It fails because you apply the model to a situation where it isn&#x27;t applicable. This isn&#x27;t very different than applying Newtonian physics with objects moving near the speed of light.<p>By the way, numbers aren&#x27;t <i>defined</i> as jars of coins. Numbers are a device to make predictions, and you can apply that device to make predictions about jars of coins.<p>I think you find it silly because you know too much about numbers and have forgotten the early years when you learned about numbers. When you teach a little kid numbers you don&#x27;t start with Peano&#x27;s axioms, you start with jars of coins and then you build an abstract model and you convince the kid that the abstract model makes accurate predictions with a series of (thought) experiments.