4 ms·

Stuff like this makes me feel like the base10 system might eventually get replaced by an even more usefull counting system.

cassepipe 3y ago
Does it not boil down to a tradeoff between the amount of symbols you are willing to learn and the space you want to use to write a number down ? Base 10 strikes me as good tradeoff
- Qem 3y ago
  Also a tradeoff with the size of the arithmetic tables one has to learn by rote. It scales with n^2. 100 entries in base 10, and just 36 in base 6, for example.
- avhon1 3y ago
  ...and also the number of integer factors of your base. 10 only has 1, 2, 5, and 10. Bases 8 and 6 have just as many. Bases 12 and 60 (used by the Sumerians and Babylonians) offer more convenient divisors.
Spivak 3y ago
Base 12! The operations humans do a lot divide by 2,3,4,12 can be done evenly. Your goal is to pack as many factors into your base as possible. They're called highly composite numbers and their big brother superior highly composite numbers. Base 10: 1,2,5,10 Base 12: 1,2,3,4,6,12 Base 60: 1,2,3,4,5,6,10,12,15,20,30,60 https://en.m.wikipedia.org/wiki/Superior_highly_composite_number https://en.m.wikipedia.org/wiki/Superior_highly_composite_nu...
- Qem 3y ago
  Children starting school would not be amused needing to learn 144 entries arithmetic tables. Lots of people were scarred already, starting with a lot of resentment against math due to sheer boredom of rote learning 100 entries tables close when they are first presented to the subject.
  - Spivak 3y ago
    Um they already do that, my elementary times tables went up to twelve. Also it's really 72 entries, and let's ignore 1's so it's 60. Unfortunately you have to memorize your times tables. There's no other way. You can't build number sense without having operations on small numbers in your meat L1 cache.
  - brianush1 3y ago
    Learning up to 12x12 is commonplace in the U.S., and apparently in other English-speaking countries, too https://en.wikipedia.org/wiki/Multiplication_table#Modern_times https://en.wikipedia.org/wiki/Multiplication_table#Modern_ti...
  - ttonkytonk 3y ago
    In base 12, the multiplication tables are (likely) easier to learn because of the increase in factors (e.g. 3 would be "3,6,9,10,13..." and 4 would be "4,8,10,14..." 8 would be "8,14,20,28..." and 9 would be "9,16,23,30,39...").
davnicwil 3y ago
I think this might be the ultimate example in human history of a 'legacy' system we are completely beyond the point of feasibility of changing in terms of cost / benefit.

cassepipe 3y ago

Does it not boil down to a tradeoff between the amount of symbols you are willing to learn and the space you want to use to write a number down ? Base 10 strikes me as good tradeoff

Qem 3y ago
Also a tradeoff with the size of the arithmetic tables one has to learn by rote. It scales with n^2. 100 entries in base 10, and just 36 in base 6, for example.
avhon1 3y ago
...and also the number of integer factors of your base. 10 only has 1, 2, 5, and 10. Bases 8 and 6 have just as many. Bases 12 and 60 (used by the Sumerians and Babylonians) offer more convenient divisors.

Spivak 3y ago

Base 12! The operations humans do a lot divide by 2,3,4,12 can be done evenly. Your goal is to pack as many factors into your base as possible. They're called highly composite numbers and their big brother superior highly composite numbers. Base 10: 1,2,5,10 Base 12: 1,2,3,4,6,12 Base 60: 1,2,3,4,5,6,10,12,15,20,30,60 https://en.m.wikipedia.org/wiki/Superior_highly_composite_number https://en.m.wikipedia.org/wiki/Superior_highly_composite_nu...

Qem 3y ago
Children starting school would not be amused needing to learn 144 entries arithmetic tables. Lots of people were scarred already, starting with a lot of resentment against math due to sheer boredom of rote learning 100 entries tables close when they are first presented to the subject.
- Spivak 3y ago
  Um they already do that, my elementary times tables went up to twelve. Also it's really 72 entries, and let's ignore 1's so it's 60. Unfortunately you have to memorize your times tables. There's no other way. You can't build number sense without having operations on small numbers in your meat L1 cache.
- brianush1 3y ago
  Learning up to 12x12 is commonplace in the U.S., and apparently in other English-speaking countries, too https://en.wikipedia.org/wiki/Multiplication_table#Modern_times https://en.wikipedia.org/wiki/Multiplication_table#Modern_ti...
- ttonkytonk 3y ago
  In base 12, the multiplication tables are (likely) easier to learn because of the increase in factors (e.g. 3 would be "3,6,9,10,13..." and 4 would be "4,8,10,14..." 8 would be "8,14,20,28..." and 9 would be "9,16,23,30,39...").

davnicwil 3y ago

I think this might be the ultimate example in human history of a 'legacy' system we are completely beyond the point of feasibility of changing in terms of cost / benefit.