One of the biggest mistakes ever made was in not listening to David Hilbert. Hilbert spelled it all out when he questioned geometry. This text would be far too long if I went into all of Hilbert's analyzing but I'll give you a small fraction of it here right now: Hilbert asked, "What is this dimensionless thing we call a point?"
Hilbert proved, beyond any shadow of a doubt, that such a conception as an imaginary point was absolutely useless when examining our entire universe because as you imagine yourself getting smaller and smaller, while trying to look at things smaller and smaller, this point must start to take on size. It must get bigger as you keep getting smaller and smaller, as you try to visualize this tiny micro world. If you could still keep getting smaller yet, then this thing that was once only a tiny point would finally take up the size of a marble, then a golfball, then a baseball, then a basketball, then eventually a lot of the room in your new universe. If you counter this argument and say, "No, it will not. It will stay at the same point size." Then if that point was at the end of a three degree angle when you got smaller then what is this same angle now that you are smaller? Sorry, you lose. Hilbert pulled the rug out of the very foundations of not only Euclidean geometry but also all types of geometry, because all types are forced to use points. Geometry is OK only if you keep your same size.
