Ramasamy’s Calculus

Foundation of mathematics is in the substance of brain

Photo credit: Hernan Pinera; www.flickr.com/photos/hernanpc

During my high school days as I was learning to do trigonometry, a question always bothered me. What prompted us to ‘create’ trigonometry? For that matter, even calculus and statistics. What drove us to create these mathematical techniques?

I have a liking for the driving that I do on Sunday mornings to work. The streets are quiet and freeways are wide and open. One day, as I was cruising between other cars and trucks, a thought struck my mind. What kind of neural process happens inside my brain during the moments when I maneuver the car to switch lanes by getting in between two moving cars? There must be some rigorous computation for such an ordinary act. Eliminate the unnecessary details in this scenario and just focus on the act of placing an accelerating object into the space between two objects with variable velocities. Most humans are capable of doing this effortlessly. However it would need an enormous amount of knowledge to program an object to do this autonomously. To arrive at a solution, a problem of this type would need computational process that includes advanced calculus and statistical approximation. Human brain computes the distance that will be covered by the moving cars over time and calculates the points in space needed for the driver’s car and places it elegantly with few coordinated movements of hands and legs!

I still vividly remember my childhood days with Ramasamy uncle. He worked as a driver for my Appa and drove our family’s first car for many years. He had no formal education but now I realize that in all those years his brain not only knew but also had practiced rigorous calculus on a daily basis. All mathematical techniques are translated form of human brain’s computational processes. Humans do not invent these methods, we merely discover them. Some sharp minds are capable of effectively translating these mental processes into symbols and mathematical operations. Calculus was extracted into symbols by Newton and Leibniz. Mathematician’s mind has the knack for discovering unknown and unexplored computational patterns that are embedded in in his brain and convert those into abstract symbols. Typically mathematicians lose this creative ability after their late 30’s or 40’s and it’s rare for humans to make any significant mathematical discoveries beyond this period.

Once our mind converts the brain’s computational model into symbols, it can be shared and also facilitates other human minds to discover it. Everything including algebra, trigonometry, statistics or geometry exist in every single human’s brain in some form. And it also probably exists in a primitive and different form in the neural structures of other mammals, birds, reptiles and insects. Mathematical tutoring helps us to discover and extract our unconscious capabilities into consciously understandable symbols. No amount of work or refinement in teaching methods will successfully make a monkey understand ‘our calculus’. You cannot teach something that is not already embedded in the brain.

Nearly 95% of human thought process is unconscious. Unfathomable amount of computation occurs in a brain during many ordinary activities like coordinating a bat against a fast moving ball. Imagine the amount of calculation that gets completed within our neural network in fraction of a second when a cricket batsman times the bat-ball interaction, strikes and places the ball in the direction of his will. Don’t tell me that he is poor in mathematics. Perhaps he can’t do rigorous mathematics consciously using symbols and operations. In fact he is better off not attempting to make this act of batting conscious. His skills will drop precipitously the moment he becomes conscious of this elegant design. Events will remain fluid as long as his unconscious brain is in control. Physicians are extremely adept in executing logistic regression unconsciously as they review the data from test results and continuously rearrange the probabilities of various diagnoses that could be causing a person’s illness. Every one of us is using advanced computational methods as we make decisions in our daily social life. Once we translate these neural processes into symbols, we can consciously understand and apply these techniques with a higher degree of accuracy to control motion and change in objects that we manipulate. We can also impregnate the methods into the circuitries of calculators and computers, and they can seamlessly perform these operations for us at the speed of electricity. Speed of neural processing, especially the ones that happens in the soup of other emotions, is ridiculously slower when compared to the unfettered flow of electricity in these circuitries.

Does mathematics lie in our brain or in the universe outside of our brain?

That art Thou