Tuesday, December 23, 2008

Selling what's rational

I had this chat with my friend "D" a few weeks back. (The carets represent exponentiation, naturally.)
(9:33:21 AM) Me: Hi. Did you know that 10^9999 is one tremilliatrecendotrigintillion? http://www.asthe.org/chongo/tech/math/number/tenpower.html
(9:35:17 AM) D: So who made up these names? It's not as if they came up in calculations frequently enough to need a name for them.
(9:35:38 AM) D: Avagadro's number is the biggest number that deserves a name.
(9:35:56 AM) Me: Well I've heard of the first few entries in the table.
(9:36:38 AM) Me: It's a cgi program, so it's all generated by algorithm. Look at 10^100
(9:38:16 AM) D: What does the column "prefix cardinal" mean?
(9:38:38 AM) Me: "determines letters before the illion" - hmm
(9:39:09 AM) D: Before the illion is a nice phrase.
(9:39:25 AM) Me: I guess when there's a 3, the name has tre or tri before the illion
(9:39:28 AM) D: Like Before the War, Before the Flood, Before the Fall.
(9:40:12 AM) Me: But 10^183 doesn't even have an illion, it ends in illiard
(9:40:30 AM) D: But 10^36 has 1 and 10 as the prefix cardinals. What does that mean?
(9:40:40 AM) Me: Oh, I'm looking at the European (or Eurpoean) system
(9:41:50 AM) Me: 1 => un, 10 => dec, thus undecillion
(9:42:43 AM) Me: I would have thought that 1 undecillion was smaller than one hundred decillion, but there you go.
The conversation then went on to other, unrelated topics, as is usually the case for us. But it set me to thinking: if they can have a star registry where you are invited to pay for a name for a star which nobody in the professional stargazing communities (whether astronomical or astrological) is ever going to use, why not have a number registry where you get to name your own positive integer with a name no mathematician would ever use. What a great idea, right?

Too late, someone already did it.

For example, imagine watching your favorite science fiction television show and hearing the starship's chief engineer shout, "Captain -- the heat from the supernova is too much for the shields! Twelve thousand degrees! Thirteen thousand! If it reaches Martin Allan Smythe, Jr. degrees, we’ll be destroyed!"
I had in mind a financial channel instead ("Unemployment is up last month to Carrie-Sue Delmonico, an increase of 14%"), but clearly my half-backed notion is far too close to this going concern and would have no chance against their first mover advantage.

But! Rational numbers (fractions, basically) are denumerable too, so one could with only a little extra effort come up with a registry for each of these as well, and they would have the advantage of having to do with something that virtually nobody understands anyway, even abroad. Exotic! And once you get past the so-called vulgar fractions ¼, ½, ¾ and a few of their relatives, you don't often encounter these in trade or commerce much any more, ever since the stock market went to decimals years ago, so some of the rules and restrictions that apply to the number registry would really not be missed. The lucky person forking over their cash for their own rational number would receive a booklet written by a professional mathematician, a wallet card, and a certificate suitable for framing.

I looked and did not see anyone else having come up with this scam concept and brought it to market. But my fallback position should such a case come to light would be to take advantage of the denumerability of algebraic numbers, so as to entice people to immortalize their loved ones forever by rechristening quantities like -3+3√43 and so forth.

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