Editing 128: dPain over dt

{{comic
| number    = 128
| date      = July 14, 2006
| title     = dPain over dt
| image     = dPain_over_dt.png‎
| imagesize = 
| 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 derivative of time is shown.  It is hoped that dPain/dt, or the change in 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 live"/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 = (-k_1 Pain + [Image of girl]) (1/(1 + e ^ -(t-k_2)/d))
:k_1=?
:k_2=?
:[Image of girl]=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 k_1 positive? Is k_2 large?
:Will I ever stop feeling like this?

{{comic discussion}} 
[[Category:Math]]
[[Category:Romance]]
@@ Line 4: / Line 4: @@
 | title     = dPain over dt
 | image     = dPain_over_dt.png‎
+| imagesize =
 | 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 derivative of time is shown.  It is hoped that dPain/dt, or the change in rate of pain (in this case, shrinking), decreases quickly so that the pain will vanish quickly.
-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>''):
+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 live"/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.
-: <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))
+:dPain/dt = (-k_1 Pain + [Image of girl]) (1/(1 + e ^ -(t-k_2)/d))
-:''k''<sub>1</sub>=?
+:k_1=?
-:''k''<sub>2</sub>=?
+:k_2=?
-:[Image of Megan]=How much she's still in my life
+:[Image of girl]=How much she's still in my life
-:Please let ''d'' only be a few days... or weeks
+: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?
+: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 ''k''<sub>1</sub> positive? Is ''k''<sub>2</sub> large?
+:Is k_1 positive? Is k_2 large?
 :Will I ever stop feeling like this?
-==Trivia==
+{{comic discussion}}
-* In ''[[xkcd: volume 0]]'', some braille is displayed prominently below the comic:
+[[Category:Math]]
-<pre>⠊⠞⠀⠞⠁⠨⠑⠎⠀⠍⠕⠗⠑⠀⠞⠊⠍⠑⠀⠞⠓⠁⠝⠀⠽⠕⠥
-⠑⠭⠏⠑⠉⠞⠀⠃⠥⠞⠀⠇⠑⠎⠎⠀⠞⠓⠁⠝⠀⠽⠕⠥⠀⠋⠑⠁⠗⠲</pre>
-*Decoding this gives:
-**"IT TAKES MORE TIME THAN YOU EXPECT BUT LESS THAN YOU FEAR."
-***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.
-{{comic discussion}}
-[[Category:Analysis]]
 [[Category:Romance]]
-[[Category:Comics featuring Megan]]