Happenings – 2011 Nov 5

This weekend – for large values of “weekend”, namely 4 days – I have a friend staying with me. I’m not really on vacation anymore – but he is.

I have made progress on regression. I now know how to completely eliminate multicollinearity from a data set – but I will not have time to write this up this weekend. In other words, expect no technical post this coming Monday. Still, I have the material for one.

My visitor pointed out that wired.com has another list of 9 essentials for geeks: 9 Equations True Geeks Should (at Least Pretend to) Know.

If nothing else, this is worth looking at for all of the comments from readers that followed.

Generally speaking, if I were to propose such a list, I would focus more on relationships than on single equations. Let me give you a few examples… although I will omit almost all of the details.

Some people suggested that the quadratic formula should be on that list. Yes… and no.

No, because the quadratic formula is high school mathematics – too elementary to be geeky. Yes, because a math geek should know that there are similar formulas for cubic and quartic polynomials – and should know that there are not, and never can be, similar formulas for polynomials of degree 5 or higher.

A formula which made the list – although I write it in a different form – is

e^{-i \pi} +1 = 0\ .

It contains 1… how droll… but it also contains 0, which the Greeks and Romans did not have… it contains not one but 2 transcendental numbers, e and pi… it contains a negative number… and the imaginary unit i.

Nevertheless, a math geek would know that that was a special case of

e^{i \theta} = cos\ \theta + i\ sin\ \theta\ .

People suggested that Maxwell’s equations for electromagnetism should have been included. Yes, but… a true math geek would know that Maxwell added the displacement current – without it, the equations are not consistent. That is, a summary of the experimental knowledge before Maxwell leads to inconsistent equations; he added a term to make them consistent.

Along the same lines, I think a math geek should know the singular value decomposition – not for its own sake, but because it generalizes to rectangular matrices the eigendecomposition of a square matrix. After all, every science or engineering major has seen eigenvalues and eigenvectors (okay, perhaps for small values of “every”) – but a math geek would know that the generalization to rectangular matrices exists.

And with that, I’m off to breakfast with my friend.

Posted in diary. 1 Comment »

One Response to “Happenings – 2011 Nov 5”

  1. probability formulas Says:

    Great to know that.You are doing good job by sharing it.

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