58 and other Confusing Numbers - Numberphile
Why Worldbuilding Stack Exchange recommends it
Worldbuilding Stack Exchange answerers point people to it when designing alien or fantasy counting systems, to show that humans have used many number bases and that ten fingers do not force base 10.
Recommended by 3 people across 3 different months, 2015 to 2019.
What it is
A Numberphile video in which Tom Scott discusses how different human languages and cultures count, including body-part counting systems and bases other than ten. It uses animated illustrations by Pete McPartlan and covers oddities such as base-27 counting in New Guinea.
What people said
Strong rec Schwern · 2019-08 · Worldbuilding Stack Exchange · on “Number of Fingers for a Math Oriented Race”
That is to say, a large reason why humans use a base 10 numbering system is because we have 10 fingers, not that we have 10 fingers because we use a base 10 numbering system. Ask any anthropologist, physiology does not constrain counting base. We like to think that base 10 is natural because we have ten fingers, and it is common, but that's not the only way humans count. Numberphile/Tom Scott has a great episode on how human societies around the world "naturally" count [this video] , and it's not all base 10. He demonstrates languages and body counting schemes of many bases, using varying parts of the body. Here's some ideas beyond just the fingers. Tips and joints on fingers Fist Knuckles Spaces
Recommends R.M. · 2015-12 · Worldbuilding Stack Exchange · on “If we had four digits on each hand”
@TomPotts I think this Numberphile video [this video] is also a good watch. Specifically because it counters, to some extent, the assumption that having four digits on your hand would naturally lead to base-four/base-eight systems. Even with standard five digitted humans, there's a variety of numbering/counting systems which aren't the standard decimal one. The 10 fingers -> decimal connection is something of a historical accident, rather than an foregone conclusion.
Recommends PipperChip · 2016-12 · Worldbuilding Stack Exchange · on “Should I use base-10 or base-12 numbers in my story?”
Use Base Twelve! There are actual [LINK] people [LINK] out there that think we, in real life, should count in base 12 [LINK] . It's called the dozenal system. People have historically counted in other units, like the Aztecs [LINK] counting in 20. A Numberphile video with Prof. James Grime [LINK] claims: the number of factors that go into 12 make it easier for multiplication and division Multiples of Three in Dozenal: 3, 6, 9, 10, 13, 16, 19, 20, 23, 26, 29, 30 ... Multiple of Four in Dozenal: 4, 8, 10, 14, 18, 20, 24, 28, 30 ... See the patterns? Most of your times tables you learn as a kid are now easy! You "don't" have .99999.... = 1 abuses [LINK] and run into as many infinitely long fract
Cites Malady · 2015-11 · Worldbuilding Stack Exchange · on “Developing Counting Systems”
Oksapmin, base-27 body part counting The Oksapmin people of New Guinea have a base-27 counting system. The words for numbers are the words for the 27 body parts they use for counting, starting at the thumb of one hand, going up to the nose, then down the other side of the body to the pinky of the other hand, as shown in the drawing. 'One' is tip^na (thumb), 6 is dopa (wrist), 12 is nata (ear), 16 is tan-nata (ear on the other side), all the way to 27, or tan-h^th^ta (pinky on the other side). Sources: [this video] & [LINK]
Cites PipperChip · 2015-11 · Worldbuilding Stack Exchange · on “Developing Counting Systems”
It’s common knowledge that (most) modern societies use arabic numerals, and moreover use base 10 for counting. That is, you count from 1 to 9 (unless you’re a programmer and you start at 0) and then you use 10, which uses that 10's place. I’ve learned about base 12 counting systems [LINK] recently, and even about how Klingon isn't that alien [this video] - because of its base 10 system! Making a counting system which is alien to humans infers not using one that has been used by humans. I can't guarantee an alien counting system unless I know what has been used. In the interest of making alien math more believable and actually alien [LINK] , what counting systems have been used by humans, and why?