Re: Natural Functorial Categorical Intuition

[posina <posina@salk.edu>]

Dear All,

My understanding, having studied in some detail the behavioural,
psychological, and cognitive scientific studies, is that a serious study of
mathematics (beginning with Lawvere & Schanuel's Conceptual Mathematics)
can inform cognitive sciences more so than the other way around, with all
due respect to Dan Kahneman and those 'where mathematics comes from' guys.

Thank you,
posina

On Tue, 27 Sep 2011 17:20:41 -0400, "Ellis D. Cooper"
<xtalv1@netropolis.net> wrote:
> My motto has been "Rigor cleans the window through which intuition
> shines." It seems to me that
> a great deal more is known about mathematical rigor than about
> mathematical intuition.
> 
> Economics Nobelist Daniel Kahneman recently published at www.edge.org
> a survey of several
> men-decades of research on flaws of human statistical intuition. A
> paper, "The Intuitive Experience" in
> "The View from Within" (Journal of Consciousness Studies, V.6 1999)
> discusses in considerable
> detail schema and methods of invocation of intuition in
> psychotherapy, art, and biology research.
> 
> My overall question is whether there really are different kinds of
> intuition depending on the research
> discipline. In particular, is there some kind of kinetic intuition
> specific to category theory that crucially
> involves visualization of time-varying diagrams? Do conjectured
> adjoint functors arise from distinct algebraic, or
> geometric, or logical intuitions? Do categorists deploy special
> methods to access their intuition, or
> do intuitions just happen to those with a knack for category theory?
> Does categorical intuition just
> develop with experience, or is there a specialized training to
> enhance it? Is categorical intuition
> any different from mathematical intuition in general?
> 
> Ellis D. Cooper
> 

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