Editing 410: Math Paper
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==Explanation== | ==Explanation== | ||
− | The math paper [[Cueball]] is in the process of describing in this comic turns out | + | The math paper [[Cueball]] is in the process of describing in this comic, turns out the be noting but an elaborate set up for a joke about {{w|imaginary friend}}s by taking the concept of "{{w|friendly number}}s" into the complex (imaginary) plane, which comprises complex numbers that have both a real and an imaginary part (see details [[#Math|below]]). |
− | Cueball | + | Such a pun is both so obvious and so terrible that Cueball's superiors, specifically the Cueball-like guy sitting at the end of the table, deem that he should no longer have a license to ''math'' and they thus revoke Cueballs "math license". |
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It is a [[:Category:Banned from conferences|recurring theme]] in earlier xkcd comics that Cueball (or [[Randall]]) ends up being banned from holding presentations at conferences after a presentation turns out to be just an elaborate pun. | It is a [[:Category:Banned from conferences|recurring theme]] in earlier xkcd comics that Cueball (or [[Randall]]) ends up being banned from holding presentations at conferences after a presentation turns out to be just an elaborate pun. | ||
− | The title text takes the joke a step further, with the added hilarity of making the audience question exactly how Cueball | + | The title text takes the joke a step further, with the added hilarity of making the audience question exactly how Cueball was able to work a {{w|striptease}} into a presentation about {{w|genetic engineering}} and {{w|astrophysical}} rocket study (or possibly genetics and rockets into a striptease) and then even manage to loose all three licenses in one go. This is what TV Tropes calls a "[http://tvtropes.org/pmwiki/pmwiki.php/Main/NoodleIncident noodle incident]". |
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===Math=== | ===Math=== | ||
− | An {{w|imaginary number}} is a number that can be written as a real number multiplied by the imaginary unit ''i'', which is defined by its property ''i<sup>2</sup> = -1'' (an impossibility for regular, " | + | An {{w|imaginary number}} is a number that can be written as a real number multiplied by the imaginary unit ''i'', which is defined by its property ''i<sup>2</sup> = -1'' (an impossibility for regular, "real" numbers, for which all squares are positive). The name "imaginary number" was coined in the 17th century as a derogatory term, since such numbers were regarded by some as fictitious or useless, but over time many applications in science and engineering have been found. |
− | An imaginary number ''bi'' can be added to a real number ''a'' to form a {{w|complex number}} of the form ''a + bi'' (the formula shown at the bottom of Cueball's slide ), where ''a'' and ''b'' are called, respectively, the real part and the imaginary part of the complex number. If ''a'' and ''b'' are both integers, the complex number is called a {{w|Gaussian integer}} (as Cueball mentions). The {{w|complex plane}} is an X-Y plot with | + | An imaginary number ''bi'' can be added to a real number ''a'' to form a {{w|complex number}} of the form ''a+bi'', (the formula shown at the bottom of Cueball's slide ), where ''a'' and ''b'' are called, respectively, the real part and the imaginary part of the complex number. If ''a'' and ''b'' are both integers, the complex number is called a {{w|Gaussian integer}} (as Cueball mentions). The {{w|complex plane}} is an X-Y plot with a on the X axis and b on the Y axis. (Such a plane is shown at the bottom of Cueball's slide). |
− | Joel Bradbury | + | Joel Bradbury has a wonderful explanation of {{w|friendly number}}s on [http://www.joelbradbury.net/notes/friendly_numbers his site]: |
:What are Friendly Numbers? | :What are Friendly Numbers? | ||
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:For each of these n, there is something called a characteristic ratio. Now that's just the divisors function over the integer itself: σ(n)/n. (This is the formula shown at the top of Cueball's slide). So the characteristic ratio where n = 6 is σ(6)/6 = 12/6 = 2. | :For each of these n, there is something called a characteristic ratio. Now that's just the divisors function over the integer itself: σ(n)/n. (This is the formula shown at the top of Cueball's slide). So the characteristic ratio where n = 6 is σ(6)/6 = 12/6 = 2. | ||
− | :Once you have the characteristic ratio for any integer n, any other integers that share the same characteristic are called friendly with each other. (This is what is written in the frame in Cueball's slide, spelling friendly numbers as ''friendly #s''). So to put it simply | + | :Once you have the characteristic ratio for any integer n, any other integers that share the same characteristic are called friendly with each other. (This is what is written in the frame in Cueball's slide, spelling friendly numbers as ''friendly #s''). So to put it simply a friendly number is any integer that shares its characteristic ratio with at least one other integer. The converse of that is called a solitary number, where it doesn't share its characteristic with anyone else. |
− | :1, 2, 3, 4 | + | :1, 2, 3, 4 and 5 are solitary. 6 is friendly with 28; σ(6)/6 = (1+2+3+6)/6 = 12/6 = 2 = 56/28 = (1+2+4+7+14+28)/28 = σ(28)/28. |
==Transcript== | ==Transcript== | ||
− | :[Cueball | + | :[Cueball holding a pointing stick is using it to point at an equation on a panel. He is looking right. There several parts of the panel that can be read. At the top there is a formula. Below is a frame with text. Below again to the left is a X-Y plot with small dots all over all four quadrants, probably indicating the complex numbers with b on the Y and a on the X axis. Finally right of this is yet another formula.] |
:Cueball: In my paper, I use an extension of the divisor function over the Gaussian integers to generalize the so-called "friendly numbers" into the complex plane. | :Cueball: In my paper, I use an extension of the divisor function over the Gaussian integers to generalize the so-called "friendly numbers" into the complex plane. | ||
:Panel: | :Panel: | ||
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::For a + bi... | ::For a + bi... | ||
− | :[The audience to the right of Cueball consist of two Cueball-like guys (one in front and one in the back) | + | :[The audience to the right of Cueball consist of two Cueball-like guys (one in front and one in the back) and between them are Hair Bun Girl, with glasses, and Megan. They sit around a table, only Hair Bun Girl is on the near side. The Cueball-like guy sitting to the right is at the end of the table, the other two are on the far side. The Cueball at the end of the table is talking, the other three have turned to look at him:] |
:Guy at the end of the table: Hold on. Is this paper simply a giant build-up to an "imaginary friends" pun? | :Guy at the end of the table: Hold on. Is this paper simply a giant build-up to an "imaginary friends" pun? | ||
− | :[Back to Cueball | + | :[Back to Cueball who stands speechless.] |
− | :[One more beat panel with Cueball | + | :[One more beat panel with Cueball who now looks down.] |
− | :[Zoom out to Cueball and the front end of the table with the Cueball-like guy who has not spoken yet and | + | :[Zoom out to Cueball and the front end of the table with the Cueball-like guy who has not spoken yet and Hair Bun Girl who now looks at Cueball. Cueball looks up again and speaks. The guy at the end of the table speaks off panel.] |
:Cueball: It <u>might</u> not be. | :Cueball: It <u>might</u> not be. | ||
:Guy at the end of the table (off panel): I'm sorry, we're revoking your math license. | :Guy at the end of the table (off panel): I'm sorry, we're revoking your math license. | ||
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[[Category:Comics featuring Cueball]] | [[Category:Comics featuring Cueball]] | ||
− | [[Category:Comics featuring | + | [[Category:Comics featuring Hair Bun Girl]] |
[[Category:Comics featuring Megan]] | [[Category:Comics featuring Megan]] | ||
[[Category:Multiple Cueballs]] | [[Category:Multiple Cueballs]] | ||
[[Category:Banned from conferences]] | [[Category:Banned from conferences]] | ||
− | [[Category: | + | [[Category:Math]] |
[[Category:Puns]] | [[Category:Puns]] |