“True knowledge exists in knowing that you know nothing” – Socrates
Like most people of my generation, I grew up confusing education with the relentless march of examinations and grades. As a student I was diligent and hard working not particularly bright. I had some bad academic years in middle school but eventually performed quite well in the examinations that ‘mattered’.
By the time I made it to College, I found that I had become numb to things like exams, tutorials, grades – the stuff of academic life. I always loved learning new things but the way they were presented in textbooks and the unwavering drone of professors made me feel completely inadequate.
Despite my good grades, I never felt I truly understood something from the basic principles. Mostly all I remembered after years of schooling and four years of engineering education were disjoint facts and big names and even those I started to forget as I began my professional life.
For some reason this always bothered me, it made me look at myself as a fake and I wanted to do something about it. One of the books I fortunately chanced upon early were the Feynman Lectures in Physics. Of course I have only read parts of it but it opened up a new way of seeing things.
For the first time I figured out what does it mean to say something is true within a framework where we have to first assume that certain fundamental truths hold good.Feynman’s engaging style and his complete abhorrence for big words reignited the joy of learning for knowledge’s sake.
One of his childhood anecdotes where his friend asks him the name of a bird and when Feynman is unable to answer, his friend haughtily says ” Your father doesn’t teach you anything!”. Feynman goes on to say that his father taught him the difference between knowing the name of something and knowing something. Its not important to know the name of the bird as long as you know what it eats, what kind of nests it builds, where does it migrate from..
I have tried to apply this principle to my own learning and found that though it is extremely time consuming and hard work but it is hugely rewarding and the kick you get in truly knowing something is unparalleled.
To cite an example of how fragile the bookish knowledge can be, I was looking over quadratic equations in my son’s high school textbook, and right there on the first page was this big, terrifying formulae to derive the 2 roots of a quadratic equation. I had never thought about where this formula comes from, though like any other student I must have solved hundreds of these quadratic equations.
So I searched online for a real math textbook and to my pleasant surprise found the famed Hall & Knight algebra series still in circulation. I had used these books during my engineering entrance days. I decided to buy a bunch of these classics – Higher Algebra, School Geometry, SL Loney’s Coordinate Geometry and Trigonometry. The Indian editions of these timeless books are priced cheaper than a cup of Cappuccino.
And so I eagerly flipped to the chapter on quadratics and found that before that chapter there was a whole chapter dedicated to the method of solving quadratic equations by completing squares and then they just extended this method and came up with the familiar quadratic roots formula. It was not only rythmic and logical but the understanding felt deep and permanent. In fact while researching this I chanced upon another beautiful proof that an equation of nth degree will have n roots.
This is certainly not the way I had learned in school. My school textbook just magically thew up this formula followed by several types of problems. No one told me to step back and think and understand why this formula worked.
Knowledge is not grades or passing of routine examinations though those are inevitable. It is something that we owe to ourselves. Quoting Feynman again “The first principle is that you must not fool yourself and you are the easiest person to fool.”.