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On salad numbers

Vel! August 18, 2012 User blog:Vel!

Have a look at this googologism. Basically, it's a bunch of existing googologisms pasted together with addition, multiplication, and exponentiation, with a factorial here and there. (The number comes from Urban Dictionary, which is mostly adolescent males turning themselves on by posting made-up words with obscene meanings.)

Here's a similar number from this wiki, created by an IP. I deleted the page due to lack of sources, but I couldn't stop laughing while doing so:

Permanentillion is equal to Grandmasteilliun with {LLL...LLL (One Housillion L's) (Meameamealokkapuwwa)}999,999 + E99#Batillion + 1987654321987654321987654321E+999...999 (59 9's) - 0.3333333333333333333333333333333333333333333333334 (One Retiring Third) x 2.718281828 (Euler Number) + Googolsuperplex (E1#15) + Googolhyperplex (E1#22) + Googolduperplex (E1#17) + 999...999 (20 Grandmasteillion 9's, Twenteen 9's) + Infinity Infinities.

Both of these numbers are humorous attempts at defining original googologisms. I've been seeing these kinds of numbers more and more frequently with budding googologists; sometimes they're half serious. If you're a new googologist, keep in mind that such numbers aren't very helpful contributions to the field: the definitions are inelegant (they have no consistency or mathematical significance) and they violate the Gentleman's Rule of large number duels. I call these numbers salad numbers — they're just a bunch of existing googologisms tossed together.

In my voyages across the Web researching large numbers, I concluded that googology is divided into two groups: syntactic and abstract googology. Syntactic googologists use creative wordplay to forge names and naming systems for large numbers (such as Andre Joyce's googo- and googolple- systems). Abstract googologists generate the largest numbers with the simplest tools (such as arrow notation). Syntacticism is whimsical and artistic; abstractism is precise and mathematical.

Despite their differences, a large part of both branches is elegance. Andre Joyce's extensions to the SI prefixes (xova-, weica-, vunda-, etc.) follow a clever "Italian forwards, alphabet backwards" pattern. BEAF generates some of the largest numbers known to googology with just three rules defining a primitive-recursive function — a definition that seems to come naturally out of the beauty of mathematics. In contrast, numbers such as googolception and permanentillion are clumsily defined; they possess no rules or consistency. ("Oooh — while we're at it, let's add a bongulus here.")

(to be continued)

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