The Universe of Discourse

Addenda to recent articles 201607

Here are some notes on posts from the last couple of months that I couldn't find better places for.

• I wrote a long article about tracking down a system bug. At some point I determined that the problem was related to Perl, and asked Frew Schmidt for advice. He wrote up the details of his own investigation, which pick up where mine ended. Check it out. I 100% endorse his lament about ltrace.

• There was a Hacker News discussion about that article. One participant asked a very pertinent question:

  I read this, but seemed to skip over the part where he explains why this changed suddenly, when the behavior was documented?

  What changed to make the perl become capable whereas previously it lacked the low port capability?

  So far, we don't know! Frew told me recently that he thinks the TMPDIR-losing has been going on for months and that whatever precipitated my problem is something else.

• In my article on the Greek clock, I guessed a method for calculating the (approximate) maximum length of the day from the latitude: $$ A = 360 \text{ min}\cdot(1-\cos L).$$

  Sean Santos of UCAR points out that this is inaccurate close to the poles. For places like Philadelphia (40° latitude) it is pretty close, but it fails completely for locations north of the Arctic Circle. M. Santos advises instead:

  $$ A = 360 \text{ min}\cdot \frac{2}{\pi}\cdot \sin^{-1}(\tan L\cdot \tan\epsilon)$$

  where ε is the axial tilt of the Earth, approximately 23.4°. Observe that when !!L!! is above the Arctic Circle (or below the Antarctic) we have !!\tan L \cdot \tan \epsilon > 1!! (because !!\frac1{\tan x} = \tan(90^\circ - x)!!) so the arcsine is undefined, and we get no answer.

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