128: dPain over dt

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dPain over dt

Title text: You laugh to keep from crying, you do math to keep from crying...

Explanation

Another one of the math-love relationship comics, a mathematical depiction of pain as a derivative of time is shown. It is hoped that dPain/dt, or the rate of pain (in this case, shrinking), decreases quickly so that the pain will vanish quickly.

If k1 was positive or if k2 was a large value, the value of dPain/dt would approach zero. Ideally, k1 would be "How much she's in my life"/Pain (which, if we assume both these values are positive, would mean the ideal k1 would be positive), while k2 would ideally be extremely large. Either of these scenarios approach what would be a situation where the value of dPain/dt is close to zero.

Transcript

dPain/dt = (-k₁ Pain + [Image of Megan]) (1/(1 + e ^ -(t-k₂)/d))

k₁=?

k₂=?

[Image of Megan]=How much she's still in my life

Please let d only be a few days... or weeks

I guess there's some kind of a cutoff after years, where it stops mattering and we can be friends. Do I want that?

Is k₁ positive? Is k₂ large?

Will I ever stop feeling like this?

 add a comment!

Discussion

== Explanation ==

Since this is my first real contribution here I'm putting everything on the talk page instead of on the article itself.

The equation describes Pain as a function of Pain, time, and several constants. This is a first-order linear differential equation with possible solution:

Pain = c_1 (e^k_2 + d e^t)^(-k_1) + (Girl)/k_1

Hopefully, d is relatively small ("days... or weeks"), thereby diminishing the time it takes for Pain to change. Significantly, k_1 needs to be positive, otherwise the first term would grow unbounded and Pain would never decrease. Assuming k_1 is positive, a larger k_2 results in a lower initial state. Again assuming k_1 is positive, the "Girl" term guarantees there will always be a nonzero amount of Pain since Pain approaches Girl/k_1 asymptotically, unless of course "How much she's still in my life" is zero. This probably gives rise to observation "I guess there's some kind of a cutoff after years."

--Smartin (talk) 02:33, 1 January 2013 (UTC)