So what can we do to prevent people creating those official coins out of thin air? If digital things are endlessly copiable, what can we do to create scarcity?
Something is scarce when there’s not an infinite or super abundant amount of it around. Gold is scarce, air is not (luckily). Pandas are scarce (too bad), mosquitos are not (also bad). There are things that are scarce naturally, and some not. Data in digital form is super abundant and easy to multiply at no cost, look at how I copy and paste this and copy and paste this and copy and paste this and copy and paste this and it costed me nothing. So, if we want our money to be both digital and scarce, so we need to create artificial scarcity.
To solve that problem we need two things, and one would not work without the other: We need people to spend something to create our money, so it’s not free to create infinite amounts of our money. And we need to ensure every coin of that money that is created is not falsifiable, so people cannot make infinite and perfect copies of it either.
The first thing we can solve it with mining. The second we can solve with magic math.