In the Wikipedia article on floaters, I discovered that if you make a pinhole and move it rapidly back and forth in front of your eye (with a light source behind it), you can see the blood vessels in your own retina! I just tried it and it works. Evidently, the reason you don't normally see your blood vessels is that they’re always there, in fixed positions, and your optic system just tunes them out. (You can experience that bit by holding very very still and staring at one spot; eventually, everything goes grey.) But the pinhole trick means that you’re only seeing the blood vessels (along with all the stuff you can see through the pinhole) very briefly, and the tune-out-everything-that-doesn’t-chance circuitry doesn’t come into play.