Saturday, February 25, 2012

Fee, fi, foe, fum

I found myself wondering about the correct pronunciation of the Greek letter φ (phi). Somehow, I acquired the habit of saying "fee." But it turns out that mathematicians say "fi" as in "fly."

It seems that in Greek, the first pronunciation is correct. However, if we were to follow that route, we'd have to pronounce π as "pee," and that just feels wrong.

A more common question is about "data." See howjsay. I pronounce data like "date-uh." I have a memory of this being drummed into me in Latin class. Perhaps we should just "say it like the Romans did," but see the above for one problem with that approach. Anyone know an authoritative source?

Wednesday, February 22, 2012

One year, one world

Yesterday was the one-year anniversary of the flag counter widget. We have 144 countries, including a new one: Cote D'Ivoire. It makes me very happy to see all these ≈25K (unique) visitors, even if I don't know that much about them.

From Google's stats, it looks like most people are interested in maybe 25-30 pages. I think there is more good stuff buried here, so perhaps I'll make a post about my favorites one of these days. What I'd love to see, is data that showed a person arriving and then poking around for a while. Sometimes you see a hint of this, but the stats really don't tell that much.

Anyway, thanks for reading! And don't forget to check out the Python book.

And, I'm still waiting for Tonga.

Wednesday, February 15, 2012

R.W. Hamming

I received a new book in the mail today. I'm a huge fan of Richard Hamming (e.g. this), and the book is everything I hoped for.

I thought I would just post a quote (from him, not one of the many interesting quotes he includes):

The taste to work on the right problem at the right time and in the right way is the secret of doing significant things.

To focus on just one aspect: what you are trying to do must be doable. Timing is (almost) everything.

Sunday, February 12, 2012


I found a nice tutorial on SVD (Singular Value Decomposition). I love the intro:

Most tutorials on complex topics are apparently written by very smart people whose goal is to use as little space as possible and who assume that their readers already know almost as much as the author does. This tutorial’s not like that. It’s more a manifestivus for the rest of us. It’s about the mechanics of singular value decomposition, especially as it relates to some techniques in natural language processing. It’s written by someone who knew zilch about singular value decomposition or any of the underlying math before he started writing it, and knows barely more than that now. Accordingly, it’s a bit long on the background part, and a bit short on the truly explanatory part, but hopefully it contains all the information necessary for someone who’s never heard of singular value decomposition before to be able to do it.

An excellent place to start. And check out the animation at wikipedia.

Saturday, February 11, 2012

MathDoctorBob and Fibonacci

I ran into an interesting page which purported to be about various ways of looking at (or deriving) the trigonometric identity

sin2 + cos2 = 1

but the site has lots of stuff including the trail I'm following here, which involves the Fibonacci numbers. Strang derives the Binet formula for the nth Fibonacci number, Fn, using linear algebra:

Fn = 1/√5 [φ1n - φ2n]

where φ1 is the golden mean or golden ratio, and

φ1 + φ2 = 1

The approach is very nice, because it uses the eigenvalues and eigenvectors of the matrix

[ 1 1 ]
[ 1 0 ]

which involves solving λ2 - λ -1 = 0, whose solutions are φ1 and φ2. That is, φ1 and φ2 are eigenvalues of that matrix.

However, I got lost in the middle of Strang's version (in the book), and cast about for another explanation. I found a great one here.

This video turns out to be one of a large number by MathDoctorBob. I am very impressed with the quality of these videos, based on the first half-dozen or so that I've looked at.

Finally, back at the first site, we use two limits (as n => ∞):

φ1n => ∞
φ2n = (1 - φ1)n => 0

and the Binet formula to get a limit for the ratio with large n:

Fn+1 / Fn = φ