

One of my favorites is the “ladder paradox” in special relativity, although I originally learned is as a pole vaulter rather than a ladder:
A pole vaulter is running carrying a pole that is 12m long at rest, holding it parallel to the ground. He is running at relativistic speed, such that lengths dilate by 50% (this would be (√3/2)c). And he runs through a barn that is 10m long that has open doors in the front and back.
Imagine standing inside barn. The pole vaulter is running so fast that the length of the pole, in your frame of reference, has contracted to 6m. So while the pole is entirely inside the barn you press a button the briefly closes the doors, so that for just a moment the pole is entirely closed inside the barn.
The question is, what does the pole vaulter see? For him, the pole has not contracted; instead the barn has. He’s running with a 12m pole through what, in his frame of reference, is a 5m barn. What happens when the doors shut? How can both the doors shut?
I will admit that I have never used this thought experiment for any practical end.
This is not the same for all crypto currency, but a bitcoin represents a “proof of work”. When people “mine” bitcoins, they are consuming computational resources, and when they find a bitcoin, it is a certification of the work that was done to find it that becomes the value of the coin. And then, as others as mentioned, people just agree that that work has a certain amount of monetary value. But the proof of work is what limits the supply and allows that value to exist. 3Blue1Brown has a really good video that goes into the technical details if you’re interested.