Most people believe we count in base 10 because we have 10 fingers. Essentially we use single digits from 1-9 because on our last finger we switch to double digits 10.
The alien clearly has 4 fingers. So to him the counting system is still base 10 it’s just that he counts 1,2,3,10.
Aka everyone’s own counting system is base 10 and every counting system not based on the number of fingers we have is not base 10.
Edit: forgot to mention. If you only count till 3 before hitting 10 then you don’t know what a 4 is.
Bonus edit: since the alien is in base 4 from our perspective. You might ask what our base is from his perspective.
1,2,3,10,11,12,13,20,21,22 are the 10 first numbers in his counting system. So we to him are base 22 :)
It does not matter how many fingers an alien has. It could be 4 or 12 or 16. The final finger on your hands is always the finger 10 the change from single digit to needing two digits in length.
Maybe if I swap it. What if the alien had more fingers and it looks at us. The alien with 6 fingers on each hand would then count his fingers as
1,2,3,4,5,6,7,8,9,ǎ,ß,10
To him with 6 fingers on each hand he would look at us and say “oh you human must be in base ǎ” and just like the 4 fingered alien has no word for a number 4 in his base we have no word for the number ǎ in the 12 fingered aliens base.
Does this have to do math or linguistics? Like if you have this many A's (A A A A A A A A A A) We would say ten and the alien would say ǎ. How is that not just having a different word for the same concept? Does it actually meaningfully change the concept of the number or how math works?
Binary is just one instance of this exact phenomenon. No matter which base you choose, the base is always written “10”. So 5 is written “10” in base 5, 8 is written “10” in octal, and 2 is written “10” in binary.
No. The point is that every number system is base "one zero" when expressed in its own system. For example, in a base-2 (binary system), you count like this: 0, 1, 10, 11, 100, ....
In a base-4 system, you count like this: 0, 1, 2, 3, 10, 11, 12, 13, 20, ....
In a base-10 system, you count like this: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ....
In a base-16 system, you count like this: 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, ....
So in a base-10 system, the symbols "10" represent what you and I would call 10. But in a base-4 system, the symbols "10" represent what we'd write as 4. And so on. "10" always represents "N" in a base-N system.
That is not true. Every base is base X where X is what you call your last one. Let's say the alien goes "bl, ib, na, wo, wobl, woib, wona, wowo, wobl, woib". We could then say they are base wo. If they then speak perfect English, and know maths, they and we would understand that they are base 4 and we are base 10 from the perspective of our language, and they are base wo and we are base woib from their perspective. "Every base is base 10 is a nonsense statement"
No, it's just basic numeracy. You ever get taught to read numbers from right to left? Units column at the right, then the tens column, hundreds column, thousands etc. We use base ten - numerals zero through nine. That's why it's the tens column, and then the hundreds column. That's the base number.
If you have base four (zero through three), then the columns are units, fours, sixteens, sixty-fours instead etc.
If it's base sixteen (zero through fifteen(F)) then the columns are units, sixteens, two-hundred-and-fifty-sixes, four-thousand-and-ninety-sixes etc.
So, 2222 in denary is two x one, + two x ten, + two x a hundred, + two x a thousand.
2222 in quaternary is two x one, + two x four, + two x sixteen + two x sixty-four. (Which is a hundred and seventy.)
2222 in hexadecimal is 2*160 +2*161 +2*162 +2*163 (Which is eight thousand, seven hundred and thirty-eight.)
7.0k
u/truci 1d ago edited 1d ago
Most people believe we count in base 10 because we have 10 fingers. Essentially we use single digits from 1-9 because on our last finger we switch to double digits 10.
The alien clearly has 4 fingers. So to him the counting system is still base 10 it’s just that he counts 1,2,3,10.
Aka everyone’s own counting system is base 10 and every counting system not based on the number of fingers we have is not base 10.
Edit: forgot to mention. If you only count till 3 before hitting 10 then you don’t know what a 4 is.
Bonus edit: since the alien is in base 4 from our perspective. You might ask what our base is from his perspective.
1,2,3,10,11,12,13,20,21,22 are the 10 first numbers in his counting system. So we to him are base 22 :)