Have you ever wondered why Banks have marble floors? You walk in, the place is decked out with fancy columns and marble everywhere. Do you value that? Your goal is to spend as little time as possible at the bank to perform some transaction, does the interior matter THAT much? You know you're paying more for that, right? That bank has to pay for the marble floors, and to do so, they must make money. So you pay more interest on your Mortgage, or get a smaller amount of interest on your savings account.

Why then does this exist in a competitive market? What would make this investment in marble floors profitable? It comes from the bank trying to signal to you their type. "Hi, I'm the good bank. I'm the only type of bank that would find it profitable to invest in lots of marble that it will take me time to repay, which means I expect to be around for a long time"

A fly by night bank, in which you put in your money, and the owner takes off, isn't going to put in marble floors. Only a bank which expects to be in it for the long haul, and expects that you won't terminate or boycott them would be willing to put in marble floors. They expect you won't terminate or boycott them because they intend to act honestly. Marble floors are a costly signal about their honesty.

If we analyze the components of this signal, we can see where the marble floor's ability to signal this honesty comes from. It boils down to a display that the bank spent time, effort, and resources, aka work, to install marble floors. Work is what we can call spent time, effort, and resources. Work tells everyone they intend to act honestly. If they don't, that work was wasted when their reputation's tarnished. Of course, not everybody can see you performing the work, so marble acts as proof that this work occurred.

In other words, marble floors are "proof of work".

It turns out that any form of proof of work has the ability to signal honesty. So long as you are able to prove resources were sunk into your endeavor, this demonstrates your expectation that you won't be terminated or boycotted.

For example, lets say that you wish to communicate with a powerful person who controls a large amount of resources. You are probably not the only person vying for their attention. They have numerous proposals and attempts at communication in their inbox, most of which are a waste of their time. But what if you were able to attach some proof of work to your email? What would this tell them, without them even reading it?

"Hi, I'm the good email. I'm the only type of email who's sender would find it profitable to give you proof of work that it will take time to replace, which means the sender expects continued interactions after you read this me".

A spam email won't have any attached any proof of work. Only an email who's sender expects to be in it for the long haul, and that you won't terminate or boycott them, would have proof of work attached. They expect they won't be terminated or boycotted because they believe their proposal to be profitable for the receiver. Proof of work is a costly signal about the profitability of reading an email.

In case you were unaware, it became possible to attach proof of work to an email with the invention of Bitcoin. Bitcoin's mining algorithm depends on computers spending energy in order to solve a hard problem. The difficulty of this problem is adjusted so that the network of computers solving this problem succeeds in finding the solution roughly once every 10 minutes. Each of these computers spends roughly the same amount of energy on solving the problem. For their effort, the individual miner which finds the solution is awarded some bitcoin. These bitcoins amount to proof of (on average) 10 minutes worth of the entire mining network spending energy to find that solution. Thus, bitcoins are themselves proof of work.

Because bitcoin can't be double spent, it becomes an investment exclusively into that email. This makes it able to send the same signal to the email recipient as marble floors are able to send to potential depositors. "I expect not to be terminated and boycotted by you because I'm honest."

While most believe that Bitcoin has no backing, it's simply not true. Most proponents argument for Bitcoin's value is pointing out that some other person is willing to accept bitcoin in exchange for goods simply because it is durable, transferable, divisible, scarce, recognizable, and fungible. Yes it it also those things, and each of those are required attributes of money. But bitcoin is also backed.