Say you convert color of the sock in the drawer to a range [0,1] on your one and only coordinate. Then you convert dirtiness of the sock to a similar range and

Say you convert color of the sock in the drawer to a range [0,1] on your one and only coordinate. Then you convert dirtiness of the sock to a similar range and just add them together. Can you differentiate between a sock that is 0.4 on color and 0.6 on dirtiness from another sock which is 0.6 on color and 0.4 on dirtiness? I suppose you could encode it all to one number so that structure is preserved, but dimensions themselves are not going anywhere, they are in your choice of encoding that must reside outside of your one coordinate.