On Jun 19, 2013, at 9:04 AM, Joe Niederberger <email@example.com> wrote:
> I'd invite you or others who don't "see it" to ponder a little more. I don't offer this as a "proof without words" that is utterly obvious. It takes, as you would agree, just a few more "ingredients" to tease the meaning out of it. And then you might have a mini-ah ha! Or not.
I got the visualization. I see the rectangles and the areas and that they represent the algebraic simplification of ln(e^pi) = pi and ln(pi^e) = e*ln(pi). You are getting off track here. The original point, my point, was the myth of "visual thinking". I asked you to justify your picture because you are one move from losing your king. I was proving that it doesn't matter if the construction is visual, symbolic or just verbose sentences. Those are just the props. To be mathematics, whatever you are doing has to be justified by a reasonable mathematical argument. The plot if you will. That is the thinking. That is not visual. It is logical.