If a currency is "backed" by something, it means the issuer is willing to exchange it for another resource, usually at a fixed ratio. For example, a gold-backed dollar (when they used to exist) could be exchanged for a certain weight of gold. There is no such thing for Bitcoin.

Bitcoins can be exchanged for the ability to add a new transaction to the blockchain, at the very least. It might be abstract and of questionable value but there is certainly such a thing.

And this is getting a bit whimsical, but why is the gold valuable?

Gold is valuable because once upon a time the government accepted gold as a tax payment. The use of gold as money lasted for so long that people began to think that there was some kind of magic behind gold. Most of today's gold prices are based on belief in that magic.

About that idea, I say that its false, and relies on misunderstanding of at least what "backed by" means for a currency, and probably a strained view of what are "established laws" of economics, as well.

Can a government "back" currency by deeming it to be valuable, without offering to exchange it for a store of value?

If not, saying that Bitcoin is "not even backed" by fiat is meaningless. If so, we are using "backed" in the wrong sense.

"That speculative credit default swaps were also backed by established laws of math and economics"?