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| date = January 27, 2006 | | date = January 27, 2006 | ||
| title = Useless | | title = Useless | ||
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| image = useless.jpg | | image = useless.jpg | ||
| titletext = Even the identity matrix doesn't work normally | | titletext = Even the identity matrix doesn't work normally | ||
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==Explanation== | ==Explanation== | ||
| − | + | [[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. | |
| + | |||
| + | This comic has been made into a [http://store.xkcd.com/products/useless t-shirt] in the xkcd store, with a {{w|Laplace transform}} in place of the bottom integral. | ||
===Basic explanations of the functions=== | ===Basic explanations of the functions=== | ||
| − | * The {{w|square root}} | + | :''Note: The Wikipedia links will provide far more detailed explanations of the mathematics.'' |
| − | * {{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). | + | *The {{w|square root}} of x is the number that, when multiplied by itself, equals x. |
| − | * 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|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). |
| − | * {{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|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. |
| − | * A {{w|Fourier transform}} converts a function from one (sophisticated) function into an endless continuous series of | + | *{{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 (more simple) 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== | ==Transcript== | ||
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:<sup>[0 1]</sup> | :<sup>[0 1]</sup> | ||
:F{♥} = 1/√2π ∫<sup>∞</sup><sub>-∞</sub>f(t)e<sup>it♥</sup>dt = ? | :F{♥} = 1/√2π ∫<sup>∞</sup><sub>-∞</sub>f(t)e<sup>it♥</sup>dt = ? | ||
| − | :[Caption below | + | :[Caption below:] |
:My normal approach is useless here. | :My normal approach is useless here. | ||
==Trivia== | ==Trivia== | ||
| − | * | + | *This was the 52nd and last comic originally posted to [[LiveJournal]]. |
| − | * | + | **The previous was [[53: Hobby]]. |
| − | + | **The next comic [[56: The Cure]] was not also posted on LiveJournal | |
| − | + | ***This thus ends this repeating trivia section that has been present for all those 52 LiveJournal comics. | |
| − | + | ***Also after this there has been no issue with comics released at two times, since they were now released only on xkcd. | |
| − | + | *This comic kept its original title: "Useless" | |
| − | + | **It is part of the last six comics on LiveJournal which all had a title without the word "Drawing" in it. | |
| − | + | **Five of these had exactly the same title on both sites. | |
| − | + | **Only 11 comics have the same title on both sites. | |
| − | + | **Apart from the [[:Category:First day on LiveJournal|thirteen first comics]] posted to LiveJournal, there were only three other comics without the word "Drawing" in the title before these last six. | |
| − | :: | + | *There was no original [[Randall]] quote for this comic. |
| − | + | *This comic was the last of the last 11 comics posted on LiveJournal. | |
| − | + | **These 11 comics were [[:Category:Posted on LiveJournal after xkcd|posted both on LiveJournal and xkcd]] after the [[xkcd]] site opened on the 1st of January 2006. | |
| − | * The | + | **The first six comics were posted on both sites on the same day. |
| − | * This | + | **And then this first happened again with this last comic. |
| + | *The version used on the [http://store.xkcd.com/products/useless t-shirt] and in ''[http://store.xkcd.com/products/xkcd-volume-0 xkcd: volume 0]'' 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}}. | ||
| + | *This comic was adapted to a wedding cake featured on [http://www.cakewrecks.com/home/2011/6/26/sunday-sweets-geek-wedding-cakes.html an installment of "Sunday Sweets"], a regular feature on popular blog [http://cakewrecks.com Cake Wrecks]. | ||
{{comic discussion}} | {{comic discussion}} | ||
| − | [[Category: | + | [[Category:Comics posted on livejournal| 52]] |
| − | [[Category:Posted on LiveJournal after xkcd | + | [[Category:Posted on LiveJournal after xkcd]] |
[[Category:Romance]] | [[Category:Romance]] | ||
[[Category:Math]] | [[Category:Math]] | ||
