Understanding our daily life problems using Integral Calculus
This article briefly discusses how integral calculus can be used for understanding problems affecting our daily life such as water scarcity.
Integral Calculus is a familiar word for anyone who at least completed their high school studies. And nowadays with the advent of IIT foundation classes, people are getting acquainted with that word from the primary school stage itself. Moreover, many of us would have solved numerous questions related to integral calculus during our pre-graduate and graduate studies. So, after spending a lot of effort in learning Integral Calculus, let’s try to apply it to have a better understanding of some critical issues existing in our society.
Apprehend Water Scarcity problem using basic integral equation
Whenever we arrive in the summer season, we come across the term ‘water scarcity ’ and the slogan ‘ Save Water ’. In our life, many people would have told us, or we ourselves would have told this slogan to many. But before we request others to practice something, we should also sensitize them about the problem and factors contributing to it. So, in this case, what are the incidents that are leading to the water scarcity problem?
Let us take a very common daily life incident which is “Keeping the tap water ON while we rub our hands with soap or brush our teeth”. It appears nothing to be wrong with that incident where a negligible amount of water (1 or 2 liters depending on the speed of flow) goes unutilized. This incident happens every day for few times (say 5 times a day) with a given person. But this small casual incident is actually contributing to a big problem we all are facing i.e, water scarcity. To understand how it happens, we need to go back to integral calculus where we learned the following:
If we apply the above principle for modeling our water scarcity discussion, then variable x is water, f(x) is our society with sufficient water resources, dx is the casual incident where a person leaves the tap water unutilized for few minutes, g(x) is our society with water scarcity problem. The integral here is the key component which is our country with a population of 140 crores. To imagine the scale of the problem caused by this small casual incident, consider that 25% of the population (i.e, 35 crores) have a habit of leaving 2 liters of tap water unutilized which happens 5 times a day and over 365 days in a year, the amount of water that goes wasted is nearly 2 x 5 x 365 x 35(10⁷) = 1.2775 Trillion Liters which is quite huge.
Another casual incident that contributes to the water scarcity problem is the usage of flush-based sanitary ware in our homes. Here, in this case, a single flush releases the same amount of water irrespective of the amount of human excreta dumped which results in wastage of a small amount of water (maybe 2 liters per flush). But again, this casual incident tends to happen every day for few times with a given person. So, in our highly populous country, we can just imagine the scale of usable water that goes into drainage without serving any purpose. So, for both incidents, we can apply integral calculus to understand the underlying concern that a casual habit of wasting few liters of water every day when integrates over the entire country will eventually contribute to the water scarcity problem.
Dirty, Unhygienic society from Integral Calculus perspective
Another common scene that happens in our daily life is throwing off our redundant pieces onto the road after consuming the item. If you look at this incident exclusively, it appears to be a very small mistake that does not go to harm much to our society. But if we look at this incident from the Integral Calculus perspective, this is the incremental step that turns our society into a dirty, unhygienic one. Thousands of Metric Tonnes of Garbage that are lying in open areas are actually the culmination of careless disposals from individuals of our society. The lack of discipline in handling the waste generated among us is actually compelling our government to allocate lakhs of crores for the Swacch Bharath mission instead of allocating them to crucial sectors like Education, etc. So, it is very disgusting to see how a casual attitude towards waste disposal turns out to be a hindrance to our economic growth.
The River Analogy
If you consider any long river like Krishna, it will have a place of origin. But if you go and look at that place, there won’t be any water generator source that produces the water flowing in the river. So how is the river that flows hundreds of km is formed? It is formed from the conglomeration of millions of small water streams produced in mountains such as western ghats, forests, etc., during rainfall. Similarly, many of our present critical issues such as water scarcity, pollution (land, water & air) are actually the integration of very small casual attitudes/incidents/mistakes that are happening with approximately 140 crores of people located all over the country.
A small stream of water can easily be controlled or stopped with simple efforts. But once a river is formed, we can only control its flow that too by constructing big dams with huge money and still cannot completely stop the flow. Likewise, if a person develops a casual (bad) habit such as leaving tap water unutilized or throwing garbage onto the street, it can be corrected with minimum effort. But when a personal bad habit turns into a characteristic of a society, it becomes a herculean task for any government to correct that. Therefore, it is very essential for us to that if we want to mitigate critical issues of our society with less effort, things have to change right from the individual level.
The way forward
There are two key takeaways from looking at our problems from an integral calculus perspective: (1) The casual attitude deeply embedded in every one of us from childhood. (2) A huge population of 140 crores. These two factors together actually distinguish our country from those countries dealing with the current problems in a better way.
“Tweaking our attitude from being casual to a bit concerned” is the single-stop solution for our crucial issues. Using this approach, we can prevent any number of COVID-19 waves and lock-downs by following covid-19 protocols such as wearing masks and maintaining physical/social distancing. And also, we can reduce petrol consumption and air pollution by walking or using bicycles to the nearest destinations. Similarly, we can save a lot of electricity with the forefinger by turning OFF the electrical appliances before exiting the rooms. All the aforesaid activities require minimal effort from each individual but the biggest hurdle here is consistency in the execution. So, a simple solution exists at the individual level for multiple crucial problems affecting our society. Its effectiveness depends upon the proportion of society that adheres to the consistent implementation of the solution.
