Platonic World

Plato thought that this world is like a shadow projected on a wall in a cave. We live in the cave just looking at the shadows. We think the shadows are our only reality. But what is it that cast the shadows? Plato thought it is the real reality which he called "Idea(イデア）".
I like this philosophical concept, especially after I learned quantum mechanics(量子力学). What it tells us is that there is actually Platonic world which is invisible to us unless it is projected to what we think is our world. This is one of the things, together with the theory of relativity (相対性理論), without which we cannot explain our world, I mean, only by our common knowledge. Time is not the same between you and me. Something is here and there at the same time! Incredible.
But what is the Platonic world like? Many scientists agree that it is like the world of imaginary number(虚数). What it suggests is that the Platonic world is made of two components; quantity and phase. In such a world, 1 + 1 is not always equal to 2, due to the phase.
Come to think about it, we studied imaginary number and we know it is the square root of minus 1. When you studied it, you must have thought what the heck was the use of this stupid idea. Me too. That's when most of the students start to hate mathematics. If only our teacher had told us that the imaginary number is the base of our real world and mastermind it. It would have made things different. At least I would have studied imaginary number more.
I would suspect that most of the mathematics teachers themselves do not understand what they are teaching. Or they do not like mathematics themselves. It is sad and tragedy for the students if their teachers do not love what they are teaching. If I taught mathematics, I could not help teaching it together with its meaning in the context of physics or chemistry, because it is so interesting for me. I love the subject after all. The quality of teachers is fatally critical to this country.
But above all the things, we must know that our visible world is a shadow of the Platonic World. We must look toward the opening of the cave where the light comes in casting the shadow, no matter how dazzling it may be.