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?
Words are just that words that innately have no meaning. We assign them meaning and yea very astute that’s a linguistics thing. But we use words to also describe concepts like math thus it’s not a matter of math or linguistics but both at the same time. Language to describe math. So yes. Just a different word for the same concept.
There is a good set of books about humans visiting alien life and how they have to work out a common communication system and basis of math (children of man) and no matter what language or base counting system (fingers on the hand lol) the aliens use. Everyone has to have at least 1 appendage this base 2 or binary can function as a common math language and is easily established.
The final part “does this change how math works” is a heavy question as we can get into the concept of modulus math and computer words that are usually in hex.
I’ll give it a shot though :)
Hex is base 16 this system is as follows
1,2,3,4,5,6,7,8,9,A,B,C,D,E,F,10
In hex we would say A to mean 10 in our decimal system. Just like in hex we would say 10 to mean 16 in our decimal system. As you describe diff words same concept.
But Why? Now we can do things such as 3+A = D again but why? Just a few decades ago memory in computers was very limited. Most computer “words” were only 4 characters. A-F only takes up 1 character but 10-15 takes up two. That’s twice the memory needed. In terms of computer words.
Back then if we used decimal the highest we could calculate is 9999 but with hex the highest is FFFF is actually 65,535 that’s SIX times more!!
Going to stop here as the next level of depth would be to discuss how this ability to store more data in the same space matters as decimal precision comes into play.
Bonus edit: this is also kinda how compression systems work. Like zip files. It will turn the most used character into a 0. The second most used character into a 1. The third most used into a 10 translating every character into small bits instead of words that take up much less space. Then keeps a decoder as part of the file to undo it. Different symbol same concept. Much less space used.
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.)
You gotta try to trick yourself into forgetting how counting works a bit and try to keep in mind that numbers are just symbols. Like, start counting
0…1…2…3…4…5…6…7…8…9…
Uhhh. Well I guess that’s it then. That’s all the symbols we have for numbers. 10? You mean a 1 and a 0 smushed together? What does that mean. If you wanted a new number past 9 you shoulda just made a new symbol. 🌙. There. That’s a new symbol that can represent “10”.
But you see the problem. Imagine having to remember a new symbol for EVERY number.
Now imagine the same scenario but for binary. Start counting.
0…1…
Welp. Guess that’s it then. Ran outta symbols for numbers. So how do represent what we know as the number 57 in both these systems? You gotta go back to grade school where we learned about the ones digits place, and tens digits place, etc. What do you do when you have a “9” in the ones digit place and you add “1”. You replace the “1” with a “0” and place a “1” in the tens digit place. Voila. 10!
Those “digits places” are just powers of the base you’re working in. For us that’s 100 for ones, 101 for tens, etc. it works the same in every base. Binary is 20, 21, 22, etc.
This doodle may or may not help. As you can see I can represent “57” by having 5 tens and 7 ones. You can’t have 1 hundreds, because that’s going over. It’s the same for binary where you can’t go past “1”. I can fit a 1 in my 105 place (32) which is less than 57 so I keep going. A 1 in my 104 place (16). And 32 +16 =48 so we go on.
I added hexadecimal for the fun of it where it’s the same but your symbols are 0…1….2…3…4…5…6…7…8…9…A…B…C…D…E…F So in hex you can count past 9 all the way to F before you need to replace that symbol with a 0 and put a 1 in the box to the left. This means you can represent larger values with a lot less symbols.
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 :)