She Loves Me, She Loves Me A Lot! . (Tags: Venus trine Moon; Jupiter trine Saturn this and that!!!) . In the spring, wrote Tennyson, a young mans fancy lightly turns to thoughts of love. Alas, his would-be partner has thoughts of her own---and the interplay between them can lead to the tumultuous ups and downs that makes True Love so thrilling, and so painful. To explain these swings, many lovelorn souls have sought answers in drink; others have turned to poetry or philosophy. We will Play it Cold in Pink Floyd colour and consult Calculus. . The analysis below is offered tongue-in-cheek, but it touches on a serious point. While the laws of love may elude us forever as a Ghost Story, the laws of inanimate things are now well understood. They take the form of differential equations, which describes how interlinked variables change from moment to moment, depending on their current values. As for what such equations have to do with romance---well, at the very least they might shed a light on why, in the words of another poet, the course of True Love never runs smooth. . To illustrate the approach, suppose Sagars is in love with Mary but that, in our version of the story, Mary is a fickle lover. The more Sagars loves her, the more she wants to run away and hide. But when he takes the hint and backs off, she begins to find in him a Strange Attractor. He, however, tends to mirror her Phase Space portrait: he warms up when she loves him and cools down when she hates him. . What happens to our star-crossed lovers? How does their love ebb and flow over time? Thats where calculus comes in. By writing equations that summarize how Sagars and Mary respond to each others affections and then solving those equations with calculus, we can predict the course of their affair. The resulting forecast for the couple is, tragically, a never ending cycle of love and hate. The incurable optimists should be happy to see that they manage to achieve simultaneous love a quarter of the time at least. . To reach this conclusion, we have assumed that Sagars behaviour can be modeled by differential equation: dS/dt= aM .....(i) which describes how his love (represented by S) changes in the next instant (represented by dt). According to this equation, the amount of change dS is just a multiple (a) of Marys current love for him. This reflects what we already know---that Sagars love goes up when Mary loves him---but it assumes something much stronger. It says that Sagars love increases in direct proportion to how Mary loves him. This assumption of linearity is not emotionally realistic, but it makes the equations with rational coefficients like Sagars rational mind much easier to solve. . (The nonlinear integro-differential version of this story with Marys emotional tantrums and irrational coefficients will be considered in next part. The final version though dealing with rationalizing the irrational denominator and transcendental numbers can not be penned down and can be best intuited by meditating on the Transcendental Love of Shiva and Parvati.) . Back to the current story, Marys behaviour, by contrast, can be modeled by the equation dM/dt= -bS ..... (ii) The negative sign in front of the constant b reflects her tendency to cool off when Sagars is chasing her. . The only remaining thing we need to know is the initial conditions (how the lovers felt about each other initially at t=0) and the boundary conditions (are they financially secure at t=T to enter into marriage.) . Then everything about their affair is predetermined. We can use a computer to inch S and M forward from the initial conditions, instant by instant, changing their values prescribed by differential equations. Actually, with the help of fundamental theorem of calculus of love and karma, we can do much better than that. Because the model is so simple and their love so complex, we dont have to trudge forward one moment at a time. Calculus yields a pair of comprehensive formulas that tell us how much Sagars and Mary will love (or hate) each other at any future time. . The above pair of coupled differential equations should be recognizable to students of physics: Sagars and Mary behave like simple harmonic oscillators. So the model predicts that S(t) and M(t)---the functions that describe the time course of their relationship---will be sine waves, each waxing and waning but peaking at different times. . The model can be made more realistic in various ways. For instance, Sagars might react to his own feelings as well as to Marys. They may share same Moon signs, they may have Saturn conjunct Venus or composite Sun conjunct Venus conjunct Neptune conjunct Ascendant from twelfth house and they lie to each other that they dont love each other while being deeply, madly, hopelessly and pathetically in love with each other. . Or Sagars might be the type of guy who is so worried about throwing himself at her that he slows himself down as his love for her grows. Or Mary might be of the other type, one who loves feeling in love so much that she loves him all the more for it. . Add to these possibilities the two ways Sagars could react to Marys affections---either increasing or decreasing his own---and you see there are four personality types, each corresponding to a different romantic style. My friends and students have suggested such descriptive names as Hermit and Malevolent House M.D who damps down his own love and recoils from Marys while remembering past Chiron break-ups. Whereas the sort who gets inspired by his own misery has been called the Hopeless and Benevolent Chris Martin who keeps creating masterpieces from a personal love to a transcendental Pink Floyd love for all. . Although these comparisons are whimsical, the kind of equation that arise in them are profound. They represent the most powerful tool humanity has ever created for making sense of the material world. Sir Issac Newton used differential equations to solve the ancient mystery of planetary motion. In so doing, he unified the earthly and celestial spheres, showing that same laws of motion applied to both. . In the nearly 350 years since Newton, mankind has come to realize that the laws of physics are always expressed in the language of differential equations. This is true for the equations governing the flow of heat, air, and water; for the laws of electricity and magnetism, for atomic realm, and even for the counter-intuitive realm of love. . In all cases, the business of theoretical physics boils down to finding the right differential equations and solving them. When Newton discovered this key to the secrets of universe, he felt it was so precious that he published it only as an anagram in Latin. Loosely translated, it reads: It is useful to solve differential equations. . The silly idea that love affairs might likewise be described by differential equations occurred to me when Mary was in love for the nth time, and Sagars for (n+1)th time. Considering himself wiser than Mary, he was baffled by her behaviour nevertheless. The cycles of their relationship drove him crazy, until he realized that they were both acting mechanically, following simple rules of push and pull. By the end of winter 2013 though, even this understanding of the equations of love had broken down, and he was more mystified than ever. Turned out that there was an important variable with unknown parameters that he had left out of the equations---Marys old love interest wanted her back. . In physics, we call this a three body problem. Its notoriously intractable, especially in the astronomical context it first arose. After Newton solved the differential equations for the two body problem (thus explaining why planets move in elliptical orbit round the Sun), he turned his attention to the three body problem of Sun, Earth and Moon. He could not solve it, and neither could anyone else till the creative genius of Pink Floyd proclaimed, And everything under the Sun is in tune but the Sun is eclipsed on Earth by the Moon... . It later turned out that the three body problem or the love triangle involving Sagars and Mary contained the seeds of Chaos, rendering its behaviour unpredictable in the long run. . Newton knew nothing about chaotic dynamics but according to trusted sources, Sagars and Mary know how to solve the nonlinear integro-differential calculus of life. Their Conscious Uncoupling and Unsconscious Coupling under the Divine Grace of Lord Shiva and Maa Parvati has already created a beautiful Grand Loop and They Live Oh So Happily Ever Now And After!!! . https://youtube/watch?v=X0j4kAB7muI .
Posted on: Wed, 21 May 2014 11:18:35 +0000
Trending Topics
Recently Viewed Topics
© 2015