The foundations of geometry have a physical significanceEinstein
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, how did we end up creating 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. 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 even lived with us. He had no formal education but now I realize that all 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. Once it is converted into symbols, it can be shared and also facilitates other human minds to discover it. Everything including algebra, trigonometry, statistics or geometry exist in all human brains in some form. And it probably exist in a much more primitive form in the neural structures of 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 calculus. You cannot teach something that is not already embodied in the brain.
Nearly 95% of human thought process is unconscious. Unfathomable amount of computation occurs in a brain during many such activities like coordinating a bat against a fast moving ball. Imagine the amount of calculation that gets completed 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. 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 his batting. 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 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.
The physical reality is an ever changing universe. In this process of evolution, nature continuously creates and destroys structures. Mathematization of natural world by the human brain improves our ability to predict outcomes of natural interactions between elements and forces. This power of prediction allows us to precisely manipulate the ‘present’ and thereby change the future ‘flow of events’, enabling us to preserve our integrity while destruction is diverted to other structures. We do not halt the flow of creative-destruction, we only alter Her direction.
Foundations of mathematics are in the substance of brain