My Chatter with My Sons

My chatter with my sons

Me: Hey Son, while we have dinner, are you interested in a story?

Son: yeah. sure. whatever. 

Me: This story is about 2600 years old. There was this philosopher in Turkey. These Greeks! They are like ‘different’. So many philosophers in Greece! Socrates and all. 

Son: What do philosophers even do! Crazy people… they give nothing to the society and only sit & think.

Me: Well, in that case son, you should listen to this story. So this guy, he was a loner philosopher in about 600BC. His name was Thales. (Thay-Leez). In those days, there wasn’t a term called ‘philosophy’. So technically he was just another guy, who was probably just smarter than most people in Europe at that time. 

Son: How so?

Me: Well, for one thing, both Socrates and Aristotle told Thales’s story many times to their students about 100 and 200 years later in their times! He was also revered as one of the ‘Seven Sages’ that have been documented in Greek history. (Saptarshi?? Jeez, draw some parallels between Greek history and Indian mythology).. Anyway, more interestingly, when Thales was about 25 years old, he decided to go study Math in Egypt. And somehow (no one knows how), he made it to Egypt and studied the pyramids. He had heard that Egyptians, Babylonian and Indians had in depth insights about Math but no one knew how they knew and not much was documented to be spread across the world in a language that was common. No translators were popular then either. No google translate hahaha. If nothing else, that knowledge was guarded as secret and not really spread out outside those countries much! Also, transportation technology wasn’t the best at that time to allow the spread much either. 

Son: ok, ok so what about this guy?

Me: yeah… Anyway, back to the story. So this guy somehow made it all the way to Egypt and there he studied the Pyramids. A philosopher, who was curious about Math, studied the pyramids!! Lol. Hmm.. but he calculated the height of the pyramids, accurately using the shadows at the time when the unit ‘Meter’ wasn’t even invented. Now even more interesting is that something that we know so well now and lovingly call it as “Geometry” and its laws and triangles and trigonometry etc and that we take for granted, was not invented yet, at least not known to wider world at least as Geometry! He did it anyway. And in the process, he gave the something really awesome to the entire world! He was the first documented person who actually connected mythology, nature, philosophy and things that were at that time considered really abstract, with his version of ‘LOGIC’ and mathematical proof. He philosophized and arrived at postulates (in math) first and then used logic to actually document the proofs and spread to the world too! Today we intuitively know that diameter bisects the circle, angles at the base of isosceles triangle are equal, when two lines interest, the opposing angles are equal, If three properties of two triangles are identical then the triangles are congruent… and finally… drum roll…. Tentenneeee…. The triangle inscribed on the circle with one side as diameter is always a right angled triangle if the vertex touches the periphery!!! We all know these like the back of our hand today. Each 7th grader is taught these, because trillions of advancements today are based on something we call as basic ‘line geometry’. This greek/turkish dude Thales is actually the father of ‘line geometry’!! Now the interesting point to note is that he is also the first documented ‘Philosopher’ in the western world!!! Socrates and Aristotle even acknowledged Thales as the very first documented philosopher in western culture. Philosophy and math hand in hand! Did you ever imagine that?

Son: yeah.. this dude seems bright. But I can bet not a lot of Philosophers are Mathematicians… he is an exception! Hahahahaha.

Me: Curious that you make that comment. Lets keep going with the story, shall we?

Son: Yeah, this sounds fun enough. What do you have?

Me: Sure, yeah… so this dude when he became a philosophy teacher, some time in 590bc or so, after he had invited the abstract line geometry, he got a student. A young dynamic brilliant guy. They became close. Thats when Thales told his student.. ‘Hey you know what, you should go to Egypt, they have good philosophy stuff there. And may be you will find something else that you may find interesting.. 

Son: Hmm let me guess, another philosopher dabbling with math… ok… keep going…

Me: Yeah. Another philosopher.. So this student of Thales goes to Egypt, again, no clue how he reached there but he did. And he studied the pyramids (yes, again). And he came up with something again that no one in the world grows up without studying! He said a^2+b^2=c^2 in a triangle that is defined by my teacher’s circle! A right angled triangle.. Any guesses what are we talking about!??

Son: Oh my god! Don’t tell me that Pythagorus was Thales’s student!

Me: Bingo!! So now you got two philosophers who were historic mathematicians! And if you look at History Son, you will find many more scientists who were actually on the edge of abstract all the time in order to pull in logical aspects and prove them. Thales once said - ‘It is not what we know, but how we know it’ and he defined right there, what science is all about!! ‘How we know it!!’ We prove what we intuitively know or feel to be probably true and we give birth to science!! So Science and Math actually so many times take birth from Philosophy, creative imagination and thought process!!!! Kekule, Tesla, Einstein, Ramanujan, used to live like that and do that day in day out!!! Is it making sense? connecting?? That’s how you invent! 

Son: OMG, never thought of it that way. May be this thinking thing or philosophy thing is rather curious, eh?

Me: So what you find common here is that it is the ‘thought process’ that is critical in all of this. Learn to think and you have the world in your pocket and If you can ‘think’, rest is all a matter of ‘what’ you are thinking!! You could think philosophy or you could think math or you could think science and invent!!! In fact, when Thales was in Egypt, inventing Geometry measuring Pyramids, (literally Geo-metry means measuring the earth)… he also predicted the dates of Eclipses and weather patterns that defined crop yields!! But that’s not it. Thales bridged the worlds of myth and reason with his belief that to understand the world, one must know its nature ('physis’ - pronounced as “Fi-sis”). He believed that all phenomena could be explained in natural terms, contrary to the popular belief at that time that supernatural forces determined almost everything. And the term Physics was born! (From physis). Can you imagine!!

Son: Jeez. Powerful.

Me: Yeah, but picture abhi baaki hai mere dost! I am so far just telling you the old stories.. that we now study in 6-7th grade math. Lets fast forward a little bit and become a tiny bit more advanced. Do you know what are Polynomials?

Son: Yeah, a set of ‘terms’ assembled in form of a function, where terms consists of variables, coefficients, exponents, constants and positive or negative signs.

Me: Very good! That’s actually a very good definition. You seem to know quite a bit!! Tell me more Son, then you must know what’s the degree of a polynomial?

Son: Duh, the highest exponent?

Me: Yes, looks like you know that as well! Very good. Then you must know about roots of a polynomial as well?

Son: Yeah, of course, those are the X intercepts or where the function / polynomial calculates to zero. 

Me: Ooh, nice, then you must know how many roots will a polynomial have?

Son: Yes, same as the degree. Boring.

Me: Hahahaha. Excellent. Are you able to determine them quickly? Like what are the actual roots of a polynomial?

Son: hahaha papa, now that part is not quiet that simple you see, Unless you are like solving a linear or quadratics (degree 1 or 2 polynomials)… they can be simple to solve.. but not always. But polynomial of any degree higher, they are just barely starting to teach that at my school and it looks a little bit intimidating! 

Me: Ok, ok, fair enough. Do you want to know a story about it though.

Son: Yeah, I can live with that. I am almost done with my dinner… 

Me: So there was this guy, about 400 years ago, a dutchman, basically a guy from France. His name was Rene Descartes. He said, I can simplify the process of finding roots of any polynomial, no matter what degree it is! And you will arrive at the solution as long as you follow my trick. And he invented something that most high-schoolers know as Descartes theorem and study it today! He said that for a polynomial you have to follow a three step process (each step is provable). Factor the number from constant divided by coefficient of the highest degree term. Determine the number of sign changes in f(x) and f(-x). And do a synthetic division. First step will give the set of first possibilities of roots (instead of infinite possibilities) and second one will give the number of roots that are positive, negative or imaginary and the third step called synthetic division will actually give you the roots when done successively! 

Me: And oh, By the way, even Rene Descartes also was a philosopher. Forgot to mention. His books from 400 years ago are still university level text books in philosophy! Meditations on first philosophy is the name of the book. Look it up!

Son: Whoa, whoa. Really! 

Me: Yeah… do you want to know more about it?…

Son: Yeah, when can we sit?

Me: Lets wash our plates and go sit.

*Mission accomplished**