Have you ever realized mankind used money for ages and our whole economy depends on it but that it actually holds no value at all, only within our system and our conventions? And yet, this world could not do without it. Money is not a mistake but to say that it actually does not hold any value is no mistake either. We only use it to 'make economies work' and that is what irrational numbers do too, they are convenient - sure - but you don't need them, they are mathematical hacks. They are not 'real' (not to be confused with mathematical real numbers).

Check out Sabine: https://youtu.be/ALc8CBYOfkw