Duality in the Context of Projective Geometry
https://en.wikipedia.org/wiki/Duality_(projective_geometry) . Except for maybe 2 classes when I took projective geometry at UCLA it was abstract algebra – didn’t look anything like GW’s works.
However it’s coming back again with virtual reality & graphics & games in the modern digital age.
Ooogie what a thought – you & I are a duality – what kind?
Here is another sense … perhaps closer to the edge that i am stufying …
thinking about that one was what got me using this hastag again. i have yet to totally digest that.
Duality is a connection between two things where the properties of one defines the properties of the other.
I feel this #duality #edge when i know that you can never have my exact qualia. You cannot have my subjective experiences. Oh sure you can have similar ones. You can also listen to my descriptions of my subjective experiences and try to duplicat them for yourself … and shucks you can come pretty close i imagine. But mine are mine … are on this side of a #duality that nature will not let you cross. Some #spriitual stories will deny and contradic that. So be it. I am in one of those #boxes … and/or you are in one of those #boxes in which that is not
you could say it the other way around too … “The #duality builds the #Ego” … not sure it matters which came first.
… the Validity or Permanence of Equivalent FORMS.GW mostly uses it for the geometry-algebra duality & it may be extended elsewhere – perhaps thinking & ideation itself.
The Ming also comes to mind in shape & meaning. Cross-ratio is one such instigation.
tag #PeacockLaw … and also via that tag … TZU & the Law of Peacock
George Peacock 1791 – 1858
The principle here indicated by means of examples was named by Peacock the "principle of the permanence of equivalent forms," and at page 59 of the Symbolical Algebra it is thus enunciated: "Whatever algebraic forms are equivalent when the symbols are general in form, but specific in value, will be equivalent likewise when the symbols are general in value as well as in form."
For example, let , , , denote any integer numbers, but subject to the restrictions that is less than , and less than ; it may then be shown arithmetically that . Peacock’s principle says that the form on the left side is equivalent to the form on the right side, not only when the said restrictions of being less are removed, but when , , , denote the most general algebraic symbol. It means that , , , may be rational fractions, or surds, or imaginary quantities, or indeed operators such as . The equivalence is not established by means of the nature of the quantity denoted; the equivalence is assumed to be true, and then it is attempted to find the different interpretations which may be put on the symbol.
… and maybe even to a natural #duality
early 15c., "correspondence, proportion," from Old French analogie or directly from Latin analogia, from Greek analogia "proportion," from ana "upon, according to" (see ana-) + logos "ratio," also "word, speech, reckoning" (see logos). A mathematical term given a wider sense by Plato. Meaning "partial agreement, likeness or proportion between things" is from 1540s. In logic, "an argument from the similarity of things in some ways inferring their similarity in others," c. 1600.
perhaps it is the form thingy. One can go as far as the Spirits of Form in RS on that one.