Just look at those crazies in their Brooks Brothers suits!

On Sep 17, 2021, at 8:04 AM, Steve Smith <sasm...@swcp.com> wrote:



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...

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".

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"?

I'm probably not reading/thinking/expressing this nearly carefully enough to be 
relevant.

bumble,

  - Steve

On 9/16/21 8:03 PM, Jon Zingale wrote:
"""
Were M absolutely, perfectly faithful to W, there would be no epiphenomena in 
M. I.e. epiphenomena do not exist...
"""

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.

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.



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