[FRIAM] Wolpert - discussion thread placeholder

[Jon Zingale]

What follows are mostly speculations:

It is possible that we do not get to have closed cartesianess (with all
of its currying and the rest) and so we do not really get to have *all*
possible worlds, perhaps only those that are symmetric monoidal. Still,
what then does this mean for us, since we can clearly posit cartesian
closed categories (like Set) and reason about them. That is, they are
somehow afforded to us like any other fiction, and like other fiction,
they play a role in our understanding of ourselves (Tennesse Williams)
and our understanding of our worlds (Noether[∫]).

Glen has me right when he suggests that I am not particularly wed to the
idea of a monism; whether it be monotheism, experience, category theory,
GUTs, etc... But I do find studying the available monoids to be as
fruitful as studying the available groupoids, etc...

In Lee Smolin's "Three Roads to Quantum Gravity", he conveys (as Hywel
often did) a skepticism toward universal acceptance of the law of
conservation, suggesting that a world with clean opposites would be a
trivial one. This has me thinking about the role duality plays in
modern mathematics (Galois theory, say) where we are not interested in
invertible maps between categories with different internal structures
(fields versus groups, say), rather we look for best approximations to
invertible maps (the adjoint functor perspective). It wouldn't surprise
me that that despite the successes of Maxwell to pin down E&M as two
faces of the same coin, that our quest for magnetic monopoles will
continue to be stymied because the duality isn't exact. That where we
attempt to reconcile two "kinds" of things, we will find subtly different,
yet corresponding algebras.

I mention some of this because duality (and symmetry more generally)
may simply be "afforded" to us and not "reality" for us. Still, the world
(and I use the term loosely) may reward those that believe (and act on)
such a fiction[Ax]. So then, many programs (it seems to me) rely on
being able to "dualize" into a larger space of possibilities/fictions,
in order to make sense out of what may be much more constrained. It may
very well be the case that the world, for instance, *must* be logically
consistent and complete and so can only support first order logics, but
assuming not, I would feel compelled to ask whether this world was one
that has the axiom of choice or not. My intuition (and preference) is to
imagine (as Glen suggests) that the in-principle ends of our questionings
do not culminate in a single monastic theory ;)

At present, I am entertaining Everett's monism, and wondering if all we
physically perceive are the moments of decoherence, and that what we
experience as particles are little more than the aliasing effects of
a wave function shedding its skin.

[∫] I am reminded of the Maria La Palme Reyes' (et al) observation in
their paper "Reference, Kinds and Predicates":

"The role of counterfactual situations in determining the actual is
further exemplified in classical Mechanics. To determine the real
trajectory of a body, we use the calculus of variations and compute the
Lagrangian of all its possible trajectories, most of which are only
logically, not physically, possible. We choose as the real trajectory
the one for which the Lagrangian has a minimum (or stationary) value.
The possible is essential to describe the real."

[Ax]. For instance, when chatting with EricS I get the impression that
linear classifiers can be unreasonably effective at sorting the bio-
chemical world. Despite the improbability of linearly evolving genes,
there is clearly a huge benefit in approximating linearity.
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