The amount of radiation from regular flying probably has no risk as well.
Aircrew have higher risk for certain types of cancers, but it's not clear if radiation plays a role in that. And of course they spend way more time on air than any regular airline customer.
At least for me, doing examples and computations is the best way to learn math, and also very important in research. Often an opaque general statement becomes clear after doing a few small examples. In linear algebra, I personally find some of the courses have too few computations, some concepts are best learned by working an hour by hand on some annoying 6 x 6 matrix..
Your guess is as good as mine. My guess is that all intelligent life in the universe would be "soooo unique", not just the one on Earth. So it would be very improbable any life form would be similar to that on Earth.
However, it could be probable that there are two life forms in the universe which are similar. But then they would probably be too far apart from each other to ever be able to communicate.
Well so far we do not know, so again this is just speculation. Your guess might be as good as mine. There does not seem to be any serious scientific results in this direction, other than nonsense like the Drake equation.
I think the variety among the possibilities for other intelligent species (if any) would far outweigh the number of them. Hence it might be probable that there would exist two similar ones, but it would be very improbable that any of them would be similar to humans.
The point about "communicating" with a piece of rock was exactly that we cannot communicate them. Even if we would run into an alien species (which seems unlikely), it seems very improbable that any meaningful communication could happen.
Even assuming that the concept of "game" would exist elsewhere seems like a ridiculous assumption. All of the things you are saying, even "purely mathematical" are just reflections of the way humans sense the world. Any alien species you are imagining here is just a reflection of mankind.
Anyway, since probably won't know anytime soon, and perhaps never, this kind of speculation is a bit useless. But if we ever found an alien species, it seems unlikely we would be able communicate with them any more than we can communicate with a piece of rock.
The Luzhin Defense is about chess. But perhaps the same novel could be written about a mathematician, I first learned about the novel while reading this article by V.I. Arnold: https://www.math.ru.nl/~mueger/arnold.pdf
> Quickly after the park was established, Whittlesly describes white superintendents trying to make the area “safe” by removing “primitive savages” from the park, claiming they didn’t live there to begin with as they were afraid of the geysers. Those claims were completely untrue; in fact, the Yosemite Indians — as well as Sheep-eaters and Mountain Shoshone tribes — lived on and revered the land, and many others also considered the geysers to be sacred. Tribes such as the Crow, the Blackfeet, the Flatheads and the Kiowa would travel through the land as well at other points of the year, for hunting or in search of obsidian for arrowheads.
> Making the land safe wasn’t the least of the problems for the Native American tribes. In a “park” now protected and preserved from “the wanton destruction of the fish and game found within said park, and against their capture or destruction for the purposes of merchandise or profit,” how were the tribes to eat, sleep, hunt, gather food, light fires? They weren’t. Forced off the land now considered a natural preserve by the government, Indians were once again removed from their ancestral home.
So sure, we could say national parks are "absolutely american"..
Aircrew have higher risk for certain types of cancers, but it's not clear if radiation plays a role in that. And of course they spend way more time on air than any regular airline customer.
https://www.cdc.gov/niosh/topics/aircrew/cancer.html