In college, I noticed that my roommate counted things in chunks of three. I had only ever counted items either individually or in chunks of two, but for most physical items I count, there are fewer than 50 of them, and counting by 3s up to that number is about as easy as counting even numbers. I was surprised to see that visually identifying three of an item was not harder than going by twos. Of course, it's also faster to count by 3 than by 2.<p>I'd be interested to know if others count by 1, 2, 3, or something else. (Another trick I learned working retail is to count out X coins, stack them vertically, and then make more stacks of the same height. Much faster than counting them all out individually!)
Base-12 is nice because, like Seximal it is divisible by both the first and second prime number (2 and 3). But it is also divisible by the first prime (2) twice, and doesn't immediately overflow into extra digits.<p>So 10 in base 12 can be exactly divided by 2, 3, 4, 6, 8, and 9.<p>Compare this to base 10 where 10 can only be exactly divided by 2, 4, 5, and 8.
Only tangentially related, but it's fascinating how number 12 emerges
in music naturally. And the fact that 12 has many divisors is a <i>big</i> coincidence without which Western music as we know it would be impossible.
I have a short write-up on this:
<a href="https://github.com/resource0x/concert0x/blob/master/doodle-script.md#chromatic-scale" rel="nofollow">https://github.com/resource0x/concert0x/blob/master/doodle-s...</a>
I was taught basic counting, addition, and subtraction using a finger-abacus system called Chisanbop: <a href="https://en.wikipedia.org/wiki/Chisanbop" rel="nofollow">https://en.wikipedia.org/wiki/Chisanbop</a><p>Now I'm plagued by off-by-one errors in my mental math, particularly when it comes to intervals. If you ask me how many days there are between now and Christmas, I will be uncertain about the answer unless I individually count them all off on my fingers.
I think hexadecimal is better, it has the advantage of super easy conversion from/to binary, the most fundamental number system.<p>We just need a good naming scheme for counting in hex :)
Human brains seem to be suited to verbally counting in base ten however. I mean, languages as unconnected as Japanese, Chinese, Russian, Finnish, Hungarian, Italian, German, English, Navajo <i>all</i> count in base ten. There are of course outliers, but those tend to be very small isolated language communities. I think the ease of communication in base ten for humans outweighs any arithmetic improvements. You can always count things in groups of 12 or 60 if you want to be able to easily divide the group, but keep the numbers in base ten.
If you want to build a new counting system, Why not use new symbols for all the numbers? I mean the practicality that 1-9 mean the samme when on their own seem completely eclipsed by the fact that any number represented by more than one symbol means something else. It’s like trying to “build a new better C” where everything works “like you’d expect from C” as long as your program is no more than 4 characters long.
Learning about positional number systems was definitely a challenge but one of the best "mind opening" experiences of my life. I thoroughly recommend reading chapter 4 of Knuth's <i>The Art of Computer Programming</i> for the history of counting systems and notation of numbers. I didn't realise how much of what I thought I knew about counting was tied to decimal notation.
I remember my maths teacher teaching that in 1995. He was pretty good at explaining it, but not as good as this video.<p>We should really be seeing a great education dividend from the availability of material these days.
There are a large number of seximalish systems. Degrees (360), hours, minutes, seconds, am/pm hours, feet/inches, troy ounces, months in a year, etc.
same person posting the same video every so often<p><a href="https://news.ycombinator.com/item?id=17083858" rel="nofollow">https://news.ycombinator.com/item?id=17083858</a>