Monday, August 24, 2009

The Count Ends at Three

My long-suffering readers might be justifiably concerned that the Radioactive brand is proliferating out of control. If so, rest assured, this third blog RadioactiveUniverse is my absolute final one. And I can even prove it mathematically.

Speaking of math class, as I often did to those suffering in the audience of my newstalk radio broadcasts, algebra was repository of many of my favorite scholastic memories. Perhaps my most inspiring moment ever in my mathematical education came, as they so often did, courtesy my all-time fave teacher in any subject, Mr. J. Harold Vaughn.
Now mind you, only about half of my math education ever took place in class; the rest came on my own via lay books which popularized the concepts which animate advanced realms like topology, nonEuclidian geometry, number theory, set theory and the calculus. But it was in Algebra II when I learned that—just as you above were surely relieved to find will be no more additional Radioactive blogs—there would be never be a need for more types of numbers beyond the so-called complex numbers.

You see, as Mr. Vaughn explained, primitive man needed only the positive integers to count his livestock, or wives, or enemies. Then commerce created a need for negative numbers—in the red to a patient neighbor for a certain number of whatever the barter currency of the day was. So they invented negative integers.

And by that point, the divvying up of certain commodities necessitated the invention of fractions. And eventually, problems like the length of diagonals of geometric figures mandated the invention of irrationals. And many of us also know of the centuries-long struggle to invent zero. And thus we had invented all the real numbers. And then when the need came along during The Enlightenment to solve equations like x times x = -1, my hero Euler invented the imaginary numbers, but, like so many 21st Century software engineers, failed to dub them with an intuitive name. So math students to this day are confused by these nominally "imaginary" numbers, when in fact they are no more or less imaginary than any of those invented prior to them.

But this process was starting to scare me. What if the further I went in math, the more types of exotic number systems they'd keep inventing and for me to increasingly struggle to understand? How could I ever sort it all out?

But as he so often did, Mr. Vaughn set my mathematical mind at permanent ease. For it turns out the Fundamental Theorem of Algebra, proved by Euler himself and many others, forever limits the need to invent new systems! This, on top of my favorite theorem's most elegant charm—that any nth degree equation has precisely n complex roots—meant the complex numbers limits forever the array of fields mathematicians must till. That is, no matter how exotic a mathematical realm you dream up, the complex numbers will be able to computationally describe it.

Likewise, my initial blog (RadioactiveSeattle, regarding the commercial newstalk radio biz) in 2007, my second blog (Radioactive Dylan, regarding Dylanology, an utterly fascinating and esoteric realm, but not for the faint-of-heart) earlier this year, and now RadioactiveUniverse, whose domain is everything else. So this third blog is, for better or for worse, it. And I intend to make it for better.

And of course, you can make it better too, with your constructive—or just vindictive—posted comments hereto. Feel free to point out typos even, if you like.


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