You can't imagine the feeling I got when I saw the next book on my list was a MATH book! Yuck! But I plowed on and found it fascinating. I'm not going to pretend I understood it all, but there were pieces where I thought "Cool!", or "That's amazing!", or even "I can see where he's going with that." Many of the Great Books that I read, I don't really follow completely but I read them anyway, taking a note here and there, and sometimes just writing "What?!" in the margins. I've learned from experience that I may not understand what I'm reading at the moment, but it is building something somewhere in my brain and days, months, or years later, I will find new building blocks to put on top of the ones I've collected here.
This book was written about 2000 years ago and it was not what I expected at all. I thought I'd find numbers and answers and proofs like I found in my math text books, but this was all words. And the math concepts were related to the world around me and philosophy, so it held my interest.
Here are my two favorite quotes.
"Without the aid of these, then, it is not possible to deal accurately with the forms of being nor to discover the truth in things, knowledge of which is wisdom, and evidently not even to philosophize properly, for 'just as painting contributes to the menial arts toward correctness of theory, so in truth lines, numbers, harmonic intervals, and the revolutions of circles bear aid to the learn of the doctrines of wisdom,' says the Pythagorean Androcydes."
What?! We should understand math to truly understand the world and what's in it? Oh, man! Now I've really got work to do. But it's not actually about the numbers exactly. It's about the relationships and that I can handle. Just don't ask me to multiply and divide in my head!
And here's my favorite.
"For it is clear that these studies are like ladders and bridges that carry our minds from things apprehended by sense and opinion to those comprehended by the mind and understanding, and from those material, physical things, our foster-brethren known to us from childhood, to the things with which we are unacquainted, foreign to our senses, but in their immateriality and eternity more akin to our souls, an above all to the reason which is in our souls."
Wow. Do we need things like a basic understanding of mathematical principles to help us understand the universe and God? After reading other books that show the magic and symbolism of numbers, I say yes. Understanding these patterns shows us the majesty of God, in my mind. It's amazing!
Oh! One more. This one relates arithmetic, geometric, and harmonic to philosophy as well.
"For the realm of the greater there arise excesses, overreaching, superabundance, and in the less need, deficiency, privation, and lack; but in that which lies between the greater and the less, namely, the equal, are virtues, wealth, moderation, propriety, beauty, and the like, to which the aforesaid form of number, the perfect, is most akin."
Just perfect. I hope next time I read this, or something like it, I can understand more of the math though. I have loads of notes, but I don't see how I can write it out on a blog. More drawings than words.