article post: "quants" and "math"

For the record, today I seem to have attended classes, a seminar, and a meeting, and have done no work yet. I was honestly expecting to do a quick e-mail check, and then get to work .. but evidently plans change. (;

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Through some digging just now, I found another article which deals with "mathematics" but I can't decide whether they actually mean statistics or applied mathematics. I suppose that for everyday life, the difference doesn't truly matter, but for those who care, it's a question of what you're doing with the data you're given.

I don't know. Here's the article; you can decide for yourself. But just to bias your reading, I found the following passage interesting:

How do you convert written words into math? Goldman says it takes a combination of algebra and geometry. Imagine an object floating in space that has an edge for every known scrap of information. It's called a polytope and it has near-infinite dimensions, almost impossible to conjure up in our earthbound minds. It contains every topic written about in the press. And every article that Inform processes becomes a single line within it.

Each line has a series of relationships. A single article on Bordeaux wine, for example, turns up in the polytope near France, agriculture, wine, even alcoholism. In each case, Inform's algorithm calculates the relevance of one article to the next by measuring the angle between the two lines.

It reminds me of sequence in infinite-dimensional spaces, and if they discuss a notion of angle, does it mean that they must use Hilbert spaces? Being a poor analyst, perhaps I can't be expected to know the intricacies of the real world, but if a boy can dream, then certainly a boy can guess .. q:

It also reminds me of this article a friend of mine (who studies library science and works as a sys.admin. for a college library) of this auto-indexing theory by Salton, Wong, and Yang; the idea is that one organises documents as vectors, where the entries are keywords. Now apply metric space theory, and you have a method of nonlinear sorting if linearity does not help.

A vector space model for automatic indexing (PDF available)

Anyways, that's their attempt at geometry. They also make some big claims, which I would rather they quantify .. but being reality and not mathematics, I may as well be asking for the moon, and maybe the rings of Saturn, while I'm at it .. \:

By the time you're reading these words, this very article will exist as a line in Goldman's polytope. And that raises a fundamental question: If long articles full of twists and turns can be reduced to a mathematical essence, what's next? Our businesses -- and, yes, ourselves.

.. This industrial metamorphosis also has a dark side. The power of mathematicians to make sense of personal data and to model the behavior of individuals will inevitably continue to erode privacy. Merchants will be in a position to track many of our most intimate purchases, and employers will be able to rank us not only by productivity, but by wasted minutes. What's more, the rise of math can contribute to a sense that individuals are powerless, a foreboding that mathematics, from our credit rating to our genomic map, spells out our destiny.

Wonderful. Shall we all become discretized and take our robot forms, now?

But just look at where the mathematicians are now. They're helping to map out advertising campaigns, they're changing the nature of research in newsrooms and in biology labs, and they're enabling marketers to forge new one-on-one relationships with customers. As this occurs, more of the economy falls into the realm of numbers. Says James R. Schatz, chief of the mathematics research group at the National Security Agency: "There has never been a better time to be a mathematician."

Whenever I see the words "mathematics" and "numbers" I cringe, because it probably means that I have to explain myself to more people about

1. why the mathematics I study contain very few numbers,
   
2. why what I do has no immediate practical applications,
   
3. or if my work does have such applications, then why I am not pursuing them ..
   

The world needs more lessons in when to use the words "mathematics," "applied mathematics," "mathematical modelling," and "statistics."

I would rant more, but that would head into careless opinions and my personal, illogical biases, so let me stop here. The article is actually quite long and makes the usual bold claims ..

.. and after all, I have work to do. Reading this article carefully can wait.