Lee - > Steve writes in relevant part: > >> My position is that I favor each and every one of us taking whatever >> responsibility for understanding our own "convex hull" of >> capability/knowledge/intuition as we are capable of and "managing" it to >> the best of our ability. > The quotation marks around the phrase 'convex hull' and the word > 'managing' presumably signal that they are being used non-literally, and > (I guess) metaphorically.
Thanks for asking (I think). I was responding to Roger's use of the term which I took to mean specifically the geometric "surface" known as a /Pareto Frontier <https://en.wikipedia.org/wiki/Pareto_efficiency#Pareto_frontier>///which is essentially a (hyper)surface (line in 2D) which describes (geometrically a containing space of) the collection of optimal solutions in a high-dimensional trade space. It *is* equivalent to the /Convex Hull / <https://en.wikipedia.org/wiki/Convex_hull#Convex_hull_of_a_finite_point_set>problem in geometry, but carries an implication for multi-objective optimization. > I would particularly like Steve, if he is > willing, to delve into the intended metaphor in the first case. On the > one hand, lots of my work uses more or less geometry; on the other, in > lots of my other work I use metaphor; and I even think and write about > metaphor. So it's likely that I'm taking the metaphor more seriously than > intended. I do believe that studying the Wikipedia articles linked above will lead to a detailed explication of what I was referring to. I will also accept responsibility for my irresponsible use of ' " ' marks. For me, it is often a shorthand for indicating that the term within the quotes is a "reserved term" (/Reserved Term/) from some /Specialized Lexicon/ which I trust the reader is either familiar with or (with my hint) recognizes as being a term with specific, intentional and likely obscure (to the casual reader) but non-trivial meaning. In other words, I'm trying to indicate that it is a very specifically /Loaded Word/ (or phrase). > With that disclaimer: in the technical contexts I'm familiar with, to pass > from something X to the convex hull of X has the effect of (1) 'filling in > holes in X', in a well-defined manner that is (2) as economical as > possible and (3) (therefore) unique. Which (if any) of those properties > are reflected, and how, in the case that X is our > "capability/knowledge/intuition"? ... I could ramble on a lot more but > will start with that. And I believe this does align with /Convex Hull/ as used above... the specific relevance to multi-objective optimization would require reference to /Pareto Frontier"/or /Pareto Surface /which (as Wikipedia elaborates well) originated in economic theory but is relevant to any multi-objective optimization problem. It could be noted that I had to go back and edit out yet more egregious uses of ' " ' in this text, using /Capitalized Italics/ in it's place. I don't know if that is ideal, but generally that would be my preferred typographical indication of a /Reserved Term/ from a /Specialized Lexicon/. I will try to be more consistent in the future, and am open to being schooled on a more proper typographical (within the realm of text consisting of the basic roman alphabet and italics/bold formatting) indication. Orthogonal to my orthographic transgressions, I admit also to playing fast and loose WITH metaphor, sometimes being whimsical about it, other times using it in a very intentional and specific way as rigid (in some cases) as a (complex) formal analogy. I would claim (following Lakoff and Nunez in _Where Mathematics Comes From_ ) that all metaphors ultimately ground in human sensations provided by our embodiment. I also work on the operational assumption the our primary mode of understanding is via (conceptual) metaphor (Lakoff & Johnson _Metaphors we Live by_)... metaphor stacked on top of metaphor which is grounded in our embodied sensuality. Near the bottom of that stack we often find metaphorical /Source Domains/ (or our /Image Donor/) from geometry. In closing, to try to tie these two points together, my /Reserved Terms/, formerly (sloppily) indicated by "scare quotes" (/Scare Quotes/?) may be from a /Specialized Lexicon/ derived from a specific (common or obscure) /Metaphorical Source Domain. / I believe that it is *more common* in /Internet Culture/ to reserve /Scare Quotes/ for sarcasm or derision, but I may not have that quite right? - Steve PS. I am given to bracketing words I intend to be read as *emboldened* with '*'s which seem to often be rendered exactly that way. I use preceding/following '_' underscore marks to indicate _Underlined Text_ which does NOT seem to be rendered that way often. And I am erratic in my use of *bold* and CAPS for simple emphasis. Also open to some improved/alternative conventions and promise to *TRY* to be more consistent.
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