But then I found out about computers. On the first day of 6.001 the professor wrote this on the board:

f(x + dx) - f(x) f'(x) = lim ------------------ dx->0 dx (define dx 0.0001) (define (deriv f) (define (f-prime x) (/ (- (f (+ x dx)) (f x)) dx)) f-prime) (define (cube x) (* x x x)) (define g (deriv cube)) (g 4) ;Value: 48.00120000993502It was the beginning of the end.

I started to unlearn math. I began seeing math through the eyes of a computer scientist. Things that I believed in stopped making sense. I used to believe that integration and differentiation were opposites: that one ‘undid’ what the other ‘did’. But look:

(define (deriv f) ...) (define (integrate f low hi) ...)The arity of

`deriv`

is 1 and the arity of
`integrate`

is 3. They *can't*be opposites!

I used to think you couldn't divide by zero. But look:

(/ 2.3 0.0) ;Value: #[+inf]

I started seeing ambiguities in even the simplest math. Is ‘x + 3’ an expression, a function, or a number? Is ‘f(x)’ a function or the value of a function at x? When I see log (f(x)) = dH(u)/du + y, are they stating an identity, do they want a solution for y, or are they defining H?

I started reading weird things like Gosper's Acceleration of Series and Denotational Semantics by Joseph Stoy and Henry Baker's Archive. These

*look*like math, but they seemed to make more sense to me.

But I drifted further away from mathematics. A few years ago a fellow computer scientist explained to me the wedge product. It is a straightforward abstraction of multiplication with the only exception being that you are not permitted to ‘combine like terms’ after you multiply (so you get a lot of irreducable terms). Then he explained the Hodge-* operator as the thing that permits you to combine the like terms and get answers. It's really not very complicated.

But then I looked it up online.

The exterior algebra ∧(V) over a vector space V is defined as the quotient algebra of the tensor algebra by the two-sided ideal I generated by all elements of the form x⊗x such that x ∈ V.And I discovered that I'm now a math idiot.

I'm probably going to have to live like this the rest of my life. I'm trying to cope by relearning what I used to know but translating it to a style I'm more comfortable with. It will be a long process, but I'm optimistic.