Goldfish are social creatures (but not schooling). They do enjoy the company of other goldfish; ask any seasoned goldfish-keeper. I've seen this firsthand with my goldfish when I removed one for a series of treatments; the other goldfish became skittish and wouldn't feed as easily. I also have heard firsthand accounts of goldfish withering away after a long-time (10+ years) friend died. They do best with company (unlike betta), but can be kept alone with no ill effects (unlike neon tetra).
That being said, unless you can get a larger tank, I would not get Aki a friend for a few reasons. The tank is just too small to safely house another goldfish. If he does have a deformity, he will be in competition with the new fish for food. The biggest problem will be the increase in bioload for your tank. If you ammonia is at 1 ppm right now with just a single fish, you will have a lot of trouble keeping it down for another fish.
Mirrors do work fine to give your goldfish some interaction. I have a friend with a ryukin that is an eye-eater, so she keeps him in his own 30 gallon tank. The back of his tank has a mirror to give him some "company" while she is away.
Last edited by thekoimaiden; 07-14-2012 at 08:43 AM.