This post deserves to be much longer and deeper than it will be, but I’m still going to post it while I have this brief opportunity.
Plato once said, “Geometry aims at the eternal.” For me, this statement was very true as a 9th grade geometry student in high school, except that it is missing a capitalization: “Geometry aims at the Eternal.”
That was an important year for me. While the years leading up to it and those immediately following it were certainly important as well, including the manner in which they complemented my 9th grade year, but that particular year saw my introduction to high school geometry. I had been a good math student, though not the self-starter I should have been, I believe. (Bad memory from 7th or 8th grade there–can’t remember which.) And I enjoyed math to a certain extent, I think. I remember in Algebra I class in Middle School finishing my work early and being allowed by the teacher to peruse some of the books on her shelf. The books were beyond me, to be sure, but the symbols I discovered there fascinated me and introduced me to the concept of mathematics as a language. I think it was the moment that I moved into a real interest in the subject, though not to the extent this would be true later.
But it was the next year–in Geometry class with Mrs. Paula Russell–that things really changed. I’m not sure if it is still as prominent today (this was before “Informal Geometry” had really caught on), but proofs were still a HUGE part of high school geometry work: assuming postulates, proving theorems, etc.
Seeing a mathematics based on clearly defined assumptions, using those to prove theorems–more complicated and less obvious statements–and then building on those theorems to prove other theorems, etc. was something transformative for me. Though mathematical points, lines, and planes were abstractions and not truly real world objects, it felt as if I were in a completely new universe with new objects to play with and examine. Yet, it wasn’t that it was a new universe that was somehow unrelated to our own. Quite the contrary: It seemed a deeper universe–something more fundamental, on which our own universe was built. A bright, glorious, beautiful place, where the pillars of reality might be seen and touched and felt in some magical way.
I had always been a “science kid” as far back as I can remember, and the idea that we live in a universe that could be mathematically described was not new. But the fact that this is an extraordinary reality about the world had not struck me, perhaps because I didn’t yet see mathematics unshackled from its applications. I don’t know. But I saw it unshackled in Geometry class. For the first time, I saw a truth such as this one I quoted from Clifford A. Pickover on Twitter yesterday:
I felt, perhaps for the first time, that I was sitting at God’s desk and looking at instruments unique to His own work. There seemed something eternal about it, as if those of us in class were simply exploring a place that, for all intents and purposes, had always existed in a way that the physical world around us simply hasn’t. A infinite place that was both workspace and playground. And there was something glorious about it.
These words and descriptions certainly didn’t come to mind back then, but the sentiment was there. And it came at an important time for me, in which my religious sentiments were undergoing a transformation, as well, and I do believe that this class played an active role in that transformation. That such ethereal objects as points, lines, and planes–postulates and theorems and proofs–could be made so very nearly tangible to me, added a tangible sense to God and His realm and thoughts to me, as well. The order in His Creation became so much more real to me that year. Well, that’s not quite right. Rather, my awareness of the reality of order seemed to change in nature a bit. I had known it was there (my science books had always emphasized that), but the fact of its presence became a startling thing–something wondrous and mysterious and not to be taken for granted.
To take things up to a melodramatic level (and I will take them back down in a moment), it reminds me of Job’s statement in chapter 42. It was not that before his trials Job did not know God–I dare say that even then he likely knew God more fully than virtually anyone reading this blog post could claim. Yet, through the trials and God’s lesson at the end of them, he makes the remarkable statement:
“I have uttered what I did not understand, things too wonderful for me to know… I have heard of you by the hearing of the ear, but now my eye sees you.” (v.3 & v.5)
Geometry class certainly did not propel me to such an understanding as Job surely had! Wow, would that be a pretentious claim. 🙂 But, it did have that sort of clarifying and enriching effect on me. The God I knew after that class was richer in detail, fuller in substance, larger in scope, and more different in kind. It’s not a coincidence to me that my 9th grade year was the year God seemed to accelerate His calling in me. It has always been a benchmark year in my life.
These thoughts have been on my mind recently, as I’ve been examining my relationship with numbers — moving from seeing them in a platonic “numbers are real” sort of sense to something else — and, thus, with mathematics, too.
And it highlights the role good teachers play, especially in mathematics. I was blessed with Mrs. Russell. In the hands of a lesser teacher, perhaps I would have been distracted by various “school dynamics” and not been free to really discover what an amazing subject I was studying. I guess I can’t know for certain, but regardless — having Mrs. Russell as my teacher was a very good thing, and I will always be grateful.
Beyond that, I think I will just say that you never know what God may use in your life to help you see Him more fully. For me, He showed up in my Geometry class, and my life has been different ever since.