Category Archives: mathematics

Categorically Not! – Ambiguity

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The next Categorically Not! is on Sunday June 8th. 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 Ambiguity. Here’s the description from K C Cole:

Nature loves ambiguity, even if human nature doesn’t. What exactly is a species? Where exactly is that subatomic particle? When did life begin? How do genes influence behavior? Why does music move us? What does that poem mean? What color is white? Is that guy flirting with me, or not? The answers are often far more indeterminate than we’d like to think. Heck, we still don’t know why the chicken crossed the road. Or what the meaning of is is.

Speakers at Categorically Not! - June 8th 2008

Bart Kosko, USC Professor of Engineering, attorney and author of best-selling books Fuzzy Thinking, Noise, and Heaven in a Chip will tell us how fuzzy math

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Categorically Not! – Puzzles!

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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 […] Click to continue reading this post →

Beyond Einstein: Fixing Singularities in Spacetime

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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

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A Delicious Fractal

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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 […] Click to continue reading this post →

Möbius Transformations

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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 […] Click to continue reading this post →

Inside Out from the Inside

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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. sandy blakesleeIt’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 […] Click to continue reading this post →

Inside Out

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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. […] Click to continue reading this post →

Categorically Not! – Inside Out

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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: […] Click to continue reading this post →

…And He Got Einstein’s Office!

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[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 … Click to continue reading this post →

Not Following the Script

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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 […] Click to continue reading this post →

Reading, Writing, and ’Rithmetic

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Yesterday (depending upon who’s counting) was 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 […] Click to continue reading this post →

Showing a Different Way

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danica mckellar from and AP articleDanica McKellar (the actress who played the girl “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 site, 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: Much 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 […] Click to continue reading this post →

E8

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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 […] Click to continue reading this post →