The Importance of Fully Comprehending

The mechanics of mathematics and arithmetic came easily to me.  I was one of three kids who were put into algebra in 8th grade at my middle school and I took calculus my senior year in high school with about twenty other kids. Yes, I know that isn’t even close to being remarkable today, but at the time it was pretty advanced!

But I was also a bit on the lazy side as far as schoolwork goes, and though I quickly learned the mechanics of solving problems and achieved good scores, I never bothered to fully comprehend the theory and deeper meaning of the mathematical concepts.  Once I arrived in college I struggled initially to keep up with the math, physics and engineering courses because of this superficial level of competency in mathematics. 

Over time I began to see the folly of my approach to learning.  I had thought I was clever when I could utilize something quickly without much effort, but I was missing the heart of the matter.  It took me a few years, but I finally realized both the necessity and the joy of fully comprehending subjects, of digging deep to master the theory, not just the basic functional pieces.

This very human tendency to acquire knowledge at a superficial level and assume one has sufficient mastery of a topic is at the heart of some of the discord we have in our society and world at large.  The Internet and AI have exacerbated this phenomenon.  People look at a YouTube or Instagram video, or read the AI-generated summary of a topic or event and assume they have ‘researched’ it sufficiently to form a strong opinion.  

Truly understanding the complex questions our society and world face requires a significant investment of time and energy.  Few have the discipline or even the desire to make that investment.  Gaining a decent comprehension of history, economics, psychology, sociology, science and politics requires both energetic inquiry and critical thinking.  

Critical thinking is the skill necessary to investigate and weigh the pros and cons of different points of view or theories in order to make a judgment about a topic.  Some subjects are not easy to fully comprehend, but once the effort is made the meaning is very clear.  Mathematics and much of the physical sciences lie in this domain.  Some scientific work has political implications and may be disputed or have varying theories (climate change, epidemiology, cosmology, vaccines, etc.) but careful analysis and resisting the tendency toward confirmation bias can help illuminate the most likely truth.

Other topics outside of math and hard science are more prone to misunderstanding or oversimplification. In interpretating history and politics one is often seduced by superficial readings and the mythology of one’s childhood or prevailing social conventions.  A healthy skepticism and determination to read more deeply will help render a more nuanced and accurate portrayal.

If more people in our society would strive to fully comprehend the critical issues of our times and avoid making superficial judgments, perhaps the partisanship and rancor would diminish somewhat.  I am not optimistic that the current trends in social media and AI will do anything to improve matters, but I would be happy to be proven wrong!