Happenings – 2011 Oct 29

OK, I’ve returned from vacation. It was good.

I haven’t touched a math book in almost two weeks, and I’m having a little trouble picking them up again. And I haven’t really seen much worth talking about today.

The good news last Saturday was that the world didn’t end on October 21 – except that it wasn’t really news, since the overwheleming majority of people didn’t expect it to. (You might – just might – recall that the man who predicted the end of the world back in May changed his prediction to Oct 21.)

While we’re looking back to May – that’s a link to my blog, and the link that follows is a recent summary – the trial is underway of those seismologists who, apparently, didn’t protest when someone summarized a meeting by saying, “We’ve reviewed the recent seismic activity here, and there’s no danger of a serious earthquake.” They’re not actually on trial for failing to predict one… and not even for saying there wouldn’t be one… but for not speaking out when someone else at the meeting publicly misrepresented their conclusions – or misunderstood them.

And that’s all for today.

Happenings – 2011 Oct 19

Well, I’m on vacation this week and next.

I had thought I would get out a technical post last Monday, but life had other ideas. I never had any hope of putting one out next Monday, and that’s still true.

I had been, however, working on three different possibilities, and I hope that one of them will be ready for Halloween.

For each of the three, I’m in the same position: I could put out a post – but there’s something more I want to figure out, even though I don’t need to understand it for the post itself.

One of the three is to construct the final tableau of a linear programming problem. Oh, yes, Mathematica® will do a fine job of solving the problem – but the final tableau contains additional information. Whether you’re trying to follow along in a text, or whether you want to do sensitivity analysis, the final tableau is a very handy thing to have.

Happenings – 2011 Oct 15

Let me finish off the story of that busy week a few weeks ago.

One of the 5 books that arrived that week was “An Introduction to the Langlands Program”, ISBN 9780817632113. (I may refer to it in this post as “the book”.) The First 8 chapters were written by one of its 6 authors… and his writing style was interesting. But let me cut to the chase. From the editors’ preface – yes, plural, there were 2 editors. (That says something about the complexity of the topic: 2 editors and 6 authors for just under 300 pages of math.)

“The Langlands program roughly states that, among other things, any L-function defined number-theoretically is the same as the one which can be defined as the automorphic L-function of some GL(n).”

That’s probably not exactly clear, is it? It certainly isn’t to me. (I can’t say it’s Greek to me… I’ve had a couple of years of classical Greek.)

Anyway, having skimmed the First 8 chapters and then some on a Friday evening, I went searching the Internet Saturday morning when I should have been drafting a happenings post. I found some very surprising links.

Andrews Curves

introduction

A long time ago, in a post about PCA (principal component analysis), I said that I did not know what Andrews curves were. (The suggestion was made that Andrews curves might help us decide how many principal components to keep. I did not understand how they were to be computed.)

Now I know. Let me show you. I will compute Andrews curves for what is called “the iris data”… for both the full data set (150 observations) and a reduced data set (30 observations). I will also show you a possible variant.

In addition, we will know that there are in fact three kinds of irises in the data – so we can assess how well the Andrews curves did. In practive, of course, we will be trying to figure out how many kinds of observations we have.

The data is here. The paper which explained Andrews curves to me is here. Andrews original paper is: Andrews D. Plots of high-dimensional data Biometrics 1972 28:125-136… but I haven’t found it freely available anywhere online.

In addition, there is a short and sweet webpage by one of the authors of the paper I read.

Happenings – 2011 Oct 1

As I was saying last week, more things happened than I cared to put into one post.

Five books arrived during the week before last Saturday’s diary post.

Two of them are new books by T.W. Körner: “Naïve Decision Making: mathematics applied to the social world”, and “the Pleasures of Counting”. He is also the author of two other spectacularly good books: “Fourier Analysis” and “a Companion to Analysis: a second first and first second course in analysis”.

I first encountered his “Fourier Analysis”. He begins the introduction, “This book is meant neither as a drill book for the successful nor as a life belt for the unsuccessful student. Rather, it is intended as a shop window for some of the ideas, techniques and elegant results of Fourier analysis.”

It is a wide-ranging book. In particular, he reviews the work of Sir Cyril Burt, knighted for his work in psychology. It has been suggested that not only did he fabricate data, but that he even fabricated co-authors for papers. On the other hand, one of his defenders has said, “I think it is a crime to cast such doubt over a man’s career.”