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.
Imagining aliens that never really get digital (finger based) math. Their math is all analog, about measurements and estimates. Their computers don't have crystals, cycles or clocks.
They find discrete math silly and amusing. Because that's not how the world is *obviously* --
The develop better understands of statistics and prediction than we've ever been able to master. But have no notion of anything like an integer or a bit.
"Sally has 4 apples Bob has 3 together..."
This is a ridiculous problem.
"Sally has 138.3495... grams of apple pulp 12.49505...grams of skin and 3.00456...grams of other apple solids-- " of course writing with our number system still causes problems.
We just don't have the precision required to convey exact irrational numbers like the aliens do.
The aliens have no idea what we mean by "irrational numbers"
Imagine if they didn't have "=" and the concept of equality. Much of our math would make no sense to them.
