Based.
Wow I never thought about that.
But it is always like this:
let there be any base "b"
That can represent a number by the sum of their positional digits:
number = sum(d_i * b ^ i)
where i is the position index and d_i is the digit at this position. (note: index starts with 0, from the least digit farthest to the right)
So the (decimal) number 4 in base 4 is then
1×4¹ + 0×4^0 = 10
And (decimal) number 8 in base 8 is
1×8¹ + 0×8^0 = 10
And 10 in base 10:
1×10¹ + 0×10^0 = 10
Plot twist: there are 8 other stones and the alien is really using base 10 (or base 30 if you use base 4)
The most reliable way to communicate bases would probably be using unary. Now if your alien is using unary, that might not work, but it should for all higher bases.
I’m not sure if I fully understand.
I was thinking, wouldn’t it be easiest to describe the system you use by taking the last number in your first decimum and then saying you increment it with one?
E.g. for base ten this would be: base 9 + 1
For binary it would be: base 1 + 1
For hexadecimal it would be: base F + 1
Etc.
But if you’re talking to an alien that uses base 4, they don’t know what you mean by “base 9+1”. Wtf is a 9?
Can we all use base 12?
It will be a shower of shit for like 50 years but then it will be marginally better for pretty much everyone.
Some people argue that it would be harder to count on your fingers but we could just surgically give everyone more?
There are 12 sections on your fingers (excluding your thumb) you then use your thumb to count to 12 on one hand.
Two hands can allow you to count to 24. Which is way higher than 10. Base 12 is better!
Billions of years ago, our collective great-great-great-[several million more]-grandparent evolved a fin with a five bone structure. That idiot didn’t know anything about common denominators, and now we’re stuck with this numeric system that can’t divide things into thirds without causing issues.
When was the last time you’ve actually needed to count something on your fingers?
I find it useful if I’m counting only specific instances of something that meet some criteria. That way my brain can focus on picking out the right things and not have to worry about keeping the current count in mind. I use the method with your thumb on each segment of your fingers though, so you can get up to twelve with one hand and 156 with both
Binary is very good for counting with your fingers. With both hands you can count to 1023. One hand is 31, which is still usually more than you typically need to count. It’s also trivial to do once you know how binary works. It takes very little thought, though potentially the decoding could take a bit depending on your proficiency.
I made it to 27 on my first attempt, so def messed up somewhere. Also, my fingers don’t want to work that way.
Doable.
Why base 12 though? Base 16 is even better. And base 60 is even better than that!
Common denominators. You can divide base 12 into half, thirds, fourths, and sixths and still use integers. I find thirds to be particularly useful, so base 16 is out. Base 60 can do it, but that’s getting unweildly.
50 years? I bet we couldn’t even agree on how to write “11” & “12” on such short notice. (See: date format, encoding, etc)
we could just go with the hexidecimal way and go with A,B,C for 10,11 and 12
42* years. Centuries are now 84 years. We are living in the 19th century! I rate this idea 12/12.