And the Babylonians, whose base-60 system's legacy lives on in our timekeeping, used the finger segments on one hand and entire fingers on the 2nd hand to count to 60.
60 has nice properties, in that it is evenly divisible by 2,3,4,5,6,10,12,15,20,30. Helpful as a base since you can divide it into smaller units easily (monetary, measurement, etc).
Funny i just started reading(half way through, its a hard book to read) Micheal Hudson book "...And forgive them their debts" talks about bronze age economics etc and debt forgiveness and how their number base was usually taken for interests calculations.
The Babylonian Base-60 also obviously survives in a lot of circle measurements: degrees, minutes:seconds. While the metric system has mostly moved on to radians, metric proponents (and esp. the French Revolution) failed to find a base-10 time system that people could agree on that matches the convenience of Base-60 minutes:seconds.
Yeah, I use that one when I need to hand-count somewhat large quantities. The Roman system is better (larger numbers), but I can't independently bend my pinky, ring or middle fingers, so it's unusable sadly.
forgive my question, I am probably missing context and I am curious: why are you hand counting large quantities?
I mean, why do you keep it on your fingers rather than just counting out loudly, or possibly just keeping on the fingers numbers up to ten repeatedly for "double checking"?
I know there are clicker tally counters which can be useful for e.g. counting cattle or people on a plane, but counting up to 60 seems feasible in your mind.
Not parent, but back when I was young and couldn’t afford a sports watch, I kept track of distance while running by counting steps. I would count up a hundred step pairs in my head, and increment a counter on my fingers on each hundred. (I also used a simple system of my own devising to allow counting up to 99 on my fingers.)
Which arguably suggests we didn't settle on base 10 because we have 10 finger as seems to be often told. We settled on base 10 likely because of politics (in the broader sense of the word)
I imagine there's a natural gravitational pull toward base 10 from having fingers, and throughout prehistory and early civilization occasionally systems deviated to suit certain purposes (like sibling comment about even divisibility of 60) but usually came back to using 10. We've always needed to count, been smart enough to count, and had 10 fingers readily accessible to count, so I wouldn't count that theory out :)
I think the biggest strength of base 10 is not hand-counting (the OP and the Babylonian/Chinese base-12 method are both superior in that regard), but ease of performing pen-and-paper operations. You can literally teach a 6-year-old to multiply huge numbers effortlessly.
Couldnt you do the same using two additional digits? Say binary and hexedicmal arithmetic are as easy as decimal if you substract the bias of being used to decimal.
If you use any other base for writing numbers down, it's just as easy to perform pen-and-paper operations. The only problem with larger bases is that the multiplication tables increase quadratically. Whereas a base-10 multiplication table has 100 entries, a base-16 table already has 256 entries.
Not quite! You can safely ignore identities (0, 1, and 10 itself) so you only have 8 numbers in your table. And multiplication is commutative so you only need 8+7+6... (= (8+1)(8/2) as per Gauss) = 36 entries.
Base 16 would have (14+1)(14/2) = 105 entries. So proportional to base-10, actually slightly harder than you said.
This video convinced me that base 6 would be even better for simple pen-and-paper math, as well as just about everything else: https://youtu.be/qID2B4MK7Y0
It was a long time ago, so not likely anybody wrote it down. But wasn't it from India? Counting-sticks in boxes, when you got to nine (maybe all that would fit in the box?) you put one stick in the next box and 'cleared' the lower-significant box. Apparently zero is a drawing of an empty box...
