>But, though we have to do it all the time, no one has ever found a perfect way of assigning scalars to vectors and no one ever will. Write the vector (x, y) i

>But, though we have to do it all the time, no one has ever found a perfect way of assigning scalars to vectors and no one ever will. Write the vector (x, y) in [0,1]^2 in its binary representation as (x0.x1x2..., y0.y1y2...), resolving any repeating sequences of 1s, and let f(x, y) = 0.x0y0x1y1x2y2... Then f is injective and therefore bijective onto its image. (I know this is incredibly pedantic and f isn't continuous/doesn't preserve whatever mathematical structure, but I think you're inviting this comparison when you write a blog post that is just saying "You can't represent everything 1 dimensionally" which everyone knows but unnecessarily couched in mathematical jargon)