Unease with adder cirtuit

My idea of Mathematics was of this beautiful tool that worked so consistantly. Something that fascinated me with mathematics in my early days of introduction of it with addition and subtraction is that there were different approaches to solving problem (adding and and subtracting which I much later now know as commutative and associative property of an additive group) and yet they always gave same result. Sometimes I secretly wished that it didn't work, I hoped that somehow we came to inconsistant result, but it was never so. Well actually at around 6th grade in school, when we first learned algebra, I knew of the bogus proof that 1:2, and there were various variants of it. This gave me a glimmer of hope that there might be inconsistancies in mathematics afterall. I later knew that each variant of this proof explotied one way or the other the use of cancellation of zeros in each side of equation, which is not allowed.[Read more on this].

During 7th grade we learned about use of algebra to solve real worl problems like finding age of people with given incomplete information of age differences with one or more people. There were various ways to solve the linear equations, again exploiting commutative and associative properties of additive group, but each always gave the same result. Mathematics was like this unmissable tool.

Then came geometry which only grew my fascination towards mathematics. It was this idea of non existant imaginary shapes in 2D(triangles rectangles ... ngons) and 3D(mostly prism, pyramid cuboid .. etc) objects of which we could calculate something like the perimeter and surface area. Being able to calculate the length of rope required to cover shapes of various shapes (some combination of rectangles/squares mostly) was again very fascinating.

I didn't straight away buy into the idea of coordinate geometry either. We used grid paper to talk about coordinates, loci of points and my un ease with the concept was that we wouldn't have those nice coordinate lying around in real live to be able to use those. I later realized that it was just matter of convention what unit we used for the coordinate measurement and specification, that I realized that no one needed to construct a grid in the space (plane) to be able to use them. One of the most satisfying excercise that I did with use of coordinate geometry was to prove that the so called chromatic abberation introduced by spherical mirrors could be overcome by use of parabolic mirror. I wrote this proof up, which is lying around somewhere

Introduction to trigonometry during 8th gade was quite boring at first, having to memorize the trigonometric ratios, some identities and using them to solve some "hard problems" was not the nicest introduction to calculus. One of the basic problems we used to asked about trignometry was to estimate the height of a building given some elevation angle to the top from certain distance. This class of problem always gave angle of elevation and decilination angle. I used to wonder in my head if only we could measure angle of elevation and declination as easily as we measured the distance from the base. Upon interrogation the teacher had said that there is something called the "sextant" that measures the angle. I hoped that I could get it. Only later did I realize that we could use the concept of similar triangles and measure the length of shadow to a given length of a pencil erect on the ground, to easily get the angle of elevation of the sun. I used to fascinate people by telling the precise height of a pole or even some tree just by measuring the length of shadow of pencil of given length by measuring the length of shadow of object under consideration.

My admiration to Mathematics only grew as I got introduced to various mathematical tools. Being able to

By 12th grade I had gotten myself familiar with some (literally) BASIC (Q-BASIC TBF) programming. Introduction to calculus was this bright revelation.

So up untill 12th grade my Idea of mathej