The arabic numererals we use in our primary base-10 system are very arbitrary. There’s no connection between the around-a-tree-around-a-tree numeral “3” we use to represent the number after the candy-cane-with-a-shoe numeral “2” and the concept of the number 3.
But it doesn’t have to be that way. What if the numerals in our base-60 system themselves followed a pattern.
One of the simpler and more straightforward ways of doing that (that might not work well in practice, at least not for hand-written numerals) would be just to make each numeral in our base-60 system be a vertical line of 6 marks, each either a dot or a dash. We could use that then to encode a single digit in our base-60 system using base-2 digits.
For instance:
. .
. _
. .
_ _
. .
Would be (1*2^1)*60^1+(1*2^3+1*2^1)*60^0 = 2*60^1+10*60^0 = 120+10 = 130.
Viola! Base-60 with (handwave, mutter, qualify) only 2 numerals!
There are downsides to this as well. For instance, you’d have to not consider certain patterns valid. Six base-2 digits can encode numbers up to 63, so you’d just have to throw away the last four and say you’re not allowed to put a 60, 61, 62, or 63 in a single digit. (Also, we’d need language to differentiate between the base-2 digits and the base-60 digits in the same exact number system.)
Not the only way it could be approached, but it’s an option.
You’re not wrong, but…
The arabic numererals we use in our primary base-10 system are very arbitrary. There’s no connection between the around-a-tree-around-a-tree numeral “3” we use to represent the number after the candy-cane-with-a-shoe numeral “2” and the concept of the number 3.
But it doesn’t have to be that way. What if the numerals in our base-60 system themselves followed a pattern.
One of the simpler and more straightforward ways of doing that (that might not work well in practice, at least not for hand-written numerals) would be just to make each numeral in our base-60 system be a vertical line of 6 marks, each either a dot or a dash. We could use that then to encode a single digit in our base-60 system using base-2 digits.
For instance:
Would be
(1*2^1)*60^1+(1*2^3+1*2^1)*60^0 = 2*60^1+10*60^0 = 120+10 = 130.Viola! Base-60 with (handwave, mutter, qualify) only 2 numerals!
There are downsides to this as well. For instance, you’d have to not consider certain patterns valid. Six base-2 digits can encode numbers up to 63, so you’d just have to throw away the last four and say you’re not allowed to put a 60, 61, 62, or 63 in a single digit. (Also, we’d need language to differentiate between the base-2 digits and the base-60 digits in the same exact number system.)
Not the only way it could be approached, but it’s an option.
Digits should be unique enough to be distinguishable with bad writing and not require you to count dots