Before a new currency exists, it doesn't exist. Someone has to mint it. It has to be inflated into existence, in the monetary sense. How is this done?

For a state or central bank the answer is obvious: The state or bank itself prints it.

For a private actor the technical means is perhaps less obvious, but the actor behind the currency obviously gets to decide.

For a decentralized open source project, it is less clear. You could do it so every node in the system gets a piece of every newly printed unit of currency, but if it is free to run a node everyone could just run a billion nodes and take all the currency for themselves.

Bitcoin solved the problem with Proof of Work, which is elegant because both the double spend problem and the minting problem is solved together. Every node has to prove it has run a unit of useless computation and inflation is spread evenly across worker nodes. This led to a split between nodes and miners with the use of specialized hardware, but the basic premise still holds.

Crypocurrencies in general are very different. Ethereum, the second most popular, was created by a private actor and the that actor decided to print 72 M for themselves and promptly sold 80+% before the release of the software which gave rise to the term ICO which was very trendy for several years. After the initial release inflation continued according to the miner model.

> Are cryptocurrencies supposed to be a potential replacement for real life cash?

They are supposed to be a medium of exchange. “Real life cash” is one of many forms of money; even for any particularly currency, like dollars, a very small fraction of use is “real life cash”. But, yes, in the most extreme visions, cryptocurrencies replace other currencies for all uses. More moderate visions, however, exist. So, as always when you use “supposed”, the answer is undefined without qualifying it as to by whom it is supposed.

> If so, why does it make sense that people can "generate" cash by proving some amount of work done?

Because there needs to be some mechanism to provide the currency supply, and also some incentive for people to provide the infrastructure on which the currency system relies. For fiat money systems the first is typical policy making in a central bank, and the second is government action to control competition in the banking space and to support banks, reinforcing the profitability of banks. Mining serves both of those functions in a cryptocurrency system (both reinforcing the profitability of transaction network participants and providing the mechanism by which currency supply is managed.)

> Is the main functionality of these cryptocurrencies supposed to be "people can send currency to each other", or "people generate currency -- a number -- and sell this currency for real life money"?

Participants in a currency system selling it for other currencies (FOREX) is a feature of every currency system in a world with more than one currency. Again, the degree to which each of those is “supposed” to be the main function depends on exactly whose supposition you are looking at it.

One of the weird things about our world is that money is central to everything, but it’s hard to understand how it works. There’s a great deal of handwaving around how, for example, dollars are created, much of which is, in fact, not correct at all (most dollars are created not by the government, or even the Federal Reserve, but by private banks, via a mechanism which I will not pretend to fully understand).

The big flaw of Bitcoin, to my mind, is that it is an inherently deflationary currency. Deflation is one of those things that seems great on the surface: prices go down, not up, but when that happens it ends up creating an economic incentive to avoid spending since why buy something today if it will be cheaper tomorrow, and this ends up causing economic activity to slow down or stop entirely. A small amount of inflation, on the other hand creates an incentive to either spend money or invest it in something that will provide a better than inflation return, whether that’s putting it in a high-yield savings vehicle or making capital or financial investments. With deflation, you can just leave your funds in cash (where they will not provoke any economic growth) and get a return.

Yes, Bitcoin is a replacement for central banking currencies. Its the first few lines of the white paper.

This is how money works. If you use a medium of exchange and unit of account for goods and services then that medium must increase at the same rate as the increase in goods and services otherwise you get second and third order effects such as inflation, contraction, rising unemployment, etc., directly impacting its ability to act as a unit of account.

In Bitcoin you don't generate cash, you earn block rewards for acting as a consensus broker which otherwise would require a central banking settlement layer. This activity, tied directly to the transaction layer, acts to maintain the equilibrium between increases in goods and services and expansion of the money supply.

Wall Street got ahold of it and now Bitcoin is primarily acting as a Store of Value for the purpose of speculative investments. Driven primarily by the fear of missing out and market manipulation since Bitcoin is heavily centralized.

> If so, why does it make sense that people can "generate" cash by proving some amount of work done?

Think of it this way: If you pay with physical cash, there are people somewhere who do the work of digging ore out of the ground, smelting it, shaping it into coins, cutting and printing paper and so on. All these people do that, because they get paid in the same currency that they themselves have minted.

It turns out that nobody has yet found a way to create a digital decentralized currency that that works without incorporating a similar concept of incentivizing the creation of currency.

Bitcoin was designed to be a replacement for real life cash, but it ultimately failed in this role. Nonetheless it was a great experiment that essentially invented the industry.

Most cryptocurrencies, if we go only by their number, are designed to make their creators rich and moderately succeed at that. This is your ERC20s, pump dot fun, et cetera.

If we only consider ones that have any serious chance of being usable as actual currencies, these days they're usually designed to run arbitrary money-like programs known as "smart contracts", of which traditional money is just one.

Money can't be sent until it's generated, that's the same whether you're talking bitcoin or dollars. There's always a rule for who gets the new money when it's created, and somehow the rule always ends up being "rich people get the new money". Dollars go to politicians and big bankers, bitcoins go to big compute farms, ethers go to big bankers, monero goes to big compute farms. The aforementioned get-rich-quick currencies go to their creators, if course.

It's just a mechanism to incentivize mining. The alternative is that miners are paid only via fees, but that risks making it prohibitively expensive to transact. Minting new coins distributes the cost of mining over all holders by inflating the currency a little bit. Fees are still necessary to avoid spamming.

You can't "generate cash" for doing some amount of random work. You are getting paid for securing the network and keeping it decentralized, and this payment is done in the native token of the network. It's an incentive mechanism, it's a reward for the people who provide the infrastructure for the network.

Broken Money by Lyn Alden is a good book on the topic

They're meant to replace the bank.

Cryptocurrencies allow market participants to communicate value to each other without having to trust other market participants or an institution. Mining verifies transactions and commits them to the public record, earning the miner a fee for their work.

> This of course cannot be done with normal cash.

Normal cash is just printed out from thin air by those who have the power. In that sense (some) cryptocurrencies are better because at least the process is open.

There are two parts of an answer to this, because your questions are somewhat divergent:

> why does it make sense that people can "generate" cash by proving some amount of work done? This of course cannot be done with normal cash.

People do generate money when they work, in a sense, because money doesn't have value. Money represents value. To really understand that you need to think about what money is and why it was invented in the first place.

Before the invention of money there was only direct exchange; I do/give something for/to you and you do/give something for/to me in return. But what if you want what I have but I don't want what you have? Or what if we want something from each other but are too far apart to make the exchange directly? Well, we find a third participant who can act as a kind of transfer agent. They could, for instance, have something I want that you don't want and also want something from you. They trade with you first so now you have something from them that you don't want that you can then trade to me for the thing you want, and everyone is happy. This extends to arbitrarily many, dozens or hundreds even, of intermediate steps.

Now it should be easy to recognize two things:

1) Everyone needing to store a bunch of stuff they don't actually want just so they can pass it on to the next person can become a huge burden for everyone. And how do you store labor anyway? You can't. You can only store goods.

2) Organizing dozens of intermediate links is an extremely difficult problem to solve just so you can get what I have.

The first one can be solved by exchanging IOU vouchers instead. The holder of the voucher becomes entitled to the thing that hasn't yet been given or done. Storing those vouchers is trivially easy compared to storing the things. And you can just as easily store vouchers for work that hasn't been done yet as you can for goods that haven't been given yet.

The second one can be solved by saying what if people put their vouchers into a central voucher bank instead of passing all their vouchers around to each other directly, and then the central voucher bank organizes all the intermediate steps for people without people needing to figure out who has the vouchers they need to complete the chain.

And then once you're there, why even use specific IOUs at all? Why not have all the vouchers be generic but you get different amounts of them instead of different kinds that you can then use freely for anything? And that's obviously what money is.

And from there a new thing should become obvious: The money itself doesn't have any intrinsic value. The labor/good behind it does. Money is just a way of representing the value of something you did/produced in a form that can be easily traded for other things. It's the medium of exchange, not the product. And when there are fewer vouchers in the system relative to what's being produced, each voucher becomes worth more (deflation), and vice versa (inflation). And then the government literally prints and destroys vouchers as needed to try to keep a balance. That is a thing that happens. And so what if there can be prolonged time delays between you doing your work and you receiving your vouchers under some systems? Time delays are not inherent, just practical for bookkeeping. And when long time delays are not practical for bookkeeping they become shorter.

> Are cryptocurrencies supposed to be a potential replacement for real life cash? This was my understanding of the motivation behind Bitcoin, at least.

Only as an unrealistic pretense in the current climate. The reality is that a currency needs to be both moderately inflationary and also very stable to be useful as a medium of exchange of goods/services. You never want it to be a better financial decision to hold onto currency forever instead of using it, and you also never want people to randomly wake up destitute. And regardless of whether bitcoin is technically inflationary in the near term, it is not practically inflationary, and it's definitely not stable.

> If so, why does it make sense that people can "generate" cash by proving some amount of work done?

Because you need an incentive for 'miners' to participate in transaction processing.

Main functionality is transactions which are not controlled by any single entity (like the government).

Most of it is speculation unfortunately, which gives it a bad name, drowning out real usecases.

They are supposed to be a replacement for suitcases of cash for illegal transactions (drugs, [kidnapping] ransoms, that sort of thing). With a side of gambling and tax evasion.

> Are cryptocurrencies supposed to be a potential replacement for real life cash? This was my understanding of the motivation behind Bitcoin, at least.

This was the original stated purpose, yes. But this works poorly in practice. Hypothesized frictionless tooling that would make it easy to make purchases with crypto has not emerged.

Nowadays it's held more like a speculative asset with value that comes from scarcity and demand, much like gold (though gold has some industrial application which Bitcoin does not).

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yes, Bitcoin was hijacked by the company, Blockstream and they injected the SegWit and RBF attacks to kill it as a currency, Bitcoin Cash still functions as Bitcoin however.

Monero is similar to Bitcoin Cash, a useful replacement for cash in most cases.