can a sword cut a strand of hair vertically into two without someone holding the hair......

I have used sword a long time now and I do not think this is possable. it is like hitting a fly with a canon.

You can still hit a fly with a cannonball, but the odds are astronomical. But my dad use to use swords when he was in the SCA,it's virtually impossible to do it.

this feat would require a sword of epic sharpness, and one that would be ridiculously impractical to use.

the other parts that are difficult:

getting a hair stood on end without any support.

even if your sword is insanely sharp, the tendency of the hair will be to bend, flex, slide, or otherwise do anything but stand still whilst you try to ut it.

and justifying any circ.umstance wherein this could possibly happen in the real world.

the sword would need to be 40X sharper that the hair is to even having a chance of cutting it long ways but its still be a 1 out of 1000 chance it would work.

a quick reference to the splitting an arrow in half lengthways myth will give you the idea...

Plus there would indeed simply be far too much tendency for the hair to just move out of the way of the blade, also the hair has neither the weight or the velocity for the blade to apply enough pressure to the hair to slice it!

You could drape a hair over a razor blade and it would not cut though it, hair has a high strength to weight ratio, you probably could get cooked spaghetti to slice through though!