Pythagoras, in establishing the primacy of the Arithmoi over geometry reveals a simple distinction between real and formal knowledge, between experience and ideation.
That which is "real" flows regardless. As Herakletos put it Panta rhei,
That which is ideation/ formal stands perfectly still as a mosaic an Arithmos of a scene..
The concept of an Arithmos as a mosaic I have discussed in previous posts. To relate the concept further to modern experience an Arithmos is a snapshot, a photograph, a single frame in a video, a 3d holograph,
We currently view things through a pixellated screen, which is a standardised Arithmos.
The Arithmoi are the collection of all such mosaic tools in our imagination. They have to be able to freeze motion.
Once I have a frozen mosaic then I can begin to define a scatter of points and establish a Metron. That done I may begin my Spaciometry and my theory of forms and ideas..
Socrates, playfully took away one freedom: to behold an Arithmoi while standing with the original.nby confining ones mind into a cave , and directing our eyes only to shadows, he takes away the artists full experience that makes it want to model or emulate.mif we accept Socrates and Plato we wander in the dark, and see shadows. But if we take his lesson and reject his cave we may wander in the light of day..
Beware though. Panta Rhein. Thus we cannot see, know or experience everything, and in that sense we are still in the dark.