## Monday, November 01, 2021

### [vrkoopsn] digits in alphabetical order

here are digits in alphabetical order by their cardinal names in English zero, one, two, three, four, five,...

8 5 4 9 1 7 6 3 2 0

it is a permutation.

by their ordinal names zeroth, first, second, third, fourth, fifth,...

8 5 1 4 9 2 7 6 3 0

Latin ordinal numbers are primus secundus tertius quartus quintus sextus septimus octavus nonus decimus (no zero).  English therefore has primary, secondary, tertiary, quaternary, quinary, then what?  probably something like sexary sextary sexnary sexanary sextanary sexenary sextenary, following Latin ordinals.  one source says "senary", but I don't trust it, probably ashamed of "sex", or fearing censorship for it.  (but "sedecim" not "sexdecim" is the Latin cardinal for 16, so there is precedent for shortening sex to se.)  this matters because "senary" sorts before "septenary" in alphabetical order, but "sexary" sorts after.  there might be similar disagreements about 7 through 9 (e.g., septenary or septinary or septary?), but they don't cause controversy in sorting.

for 0, we invent zeroary, because "nullary" belongs to a different sequence (with unary not primary, see below).  zeroary means "the thing before primary", which seems nonsensical, but maybe there's a situation in which it makes sense.  here are alphabetized Latin ordinals and zeroary:

9 8 1 4 5 2 7 6 3 0

but if we nevertheless use nullary instead of zeroary:

9 0 8 1 4 5 2 7 6 3

nullary, unary, binary, ternary, then Latin ordinals:

2 9 0 8 4 5 7 6 3 1

octal and octonary sort the same.  (digression: it really should have been sedenary, not hexadecimal, but early computer scientists mixed up Greek and Latin.)  but in that vein, if we let hexal and heximal win the battle between sexary and senary:

2 6 9 0 8 4 5 7 3 1