One of our cats is called Microsoft; another is called Patches.
I chuckle about that, sometimes.
Above is a picture of Patches, transformed by a java applet that can be
found here.
It appears that the original intent of the program was to
transform human faces to resemble those found among persons of
different ethnicities. However, they added some artistic
transformations as well. One option is to view a face as is
might have been portrayed by
href="http://www.ibiblio.org/wm/paint/auth/modigliani/">Modigliani.
HT:
href="http://climactericclambake.blogspot.com/2006/07/i-am-work-of-art.html">Climacteric
Clambake.
More like this
Most textbooks, especially ones not aimed at college math majors, give a definition of "function" that seems quite intuitive. They'll say something along the lines of: a function is a rule that takes an input x and turns it into an output f(x).
Today's contribution on category theory is going to be short and sweet. It's an example of why we really care about [natural transformations][nt]. Remember the trouble we went through working up to define [cartesian categories and cartesian closed categories][ccc]?
The thing that I think is most interesting about category theory is that what it's really fundamentally about is structure. The abstractions of category theory let you talk about structures in an elegant way; and category diagrams let you illustrate structures in a simple visual way.