Editing 55: Useless

{{comic
| number = 55
| date = January 27, 2006
| title = Useless
| before    = <big><big><span class="plainlinks">[https://web.archive.org/web/20060529063441/http://xkcd-drawings.livejournal.com/#:~:text=4%3A38%20am-,Useless,-(3%20Comments LiveJournal title</span>]: '''Useless'''</big></big>
| image = useless.jpg
| titletext = Even the identity matrix doesn't work normally
}}

==Explanation==
This was the fifty-second and last comic originally posted to [[LiveJournal]]. The previous one was [[53: Hobby]], but the next comic, [[56: The Cure]], was never posted to LiveJournal. It was among the [[:Category:Posted on LiveJournal after xkcd|last eleven comics]] posted both on LiveJournal and on [https://xkcd.com xkcd.com] after the new site was launched. This comic was published on the same day across both sites, but not all of them shared the same posting day.

[[Randall Munroe|Randall]] is attempting to apply mathematics to the concept of love to no avail. Specifically, he is attempting his "normal approach", which is a term used in mathematics for the method one typically uses to solve a certain type of problem. However, as love is not a well-defined mathematical entity, his normal approach is useless. Simply put: he's saying he has found no way of describing love using only the tools of mathematics.

From the top, moving left to right, he tries the {{w|square root}} of love, the {{w|cosine}} of love, and the {{w|derivative}} of love with respect to x. He then attempts to left-multiply love by a 2x2 {{w|identity matrix}}, and finally he defines a {{w|Function (mathematics)|function}} of love as a {{w|Fourier transform}}. These are all "normal approaches" to solving certain math problems. The message of the comic is that for someone who uses math to solve all their problems, defining love is impossible.  It also indicates that love is not always a rational (or irrational) phenomenon.

===Basic explanations of the functions===
* The {{w|square root}}s of x are the two numbers (positive and negative) where each multiplied by itself equals x. Often only the positive answer is quoted.
* {{w|Cosine}} is a {{w|trigonometric function}} that, when given the measure of an angle in a {{w|right triangle}} as an input, outputs the ratio of the lengths of two sides of that triangle (for cosine, it is the non-{{w|hypotenuse}} side adjacent to the angle and the hypotenuse).
* A {{w|derivative}} of a function is the rate of change of that function at a given value of x. It is a primary focus of {{w|calculus}}. A basic example is where "velocity" is the rate of change of displacement at a given time, the derivative of velocity is "acceleration", which is the rate of change of velocity at a given time. 
* {{w|identity matrix|Identity matrices}} are {{w|matrix (mathematics)|matrices}} that consist of only zeros and ones, with zeros everywhere except along the {{w|main diagonal}}. Multiplying a matrix by the equal-sized identity matrix will result in the same output in the same way that multiplying a non-matrix by 1 does not change the original term. The title text suggests that multiplying love by the identity matrix does not return the same "love" value.
* A {{w|Fourier transform}} converts a function from one (sophisticated) function into an endless continuous series of simpler functions, where each next part is bringing the equation closer to the real result. This means that you can stop your calculations after a few iterations and you are very close to the real result, and it also can be used to deconstruct signals.

==Transcript==
:[Different mathematical equations, all with a heart on left side, and all ending up with question marks.]
:√♥ = ?
:cos ♥ = ?
:d/dx ♥ = ?
:<sub>[1 0]♥ = ?</sub>
:<sup>[0 1]</sup>
:F{♥} = 1/√2π ∫<sup>∞</sup><sub>-∞</sub>f(t)e<sup>it♥</sup>dt = ?
:[Caption below the equations:]
:My normal approach is useless here.

==Trivia==
* In the book ''[[xkcd: volume 0]]'', this comic is slightly different. The derivative is with respect to time (''t'') instead of ''x'', and the function at the bottom is a {{w|Laplace transform}} instead of the bottom integral.
* Also in the book, a cipher is displayed prominently below the comic:

<pre>
CY-O CMLROOCXN. YR M.AOGP. NRK.W ABE ,CYDRGY M.AOGP.M.BY YD.P. JAB X. BR OJC.BJ.V <D.B CY JRM.O YR NRK.W ,.-P. ANN CB YD. EAPTV [[TCBO.F
</pre>

:This is a Dvorak to Qwerty cipher. Undeciphered, it reads:

::it"s impossiblE to mEasurE lovE, and Without mEasurEmEnt thErE can bE no sciEncE. whEn it comEs to lovE, WE"rE all in thE dark. __kinsEy
::: It's impossible to measure love, and without measurement there can be no science. When it comes to love, we're all in the dark. --{{w|Kinsey_(movie)|Kinsey}}
<!--(Although it is worth noting that this was never said verbatim, Alfred Kinsey is quoted as saying this.)
The quote in question: [https://en.wikiquote.org/wiki/Kinsey_(film)]-->
* The modified book version used to be [https://web.archive.org/web/20211215085605/https://store.xkcd.com/products/useless available as a T-shirt] in the xkcd store before it was [[Store|shut down]].
* This used to be one of the [[Footer comics|footer comics]] featured in the bottom segment of [https://xkcd.com xkcd.com].

{{comic discussion}}

[[Category:Posted on LiveJournal| 52]]
[[Category:Posted on LiveJournal after xkcd]]
[[Category:Romance]]
[[Category:Math]]
[[Category:Footer comics]] <!-- in footer staring around Oct 13, 2006 -->
[[Category:Comics with xkcd store products]]
[[Category:Comics with lowercase text]]