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Differential love April 12, 2007

Posted by Sharath Rao in reminisces-1990s.

This post makes me extremely nostalgic…when was the last time I used differential equations, one of my favorite topics. Abhinav links to a page where they model romantic love using a simple differential equation model. You should probably visit that and return. Solution to the problem ? Well, abhinav gives a qualitative explanation, here is the math.

Ofcourse, what you do is differentiate both sides, that will help you express it as a single variable. So lets say it becomes,

dG-squared/dt-squared=n*m*G ; dG-squared/dt-squared-n*m*G =0

If n*m less than 0, then we can write that as :
dG-squared/dt-squared+kG =0 where k=n*m.

This is the famous mass spring oscillation system equation and has a complex form solution. G is a sinosoid with a frequency of squared root of -k, and since B is a derivative of the sinosoid, its also a sinosoid but with a phase difference of 90 degrees. That is what Abhinav means by one follows another but never quite in sync.

Now, if n*m > 0, then it becomes unstable because the solution has an exponential form ( which is what Abhinav means by unstable – you love each other so much that you have no more love left to give OR you love each other so little that you love each other even lesser, eventually reaching zero).

And for the trivial case of n*m=0, ofcourse there is no love at all.

Irrespective of the utter simplicity of the modeling and somewhat hopeless domain to apply it to, I think it is useful to explain teenagers about differential equations šŸ˜‰

In some sense I feel sad because of my inability to solve without some sort of reference any common differential equation which would be solvable less than a minute about 4 years back. Ofcourse I can brush up techniques and get back in normal in less than a day, but still having differential equations as second nature, those days are gone. There used to be a thrill in seeing an equation and knowing almost immediately how it would unravel. Aaaah, applied calculus !! only now I realize how much I have forgotten so much that so absolutely loved !!



1. Abhinav - April 12, 2007


Glad you took the time and effort to explain the simple model mathematically. I didn’t wanna do that on my blog as it can be a real killjoy for a lot of people. If math were a person, trust me, it would be right in the upper echelons of the top 10 list of the most hated people. Ever.

It is truly amazing to realize the potential of Applied Calculus. One qn: I get the hint that you appreciate the fundamental sciences. I wonder why did you venture into Computer Science? Not that I’m against that but just curious.

And thanks for visiting my blog:)


p.s.- Your LA trip was fab! Didn’t comment but read your posts.

2. Sharath Rao - April 12, 2007

loved calculus, physics and organic chemistry …long story that, another day šŸ™‚

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