On Jul 11, 2013, at 10:30 PM, "Louis Talman" <firstname.lastname@example.org> wrote:
> Has it occurred to you that you may lack a sense of visualization that Joe possesses?
In the beginning of the conversation that was a possibility I suppose, but everything Joe has described thus far isn't unlike anything I have done a thousand times before.
It appears that we are talking about the exact same process, but he is clinging to this notion that because the rationalization involves a visualization then it is a visual rationalization, aka visual thinking. I claim that the simpler and more correct interpretation is that it is a rationalization of a visualization. Moreover, the visual senses involved are not rational and that the rationalization component of the experience is provided by the same rational senses that one uses to justify an algebraic derivation.
A very simple example of what I am saying...
Suppose I show you a bar 4 units in length next to a bar 5 units in length and then ask "Which is greater? 5 or 4?" Obviously, you will pick the bar that is 5 units in length. But you would have even done this even if I placed the two bars next to each other without any mention of 4 and 5. This is what I am calling "rat-sense". This is not rational.
If however, in this example you justify to yourself the general association of each bar with its length in units (a measure) and then justify to yourself that the visual comparison of length is equivalent to the abstract comparison of length (a measure), then it is rational. In particular it is a rationalization of a visualization or if you prefer, a rationalization of a visual experience.
 rational: based on or in accordance with reason or logic.  justify: show or prove to be right or reasonable.  measure: the association of number with size.