It's like a 16 bit integer, you can only store so much…
Re:Cistercian Numerals
by college_physics on Tuesday January 31, 2023 @07:07AM
(#34594064)
> The problems are that this is 1) hard to use for arithmetic, and 2) brittle.
I wonder if these constraints are inate to the problem (inescapable trade-offs) or circumstantial to the particular choices of the Cistercian monks...
Re:Cistercian Numerals
by AnimalMuppet on Tuesday January 31, 2023 @01:01PM
(#34598927)
Any fixed-number-of-digits (or bits, or whatever) system is brittle against overflow.
Any compressed format is hard(er) to use for arithmetic. Pretty much any grade-school kid can memorize the addition table, and can work it out on their fingers if they forget. But that table only has 100 entries. The addition tables for Cistercian numbers has 100,000,000 entries; nobody will memorize that.
But maybe I'm thinking wrong. Cistercian numbers really only have 0-9, in four possible orientations. So maybe you can just add them, going from units up through thousands, writing down each quadrant as you go. (Multiplying still looks like a mess, though...)
"Brittle" because you're peacefully sitting there at 9999 coins or whatever, and you earn another one, and suddenly you can't represent it. Arabic (Hindu) numerals just slap another digit to the left, but Cistercian numerals break.
(You could fix that by using an Arabic notation - two Cistercian numbers, with the left one meaning "multiply this by 10,000". At that point, Cistercian numbers become a compressed Arabic notation. Still harder to use for arithmetic, but that's true of many compressed formats.)