I have often noticed that when people come to understand a mathematical proposition in some other way than that of the ordinary demonstration, they promptly say, "Oh, I see. That's how it must be." This is a sign that they explain it to themselves from within their own system.
Georg C. LichtenbergDiogenes, filthily attired, paced across the splendid carpets in Plato's dwelling. Thus, said he, do I trample on the pride of Plato. Yes, Plato replied, but only with another kind of pride.
Georg C. Lichtenberg