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Lee -<br>
<blockquote type="cite"
cite="mid:55917.73.182.196.159.1552097055.squirrel@webmail.meganet.net">
<pre class="moz-quote-pre" wrap="">Steve writes in relevant part:
</pre>
<blockquote type="cite">
<pre class="moz-quote-pre" wrap="">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.
</pre>
</blockquote>
<pre class="moz-quote-pre" wrap="">
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.</pre>
</blockquote>
<p>Thanks for asking (I think).</p>
I was responding to Roger's use of the term which I took to mean
specifically the geometric "surface" known as a <i><a
moz-do-not-send="true"
href="https://en.wikipedia.org/wiki/Pareto_efficiency#Pareto_frontier">Pareto
Frontier</a></i><i> </i>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 <a moz-do-not-send="true"
href="https://en.wikipedia.org/wiki/Convex_hull#Convex_hull_of_a_finite_point_set"><i>Convex
Hull </i></a>problem in geometry, but carries an implication
for multi-objective optimization.<br>
<blockquote type="cite"
cite="mid:55917.73.182.196.159.1552097055.squirrel@webmail.meganet.net">
<pre class="moz-quote-pre" wrap=""> 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.</pre>
</blockquote>
<p>I do believe that studying the Wikipedia articles linked above
will lead to a detailed explication of what I was referring to.
<br>
</p>
<p>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" (<i>Reserved Term</i>)
from some <i>Specialized Lexicon</i> 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 <i>Loaded Word</i> (or
phrase).
</p>
<blockquote type="cite"
cite="mid:55917.73.182.196.159.1552097055.squirrel@webmail.meganet.net">
<pre class="moz-quote-pre" wrap="">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.</pre>
</blockquote>
<p>And I believe this does align with <i>Convex Hull</i> as used
above... the specific relevance to multi-objective optimization
would require reference to <i>Pareto Frontier"</i>or <i>Pareto
Surface </i>which (as Wikipedia elaborates well) originated in
economic theory but is relevant to any multi-objective
optimization problem.</p>
<p>It could be noted that I had to go back and edit out yet more
egregious uses of ' " ' in this text, using <i>Capitalized
Italics</i> in it's place. I don't know if that is ideal, but
generally that would be my preferred typographical indication of a
<i>Reserved Term</i> from a <i>Specialized Lexicon</i>. 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.</p>
<p>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. <br>
</p>
<p>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 <i>Source Domains</i> (or our <i>Image Donor</i>)
from geometry. <br>
</p>
<p>In closing, to try to tie these two points together, my <i>Reserved
Terms</i>, formerly (sloppily) indicated by "scare quotes" (<i>Scare
Quotes</i>?) may be from a <i>Specialized Lexicon</i> derived
from a specific (common or obscure) <i>Metaphorical Source
Domain. <br>
</i></p>
<p>I believe that it is *more common* in <i>Internet Culture</i> to
reserve <i>Scare Quotes</i> for sarcasm or derision, but I may
not have that quite right?</p>
<p>- Steve</p>
<p>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.<br>
</p>
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