Math-The language of patterns
“Dad, look! A car shaped cloud”. The four-year old’s excitement went unnoticed by his dad. He is in a hurry to drop his son off at school and then rush to his office. He is visibly irritated with all the traffic on the road, honking of the cars, and the dust. “What’s with Mondays and people getting blues about it. Everyone seems to be in a bad mood. God! Mondays are so annoying”, he just was thinking to himself. The next weekend is not until 5 more days. He somehow has to drag himself through the week to the other end when he can enjoy some peace. The watch on the dashboard was signalling ten minutes past eight. He knows that the watch is set 15 minutes faster than the correct time and it is actually just five minutes to eight right now. So, he still has enough time to drop his son and reach office by eight thirty.
Isn’t this a common scene in most of our lives?
But let’s look at some basic observations here. Why does the boy see it as a car shaped cloud and not just a cloud? Why should people get worried about a Monday and not a Thursday? Why do we always count time until the next weekend? Why do people set their watches faster when they know and calculate the right time despite that?
The answer is quite simple. We are wired to seek patterns in everything around us. Whether it is physical shapes, time, or space. Our natural tendency is to convert any abstract information into known patterns and then perceive them using our existing mind maps about the world. This is true for everything that we learn from how to walk to how to learn complex concepts in various domains that we are interested in.
Now, let us apply this idea to how we perceive math. By nature, math is a language of repeated patterns. All the theorems and concepts that we learn from school until the time we graduate are all patterns that repeated themselves. For example, Pythagorean Triplets are three sides of a triangle that repeatedly fit a pattern if the triangle happened to be right-angled; progressions are a series of numbers that repeatedly occur in a specific pattern for a given condition.
Shouldn’t we be left alone to explore patterns like these and learn from the maps we make? Why is it that we are forced to learn math as a series of factoids that have no pattern? This method of forcing the abstract ideas by discounting the obvious patterns that they occur in makes math a dull and boring subject to learn.
The “Nash Equilibrium” that earned John Forbes Nash Jr. a Nobel prize in economics for his contributions to game theory, Alan Turing’s breakthrough on deciphering the code for Enigma during second world war which aided in a somewhat positive outcome to end the war; and even the proof of sum of n natural numbers is “-1/12” submitted by Srinivas Ramanujan to his mentor Dr. Hardy in Cambridge university are all classic examples of how seeking patterns in mathematics will lead to solving unsolved problems.
Most of the extraordinary mathematicians had someone who recognized and supported their ability to see and explore patterns. Those are some examples of the mathematicians from pop-culture, but if you dig deeper, you will find that all patrons of math have become so, because they got a chance to wonder, explore and discover the patterns themselves.
So, here’s the closing thought: Go out there and find mathematical patterns in the most mundane things. Savour the taste of those orderly structures from the chaos of life. Who knows, you may stumble upon on a pattern that has never been seen before.