[perihelions]

Indeed.

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.

[meroes]

But we can distinguish i and -i by convention and keep consistent right? Akin to sending the distant alien a sample? It’s in the abstract that we can’t really tell them apart. But as soon as we are given any kind of starting point to form a convention, like the first mathematical textbook tells us which is i and which is -i, we have enough?

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?

[AaronM]

I attempted to explain my thought process further up