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Just look at those crazies in their Brooks Brothers suits!<br>
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<blockquote type="cite">On Sep 17, 2021, at 8:04 AM, Steve Smith <sasmyth@swcp.com> wrote:<br>
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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...
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<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>
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<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>
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<div class="moz-cite-prefix">On 9/16/21 8:03 PM, Jon Zingale wrote:<br>
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Were M absolutely, perfectly faithful to W, there would be no epiphenomena in M. I.e. epiphenomena do not exist...<br>
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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>
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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>
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