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−
| number    = 128
 
−
| date      = July 14, 2006
 
−
| title    = dPain over dt
 
−
| image    = dPain_over_dt.png‎
 
−
| titletext = 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 {{w|differential equation}} 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. He's hoping the value for ''d'' will not be larger than a few days or some weeks. Assuming that ''How much she's still in my life'' is a constant [Megan], [http://www.wolframalpha.com/input/?i=dP%2Fdt+%3D+%28-k1*P%2BG%29*%281%2F%281%2Bexp%28-%28t-k2%29%2Fd%29%29%29 solving the differential equation] leads to the following solution (with unknown ''c<sub>1</sub>''):
 
−
: <math> Pain(t) = {c_1 \left(e^{k_2/d} + e^{t/d}\right)}^{-dk_1} + \frac{[\text{Megan}]}{k_1}</math>
 
−
 
 
−
If ''k<sub>1</sub>'' was positive or if ''k<sub>2</sub>'' was a large value, the value of ''dPain/dt'' would approach zero. Ideally, ''k<sub>1</sub>'' would be "How much she's in my life"/''Pain'' (we assume both these values are positive), while ''k<sub>2</sub>'' 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. But we don't know the meaning of ''k<sub>1</sub>'' or ''k<sub>2</sub>''; these variables are just unpredictable.
 
−
 
 
−
In the title text, [[Randall]] changes the famous "laugh to keep from crying" statement to math.
 
−
 
 
−
==Transcript==
 
−
:dPain/dt = (-k<sub>1</sub> Pain + [Image of Megan]) (1/(1 + e ^ -(t-k<sub>2</sub>)/d))
 
−
:''k''<sub>1</sub>=?
 
−
:''k''<sub>2</sub>=?
 
−
:[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 <u>want</u> that?
 
−
:Is ''k''<sub>1</sub> positive? Is ''k''<sub>2</sub> large?
 
−
:Will I ever stop feeling like this?
 
−
 
 
−
{{comic discussion}}
 
−
[[Category:Analysis]]
 
−
[[Category:Romance]]
 
−
[[Category:Comics featuring Megan]]
 

Revision as of 21:21, 4 May 2022

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