If you do have a multimeter, set it to Ohms. Put one test lead
on the center conductor of the light socket (where the tip of
the light bulb makes contact) and check for continuity to each
of your wires. Whichever one shows 0 is the hot side. Wrap a
turn of black electrical tape around the wire to identify it.

Note: you don't even need an Ohmeter if you can visually trace
which wire goes to the center conductor.

It's wired this way to give you a fighting chance should you ever
stick a finger into a live empty socket. If you touch the outer
conductor (the threaded sleeve) you won't get zapped. You have to
poke all the way in and touch the nub at the bottom.

Thank you very much for the help! I can't actually trace the wires
because the two white wires are actually connected together (or their
plastic covers are) lower down in the fixture, and the light is a
complicated sputnik design, so I can't see the wires for most of their
length, and can't tell if they twist around in there. But I will see
if I can get my hands on a multimeter. That's a big help. Thanks
again!