The Magical Mathematics of Numb3rs
math-blog.com
math-blog.com
This is the only bit I disagree with. Math is his life.
Baseball fans know an amazing array of statistics about ALL major baseball teams. They can quote all kinds of crazy things.
Epps does the same thing, but with mathematical theories. It doesn't surprise me a bit for a single person to know about all those techniques.
Successfully implementing a given one within 24 consecutive hours is another story altogether. But that's already addressed.
Knowing of something is very different from properly understanding it to the extent of being able to contribute meaningfully with it. The difference between data and knowledge. The amount of information out there is growing exponentially. The amount that needs to be known before you can contribute keeps exploding with each generation. Such that the practitioner might know just as much if not more than their predecessors but the scope of their knowledge as a fraction of the full body is many orders of magnitude smaller.
It is not just a matter of will but of physics of time and the chemistry of the brain. Underutilized connections fade such that unless you spent time actively practising the wide skill sets to sufficient depth they will fade. But there is not enough time to be able to do that.
I do think that more must be done in enabling bridges as a counter to this. It is a shame category theorist must wrap their material in such obtuse language as it seems that it would be just the tool for the job.
I think people don't understand how broad a field mathematics itself is. In graduate school, one will gain a broad knowledge of one particular subfield (e.g. algebra, analysis, topology/geometry, or discrete math, for instance), a very deep knowledge of a particular subject within that subfield (e.g. sheaves of smooth functions on manifolds), and become the world's leading expert on a particular subject (the dissertation). Along the way, one will certainly pick up at least a couple of courses in perhaps 2 or 3 other major subfields sufficient to pass the comprehensive exams set by the department, but that's it.
So, a mathematician graduates knowing a lot about very little compared to the whole of mathematics. Over the course of an entire career, one will usually pick up bits and pieces that were neglected in grad school, and perhaps enough knowledge to contribute in maybe one or two additional subfields.
This, of course, is how it works for an average mathematician -- the average Joe or Jane who makes it through grad school. Superior mathematicians might contribute more broadly (Erdos comes to mind), but they're sufficiently rare that we can practically discount them. Charlie Epps goes beyond this because dramatic license allows (indeed, practically requires) him to.
It's not just another illusion we have conjured to make sense of our perceptions, to organize them?
In some respects, that's like expecting someone whose "life is languages" to be able to speak every language on the planet fluently. Math is definitely a coherent whole with the different subfields like algebra and analysis being a part of it but, at the same time, there are enough differences between them and enough depth in each that we're not going to see anyone remotely close to the level at which Eppes is portrayed.
Likewise, a linguist would know the differences between languages without actually being able to speak all the languages in the world. If a relatively-unknown language had a special property that no other language did, I'd expect serious linguists to know that. Eventually, anyhow.
* Time frame for both gathering data and performing analysis
* The incredible depth and breadth of Charlie's knowledge
To enjoy the show, you simply have to think of Charlie as a superhero and suspend your disbelief as if you were watching Spiderman or Superman.
However, the author spends a good chunk of the post attempting to persuade readers that Numb3rs can be thought of as a propaganda vehicle for persuading the masses that a math-based surveillance society is good and necessary. I disagree.
First, there are several episodes featuring poor ethics at the FBI, NSA, prison officials, etc. which sometimes includes manipulating surveillance information (i.e. 216 Protest, 310 Brutus, 313 Finder's Keepers, 608 Ultimatum).
Second, one of the great appeals of the show in general is intense exploration of ethics, with the father and two sons of the Epps family frequently challenging each other and themselves.
Third, and perhaps most importantly, this show appeals to geeks (most people I know who love this show are math/engineer/computer enthusiasts or close to it). You don't get into the hearts and minds of the populace at large by doing virtuoso math demonstrations tied with intense discussions of ethics.
Though I disagree with the propaganda angle (and the off-hand comments about how Numb3rs-type thinking is partly responsible for the house boom and bust), I think it was a great, thought-provoking post, which did a good job of listing out the elements of numbers which stretch the bounds of credulity.
EDIT: typos, inserted specific show names