That’s incorrect. Any base system has the same property. For base 12, we would just have two extra digits, and we would be counting powers of 12 instead of powers of 10. Let’s say those extra digits are X for ten and Y for 11. We would write numbers like so (starting with zero and incrementing by one): 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, X, Y, 10, 11, 12, …, 18, 19, 1X, 1Y, 20, 21, …, 29, 2X, 2Y, 30, …
For example, in base 10, a number 265 means we have 10² twice and 10¹ six times and 10⁰ five times (100 + 100 + 10 + 10 + 10 + 10 + 10 + 10 + 1 + 1 + 1 + 1 + 1).
Same number in base 12 has 12² once and 12¹ ten times and 12⁰ once (144 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 1).
A “round” four-digit number in base ten is written as 1000 (written in base twelve as 6Y4). If we subtract one, we get a three-digit string of nines (highest single digit): 1000 - 1 = 999 (written in base twelve as 6Y3).
A “round” four-digit number in base twelve is written as 1000 (written in base ten as 1728). If we subtract one, we get a three-digit string of Ys (highest single digit): 1000 - 1 = YYY (written in base ten as 1727).
I hope this shows you how there’s symmetry between the bases and there is nothing special about base 10 other than we’re familiar with it. If we were familiar with base 12, the “round” numbers for us would be (writing in base 10 here): 12, 144, 1728, … which we would be writing as 10, 100, 1000, …
That would be the case for any base system. Do you know what a base system is? It’s basically how many values before you go to the next place. So base 2, or binary, is 0 and 1. Counting goes 0, 1, 10, 11, 100, … Base 16 is generally 0-F. Counting goes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1A, 1B, 1C, 1D, 1E, 1F, 20,…
The way base 12 would work is that you’d add 2 characters and you would write “12” as 10. Which looks really confusing because we’re all used to base 10. If you were then to do 1010 in base 12 (so in base10 that would be 1212) you’d get 100 (144 in base10) so this still stands whatever base you use.
True! And that’s probably why we use base 10, also we have 10 fingers. But that’s usually the argument for base 12. I think we do ok using it in just certain cases, like time and inches.
but 10 exponentially speaking is more sound 10 100 1000 10000 100000 etc
That’s incorrect. Any base system has the same property. For base 12, we would just have two extra digits, and we would be counting powers of 12 instead of powers of 10. Let’s say those extra digits are X for ten and Y for 11. We would write numbers like so (starting with zero and incrementing by one): 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, X, Y, 10, 11, 12, …, 18, 19, 1X, 1Y, 20, 21, …, 29, 2X, 2Y, 30, …
For example, in base 10, a number 265 means we have 10² twice and 10¹ six times and 10⁰ five times (100 + 100 + 10 + 10 + 10 + 10 + 10 + 10 + 1 + 1 + 1 + 1 + 1).
Same number in base 12 has 12² once and 12¹ ten times and 12⁰ once (144 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 1).
A “round” four-digit number in base ten is written as 1000 (written in base twelve as 6Y4). If we subtract one, we get a three-digit string of nines (highest single digit): 1000 - 1 = 999 (written in base twelve as 6Y3).
A “round” four-digit number in base twelve is written as 1000 (written in base ten as 1728). If we subtract one, we get a three-digit string of Ys (highest single digit): 1000 - 1 = YYY (written in base ten as 1727).
I hope this shows you how there’s symmetry between the bases and there is nothing special about base 10 other than we’re familiar with it. If we were familiar with base 12, the “round” numbers for us would be (writing in base 10 here): 12, 144, 1728, … which we would be writing as 10, 100, 1000, …
Works with base 12 too, look: 10 100 1000 10000 100000 etc.
That would be the case for any base system. Do you know what a base system is? It’s basically how many values before you go to the next place. So base 2, or binary, is 0 and 1. Counting goes 0, 1, 10, 11, 100, … Base 16 is generally 0-F. Counting goes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1A, 1B, 1C, 1D, 1E, 1F, 20,…
The way base 12 would work is that you’d add 2 characters and you would write “12” as 10. Which looks really confusing because we’re all used to base 10. If you were then to do 1010 in base 12 (so in base10 that would be 1212) you’d get 100 (144 in base10) so this still stands whatever base you use.
True! And that’s probably why we use base 10, also we have 10 fingers. But that’s usually the argument for base 12. I think we do ok using it in just certain cases, like time and inches.
Actually this works fine in base 12 too! See my other comment for a more in-depth explanationz