NOTE: We don't inhabit a fragmented reality. Nothing around us can be isolated from the catastrophic effects of the pandemic we're witnessing. All further posts on this blog will carry this caveat until there is some reasonable accountability established and substantial actions taken against the state's criminal abdication of responsibility.
Before undertaking the seemingly bizarre proof, let me give you some context of how the problem came about. A few days ago, I was strolling on my terrace and my mind kept going back to why humans have an urge to couple with other humans and enter into relationships. I have written earlier why I think so - like many other of our other habits, this too is built on propagation of our species. But non hetero relationships show us that the urge to be with someone does not vanquish if a child is not or can not be the intended objective of such an association. (I would have argued that even hetero relationships serve as an example since most of us don't enter into them thinking about having kids with our partner, and thus at least on some decisional level we're not always thinking kids and family when entering relationships. But the hetero urge for association primarily is in fact driven by genetically encoded instruction to reproduce. Richard Dawkin's book The selfish Gene is a great explainer of how genes control us).
Long story short - I was thinking about relationships. I then started to analyze romantic relationships as a resource solution problem i.e. I asked myself the question - "which problems does a relationship solve for"? (So one way I look at how our brain makes decisions is to ask the question that if our brain made a decision X, which problems does that decision solve? Every decision you take in your daily life is taken to solve a problem. You cooked a meal? You solved the hunger problem. You switched on the TV? You solved the boredom problem. You studied and completed the essay that is due tomorrow? You solved the productivity problem. Of course some decisions solve much larger problems - such as taking up a student loan to study at a good university so that you can solve career problem, social security problem, and the loan problem itself. A good mental model when making decisions is to take that course that gives you more leverage in the long term rather than pleasure in the short term.
I think a relationship solves primarily two problems. Emotional and sexual. I'm interested in evaluating the first problem and how a relationship solves it while interacting with other variables in ones life. My original line of enquiry is this. What is something so elusive and unique that a romantic relationship gives you in terms of emotional comfort that nobody, neither you best friends, childhood friends, your family, your mentor - nobody can provide for. Alternatively, why is it that irrespective of how close you are with others in platonic relationships (with maybe a childhood friend who you've been friends with almost all of your life) - the moment you enter into a romantic relationship, it de facto becomes the place where you can be and choose to be the most vulnerable. Because if you think about it, prima facie it doesn't make sense . Imagine X is friends with Y since 18 years. They have gone through thick and thin and have made countless sacrifices in their friendship, pulled each other from depths of darkness and pushed each other to greatness. And yet, the moment Z (a romantic partner) enters into X's life -- Z de facto becomes the closest emotional confidant to X, laving behind Y. You might even ask the question of whether such a behavior is fair to Y. (by the way this reads dangerously close to the script of Sonu ke Titu ki Sweety. That is indeed the problem statement I am proposing, sadly.)
The closest explanation to an answer that I have is that maybe because when one enters into a relationship, more often than not one enters thinking or at least hoping that this will be the last relationship they'll have to ever enter into. So one is incentivized to build that kind of robust emotional foundation with their partner to last a lifetime. Because no matter how many years you've been someone's friend, assuming that an average male marries at 29 and lives up to 75 - the person you'll associate the most with and inhabit the most same spaces with is going to be your partner. So it makes sense for a relationship to de facto become the prime emotional sharing and comfort place. This previous line of reasoning got me thinking about how humans are dynamic in their emotional needs and wants. For example, X might have an emotional need to talk to Y whenever something major happens in X's life. But when Z enters into X's life - X now has an incentive to share that information with Z instead of, or along with X. At some point in time, Z will surpass Y in terms of the emotional comfort and association with X. (I was actually thinking hard about how much time such a process would take realistically. And by the way none of this is to suggest that when you have a significant other you automatically devalue your friends. My only argument is that one overtakes the other in terms of emotional proximity at some point in our lifetime).
So now lets use Calculus to analyze this situation. Our emotional needs and wants and associations are part of what I have earlier characterized as the 'emotional resource problem'. Imagine that it is a quadratic equation in one variable (quite fitting since it is a problem). A quadratic equation in one variable looks something like this: ax² + bx + c = 0. (I actually do not know at what point in time is concept of a quadratic equation taught across various school boards. I attended a CBSE school and we learnt quadratic equations in class VIII. Regardless, if you haven't read quadratic equations or have lost your touch - I will explain it).
So a quadratic equation is a mathematical problem. As is the case with every problem, it has a solution. A quadratic equation has two solutions. Which means that there are two values of x that solve for the mathematical expression ax² + bx + c = 0. To solve for a mathematical problem means to find out the value of the variable (x in this case) for which the stated expression will be true. So basically a solution is that value of x for which if inserted in the above expression will lead to the RHS being zero. Anyhow, the only thing you need to remember is that there are two solutions to a quadratic equation.
Now let's go back to our description of one's emotional needs and wants as being a quadratic problem. So the logical conclusion from the discussion above is that there are two solutions to this emotional resource problem. In the example above, X's emotional resource problem (a quadratic equation. Remember this detail) has two solutions - Y and Z. They are solutions because they solve for X's emotional needs and wants. (solving basically means offering emotional comfort and support). So the two solutions to the problem are the emotional contributions by Y and Z. Now an individual's emotional needs and wants changes with time. One's emotional needs at 15 are very different from when they're at 35 and consequently at 65. Therefore the emotional resource problem is dynamic and not static. In other words, the quadratic equation is time dependent. For a mathematical expression to be time dependent means that the value of that expression changes with time. Humans are dynamic creatures with changing emotional needs and as a consequence the emotional resource problem is dynamic.
Now if the problem itself is time dependent - it means that its solution will change over time too. Let's simplify this further. Let the initial quadratic equation to be 3x² + 2x - 1 = 0. The solution to this equation are 1/3 and -1. If the quadratic equation is time dependent it would mean that the value of the constants and consequently the variable will change over time. Let 't' amount of time pass, and since the equation is time dependent - it will change with time as well. Let the equation after time 't' be: 6x² + 7x + 2 = 0. The answers of this equation now are -2/3 & -1/2. So you can observe that for a time dependent equation, its corresponding solutions change their value with time as well. Therefore the emotional resource problem also changes its value by virtue of its time dependent nature. Thus the 'solution' of the emotional resource problem will change with time too. Correspond the solution values in earlier problem with Y and Z's absolute contribution towards solving for X's emotional resource problem (go back to our definition of solving as offering emotional comfort and support). The changing solution over time reflects the changing contribution of emotional support by Y and Z towards X. Strictly mathematically speaking, the only reason the solution of a time dependent quadratic equation changes over time is because of the changing nature of the quadratic equation itself - which if applied strictly in this case would mean that the only reason emotional contribution by Y and Z changes over time is because X's emotional wants and needs changes over time. Such reasoning even though true is not the only reason. The 'solution' i.e. the emotional contribution by Y and Z towards Z also changes with time because Z and Y themselves are dynamic individuals whose emotional needs, wants and attitudes change over time as well.
WE have now mathematically confirmed the dynamic nature of Z and Y's emotional contribution towards X by stating X's emotional resource problem as a quadratic equation in single variable with two dynamic (time dependent) solutions i.e. Z and Y's emotional contribution towards X. This analysis gives rise to two further observations. First, that even if someone's partner starts by offering less contribution to the emotional needs and comfort of the individual as compared to say the individual's other long term friends, because such contribution is dynamic (as shown by how the solution of the problem changes with time) there will come a point in time where the partner will overtake the best friend as being the primary emotional confidant (We earlier discussed the incentive of a person to confide more in their partner than in their friend). And because the quadratic problem (emotional resource problem in this case) is not only time dependent but also dependent on other aspects, inter alia - physical location, emotional disposition of the person, childhood upbringing, attitude of the person - basically anything that can be argued to have an effect on a person's emotion needs and wants - such a point of overtake will occur at different times in relationships for different people. But most likely occur it shall. (Of course I'm not accounting for failed relationships or those relationships that were either of such nature or of such short duration that such a point of overtake did not occur).
Basically the gist of this enquiry is that if you model your emotional needs and wants as a time dependent quadratic problem - it elegantly shows and confirms the dynamic nature of human beings and their relationships.
Side Note 1: The non exhaustive list and the over inclusive category of 'basically anything that affects a person's emotional needs and wants' is indicative of why mathematical and computational modeling of human consciousness is arguably the hardest problem for humanity.
Side note 2: If you're feeling mathematically adventurous you might want to check out the millennial mathematics problems. They are a set of seven unsolved problems in mathematics and anyone who solves either of the problems gets 1M dollars. One person solved one of these problems - the Poincare conjecture and later refused to accept the prize money. He is Grigori Perelman.
Image only for thumbnail purposes. I miss calculus.
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