The joke: In any base X, the Xth number is always the first number to require a second digit. Base 4 goes 1,2,3,10,11,12,13,20,21,etc. Base 7 goes 1,2,3,4,5,6,10,etc.
That alien doesn’t even have a numeral for 4, so it wouldn’t have a word for it either. If it speaks English, uses base 4, and uses the same words we do for numbers, it would sound like this when counting rocks: “One, two, three, ten, eleven, twelve, thirteen, twenty…”. But when it says “twelve”, it means the same thing as when we say “six”.
If you want another example, try counting to 10 in hex (base 16).
Also, base 10 is always base 10, but “10” in base 2 is 2 in all counting systems above base 2 (since base 2 doesn’t actually include 2, just like base 10 doesn’t include “A”). Likewise, 10 in base 10 represented in base 2 would be 1010. ;)
Base 1 usually uses ones, because it represents summation at that point. Using zero as the numeral would be a bit awkward. Also historically zero is pretty new.
Numbering systems all essentially evolved from base 1. People started out keeping track of wheat/barley using tally marks representing a single stalk, then creating different tally marks representing bushels, baskets, etc. More intentionally designed number systems based on things like the number of fingers on our hands came later.
The joke: In any base X, the Xth number is always the first number to require a second digit. Base 4 goes 1,2,3,10,11,12,13,20,21,etc. Base 7 goes 1,2,3,4,5,6,10,etc.
But the joke would only work written, not spoken first contact? Base five we would still say five just the numerals would show 10.
That alien doesn’t even have a numeral for 4, so it wouldn’t have a word for it either. If it speaks English, uses base 4, and uses the same words we do for numbers, it would sound like this when counting rocks: “One, two, three, ten, eleven, twelve, thirteen, twenty…”. But when it says “twelve”, it means the same thing as when we say “six”.
So the base is always written as base 10 in the native base. So base 2 (in decimal) is base 10 (in base 2)
If you want another example, try counting to 10 in hex (base 16).
Also, base 10 is always base 10, but “10” in base 2 is 2 in all counting systems above base 2 (since base 2 doesn’t actually include 2, just like base 10 doesn’t include “A”). Likewise, 10 in base 10 represented in base 2 would be 1010. ;)
Base 1 is “base 0”.
0 is expressed as .
1 is 0.
2 is 00, and so on.
Base 1 usually uses ones, because it represents summation at that point. Using zero as the numeral would be a bit awkward. Also historically zero is pretty new.
Tally marks are essentially a base 1 system.
Numbering systems all essentially evolved from base 1. People started out keeping track of wheat/barley using tally marks representing a single stalk, then creating different tally marks representing bushels, baskets, etc. More intentionally designed number systems based on things like the number of fingers on our hands came later.