I just finished reading a book called Is God A Mathematician? by Mario Livio. (I'll be reviewing it for the A.V. Club soon.) It's an entertaining historical guide to the debate between formalists -- those who believe mathematics is a human construct that we apply to the world -- and realists -- those who consider math the inherent language of nature itself.
It's hard not to think of Archer while exploring both sides of this debate. This morning Archer was talking about words that don't count in Scrabble, and Noel commented that some proper nouns are also words in the dictionary -- like "archer." Archer immediately jumped in: "Yeah, and Archer scores 1 -- 2 -- 5 -- 9 -- 11 points." It's a source of endless delight to him that almost everything he encounters can be associated with a number or equation.
I asked Archer this past week, after a similar conversation, whether it made him happy that the world comes equipped with numbers, and he assented with his usual, "Oh, yeah." In some ways I thank my lucky stars that Archer is growing up in a world where so many numbers are already assigned to its features -- highways, temperatures, addresses, library books, schedules, sports. Time and space are mapped onto Cartesian coordinates, and everything you consider can be delineated by an integer, and those integers can be manipulated and explored in innumerable ways.
In another time or place, he might have had to assign his own numbers to the elements of his environment. Or maybe there would not have been enough enumeration in his culture to allow his fixation on mathematics to bloom and grow. Whether the numerical nature of the world is discovered or invented, it exists for him, and it's allowed him to be who he is. And I wouldn't have it any other way.