The Norse Gods and the Calculus

The Wrath of the Norse Gods,
originally uploaded by Stuck in Customs.

Compare and contrast

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.

Synaesthetic dessert

Cuisenaire rods,
originally uploaded by your neighborhood librarian.

One is white, two bright red, three lime-green and so on. When I first heard about the synaesthetic association between numerals and colors, something like this came to mind, but it wasn't until later that I could identify the source: Cuisenaire rods. How like a perfectly-trimmed carrot stick the mighty orange Ten looked! The succulent purple grape color of the Four!

I think it might be a nice idea for a primary-school teacher's going-away party to make edible Cuisenaire rods out of agar, fruit juice, and appropriate coloring. Arrange the rods to illustrate mathematical problems, but be prepared for the guests to play with their food afterward.
Has someone already done this? I would like to see how it turned out.

Axiomatic Mexican platter theory, with Elvis

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Combo Platter,
originally uploaded by egseah.

At Marginal Revolution there is a post up about the phenomenon of random combination platters at Tex-Mex restaurants. It does seem as if as if this is more characteristic of those sorts of restaurants than those of other types.

Rather than the economic perspective they adopt, I prefer to think of it from a mathematical point of view. Consider S, the set of all n individual dishes they sell on the menu. The maximum variety of combination platters which could be assembled from these is the set of all subsets of S, known as the power set of S, P(S) and has 2ⁿ elements, ranging from an order of no dishes at all ("I'll just have a coffee, thanks.") to one comprising all the dishes at once ("One of each, please.")

Thus a restaurant with five house specialties could post an exhaustive menu of platter combinations thereof:

{}, {chile rellenos}, {elvis green chile fried chicken}, {chile rellenos,elvis green chile fried chicken}, {chicken flautas}, {chile rellenos,chicken flautas}, {elvis green chile fried chicken,chicken flautas}, {chile rellenos,elvis green chile fried chicken,chicken flautas}, {chuychanga}, {chile rellenos,chuychanga}, {elvis green chile fried chicken,chuychanga}, {chile rellenos,elvis green chile fried chicken,chuychanga}, {chicken flautas,chuychanga}, {chile rellenos,chicken flautas,chuychanga}, {elvis green chile fried chicken,chicken flautas,chuychanga}, {chile rellenos,elvis green chile fried chicken,chicken flautas,chuychanga}, {steak burrito}, {chile rellenos,steak burrito}, {elvis green chile fried chicken,steak burrito}, {chile rellenos,elvis green chile fried chicken,steak burrito}, {chicken flautas,steak burrito}, {chile rellenos,chicken flautas,steak burrito}, {elvis green chile fried chicken,chicken flautas,steak burrito}, {chile rellenos,elvis green chile fried chicken,chicken flautas,steak burrito}, {chuychanga,steak burrito}, {chile rellenos,chuychanga,steak burrito}, {elvis green chile fried chicken,chuychanga,steak burrito}, {chile rellenos,elvis green chile fried chicken,chuychanga,steak burrito}, {chicken flautas,chuychanga,steak burrito}, {chile rellenos,chicken flautas,chuychanga,steak burrito}, {elvis green chile fried chicken,chicken flautas,chuychanga,steak burrito}, {chile rellenos,elvis green chile fried chicken,chicken flautas,chuychanga,steak burrito}

Fudging the prices somewhat would make it just about impossible for one to tell easily what the best deal for the money would be.

Having made it through the entree, one could then work one's way through the combinations of the 31 flavors of ice cream offered.

Fun with negative numbers

This is a screenshot of part of my browser today after I'd clicked on a message in Yahoo Mail. I am eagerly waiting to see whether when I get a new email, that will bump the total up to "0 unread."


More useful would be to have the Spam folder total reported as an imaginary number.