I believe in understanding and consistency. Joy in life is found in learning, and learning is done in steps. It is those “ah-ha” moments that are the most thrilling. Academicians have different names for this, but we all know what those moments feel like. You can’t go looking for them; at least not specifically. You might be searching for something else, trying to understand something wholly unrelated. And yet, there it is, and you never forget the feeling.
I was in my second year of undergraduate school when I faced an unforgettable ah-ha. Faced with many esoteric studies, I was immersed in the 3rd of 5 semesters of calculus. By way of demonstration one day, my professor decided to show the power of Newton’s mathematical tools. Starting with the simple F=ma, and in taking about an hour using simple integral and differential calculus, I discovered, there on the chalkboard (and subsequently in my class notes) the three Keplerian laws of planetary motion.
The impression this made was unforgettable because of the story it told, and that it told a story without using any words. You see, Johannes Kepler developed these laws of planetary motion over 400 years ago. There is nothing particularly new or revolutionary in them now. In fact, we use these very laws as tools to travel to the moon and to send robots to the planets. We use them in detail each time we travel in space, or make observations of the heavens. But Kepler deduced these laws empirically – that is to say he studied very detailed observations of Mars recorded by Tycho Brahe, a contemporary Danish astronomer of Kepler’s time. This study took most of Kepler’s life, and he was meticulous about his search for these laws. Kepler couldn’t have done what was in front of me, though, because Newton had not yet invented a new branch of mathematics: the calculus. Had Kepler known what I now had before me, he would have saved himself 40 years of painstaking work. What work could his brilliance have turned to, and what advances could have been made because of that?
The ah-ha made its next appearance to me not a year later when, in my 3rd and final semester of physics class, the professor culminated a two day long lecture with the stark conclusion that one does not equal zero. Now, if there was ever an ah-ha announcement, surely this was it. The professor simply waited, and looked for a reaction. Understandably, it took a little while; it wasn’t exactly clear where we’d been, or where this mathematical construct came from. Upon some review, we all discovered that he had simply demonstrated (with no words, of course) that observation of subatomic particles necessarily disturbs their state. In other words, you can’t know the energy of an electron at the same time you know its position.
This is the Heisenberg Uncertainty Principle, a cornerstone of modern particle physics. And there it is, in all its glory, on the chalk board (and in my class notes) for all to see. Werner Heisenberg won a Nobel Prize at least in part for what was now in my class notes.
In neither case did I go looking for this understanding. I knew it when I saw it. I knew there was deep understanding in brief passages before me. Yet, I’ve known understanding from mistakes as well. I once had a flight student that would repeatedly deploy flaps outside the white arc; that is to say at too high an airspeed. While we were never in danger when this was done, it was simply bad form, and not a habit I wanted to disregard or tacitly encourage. After commenting on the practice several times, the next time it happened, I angrily reached for the controls, and sharply pulled the nose of the aircraft up to quickly slow the aircraft to the proper speed. My reaction was an impatient and ill advised reaction of frustration.
I remember my student’s reaction: it scared her. The aircraft, and her instructor, had just done something unpredictable. She was not ready for this, and withdrew for a few seconds. This is understandable and predictable. I believe in both, and that my impatience and frustration allowed me to circumvent an opportunity to break several instructional maxims was disappointing. On the ground, and during our usual extensive post-flight debriefing, I apologized. I’ll never forget that incident, and I’ll never repeat that mistake.
I’ve often thought that understand and consistency come with age, but this isn’t necessarily so. I feel the fate of the ages descend upon me as I trade the energy and exuberance of youth for the wisdom that is supposed to come with advancing years. To paraphrase Oscar Wilde, I’m discovering that I’m not young enough to know everything (although I’m certain at one time I was.) I’m a lifelong learner, and have observed that our search for knowledge is often compartmentalized into quanta of educational delivery. You don’t need to be in a classroom or in front of an instructor to be garnering knowledge. In fact, my most lucid memories of learning are as a teacher. Nothing like having a student ask you to explain it again do you realize just how hard it is to say the same thing twice, but say that same truth twice. Being consistent allows others to search out their learning process. Everyone’s is different, and only by knowing their own can the incoming knowledge become workable, useful tools. Knowing to recognize others will challenge your ability to describe knowledge, to be consistent, to anticipate their questions, their building blocks of insight, their processes. When you get good at it, and can anticipate its arrival, seeing someone else have an ah-ha is satisfying indeed. For me, this is the -ber ah-ha.
Consistency is not predictability. Logic and reason must prevail, and unsupported or unsupportable premises must be discarded. My students often search for knowledge through a “google” search. I have no objection to finding references this way, but oddly enough, these resources have made it possible to proliferate more fiction than fact. I’ve had many a discussion with students caught in the trap of wanting to find support for a premise in literature, only to fail to disclose the source. This, I warn them in stern tones, is plagiarism. Worse, failing to attribute to a reputable source makes their assertion less convincing, rather than more so. As someone once pointed out it is easier to stick to the truth, if for no other reason than it is easier to remember.
Contradictions can be inevitable. I find the practice of the death penalty untenable, as it strikes me as purely about revenge and retaliation. I recognize the power of martyrdom, but I can also recognize that an imprisoned prophet can motivate dedicated disciples.
I believe in a woman’s right to choose, and there are those that question my consistency as irreconcilable with my rejection of the death penalty. I find no such contradiction, as those who are most reverent about opposing this right of choice most often cite a religious, non-scientifically supported justification for their position. I find all such positions untenable, inconsistent, and contrary to the path to greater understanding. I reject them outright.
The path to knowledge requires consistency, but consistency will not necessarily lead to knowledge. Knowing is not a destination, but a path. A Native American proverb points out that you don’t need to know where your path leads, only that you are on it. Just as the path has an unknowable destination, others may choose to walk the path with you. You will see the world differently once you recognize the path of knowledge, and see others joining you along the way.
Just enjoy the ah-ha’s together.
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