How does those numbers look in base 8 or 12.
Since I learned about base 2, etc, long ago, I always thought there was something magically elegant about base10 and never understood this? The explanation I've always heard, being 10 fingere, doesn't seem to explain all the elegance with base 10 being easy to work with?..?
In fact, every number base is base "10" when you interpret the "10" in that base.
10 binary is two.
10 octal is eight.
10 hexadecimal is sixteen.
This is the very definition of a number base: it is the multiplier that you represent by appending "0" to a string of numeric characters in that base.
So that is where the fundamental and special nature of "10" comes from; it's not because it happens to mean "ten" in our customary number base.
Ten is nothing special, "10" is. "10" is simply the way you write N where N is whatever number base you're working in. It's just as special in every number base!
p.s. I'm sorry you were downvoted so heavily for asking an honest question. You can't be the only one who has wondered about this, and your question led to an interesting discussion.
Your reasoning seems quite obvious now with hindsight after having given it some thought; and yet, even still I have such a strong inclination that ".........." is a special number? Why? I guess it really is entirely my cognitive bias, because I can't find a reason for it.
But I should have known better as I've--probably obviously being a user here--encounteted binary more than just a few times. And even still, it never occurred to me that 10 in binary is just ".." And then 100 in binary is 1 order of magnitude of "..," 4. And 1,000 is just two orders of magntiude, 8. But still, intuitively this does not seem as natural as 10, and I guess that is completely cognitive bias.
Am I retarded to not have realized this? Maybe, but I actually was so curious about this that I tried to quiz some colleagues by asking what 1000 and 1001 is in binary and only one person got it right immediately, probably by understanding orders of magnitude and not by rote memorization. All the others got it by counting in binary, and one final person was annoyed and questioned why I was asking about binary (oops, sometimes being inquisitive is not socially acceptable). By the way, I work with app developers, most of whom do not have backgrounds in computer science, same as myself.
Past cultures thought even more factors were good, e.g. sexagesimal with 2, 2, 3, and 5. It means that e.g. the expansion of 1/3rd and 1/6th don't form a repeating fraction in sexagesimal notation.
This is the basis for the 12-tone equal temperament scale in music, and it only works if you use base-12. So if we used base-12 for our numbers then someone would have the bright idea to name all of our musical notes with numbers and we could just do a key change (or chord formation) by addition.
I'd wager Gawsh made the best system S/He could given product constraints (completely unfocused if you ask me [which I know no one did]) and the real need to deliver (take it easy over there Leibniz, the world is still crap as evidenced everywhere).
Anyway, can't knock it 'til you've built it.
This is an interesting article:
> Is there really any good evidence that five, rather than, say, four or six, digits was biomechanically preferable for the common ancestor of modern tetrapods? The answer has to be "No,"
Base 11 is the natural base for a ten fingered person: Base 11 has a distinct symbol for ten, base 10 does not.
[A prime base has quite a few practical disadvantages... and their advantages are fairly esoteric...]