Friday, November 18, 2011

in which some constructions are "natural" ..

perhaps all of you knew already, but today i learned that "magenta ain't a colour" in the sense that it cannot be created with a single wavelength from the visible light spectrum.

however, since the human eye processes colors in terms of opposites, so magenta appears as the complementary color to green.
initially i nodded,
thought it was a neat factoid,
and went back to wasting time on the internet ..

.. but then it occurred to me: 
this is exactly the 1-point compactificatiοn of the real line [1]!
despite the abstract nature of lοcally cοmpact Hausdοrff spaces, this is a concrete example that some ideas in tοpology sit naturally in the real world ..

this is just as cool as when i learned that the video game "asteroids" is played on a torus ..

[1] yes, for the record the visible spectrum is a bounded interval, not the whole real line .. q-:

1 comment:

Daniel said...

1 point compactifications are completely natural. Above and beyond the homomorphism between the one point compactification of the real line (or an open interval in the real line in this case) and the circle, the notion of a 1 point compactification is still pretty natural. The dynamical systems bias in me is thinking of the point that occurs when a system diverges to infinity. You can (loosely) define a compactification by adding the point that systems that go far away from everything else converge to.