Let's return to the Baylonians' base-60 system. https://en.wikipedia.org/wiki/Babylonian_cuneiform_numerals

I'm not sure we would be any more advanced. Anyone to whom binary conversion is relevant has sufficient intelligence to not need the convenience of base 8. For practical needs, convenient representation of repeated doubling and halving are of limited use. Much more relevant to the daily needs of actual people for most of history was the ability to reckon measurements using common objects such as the human body, hence the bewildering diversity of different measurement systems across different peoples, see e.g. https://en.wikipedia.org/wiki/Medieval_weights_and_measures. The base of the number system was a non-factor.

> I know some people say base-12 would be better, as it has lots of integer divisors

IF people with an extra digit on their hand were more common and they were somehow elevated to a priestly / godly class at some point by a dominant tribe ... we would pronbably have had base-12 number system

You can count to 12 on one hand pretty easily without any extra digits: https://m.youtube.com/watch?v=pUZwv9oFbI8

Or we could adopt a number system that has actual, proven arithmetic benefits. See the Kaktovik numerals (https://en.wikipedia.org/wiki/Kaktovik_numerals). As a bonus the numerals are all one single stroke, so it's super fast to write!

Though, the benefits to calculation come from the fact that the numerals are iconic, not due to it being base-20.

[delayed]

We have 10 fingers. the thumb is a finger too. Better stay with base 10

My point was that you could imagine an alternate history where people landed on base-8 (which of course would still be called "base-10" in that timeline) because of 8 fingers ignoring thumbs. And that that would have had some advantages. Obviously society isn't going to change now.

It is an interesting thought experiment to wonder if certain things were discovered earlier or later owing to a particular type of maths that we practiced.

I was amused to learn that there are societies dedicated to the cause of dozenal system who write papers and books urging everyone to switch. On the other hand, I don't know if it is exaggerated but French revolutionist had grand ideas of creating decimal based systems even for time. But better sense prevailed in the long run!

It is interesting to think how can changes of the form "if we can align everyone to change and adopt this new way" can be brought about at any scale beyond a few thousand folks. I think large mass adopted switches (horses to cars, smart phones) have been about incentives and convenience demonstrated by some early adopters. But for basic arithmetic this seems impossible to pull off!

Yes, it's a coordination problem where the incentives for a single individual don't match the optimal global solution. Aka trapped by network effects. You don't see this problem with cars or smartphones because the benefit to the individual is obvious and independent of other people's choices.

https://en.m.wikipedia.org/wiki/Coordination_failure_(econom...