Why is Hash Valuable?

Hashing as performed by bitcoin mining is the equivalent of digging ditches in the yard and then filling them in. Day in day out. It is “make work” in it's purest form. Quite early in the bitcoin learning curve, people usually come across this idea in some form or another. Wait a minute, all the miners are doing is hashing? What good is that? Well nothing really. It is inherently worthless. How could this coin be valuable?

Well the story brings us back to Marx, who wrote that currency should be tied to labor. Work. Proof of work. (Not proof of stake)

So the trouble is, how do you prove labor? If we tie currency to digging ditches, a crew could appear next to a ditch which has already been dug and claim work, effectively double spending the digs. And how can you tell that a ditch has been dug and refilled 35 or 36 times? It turns out that if hash functions work as advertised, that is if they are perfect random oracles, one can “prove” that specific make work has been done.

Don't believe me? Then you should try to come up with a list of 300,000 numbers which have double SHA256 hashes lower than those of the BTC blocks. When you try you will realize that this is going to take a lot of guesswork.

So the answer is simply that used hash has value simply because it is provable. Sure it's make work but at least you have proof that you did it.  Proof that energy was expended.  If you can come up with any other way in the world to prove that you applied a force over a distance, please let me know.