The opening words
If you can look at an equation and, without anybody guiding you, see for yourself why that equation is true and self-evident—not as a sequence of mechanical steps, but as a holistic, self-evident truth—that’s a level of mathematical ability to aspire to.
You may be able to calculate all kinds of things, pass most tests, but have very little understanding why that mathematics, existentially, is a fact in actuality.
Then equations become poetry. Descriptions of something beyond description. Like a sunset: you can describe its colors, its textures, its feelings, all of it. But it alludes to something beyond description. Something that is so simply actual that it cannot be encompassed in words, because a word is not the thing. A poem is not the thing it describes. An equation is not the thing it alludes to.
I tell you this because I do this all the time. This is my practice. It’s part of my practice. I looked at that hypercube equation, and I said, “Oh, that’s an interesting pattern.” And I meditated on it. And now I can see, since our last session, why it’s true.
That’s pretty cool.
I lay in bed. I sat at the park. I closed my eyes, and it dawned upon me why that equation describes the actuality of the hypercube and its family of n-dimensional polytopes.
So when we work together, we’re holding you to a standard much, much higher than most teachers will even consider possible.
You see Pythagorean theorem. You say, “Okay, well, I see it’s true, but why?” You see some algebraic equation. You say, “Well, can I factor that?” Okay, but why is that true, right?
And that’s what I’m trying to teach you, because then all of your math is founded upon an actual knowing.
And here’s the one great benefit. The central benefit is you get to know math. Not simply do it and go through the motions, but you get to actually know math more deeply. It touches your soul more completely. It becomes your mind. Your mind takes the form of what you focus on, and you become math instead of some mechanical technique.
And I feel you could do it.