11:16 February 12, 2012

There is a disparity of thought that the word circle can mean either the 1-dimensional curvature, x^2 + y^2 = r^2 , or the area contained therein, whereas a sphere is usually thought of as the 3-dimensional space versus the 2-dimensional membrane confining it.

The argument can be made that this is innate to human thought, but I would contend that we (as only an English speaker, I will confine the first-person plural to that) have muddled the language with this ambiguity. Since 2-dimensional drawing has been available since pre-history, this mode of ambiguity comes from the ability to have define a region with a circle (the 1-d variety), whereas having no drawing mode in three space commonly available in 3-space the sphere is realized through abstract thought.