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<p>My first thought in reading this (Glen and Jon in
response/elaboration) is that we are discussing whether the
universe of comprehensions is (fully) metrizeable or not. I have
some conjectures about (weighted) graph and network metrization
which may or may not have a play in this. I'm not enough of a
math-hole to really properly think (much less speak) about the
higher order abstractions of topology that are invoked/implied in
all this... <br>
</p>
<p>I'm also puzzled by the distinction between epi-phenomena and
phenomena. I suspect the principals in this discussion here to
be using similar but different reserved terms from overlapping but
distinct lexicons. My entirely intuitive/vernacular response to
this is that it feels like epi-phenomena "all the way down". <br>
</p>
<p>Glen invoked "epi" as "nearly" and yet in vernacular use, I feel
it always carries the extra connotation of "on top of" or "in
addition to" or "composed with". Cycles and epicycles in the
copernican sense? Isn't the "billiard ball model" of molecular
dynamics an "epiphenomen" when compared to a quantum wave
formulation of the "phenomenology of particle physics"?</p>
<p>I'm probably not reading/thinking/expressing this nearly
carefully enough to be relevant.</p>
<p>bumble,</p>
<p> - Steve<br>
</p>
<div class="moz-cite-prefix">On 9/16/21 8:03 PM, Jon Zingale wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CAH5Jek1F-jVN2q=zRas+s55LtgsHh4a+S9o2DDFE8F_oc3x-7g@mail.gmail.com">
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<div class="gmail_default"
style="font-family:verdana,sans-serif;font-size:small;color:#333333">"""</div>
<div class="gmail_default"
style="font-family:verdana,sans-serif;font-size:small;color:#333333">Were
M absolutely, perfectly faithful to W, there would be no
epiphenomena in M. I.e. epiphenomena do not exist...<br>
"""</div>
<div class="gmail_default"
style="font-family:verdana,sans-serif;font-size:small;color:#333333"><br>
I read Glen as saying that the collection of all
comprehensions forms a space equipped with a meaningful notion
of distance, and that if one were to treat the space
analytically, one can arrive at a satisfactory definition of
local epiphenomena.<br>
</div>
<div class="gmail_default"
style="font-family:verdana,sans-serif;font-size:small;color:#333333"><br>
</div>
<div class="gmail_default"
style="font-family:verdana,sans-serif;font-size:small;color:#333333">For
what it's worth, I still feel that free-constructions may be
an insightful way to model epiphenomena, or maybe even (as in
EricS's t-shirt post) the relationship that Lie groups have to
their algebras.</div>
</div>
<br>
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