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#notetype:Basic
#deck:Math::Learning to learn::Day or night
#tags:math learning dichotomy
#columns:Front	Back	Tags
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What does a yes/no word on a continuous quantity need before it can answer?	A cutoff: a value of the quantity on one side of which the answer is yes.	definition
Is it night iff the sun is below c: a theorem or a definition?	A definition, so an if and only if by agreement; changing c changes the word, not the sky.	definition
Sun heights of the four standard cutoffs	Sunset -0.833 deg, civil dusk -6, nautical dusk -12, astronomical dusk -18.	twilight
Why is sunset at -0.833 deg and not 0?	The sun's radius (about 0.27 deg) plus refraction by the air (about 0.57 deg): the top edge disappears when the centre is 0.833 deg below.	twilight
Starbuck, WA, 21 June 2026: when does night begin?	20:49 by sunset, 21:28 civil, 22:22 nautical, 23:39 astronomical: four exact answers to four questions.	twilight
At 22:00 in Starbuck one person says night and another says not yet. What do they disagree about?	Not the sky (it is at -9.74 deg for both) but the cutoff: civil says night, nautical says not yet.	trap
What is the sorites paradox, for dusk?	It is day at sunset; one minute never turns day into night; so it is never night.	sorites
Where does the dusk sorites go wrong?	Once a cutoff is named, one minute does turn day into night: the premise is false at exactly one minute.	sorites
Lowest sun at local midnight on the June solstice	-(90 - latitude - 23.45) degrees.	twilight
Where is there no astronomical night in late June?	North of about 48.55 deg N, where the sun never gets to -18 deg.	twilight
In fuzzy logic, what is the value of day and not day?	min(day, 1 - day): 0 at noon and midnight, up to one half at dusk.	fuzzy
Is a fuzzy degree of day vaguer than a cutoff?	No: it is an equally precise choice, a number in [0, 1] instead of a bit.	fuzzy
First step when two people argue over a dichotomy	Name the quantity underneath and the cutoff each side is using.	trap