On Jul 11, 2013, at 12:16 PM, Joe Niederberger <firstname.lastname@example.org> wrote:
> I can reason about it, visually.
Everything else you wrote I agree with, except this line. We both agree that we reason, and I think we both agree that if there is no reasoning then it isn't mathematical.
But then you say that you reason visually.
And then I ask "Really? What's that like?"
You say "It's super duper trooper."
I say "No. I mean how does it work?"
You say "log(x)"
I say "Huh?"
You say "The graph of log(x) proves that e^pi > pi^e?"
Renfro says "Huh?"
I say "You mean like this, with rectangle's and such?"
You say "No, dumb ass! If you use algebra to reduce the expression to logarithms and then use calculus to take the derivatives of that and understand that this is the slope of the tangent that touches the graph here, here and there, then it becomes intuitively obvious that e^pi > pi^e"
I say "Oh! So you mean reasoning applied to a visualization, not visual reasoning."
You say "No! I mean visual reasoning."
I say "Can you somehow differentiate that from just reasoning?"