can it be? It is not April 1st, so my only explanation is that it is an Onion article that somehow was picked up by the BBC. What do you think? It reads exactly like one, right down to the picture of the pleasant bearded academic at the board, the well-scrubbed English schoolchildren, and the quotes from the children. The only thing missing is the page with the three heads (whose names and occupations change every week) making comments on the story. (Be sure to watch the video links of the demo too!)

This is the sort of science/mathematics reporting that I usually expect to read in the Continue reading ‘BBC Publishes Onion Article?’

Poincaré In Our Time

by
Clifford
on November 20, 2006
in mathematics, science and science in the media
. 6 Comments

I don’t know whether you caught this already, but if not, do consider listening to the 2nd November edition of BBC Radio 4’s “In Our Time”. It is about Poincaré, his work, and the famous conjecture. From their website’s page on the programme:

The great French mathematician Henri Poincaré declared: “The scientist does not study mathematics because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would not be worth knowing and life would not be worth living. And it is because simplicity, because grandeur, is beautiful that we preferably seek simple facts, sublime facts, and that we delight now to follow the majestic course of the stars.”
Poincaré’s ground-breaking work in the 19th and early 20th century has indeed led us to the stars and the consideration of the shape of the universe itself. He is known as the father of topology – the study of the properties of shapes and how they can be deformed. His famous Conjecture in this field has been causing mathematicians sleepless nights ever since. He is also credited as the Father of Chaos Theory.

So how did this great polymath change the way we understand the world and indeed the universe? Why did his conjecture remain unproved for almost a century? And has it finally been cracked?

It is a particulalry good programme this time. This is a programme that focuses mostly on philosophy, and is often accused of being only rather superficial when it comes to covering the more hardcore and up-to-date science, but not this time. The guests are Continue reading ‘Poincaré In Our Time’

A Man Out Standing In His Field

by
Clifford
on November 8, 2006
in Los Angeles, academia, mathematics, science and science in the media
. 9 Comments

Two of our colloquia this semester were concerned with work very much in the public eye this year. The first was from Francis Bonahan of the Mathematics Department here at USC.

F bonahan colloquium

He talked about the work that won the Fields medal - the proof, by Grigori Perelman, of the Poincaré conjecture. Or better, I should say the work toward the proof, since the citation does not explicitly mention the conjecture, but his larger body of work. (MathWorld link, Wikipedia link.) In fact, Francis spoke about a lot more than just the Poincaré conjecture.

F bonahan colloquium

He talked about the larger setting in which that work fits, something mathematicians call the “geometrization conjecture”, which Mathematicians care a lot more about. Perelman’s work does more than just prove the Poincaré, it addresses the whole (3-)ball of wax, so to speak. He told us quite a bit about that in the talk, spending most Continue reading ‘A Man Out Standing In His Field’

A Positive Sign

by
Clifford
on October 25, 2006
in fun, mathematics, science and society, science education and travel
. 8 Comments

positive sign I’m always pleased to see this sign. It is at Heathrow, on the walk down the perpetually dingily lit underground corridors connecting the terminals, the tube, the extortion Heathrow express, and the parking lots.

For a start, I generally like the idea that the ground floor of a building (the one you walk onto off the street) is the “zeroth” floor. (I mean no disrespect to this splendid country I live in, that has largely chosen otherwise, although every now and again in older buildings you see it.) So it is just great to see a (-1)th floor, and all the more pleasing that it is not considered odd to have that. No worries about people being confused about what a negative number is. I know it sounds trivial, but when you see basic mathematics and science literacy seemingly getting worse all around -on both sides of the Atlantic, mark you- …when you think something shouldn’t or can’t possibly get “dumbed down” any further for the general public, and then it gets “dumbed down” anyway… seeing this sort of thing is a relief.

Every time I see it, once the above has flashed through my mind, you know what I think next, every single time? Wouldn’t it just be great if elevators went horizontally too?! Then we could have the imaginary axis as well! But that will have to remain just in my, uh, imagination.

-cvj

Those Self-Fulfilling Prophecies

by
Clifford
on October 20, 2006
in academia, black people in science, mathematics, minorities in science, science and women in science
. 13 Comments

You may recall that we were recently discussing stereotypes as a result of an earlier post. Particularly, I was talking about the effects those sterotypes can produce as a result of modifying the expectations of others, making it hard for some people to be taken seriously, and resulting in them having to go that extra mile (or several) as a result.

Well, I’d like to point your attention to a recent study about the direct effects of those stereotypes on the stereotyped. Quoting from an article by AP science writer Randolph E. Schmid:

[Steven J.] Heine and doctoral student Ilan Dar-Nimrod wanted to see how people are affected by stereotypes about themselves. They divided more than 220 women into four groups and administered math and reading comprehension tests between 2003 and 2006. Their results are reported in Friday’s issue of the journal Science.

What they actually did was to provide the different groups with different images and reading materials before they did the tests. They seem to have found significant differences in the results that suggest that having a negative stereotype of yourself in mind actually makes things worse. In other words:

It’s a process psychologists call a stereotype threat, Heine explained. “If a member of a group for which there is a negative stereotype is in a position to test the stereotype, they are likely to choke under the pressure.”

So reminding them of the stereotype affects them.

Here’s what they found:

Continue reading ‘Those Self-Fulfilling Prophecies’

Manifold Yau

by
Clifford
on October 16, 2006
in academia, mathematics and science in the media
. 30 Comments

calabi-yau sliceWell, here’s yet another discussion of Yau to gobble up. It is a New York Times article by Dennis Overbye on Yau, his life and work*. I’ve no idea why this was written, or what the timing was. I’d like to believe that it was just because it is a good subject -because it is- and that it is worthwhile to do an article about a Mathematician of considerable stature in the field, and about the ins and outs of the world of Mathematics -because it is. But I can’t help but wonder if this would have seen the light of day if there was not the big argument going on about the New Yorker article and Yau’s displeasure with its contents. (Image on the right -click for larger- was taken from this site. It is a slice of a Calabi-Yau manifold. There’s more in the article about Yau’s work on those.)

Well, I don’t care what the reason is. I love to see articles of this type written about this Continue reading ‘Manifold Yau’

The Letters Keep Coming

by
Clifford
on October 15, 2006
in mathematics and science in the media
. 12 Comments

I just checked the website of Yau just now, for more developments on the argument with the New Yorker. It seems that since Hamilton’s strong letter, there have been several more, from various luminaries in the field. You can find them all on the site.

-cvj

Giant Still Standing

by
Clifford
on October 8, 2006
in mathematics and science
. 2 Comments

The giant still stands, at least for now. From the preprint site:

This paper is being withdrawn by the author due a serious flaw.

I would not be surprised to learn later that her work, even if flawed, has led the way to helping solve this long-standing problem.

-cvj

(Thanks, Say Lee!)

Update on the Giant-Killers

by
Clifford
on October 5, 2006
in mathematics and science
. 16 Comments

navier-stokes flowGood News Everyone! I learned just now from Good Math, Bad Math there may well be a successful proof of yet another of the great Millennium problems. This one pertains to solutions of the Navier-Stokes equations which are of central importance in fluid dynamics, for example. (The figure to the left -click for larger- is from a computer simulation, by Greg Ashford, of the airflow around an aircraft wing (in cross section) and the foil that it uses to change the overall shape of the wing for maneouvering. I got it from a site linked here.)

Penelope Smith, at Lehigh University has presented a preprint with her proof, which Continue reading ‘Update on the Giant-Killers’

Irrational Memories

by
Clifford
on October 4, 2006
in academia, architecture, art, fun, mathematics, nature and science
. 14 Comments

Back when I was young enough to care to try to list such things, I had a favourite number. Really, really faourite. I lived and breathed that number for a while. Today’s session in the freshman seminar “The Art and Science of Seeing and the Seeing and Science of Art”, about which I have blogged here and here, was all about it. Rather than do chapter and verse about it (don’t get me started!), I will instead leave you with the image that I ended with…

penrose tiling

… and let you tell me and other readers - if you like - what you think the number is, what it means to you, and perhaps share whatever you like (or hate) about it.

-cvj

Scary Statement

by
Clifford
on September 30, 2006
in mathematics, science and science and society
. 7 Comments

Anton Kapustin, yesterday, in the middle of what he called (not seriously) “the scary statement” of the Geometric Langlands duality….

kapustin langlands

Part of the audience, receiving the news….

SCSS audience

The SCSS is going well. More later. Must go get my bus now so that I can start the Saturday session…

-cvj

Hamiltonian Support

by
Clifford
on September 27, 2006
in mathematics and science in the media
. 7 Comments

In the continued public discussion of the treatment of Yau’s reputation by the New Yorker article (by Sylvia Nasar and David Gruber), to which I earlier referred (see here, and see the post about Yau’s response here), there has been a recent significant development. I don’t mean the press conference of last week, held by Yau’s entourage (…did anyone see that? I could not log on… there is archived video avaialble here. I still can’t view it…reports are welcome).

No, I’m talking about the public letter attributed to Richard Hamilton, the mathematician at Columbia University who is another major player in the story of proving the Poincare conjecture. He does a great job of supporting Yau, and setting the record straight about his numerous contributions to the field in general, and to the proof of the Poincare conjecture in particular. You can see the whole letter here.

It starts:

I am very disturbed by the unfair manner in which Yau Shing-Tung has been portrayed in the New Yorker article.

and there are detailed descriptions of Yau’s early recognition of the importance of Hamilton’s Ricci flow technique, ending in:

Without Yau’s guidance and support at this early stage, there would have been no Ricci Flow program for Perelman to finish.

He then goes on to describe Yau’s contributions to the field through his encouragement and support of several young researchers in the Ricci flow program, and other key work that he and Yau did in the area, in addition to other key Continue reading ‘Hamiltonian Support’

Go Figure!

by
Clifford
on September 21, 2006
in Los Angeles, art, design, mathematics, science, science and society and work
. 12 Comments

hyperbolic crochetSo I think maybe I died and went to cvj heaven. Let me explain. I mentioned to you a while ago the freshman seminar entitled “The Art and Science of Seeing and the Seeing and Science of Art”, for which there was an enrollment snafu. Well, it is continuing, and on Wednesday afternoons, I sit under the trees with two students for an hour and a half (KC Cole pulled out, since it would be a ridiculous professor-student ratio otherwise) and talk about a huge spectrum of things that fall into this category, as well as some of the things that come up in the Visions and Voices series.

Last week and this week, we discussed -with illustrations- two pretty obvious topics that come up first in people minds when the words “Science” and “Art” are in the same sentence. Those two topics are Fractals, and Escher. Quite obvious as “science-meets-art” topics go (and tiresomely so sometimes) but nontheless I believe it would be neglectful of us not to explore some of the interesting and wonderful themes, images, and techniques that those topics touch upon. Escher last week, Fractals this week. It was a lot of fun. I will tell you a bit about it later, in view of the lack of time (I had a breakthrough in a little computation that I really should get back to before I have to prepare a class).

Anyway, I come away from these sessions thinking how great it is to let oneself broaden the canvas upon which one can jot down one’s reflections upon and reactions (emotional, intellectual, otherwise) to when one looks at a piece of art. The broadening I refer to means simply to include science. Either directly or indirectly. This is the tack we’ve been taking in this seminar, and so far I think we’ve been having a lot of fun and learning a lot. I’ve been reflecting on how wonderful it would be if more people, in the context of art appreciation, would allow themselves the latitude to do this. Sadly, ignorance of what science is about, and the fear of science, topics that I talk about a lot on this blog, maintain huge barriers between art and science in most people’s minds, and so there is a whole dimension of appreciation that goes unlocked as a result (not just in the obvious context of Escher, etc, but in appreciating any art form). It was especially sad to see six freshmen disappear from the enrollment on the class principally because the word “science” was inserted into the title of what they thought would be an art appreciation seminar. Well, it is still an art appreciation seminar, but those who are coming are learning to look at art, and the world around them, with new eyes, and maybe seeing a broader and/or deeper spectrum.

So I go into “What if…” mode for a while on my ride back to my office and feel a little sad that even bright young people who are on campus to learn new things are selecting themselves out of such opportunities to engage with their world because of the word “science”. Sigh.

So imagine my delight last night (having finished a seminar on fractals earlier that day, pointing out several examples of “fractal geometry” in art and nature) when and architect friend of mine* emailed me a link to an institute, right here in LA, that seems to be right on the same track I’m talking about!

It is the Institute for Figuring, (founded by science writer Margaret Wertheim) right Continue reading ‘Go Figure!’

Yau Fights Back?

by
Clifford
on September 18, 2006
in academia, mathematics and science in the media
. 32 Comments

Well… yikes! Remember my article on the New Yorker piece on the Fields Medal, the Poincare Conjecture, and the mathematicians Perelman and Yau? Remember that I said:

I cannot comment upon whether the hero of the story (Grigory Perelman) is as heroic as painted, or whether the villian of the piece (Shing-Tung Yau) is really as villainous. The anecdotes that are used to do the painting may well be able to be supplemented by other anecdotes that tell another story, as is sometimes the case. I simply don’t know.

Well, it seems that Yau is quite sure that it is not going to stop there. There was a letter sent to the New Yorker and the authors of the article (apparently) on his behalf by legal counsel. It is discussed and can be found on a web page under Yau’s name. The page is in the form of a press release, and I quote:
Continue reading ‘Yau Fights Back?’

Epic Struggles in Mathematics

by
Clifford
on September 9, 2006
in mathematics and science in the media
. 12 Comments

fields medal frontI have this problem: I don’t really have enough hours in each day. One of the symptoms of this problem is a huge pile of unread or partially read issues of the New Yorker. Sometimes I try to catch up. This catching up is incomplete, of course, and sometimes I miss articles of direct relevance to my field. Sometimes I miss them even when they are in an issue I skimmed through, promising to read later more thoroughly. This time, I missed the August 28th article called “Manifold Destiny” (by Sylvia Nasar and David Gruber), about the quest of some mathematicians to understand the Poincare conjecture. The subtitle of the article in the table of contents is “Who really solved the Poincare conjecture?”. The story starts out with a report on a talk at the Strings 2006 conference in Beijing.

[Update: After reading the below, do read this post about the letter (apparently from Yau’s lawyer) about the issue. His being painted in the role of villain may have been rather over the top, and the writers may have not behaved very well at all… so the word “masterpiece” I used below may well be totally wrong. I’m so glad that I wrote the cautionary remarks at the end now.]

As a piece of writing for the non-mathematician’s consumption, it is another New Yorker masterpiece. It is of course several pages long, and so there’s plenty of meat Continue reading ‘Epic Struggles in Mathematics’

The Science, Art, and Mathematics of Origami

by
Clifford
on September 9, 2006
in Los Angeles, art, mathematics, science and science education
. 4 Comments

origami dancing craneOne of my hobbies for a while when I was a young ‘un was origami. It was swiftly overtaken by other arts and crafts, and these were hobbies long before I started taking apart cameras and radios, and the like, to see how they worked, and collecting pondwater and pressing leaves and…

In retrospect, I think it might be obvious that (obstacles aside) I had a good chance of becoming a theoretical physicist. A lot of those arts and crafts hobbies were all about intricate patterns of one sort or another. I loved that stuff, although I did not think of it as mathematics… just a nice pattern. And I was drawn to playing with and creating those patterns. Some of them are amazing, as you know from staring at whatever your mum or grandmother is working on right now. Or perhaps you. I’ll tell you about more of that some other time. Let’s get back dancing crane pattern to origami. I stumbled upon (via NPR) an excellent website, that of Robert J. Lang. It is quite wonderful. The site tells you about Lang’s work, and shows you a ton of it. But the best thing of all is that it tells you about the Art, Science and Mathematics of it all together. The engineering applications of origami are growing as well. These include developing the best way of folding airbags for ready deployment, and the problem of how to fold up a giant array of solar panels on a spacecraft so that they can be successfully unfolded and put into use once the craft gets into space.

Imagine also the problem in a scientific context of how to design arrays of mirrors with Continue reading ‘The Science, Art, and Mathematics of Origami’