Base 6 would be better and maybe even base 12 could be too. Luckily the United States customary units already use a lot of numbers with more useful prime factorization than 10 like 4 and 3 and even 120.
Babylonians were obsessed with divisibility, so they went with a base 60 system. That’s why we still have 60 minutes 60 and seconds. Also the 360 degrees of a circle fits that ideology, because 6*60=360.
Was it really base-60? Like “10” in Babylonian was 60 and they had 59 individual symbols for the digits lower than that? If so, that’s a lot of digits to learn.
To represent a number using Babylonian Cuneiform Numbers, you choose a symbol to represent 10 ((2*2*2)+2) and a symbol to represent 1, and you create them combined in groups that are summed together to represent numbers up to 59 (10+10+10+10+10+1+1+1+1+1+1+1+1+1). When one group is to the left of another, the group to the left represents a number that is 60 times greater than it would if the group to its right hadn’t been created. A symbol representing a group that sums to 0 was sometimes used.
The Numberphile channel created videos on this topic: https://www.youtube.com/watch?v=RR3zzQP3bII https://www.youtube.com/watch?v=R9m2jck1f90
You’ve almost got it right, but in the opposite way. “10” in Babylonian would just be one character. They would have a different character for every number 0-59 and at 60 it would become two characters.
I like hexadecimal because since it’s (22)2 so it works with computers pretty well. 2^2 is too few symbols, it would make writing numbers unnecessarily long. And ((22)2)^2 is too many symbols to easily memorize.
Binary is really good for signal processing, because you need to worry about two distinct states. Could be two voltages, two currents, two frequencies, two anything. If you use base n in your system, you would need to make sure those n states are pretty much guaranteed to be separate at all times, and that’s surprisingly difficult. Binary is very wasteful, but it is also very robust.
If your numbers need to exist on paper, then binary isn’t a very appealing option. If you’re limited by the space on your golden paper, then base million or something like that would be ideal. If you’re limited by human brain capacity to learn digits, then binary would be great, base 10 is ok, base 20 might be kinda pushing it and base million is out of the question.