Inverse Proportions- Beyond the Mathematical Perspective


What seemed to be an unending struggle with comprehending proportions dates as far back as my fourth year in primary school. I occasionally came across them in algebra but never knew them for what they really were.

Evidently, this math concept wasn’t done haunting me. It surfaced once again during my third year in secondary school. But this time around, it looked meaner than usual and it managed to carve out a topic for itself — Variations. Since only little had changed about me since elementary school; I only took a superficial approach to its understanding.

Allow me say that I come from an educational system where one progresses to one of  three fields upon completion of the first phase of secondary school education. But for some reason which I find unclear till date, I opted to go into the sciences. Probably because I felt science was much cooler or my initial distaste for the arts got the better of me .

Few weeks into my Chemistry class, my teacher walked into the class and introduced the “Gas Laws”- eight of them; which basically discussed the various relationships and proportions between the properties of gases. During the lesson, some voice at the back of my head made it clear that proportion was like a shadow i could not hide from. Surprisingly though, I still managed to scale through without really comprehending what proportions really signified.

Fast forward to first year in college while I was burrowing into my soul as well as watching tender snowflakes drop on the ground far below- It was then I struck gold. I was eventually able to conceptualize the very meaning of proportions—Inverse Proportions. I finally was able to see through the confined horizons of mathematics and perceive it for what it truly meant. I see inverse relations to mean the relationship between 2 quantities where they pest on each other for survival; where an increase in one quantity will evoke a corresponding decrease in the other and where one quantity wants the best for itself without caring whose ox is gored in the process.

I initially tried to explain simple situations with it; but surprisingly, this system jibed with every possible scenario I threw at it. But the first thing I did was to borrow the notorious Law of Conservation from science which states that there is no such thing as creation or destruction; everything merely shifts from phase to phase. Things also got less tedious when I decided to view occurrences as a Universal Set with just two large subsets without intersections or mutual compliments.

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Inverse proportions

My thoughts were mainly about happiness and sadness, time management and time wastage, love and hate, and a host of other scenarios I thought are in tandem with each other. Even most of the issues that plague our society can be exemplified through this very concept. Talk about power structures among nations, climate change versus industrialization, resurgence of imperialism and what not.

It is totally fine should this come off as rather basic; but major flaws are born not only because we decide to depart from the rudiments but also because we tend to treat potential mistakes as insignificant.

And speaking of rudimentary mistakes, what better example to cite than the Leaning Tower of Pisa in Italy. Wikipedia tells me that a mere 4 degree angular deviation at the base made a 3.9 meter offset at the top of the tower. This means that the top of the tower is about 4 meters from where it would stand if it were totally vertical.

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Yeah, that’s the power of  only 4 degrees



Over time, Mathematics- in its finite mercies- has provided us with the luxury of expressing ourselves in more ways than one.  For instance:

      You = 1 / Your misery      and         You * Your misery =1   

The concept of cross-multiplication shows that these above expressions preach the same gospel. But a lot of people err in thinking that this mathematical model bears semblance to the real world. I am afraid this is one of the few places where math will come off as rather disappointing. My little insight as to why our world has degenerated to such levels is because we refuse to create a fine line between ourselves and our stumbling blocks. We always try to co-exist with our respective albatrosses because we come up with this self-imposed delusion that we are in control. We never are. If anything, we should be wise enough not to place “what we are” and “what we are not” on the same side of the equation.

Choosing a preferred side always seems to be easy; but the crux of the matter lies in keeping each side in its domain. But now that I think about it, isn’t that what the equality sign was destined for in the first place?

But then again, like every article of this kind that floods the cyberspace, I believe the bigger problem here is not one of comprehension but one of application.





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