[FRIAM] towards a description of a goal-function relation

[Jon Zingale]

Thank you, Nick and Eric, for the corrections, direction, and help as I
grapple with these ideas that you both are so familiar with. Taking a
step back, it appears that evolutionary theorists identify *function* in
the *epiphenomena* arising from *underlying mechanisms*. What connection the
epiphenomena have to the mechanisms can often be elusive, illusory, and
hotly debated. Must the mechanisms related to a flowing river give rise
to a meaningful[Ȣ] function? Moreover and seemingly less to the point,
evolutionary functions are sought after that can be identified as being
preserved inter-generationally in some sense. The survival of gulls is
an *unintended consequence* of selection upon eggshell removal.

While *goals* are related to the satisfaction of the individual, the
*function* is not so simply defined. As Nick has pointed out many times in
our conversations, *function* may better be understood in relation to a
concept of *design*[‖]. Perhaps it would be better to imagine *function* as
needing to satisfy the specification of some *design*[※]. The styrofoam
herding robot *knows nothing* of styrofoam, the bent metal in my thermo-
stat *knows nothing* of comfort, the maple pod *knows nothing* of the
journey or what it means to be distributed evenly, and the gull makes
no connection between removing shells and predation. However the theory
is to account for function, it will need to be in a language capable of
describing *side effects* as *first-class citizens*.

Eric relates the discovery of a goal-function distinction in evolutionary
theory to the discovery of the surface tension-PH distinction in chemistry.
Whether intentionally identified or just a side effect of his argument,
surface tension and PH are decidedly examples of intensive quantities and
so are of a type best characterized by contravariant functors[⁂]. The
connections here to contravariant logical notions (pullbacks, sections,
equalizers, finite limits, etc...) may have very real manifestations wrt
how we *must* investigate such ideas *empirically*. Ideas like this are
hinted at in Lawvere's work, but also seem to trace back further to
thinkers like Clifford Truesdell and others that struggled with rational
thermodynamics. From what I gather from those works, there ought
to be a tight connection between the logic of a notion and the methods
we employ in coming to understand the notion.

To the extent that this much may be passable, I hope to find some time
this week to work through the possible connection to contravariant
functors, to reason further in analogy to free constructions, and extend
the analogy to *exaptations* and *spandrels*. Again, I invite additional
corrections, comments, and nuance.

Jon

[Ȣ] By meaningful I exactly mean non-arbitrary. I would say that notions
like *energy* and *momentum* are *meaningful* to the physicist, for
instance,
not because they are *arbitrary* but because they have a *privileged* place
relative to the *art* and the artisans that work there. The scientific
enterprise is a meaning-making enterprise and to say that such-and-such
idea is meaningful to the artisan is to emphasize its value relative to the
art.

[‖] In a parallel post, I attempt to spell out a mathematical construction
that I believe can be an example if not a template relating design,
epiphenomena, and higher-order structure in mathematics. That this
construction can alternatively be interpreted as a post hoc justification,
gives a limiting case for not needing a designer to have a *design*.
http://friam.471366.n2.nabble.com/How-is-a-vector-space-like-an-evolutionary-function-td7597965.html

[⁂] Footnoted again, but this time with an added emphasis on page 20:
https://altexploit.files.wordpress.com/2017/06/1992-categories-of-space-and-quantity.pdf
"


*By contrast, an intensive quantity-type is a contravariant functor,taking
coproducts to products, from a distributive category, but now afunctor
whose values have a multiplicative structure as well as anadditive
structure.*"

[※] To act as touchstones, I am adding this list of functions:
1. herd styrofoam (http://www.verena-hafner.de/teaching/didabots.pdf)
2. maintain a comfortable temperature in the house
3. spread seeds far and evenly
4. avoid predation
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://redfish.com/pipermail/friam_redfish.com/attachments/20200726/655dfa94/attachment.html>