Editing 2595: Advanced Techniques
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An alternative view is that Randall is referring to {{w|Arthur C. Clarke}}'s {{W|Clarke's three laws|third law}} that ''Any sufficiently advanced technology is indistinguishable from magic'', as re-framed for mathematics. What [[Randall]] would be implying is that all advanced math techniques look like magic to non-mathematicians. (Another advanced and somewhat magical math technique is deployed by Miss Lenhart in [[1724: Proofs]].) | An alternative view is that Randall is referring to {{w|Arthur C. Clarke}}'s {{W|Clarke's three laws|third law}} that ''Any sufficiently advanced technology is indistinguishable from magic'', as re-framed for mathematics. What [[Randall]] would be implying is that all advanced math techniques look like magic to non-mathematicians. (Another advanced and somewhat magical math technique is deployed by Miss Lenhart in [[1724: Proofs]].) | ||
− | 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, | + | 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, 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. 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. |