Talk:S-expression: Difference between revisions

(6 intermediate revisions by 3 users not shown)

Line 61:

: If that still doesn't make sense to you, think of <math> {\rm So}(k) = h_k^2 h_{k-1}^{-1} h_{k+1}^{-1} </math> as the "source" of its squareness (as h<sub>k</sub> is the analogue of the ''k''th harmonic so this is the direct analogue of k<sup>2</sup>/(k+1)/(k-1)). Ideally, for the analogy to be perfect, So''k'' would be odd-particulars (as it'd be impossible to have them be superparticular when they are defined entirely in terms of ratios between odd numbers), but quodd-particular is thus the next best thing.

: Hope that clarifies. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 22:31, 5 July 2024 (UTC)

: I should note that "S" stands for "(Shorthand for) Second-order/Square Superparticular", so by analogy and contrast:

: you can think of "So" as standing for ""(Shorthand for) Second-order/Square Odd-particular". --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 13:17, 6 July 2024 (UTC)

== No monzos? ==

Why --[[User:Eufalesio|Eufalesio]] ([[User talk:Eufalesio|talk]]) 15:04, 26 May 2026 (UTC)

: There used to be a section on what I call "S-factorizations" (formerly S-monzos before realising that term was taken), but it was moved to [[S-expression/Advanced results]], but S-factorizations are mentioned on the page so probably it should be moved back onto the page, leaving the mathematical derivations section and the abstraction section there. You might ask why not use normal monzos and the answer is it's clearer for the way S-commas work, and this sense is illuminated if you understand the abstraction section whereby you can understand how each infinite comma family of an S-expression is actually readable in a generalised sense based on an abstract harmonic series. But probably that should stay there with the mathematical derivations at least as long as I've written it in terms of group theory. But it does give an additional answer to the question (which also isn't useless as the two examples of potentially interest show), so I wonder if including it might be acceptable under some collapsable section? (IDK if those are possible on MediaWiki...) --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 23:02, 26 May 2026 (UTC)

@@ Line 61: / Line 61: @@
 : If that still doesn't make sense to you, think of <math> {\rm So}(k) = h_k^2 h_{k-1}^{-1} h_{k+1}^{-1} </math> as the "source" of its squareness (as h<sub>k</sub> is the analogue of the ''k''th harmonic so this is the direct analogue of k<sup>2</sup>/(k+1)/(k-1)). Ideally, for the analogy to be perfect, So''k'' would be odd-particulars (as it'd be impossible to have them be superparticular when they are defined entirely in terms of ratios between odd numbers), but quodd-particular is thus the next best thing.
 : Hope that clarifies. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 22:31, 5 July 2024 (UTC)
+: I should note that "S" stands for "(Shorthand for) Second-order/Square Superparticular", so by analogy and contrast:
+: you can think of "So" as standing for ""(Shorthand for) Second-order/Square Odd-particular". --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 13:17, 6 July 2024 (UTC)
+== No monzos? ==
+Why --[[User:Eufalesio|Eufalesio]] ([[User talk:Eufalesio|talk]]) 15:04, 26 May 2026 (UTC)
+: There used to be a section on what I call "S-factorizations" (formerly S-monzos before realising that term was taken), but it was moved to [[S-expression/Advanced results]], but S-factorizations are mentioned on the page so probably it should be moved back onto the page, leaving the mathematical derivations section and the abstraction section there. You might ask why not use normal monzos and the answer is it's clearer for the way S-commas work, and this sense is illuminated if you understand the abstraction section whereby you can understand how each infinite comma family of an S-expression is actually readable in a generalised sense based on an abstract harmonic series. But probably that should stay there with the mathematical derivations at least as long as I've written it in terms of group theory. But it does give an additional answer to the question (which also isn't useless as the two examples of potentially interest show), so I wonder if including it might be acceptable under some collapsable section? (IDK if those are possible on MediaWiki...) --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 23:02, 26 May 2026 (UTC)