Everyone assumes aliens will know higher math. So much so that some people think encoding the orders of the first 26 sporadic groups would be obvious. (IDK why this is better than a list of primes)
But would it, though?
We name the groups by their orders, and think it's neat that exactly 26 are special in this way, like the 5 platonic solids.
But couldn't you do a lot with math and never really focus on these facts? It's not free from culture. math has a culture.
@futurebird I think the trick here is that what call math is really just a language to express things that Already Exist in nature. There is a famous Jordanian mathematician who was "discovered" by travelers, living in the highlands, herding goats. He had written his Own system of math, and had in the process re-invented Calculus. "Math" isn't cultural. How we apply it though, certainly is.
How we describe it, apply it AND what we choose to pay attention to or ignore.
That last one is the big one IMO. There are all kinds of math questions that just don't matter, or are too hard to formulate, or everyone gets frustrated in the definition stage.
Here is a question I've had for a long time that just hasn't fit in anywhere:
https://math.stackexchange.com/questions/34452/yarn-like-functions
@futurebird @VaylLarkinPoet If a civilization had encountered them, our knowing the orders of the first 26 sporadic groups would be extremely strong evidence of high mathematical intelligence. But indeed there's no reason an advanced civilization would have encountered them. On opposite end of spectrum, any should know primes, but they don't demonstrate high mathematical intelligence and could even plausibly emerge from some physical process without intelligence taking part.
If a natural system makes primes it's just as worthy of research as aliens. It's a good "hey look over here" either way.
@futurebird @dalias @VaylLarkinPoet Like periodic cicadas?
