Nyarly's Journal: Philosophy of Mathematics

(Once again, the topic isn't right, but Slashdot lacks a Pointless Pedantry topic. Probably with good reason.)

Is there any existing mathematical system, I ask myself and my friends, which includes the idea of the empty slate? Not the null set, or zero, but that to which every symbol is added, the place where the signified interacts.

By analogy, if I were writing a really good calculator, I'd probably write (or integrate) a parse tree with the various operators and constants and whatnot. There would be, one way or another, an entity to represent addition, which would be created and added into the tree whenever the symbol + was encountered. Once an expression was parsed, I'd have an internal representation that I could operate on. In OO, I'd most likely use some version of the Composition and Visitor patterns to be able to simplify or integrate or whatnot. And on some level, the objects exist in a memory space, and their signifiers exist on a command line. In many languages, I'd be able to refer to both the memory space (or even all memory) and to the terminal (or the abstration of a CLI.)

But in my undergraduate nickle tour of mathematics, I can't recall any case in which it was possible to refer to either the empty page, or to whatever metaphorical place in which the ideas of addition and the unit and equality could composite into something like "1+1 = 2."

Is there any point to being able to make such a reference?

Depends

[Planesdragon]

Is there any point to being able to make such a reference?

Mathematically or computationally?

For making the calculator, I assume that it'd be relevant--but not for the underlying mathematics.

You might as well say "how do I give directions to a nonexistant space?" Mathematics is a logical language that describes Things, and mathematics has no reason to refer to things that are not Things.

Re:Depends

[Nyarly]

Computational, it would probably be relevant - if I wanted the calculator to be efficient. The the computation example was mostly by way of analogy. I don't really care about the computational case.

Isn't no-place a concept, and thus a Thing? Can't I draw the analogy of "arithmetic deals with numbers - none isn't a number, so what good is this zero thing?" (Or as a grade school teacher once told me "White isn't a color.")

Zero matters, right? Why not the empty expression?

Re:Depends

[Planesdragon]

Isn't no-place a concept, and thus a Thing? Can't I draw the analogy of "arithmetic deals with numbers - none isn't a number, so what good is this zero thing?" (Or as a grade school teacher once told me "White isn't a color.")

Zero matters, right? Why not the empty expression?

Zero is the "empty expression." If you have no Things and are owed no Things, you have 0 Things.

If you don't know how many things you have, you have a variable.

Oh, and your grade school teacher was blowing smoke and should be sma

Your post made my head hurt.

[ellem]

And now I'm sure that either God doesn't exist or a Flat Tax is impossible, but I'm not really sure which.

Thanks.