In the 300 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.To illustrate love in a mathematical approach the following example can be taken.
suppose Romeo is in love with Juliet, but in our version of the story, Juliet is a fickle lover. The more Romeo loves her, the more she wants to run away and hide. But when he takes the hint and backs off, she begins to find him strangely attractive. He, on the other hand, tends to echo her: he warms up when she loves him and cools down when she hates him.
By writing equations that summarize how Romeo and Juliet respond to each other’s affections and then solving those equations with calculus, we can predict the course of their affair. The resulting forecast for this couple is, tragically, a never-ending cycle of love and hate. At least they manage to achieve simultaneous love a quarter of the time.
For readers who are curious about the math used here:
In the first story above, Romeo’s behavior was modeled by the differential equation dR/dt = aJ. This equation describes how Romeo’s love (represented by R) changes in the next instant (represented by dt). The amount of change (dR) is just a multiple (a) of Juliet’s current love (J) for him. This equation idealizes what we already know – that Romeo’s love goes up when Juliet loves him – by assuming something much stronger. It says that Romeo’s love increases in direct linear proportion to how much Juliet loves him. This assumption of linearity is not emotionally realistic, but it makes the subsequent analysis much easier. Juliet’s behavior, on the other hand, was modeled by the equation dJ/dt = -bR. The negative sign in front of the constant b reflects her tendency to cool off when Romeo is hot for her. Given these equations and an assumption about how the lovers felt about each other initially (R and J at time t = 0), one can use calculus to inch R and J forward, instant by instant. In this way, we can figure out how much Romeo and Juliet love (or hate) each other at any future time. For this elementary model, the equations should be familiar to students of math and physics: Romeo and Juliet behave like simple harmonic oscillators. read more..
suppose Romeo is in love with Juliet, but in our version of the story, Juliet is a fickle lover. The more Romeo loves her, the more she wants to run away and hide. But when he takes the hint and backs off, she begins to find him strangely attractive. He, on the other hand, tends to echo her: he warms up when she loves him and cools down when she hates him.
By writing equations that summarize how Romeo and Juliet respond to each other’s affections and then solving those equations with calculus, we can predict the course of their affair. The resulting forecast for this couple is, tragically, a never-ending cycle of love and hate. At least they manage to achieve simultaneous love a quarter of the time.
For readers who are curious about the math used here:
In the first story above, Romeo’s behavior was modeled by the differential equation dR/dt = aJ. This equation describes how Romeo’s love (represented by R) changes in the next instant (represented by dt). The amount of change (dR) is just a multiple (a) of Juliet’s current love (J) for him. This equation idealizes what we already know – that Romeo’s love goes up when Juliet loves him – by assuming something much stronger. It says that Romeo’s love increases in direct linear proportion to how much Juliet loves him. This assumption of linearity is not emotionally realistic, but it makes the subsequent analysis much easier. Juliet’s behavior, on the other hand, was modeled by the equation dJ/dt = -bR. The negative sign in front of the constant b reflects her tendency to cool off when Romeo is hot for her. Given these equations and an assumption about how the lovers felt about each other initially (R and J at time t = 0), one can use calculus to inch R and J forward, instant by instant. In this way, we can figure out how much Romeo and Juliet love (or hate) each other at any future time. For this elementary model, the equations should be familiar to students of math and physics: Romeo and Juliet behave like simple harmonic oscillators. read more..
hei hajju......nice one.....hehe
ReplyDeletedifferential equations in love....:p eheh
nice one
ReplyDelete-intox