2595: Advanced Techniques - Revision history

Bence98: Added mathematical relevance of arrows

2025-02-22T23:50:16Z

Added mathematical relevance of arrows

172.71.254.15: /* Explanation */ italics

2023-03-13T18:58:17Z

‎Explanation: italics

Account: /* Explanation */ Removing some stale incomplete tags

2022-07-02T20:40:54Z

‎Explanation: Removing some stale incomplete tags

Natg19: Undo revision 277063 by Donald Trump (talk)

2022-05-26T17:42:57Z

Undo revision 277063 by Donald Trump (talk)

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Donald Trump: Crapped page

2022-05-26T16:45:07Z

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172.70.230.63: Undo revision 266271 by 👖🔥 (talk)

2022-05-11T18:18:17Z

Undo revision 266271 by 👖🔥 (talk)

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👖🔥 at 17:38, 11 May 2022

2022-05-11T17:38:04Z

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Jacky720: rv

2022-05-04T21:56:55Z

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Ex Kay Cee Dee at 21:52, 4 May 2022

2022-05-04T21:52:42Z

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Jacky720: rv

2022-05-04T21:10:50Z

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 Invocations are a common classification for spoken or vocalized types of spell. In the logic Miss Lenhart used, 'invoking' Gauss's operator may refer to casting a magical spell with verbal components (such as [https://roll20.net/compendium/dnd5e/True%20Polymorph True Polymorph]). The operator is presumably named after the famous German mathematician {{w|Carl Friedrich Gauss}}. There is nothing on Wikipedia called Gauss's operator, but there is both {{w|Gauss's law}} and the {{w|Gauss–Kuzmin–Wirsing operator}}. As neither can transform an equation into a dragon,{{Citation needed}} it's clear Randall is making a joke.
-Slaying the dragon with Hilbert's arrow indicates that the arrow has some magical properties. The arrow is presumably named after {{w|David Hilbert}}, known for many mathematical developments including {{w|Hilbert's problems}} and {{w|Hilbert spaces}}. A Hilbert space converts subsets of an infinite vector space into a complete metric space, allowing the use of linear algebra and calculus methods which might otherwise be applicable only to finite Euclidean spaces. Vectors could be compared with an arrow. Magical arrows are frequently used to slay dragons in myth and role-playing games. Magical items in RPGs such as {{w|Dungeons & Dragons}} are often named after a creator or famous user; hence, a magical "Arrow of Hilbert" might traverse infinite spaces or affect targets for which one or more stats are effectively infinite.
+Slaying the dragon with Hilbert's arrow indicates that the arrow has some magical properties. Mathematical notation uses arrows for certain relations and operations, for example for expressing {{w|Limit (mathematics)|limits of a series or function}}, or {{w|Knuth's up-arrow notation}} used for denoting {{w|Hyperoperation|hyperoperations}} more complex than multiplication (i.e. exponentiation, tetration, pentation etc.). The latter is usually used for concisely describing huge numbers that would otherwise be impossibly difficult to write out, like {{w|Graham's number}}. Vectors are also frequently represented as arrows. This (fictional) arrow is presumably named after {{w|David Hilbert}}, known for many mathematical developments including {{w|Hilbert's problems}} and {{w|Hilbert spaces}}. A Hilbert space converts subsets of an infinite vector space into a complete metric space, allowing the use of linear algebra and calculus methods which might otherwise be applicable only to finite Euclidean spaces. Another observation to note is that in 1928, one of Hilbert's students, {{w|Wilhelm Ackermann}} introduced the Ackermann function, a fast-growing function very similar in function (pun intended) to Knuth's up-arrow. Magical arrows are frequently used to slay dragons in myth and role-playing games. Magical items in RPGs such as {{w|Dungeons & Dragons}} are often named after a creator or famous user; hence, a magical "Arrow of Hilbert" might traverse infinite spaces or affect targets for which one or more stats are effectively infinite.
 There is in fact a class of {{w|Dragon curve}}s, which do have the sort of S-shape shown on the whiteboard, but they have no connection to Gauss's operator, and are not actual dragons that need slaying.

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 In typical [[Miss Lenhart]] fashion, she is teaching a mathematics class where she outlines a process by which a mathematical result is achieved through steps which sound suspiciously like magical {{w|Role-playing game|RPG}} logic. She includes both a dragon and arrows to slay it.
-One of her students asks if this is a metaphor for the technique, but her rather tetchy reply "Does this look like English class?!" seems to imply that she literally means that dragons and arrows will be employed in the resolution of the problem. It is also clear from the slide she is pointing at that she has drawn a dragon and a man with a bow that is aiming an arrow at the dragon. Whilst metaphor is an important part of many languages, and so is definitely taught in language classes, it is not usually used in math classes.
+One of her students asks if this is a metaphor for the technique, but her rather tetchy reply "Does this ''look'' like English class?!" seems to imply that she literally means that dragons and arrows will be employed in the resolution of the problem. It is also clear from the slide she is pointing at that she has drawn a dragon and a man with a bow that is aiming an arrow at the dragon. Whilst metaphor is an important part of many languages, and so is definitely taught in language classes, it is not usually used in math classes.
 The caption beneath the comic states that this approach describes "All advanced math techniques." This could be a reference to the now-common approach in higher mathematics in which a problem is transformed into another domain where it is easier to solve, then transformed back. For instance, in {{w|Fourier analysis}}, commonly used for analyzing the behavior of signals or dynamical systems, a problem can be transformed from the time domain to the frequency domain, solved, and then transformed back again. A (much) more complex example is Andrew {{w|Wiles's proof of Fermat's Last Theorem}}, which uses {{w|modularity theorem|modularity lifting}} to transform the problem. Here Miss Lenhart says she will transform a math problem into an actual dragon, slay it, and transform the corpse back into mathematics.

← Older revision		Revision as of 20:40, 2 July 2022
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	==Explanation==		==Explanation==
−	~~{{incomplete\|Created by AN EULISH CLAUSS- Please slay the CORRECT dragon when editing this page. Do NOT travel to the Noetherworld. Do NOT pass Go. Please collect the correct sedenion.}}~~
	In typical [[Miss Lenhart]] fashion, she is teaching a mathematics class where she outlines a process by which a mathematical result is achieved through steps which sound suspiciously like magical {{w\|Role-playing game\|RPG}} logic. She includes both a dragon and arrows to slay it.		In typical [[Miss Lenhart]] fashion, she is teaching a mathematics class where she outlines a process by which a mathematical result is achieved through steps which sound suspiciously like magical {{w\|Role-playing game\|RPG}} logic. She includes both a dragon and arrows to slay it.