https://www.explainxkcd.com/wiki/api.php?action=feedcontributions&feedformat=atom&user=YadierWikiexplain xkcd - User contributions [en]2026-04-29T13:50:18ZUser contributionsMediaWiki 1.30.0https://www.explainxkcd.com/wiki/index.php?title=128:_dPain_over_dt&diff=386575128: dPain over dt2025-09-14T04:20:44Z<p>YadierWiki: /* Trivia */</p>
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<div>{{comic<br />
| number = 128<br />
| date = July 14, 2006<br />
| title = dPain over dt<br />
| image = dPain_over_dt.png<br />
| titletext = You laugh to keep from crying, you do math to keep from crying...<br />
}}<br />
<br />
==Explanation==<br />
<br />
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], [https://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>''):<br />
: <math> Pain(t) = {c_1 \left(e^{k_2/d} + e^{t/d}\right)}^{-dk_1} + \frac{[\text{Megan}]}{k_1}</math><br />
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Note: In reality, "Megan" is not likely to be a constant.<br />
<br />
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.<br />
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In the title text, [[Randall]] changes the famous "laugh to keep from crying" statement to math.<br />
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==Transcript==<br />
:dPain/dt = (-k<sub>1</sub> Pain + [Image of Megan]) (1/(1 + e ^ -(t-k<sub>2</sub>)/d))<br />
:''k''<sub>1</sub>=?<br />
:''k''<sub>2</sub>=?<br />
:[Image of Megan]=How much she's still in my life<br />
:Please let ''d'' only be a few days... or weeks<br />
: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?<br />
:Is ''k''<sub>1</sub> positive? Is ''k''<sub>2</sub> large?<br />
:Will I ever stop feeling like this?<br />
<br />
==Trivia==<br />
* In ''[[xkcd: volume 0]]'', some braille is displayed prominently below the comic:<br />
<pre>⠊⠞⠀⠞⠁⠨⠑⠎⠀⠍⠕⠗⠑⠀⠞⠊⠍⠑⠀⠞⠓⠁⠝⠀⠽⠕⠥<br />
⠑⠭⠏⠑⠉⠞⠀⠃⠥⠞⠀⠇⠑⠎⠎⠀⠞⠓⠁⠝⠀⠽⠕⠥⠀⠋⠑⠁⠗⠲</pre><br />
*Decoding with a braille translator will give you this message:<br />
**"IT TAKES MORE TIME THAN YOU EXPECT BUT LESS THAN YOU FEAR."<br />
***This seems to be a message from Randall about breakups such as this one, assuring readers going through similar situations that it will not last forever.<br />
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{{comic discussion}}<br />
[[Category:Analysis]]<br />
[[Category:Romance]]<br />
[[Category:Comics featuring Megan]]</div>YadierWiki