# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Kollsman periscopic sextant mount
From: Peter Hakel
Date: 2020 Sep 23, 06:37 -0700

If I want to do a temperature-dependent refraction correction of a sextant altitude, temperature readings in Celsius and Fahrenheit are equally useful (Kelvin is possible but not necessary). However, when we do scientific or engineering calculations combining various “silos” (mechanical, electrical, etc.) and potentially across many orders of magnitude, we need a self-consistent system of measurement for all such quantities; these “silos” are an artificial human invention after all, it’s all one Universe to Mother Nature. It’s also then useful to make such a system international (hence SI), and metric (to work well with our base-10 math system).

Speaking of math, it tells us that:
exp(x) = 1 + x + x2/2 + x3/6 + …

which, combined with the imaginary unit i = sqrt(-1), becomes:
exp(ix) = 1 + ix - x2/2 - i x3/6 + …  =  cos(x) + i sin(x)

where those trig function (familiar to celestial navigators) must take “x” in radians for this very powerful formula to work.

Human convenience (e.g., sextant readings in degrees) versus Nature’s design (angles in radians, necessary for certain calculations) can sometimes be at odds and we need to find some reasonable middle ground. It is fine to return a kickoff 99 yards for a touchdown, but I prefer my flu shot dose measured in cc’s.

Peter Hakel

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