Talk:S-expression: Difference between revisions

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: 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 Oddparticular". --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 13:17, 6 July 2024 (UTC)

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 : 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 Oddparticular". --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 13:17, 6 July 2024 (UTC)