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Hermann Weyl is widely reported as making the following observation about a compact space:

"If a city is compact, it can be guarded by a finite number of arbitrarily near-sighted policemen."

This was reported in a paper by Edwin Hewitt in a 1960 paper in AMM, and hence more widely propagated since. (I first encountered it in W.A. Sutherland's "Introduction to Metric and Topological Spaces" (Oxford Science Publications, 1975).)

However, I am having difficulty tracking down the precise origin. (Weyl wrote prolifically.)

Does anyone know where he first made that remark?

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  • $\begingroup$ @ConsigliereZARF Aha, wonderful. I will follow that up then. $\endgroup$ – Prime Mover Jan 15 at 20:06
  • $\begingroup$ @ConsigliereZARF Now I've checked that source you cited, and I need now to consider the question: how certain are we that this is the actual quote that Hewitt was citing, and not another similar one? Either Hewitt paraphrased drastically, and his was the version that got spread widely, or Weyl made the same observation using different words at another time. I am going to keep this open in case something else turns up. $\endgroup$ – Prime Mover Jan 15 at 20:19
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The closest match I could find is in H. Weyl, "Harmonics on homogeneous manifolds." Annals of Mathematics, Second Series, Vol. 35, No. 3, July 1934, pp. 486-499, as reproduced in K. Chandrasekharan (ed.), "Hermann Weyl: Gesammelte Abhandlungen Band III," Springer 1968. On page 389 of "Gesammelte Abhandlungen":

A "finite" country can be watched by a finite number of policemen, however small the radius of action of the single policeman may be!

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    $\begingroup$ Thank you, that seems a popular suggestion -- I'm beginning to wonder whether Hewitt deliberately rewrote / paraphrased Weyl's statement to make it more picturesque. $\endgroup$ – Prime Mover Jan 16 at 16:20

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