Editing 2595: Advanced Techniques
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==Explanation== | ==Explanation== | ||
− | 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 | + | {{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. Do not collect the square root of minus one pounds}} |
+ | 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 both includes dragons and arrows to slay it. | ||
− | One of her students asks if this is a metaphor for the technique, but her rather tetchy reply | + | 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. |
− | The caption beneath the comic states that this approach describes "All advanced math techniques." This | + | The caption beneath the comic states that this approach describes "All advanced math techniques." This is probably a reference to {{w|Arthur C. Clarke}}'s {{W|Clarke's three laws|third law}} that ''Any sufficiently advanced technology is indistinguishable from magic'', but re-framed for mathematics. What [[Randall]] is implying is that all advanced math techniques looks like magic to normal people. |
− | + | Whilst metaphor is an important part of many languages, and so definitely taught in for instance English and French classes, it is not usually used in math classes. The process of algebra denoting variables with letters could though be considered related to metaphorical thinking. | |
− | 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 | + | 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 named after the famous German mathematician {{w|Carl Friedrich Gauss}}. There is nothing on Wikipedia called Guass'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, it is not certain what, if anything real, Miss Lenhart references. |
− | Slaying the dragon with Hilbert's arrow | + | Slaying the dragon with Hilbert's arrow, indicate that the arrow has some magical properties. The arrow is names after {{w|David Hilbert}}, for instance now for {{w|Hilbert space}}. Hilbert space converts subsets of an infinite vector space into a complete metric space, allowing the use of linear algebra & 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. | |
− | The title text contains two puns and a reference. The phrase "{{w|Cutlass}} of Variations" is a pun on the mathematical technique called "{{w|Calculus of variations}}". The word "Noetherworld" is a pun on "{{w|underworld|netherworld}}". The reference is to the mathematician {{w|Emmy Noether}}, a giant in the field of abstract algebra | + | {{w|Conway chained arrow notation}} (2→3→4) is a means of expressing extremely large numbers and one of many uses for arrows in mathematics. |
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+ | 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 which need slaying. | ||
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+ | Basically Miss Lenhart will turn the unsolvable equation into a dragon using Gauss's operator, then kill it with Hilbert's arrow. The now dead dragons corpse will then be transformed into the solution of the original equation, QED. | ||
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+ | Miss Lenhart could be describing techniques like {{w|Fourier analysis}}, in which a problem is transformed from one domain into another which is more tractable (e.g. from the time domain to the frequency domain, commonly done for analyzing the behavior of signals or dynamical systems) and then back again. | ||
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+ | The title text contains two puns and a reference. The phrase "{{w|Cutlass}} of Variations" is a pun on the mathematical technique called "{{w|Calculus of variations}}". The word "Noetherworld" is a pun on "{{w|underworld|netherworld}}". The reference is to the mathematician {{w|Emmy Noether}}, who was a giant in the field of abstract algebra. Furthermore, so-called {{w|Noether's Theorem}} is used in the Calculus of Variations. She was previously referenced as one of many important women in science back in [[896: Marie Curie]]. | ||
==Transcript== | ==Transcript== | ||
− | :[Miss Lenhart is using a stick to point at a whiteboard | + | {{incomplete transcript|Do NOT delete this tag too soon.}} |
+ | :[Miss Lenhart is using a stick to point at a whiteboard with a drawing of a dragon, an archer, and rows of text on it, while facing, presumably, a crowd of students.] | ||
:Miss Lenhart: To solve this equation, we invoke Gauss's operator to transform it into a dragon. | :Miss Lenhart: To solve this equation, we invoke Gauss's operator to transform it into a dragon. | ||
:Miss Lenhart: Then we slay the dragon with Hilbert's Arrow, and transform its corpse back into the solution. | :Miss Lenhart: Then we slay the dragon with Hilbert's Arrow, and transform its corpse back into the solution. | ||
− | : | + | :Voice off-screen: Just to be clear, this is a metaphor, right? |
− | :Miss Lenhart: Does this | + | :Miss Lenhart: Does this '''look''' like English class?! |
:[Caption below the panel:] | :[Caption below the panel:] | ||
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{{comic discussion}} | {{comic discussion}} | ||
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[[Category:Comics featuring Miss Lenhart]] | [[Category:Comics featuring Miss Lenhart]] | ||
[[Category:Math]] | [[Category:Math]] |