Is my goldfish dying?

welcome to a2k fiddlesticks. Sorry your first post should be so serious.

I really have no idea whether the fish is dying or whether he is trying out a new swimming style.

Is the tank well oxygenated? Perhaps he's lethargic.

It sounds like swimmers bladder.
Swimming upside down in strange patterns, not being able to turn over, but NOT dead. Actually appearing very ALIVE... just upside down?

Go buy a small bag of frozen peas.
Start putting 2 in his bowl every day. Mash them of course.. :-)

Swimmers bladder is quite common in goldfish and is sometimes caused by over feeding of dry foods. One gold fish should only be eating about 4 flakes of dry food once a day. If you are feeding more then that, you need to stop. They ALWAYS appear hungry so dont worry, you wont be starving your fish.
Goldfish ( and most all fish for that matter) only have a memory of about 20 seconds. It is a survival technique. In the wild, if they remember they have eaten, on the rare occasion they will FIND food, they may not eat. Forgetting ensures they will always hunt for food. ( silly analogy.. but! )
You can do a google search for Swimmers bladder + goldfish and get some more info if ya need it.
good luck . :-)