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
- .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/
