I thought about this for a bit. One easy to use explanation for left and right is a number line. Smaller numbers are on the left and larger numbers are on the right. It's still an assumption that alien species would count that way.
There's nothing you possibly draw on paper that answers the question, in isolation. A diagram on paper means exactly the same thing if you simultaneously (i) flip it, and (ii) flip your mental interpretation if it.
Or: if you run a software program on a raster image, there exists a different program that returns identical output given an input image which is mirror-flipped copy of the first one. (It's just the first program, plus a pre-processing step that flips its input (which is computable). If f is a computable program, and f(img) = "left" and f(flip(img)) = "right", there exists a computable program g=f∘flip such that g(img) = "right" and g(flip(img)) = "left").
Similarly: there's nothing you can do in complex analysis that can distinguish the case where all +sqrt(-1)'s are swapped with -sqrt(-1)'s. Nor can you invent any math whatsoever that has an isomorphism to the plane, that works differently if the plane is mirror-reversed.
I think of an unlabeled, unconnected graph of two vertices. If I just pick one and call it A say by pointing to it, that’s enough. The trick is to do it for limited communication partners like the alien right?
Edit: it's a bit silly though, I think if they could understand our language well enough to convey complex scientific ideas like an atom and its size, then smart people could probably find a good way to convey direction
You completely missed the point of the original thought experiment. The whole experiment already assumes that the Martian understands the concept of direction perfectly. That's the premise of it.
The hard part is to convey which direction is which. It's a completely different thing from the concept of direction.
It's not about Martians is so stupid and we need to try very hard to make them even understand what direction is. It's about whether there is a universal and fundamental (as fundamental as elementary particles) reference to distinquish left and right.
> Now you say if you are standing left side of the line looking left to right the numbers would go 3,2,1 if you are standing on the right side looking left to right the numbers would go 1,2,3
The Martian doesn't know how to "looking left to right". He doesn't know which side is left. That's the whole point.
Very interesting thought experiment while drinking my coffee this morning!