I couldn’t believe my eyes. I was watching an episode of numb3rs, ‘undercurrents’ to be precise, and there it was, circled in the middle of the blackboard, CEILIDH, together with some of the key-exchange maps around it…

Only, the plot doesn’t involve any tori-crypto… okay, there is an I-Ching-coded-tattoo which turns out to be a telephone number, but that’s all. Still, this couldn’t just be a coincidence. Googling for ‘ ceilidh+numbers‘ gives as top hit the pdf-file of an article Alice in NUMB3Rland written by … Alice Silverberg (of the Rubin-Silverberg paper starting tori-cryptography). Alice turns out to be one of the unpaid consultants to the series. The 2-page article gives some insight into how ’some math’ gets into the script

Typically, Andy emails a draft of the script to the consultants. The FBI plot is already in place, and the writers want mathematics to go with it. The placeholder “math” in the draft is often nonsense or jargon; the sort of things people with no mathematical background might find by Googling, and think was real math. Since there’s often no mathematics that makes sense in those parts of the script, the best the consultants can do is replace jargon that makes us cringe a lot with jargon that makes us cringe a little.
From then on, it’s the Telephone Game. The consultants email Andy our suggestions (”replace ‘our discrete universes’ with ‘our disjoint universes’”; “replace the nonsensical ‘we’ve tried everything -a full frequency analysis, a Vignere deconstruction- we even checked for a Lucas sequence’ with the slightly less nonsensical ‘It’s much too short to try any cryptanalysis on. If it were longer we could try frequency analyses, or try to guess what kind of cryptosystem it is and use a specialized technique. For example, if it were a long enough Vigenere cipher we could try a Kasiski test or an index-of-coincidence analysis’). Andy chooses about a quarter of my sugges- tions and forwards his interpretation of them to the writers and producers. The script gets changed, and then the actors ad lib something completely dif- ferent (’disjointed universes’: cute, but loses the mathematical allusion; ‘Kasiski exam’ : I didn’t mean that kind of ‘test’).

She ends her article with :

I have mixed feelings about NUMB3RS. I still have concerns about the violence, the depiction of women, and the pretense that the math is accurate. However, if NUMB3RS could interest people in the power of mathematics enough for society to greater value and support mathematics teaching, learning, and research, and motivate more students to learnthat would be a positive step.

Further, there is a whole blog dedicated to some of the maths featuring in NUMB3RS, the numb3rs blog. And it was the first time I had to take a screenshot of a DVD, something usually off limits to the grab.app, but there is a simple hack to do it…

Mark J. Penn wrote Microtrends: The Small Forces Changing the World. He argues that the most important trends in the world today are the smallest ones. Such as… declining standards in math education!

What should you do on the educational front if you have a child with an aptitude for numbers, as mine does? Both of you had better get cracking, because American college students are studying less math. As an example, “Microtrends” says Harvard has only 77 math majors out of 6,700 undergraduate students.
The math story is different in China and India, which are graduating as many as 950,000 engineers a year. Granted, both nations are far more populous than the United States, but that is a lot of engineers.
Mr. Penn notes that a 2001 bipartisan commission “said that the greatest threat to American national security - behind only terrorist attacks - was the threat of failing to provide sufficient math and science education in America.”

I haven’t read the book yet but it’s high on my wish-list after reading the NYT-article Why There’s Strength in Small Numbers and the Introduction of the book.

Hey, here’s an idea : The Text-Math Book! Trying to promote mathematics while at the same time acknowledging the fairly limited attention-span of the intended generation, let’s try to write a book on serious maths following just one rule

EVERY DEFINITION, THEOREM AND PROOF IN THE BOOK SHOULD NOT BE LONGER THAN A TEXT-MESSAGE (ie. 160 chars)

I don’t even own a cell phone¹, so PLEASE educate me youngsters! SMS your contribution, either as a comment left here or hosted at your own blog (please link, so that I can learn…, a full text explanation of abbreviations used will be applauded.)

1. waiting for the iPhone to arrive in Belgium [↩]

A first year-first semester course on group theory has its hilarious moments. Whereas they can relate the two other pure math courses (linear algebra and analysis) somewhat to what they’ve learned before, with group theory they appear to enter an entirely new and strange world. So, it is best to give them concrete examples : symmetry groups of regular polygons and Platonic solids, the symmetric group etc. One of the lesser traditional examples I like to give is Nim addition and its relation to combinatorial games.

For their first test they had (among other things) to find a winning move for the position below in the Lenstra’s turtle turning game. At each move a player must put one turtle on its back and may also turn over any single turtle to the left of it. This second turtle, unlike the first, may be turned either onto its feet or onto its back. The player wins who turns the last turtle upside-down.

So, all they needed to see was that one turtle on its feet at place n is equivalent to a Nim-heap of height n and use the fact that all elements have order two to show that any zero-move in the sum game can indeed be played by using the second-turtle alternative.¹

A week later, one of the girls asked at the start of the lecture :

Are there real-life applications of group-theory? I mean, my father asked me what I was learning at school and I told him we were playing games turning turtles. I have to say that he was not impressed at all!.

She may have had an hidden agenda to slow me down because I spend an hour talking about a lot of things ranging from codes to cryptography and from representations to elementary particles…

For test three (on group-actions) I asked them to prove (among other things) Wilson’s theorem that is

for any prime number . The hint being : take the trivial action of on a one-element set and use the orbit theorem. (they know the number of elements in an -conjugacy class)

Fingers crossed, hopefully daddy approved…

1. for the curious : the answer is turning both 9 and 4 on their back [↩]

Here a list of pdf-files of NeverEndingBooks-posts on general topics, in reverse chronological order.

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