In the context of Mean Curvature Flow (MCF), it's explained that in order to study the development of singularities, two tools are necessary: the monotonicity formula of Huisken and the rescaling procedure. However, I cannot understand... why does rescaling allow us to understand something about the singularities? What are we actually doing?
I would be grateful if someone could clarify this for me, even without excessive mathematical formalism. It's the intuitive concept that I lack.