A man is told to make a circle
He makes this:
Where is the man?
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asked Feb 11, 2018 at 3:54
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7$\begingroup$ And this is an even-looking circle: ⃝. $\endgroup$– CJ DennisCommented Feb 11, 2018 at 9:47
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4 Answers
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In Manhattan, because that is what a "circle" (defined to be the set of points of a certain set distance d away from a given point) looks like when using the taxicab (or Manhattan) metric.
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He has made a rapid escape from the scene because he actually didn't know what a "circle" was.
No wait.
He makes it.
Well, he draws a circle.And then he makes the diamond...
So where is the man?
Think what I have just done.
I am that man.
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6$\begingroup$ That's a..... cheeky ..... answer :) $\endgroup$– Brian JCommented Feb 12, 2018 at 13:53
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3$\begingroup$ But we still don’t know where you are! :-) $\endgroup$ Commented Feb 13, 2018 at 16:11
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Clearly the man is
in $L^1$ space.
He was asked to draw a circle, namely the set of all points at distance $1$ from a fixed centre.
We imagine this as looking round, because we live in Euclidean $L^2$ space. But this man lives in $L^1$ space, in which the unit circle is a square box because the concept of 'distance' is defined differently. More generally, unit circles in $L^p$ space look like this for assorted values of $p$:
answered Feb 11, 2018 at 14:22
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7$\begingroup$ So he could also be in L^inf space, just with is head tilted? $\endgroup$– Dale CCommented Feb 12, 2018 at 2:10
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He's in another distance metric, one where distance is determined by the addition of coordinates, instead of pythagorean theorem.
