Heh, I hit that next year. This last birthday, it occurred to me that the Hamming weight (popcount) of my age in years was the largest it would ever get, barring me living to a really unlikely age.
I did some research on this for my CSS framework, I didn't want to have a max-h-1rem type value for every single number, just a small subset that is easy to remember.
5-smooth numbers and practical numbers overlap with the highly composite, but include more of the common "Numbers you see everywhere that people seem to like".
We are obsessed with anything divisible by 10, which is our counting base. So a decimal system is most logical.
It is highly unfortunate, though, that we used the number of our fingers for that base. Have we gone for the phalanges (sans content then with a thumb) we would end up with 12, divisible by 2, 3, 4, 6.
Since we would just use one hand for counting, we would easily end up with 12x12=144 without any effort.
I completely agree, finger counting makes much more sense, smaller times-tables, etc, but I don't like the naming, using existing numbers, or 1000 groupings.
One problem with all these alternative base number systems is they reuse our base-10 digits.
To me '10' instinctively means 'ten', '13' is automatically read as thriteen, and so on. They need to use a completely different set of digits (and names) so that you 'feel' the new base, and avoid confusion.
There are already proposed names for exponents; "nil", "un", "bi", "tri", "quad", and "pent" - those should be the names of the numbers too, and the exponents should be direct rather than x3, ie "unex" is sixes, bi-ex is 6x6s, tri-ex is 6x6x6s, etc.
"objectively" and "best" are almost opposites. Best depends on the chosen criteria, and how you weight them. And that selection is subjective.
Maybe it works for an alien civilization, or a lost tribe that never had contact with our culture. But for us our culture count, and it is not just how today we represent numbers.
And we are closer for a cultural shift for going to hexadecimal than going to seximal. But in any case, if we would go to seximal, I would use a different set of symbols for digits, or at least way to present them.
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[ 37.4 ms ] story [ 1077 ms ] threadIf we were all polydactyl it would be easier to use base-6.
Why? Five fingers are the perfect amount for base six, which has digits from zero to five.
4ft = 48" which is evenly divisible by 2, 3, 4, 6, 8, 12, 16, and 24. This makes math easy and significantly minimizes cutting and waste.
3, 9, 12, 24, 48, 56, 72, 96, 480, 600 etc
There are many other factors which result in these as well though
5-smooth numbers and practical numbers overlap with the highly composite, but include more of the common "Numbers you see everywhere that people seem to like".
It is highly unfortunate, though, that we used the number of our fingers for that base. Have we gone for the phalanges (sans content then with a thumb) we would end up with 12, divisible by 2, 3, 4, 6.
Since we would just use one hand for counting, we would easily end up with 12x12=144 without any effort.
One problem with all these alternative base number systems is they reuse our base-10 digits. To me '10' instinctively means 'ten', '13' is automatically read as thriteen, and so on. They need to use a completely different set of digits (and names) so that you 'feel' the new base, and avoid confusion.
There are already proposed names for exponents; "nil", "un", "bi", "tri", "quad", and "pent" - those should be the names of the numbers too, and the exponents should be direct rather than x3, ie "unex" is sixes, bi-ex is 6x6s, tri-ex is 6x6x6s, etc.
https://en.wikipedia.org/wiki/Balanced_ternary
It once made an appearance in a computer:
https://en.wikipedia.org/wiki/Setun
Maybe it works for an alien civilization, or a lost tribe that never had contact with our culture. But for us our culture count, and it is not just how today we represent numbers.
And we are closer for a cultural shift for going to hexadecimal than going to seximal. But in any case, if we would go to seximal, I would use a different set of symbols for digits, or at least way to present them.