Maybe the point is supposed to be a metaphor for a fertilized egg. Unless we read the DNA of the egg we have no way of knowing what it is going to differentiate itself to become. In the same way, unless we read the equation of the geometric shape, we have no way of knowing whether the point is going to grow up to be a baby circle or a baby square. Until then it's just a point.
But they cannot be the 'same' point, seed, egg, etc…
If we all were to wear the same genes it might make our butt look big…