Schmoodle
Bzzt, just realized that a fantastically simple theorem (well known in coupled-oscillations lit) has application to coordinated control of unmanned vehicles.
Let S be homeomorphic to the unit circle, and let f be a function from S x S -> S.
Suppose f has the following properties:
1) interchange of variables does not change the result, i.e. f(x,y) = f(y,x)
2) if x = y, then f(x,y) = x = y.
Then f cannot be continuous, no matter how hard it tries to be.
Proof is simple, based on a winding number argument, and the non-retraction theorem of topology (equiv to Brouwer's fixed point thm).
Why does this pop up when I'm trying to finish writing a thesis full of old ideas and boring results?
Hopefully no one else has thought of it...
(first published on the internationally acclaimed research journal GO MORON!)
A photo? Hmm... old favourite, Bernie after a heavy night:
Let S be homeomorphic to the unit circle, and let f be a function from S x S -> S.
Suppose f has the following properties:
1) interchange of variables does not change the result, i.e. f(x,y) = f(y,x)
2) if x = y, then f(x,y) = x = y.
Then f cannot be continuous, no matter how hard it tries to be.
Proof is simple, based on a winding number argument, and the non-retraction theorem of topology (equiv to Brouwer's fixed point thm).
Why does this pop up when I'm trying to finish writing a thesis full of old ideas and boring results?
Hopefully no one else has thought of it...
(first published on the internationally acclaimed research journal GO MORON!)
A photo? Hmm... old favourite, Bernie after a heavy night:
posted by I-Rock at 3:28 PM
5 Comments:
ian, it's time to finish that thesis and perhaps get into the real world...well, for at least a few weeks before you leave for sweden!
I've no idea, but now is not the time to be distracting me with problems that seem infinitely more interesting...
Are they New Scientist magazines?
Just a not-so-subtle dig...
alex: the real world is a fictional place made up to scare children into behaving, like hell, or the sutherland shire.
cok: I'm convinced that good ideas only ever come when you're supposed to be thinking about something else.
chia: I have nothing to say at this point in time.
bernie looks like a fun guy - bring him to my party.
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