Mobile-friendly sidenotes, and distance estimation with milliradians
We learn how to make mobile-friendly sidenotes without requiring JavaScript (though requiring some HTML templating.) We also learn to estimate distances with no external tools but our hands and a little mental arithmetic!
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Sidenotes, Footnotes, Inlinenotes
I have had so many questions on how the sidenotes on Entropic Thoughts work. This is a brief description that ought to be enough to get the interested going.
Full article (2–4 minute read): Reading GHC Errors
Flashcard of the week
Here's a neat trick!
If a width downrange is estimated to be roughly 50 metres long, and its subtension is 60 milliradians, how far away is it?
This might describe a situation where we are looking at a road far away at a right angle – the distance between full-size street lights is typically 50 m (at least where I live). We can estimate the subtension by holding up our hand at arms length from our face. Each knuckle is roughly 30 milliradians.
It is around 800 m from us.
The underlying relationship here is width downrange in metres = subtension in milliradians × distance in kilometres. That relationship is not exact, but for subtensions that are small enough to be measured in milliradians the inaccuracies are smaller than those introduced during estimation.
Toying with a few examples of this also helps get a good grip for why radians are a fundamental unit of angle! If we measure both width downrange and distance in the same unit, the relationship holds true for radians rather than milliradians. And it's only true approximately because the object is tangent to a circle but we are pretending it is an arc length. This is fine for small angles.
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