Glen, I very much agree that questions of a *formality-informality* spectrum will weave itself throughout *the work*. It seems to me that the informality ought to provide a *place* for birds to make a nest, a *bellybutton* for lint to collect, and a *place* for rust to never sleep. To my mind, it is not necessarily the formality that chokes development. Rather, I think of formality purely as description and one among many valid and possibly incongruous descriptions. Here is a place that I would again emphasize Rota's take on eidetic variation. For Rota, the eidetic variation includes all of the counterfactuals, contradictions, and messiness that we develop/uncover as we vary in our minds an object of interest. It is not necessary that we cut away* babies from bath waters*, but rather recognize that the concepts are complex. I believe that the development of a concept can especially choke when we fail to recognize that a concepts formal description has a *combinatorial explosion*. A good example is a way the concept of random number can be used, ironically enough, *informally* to mean a number I can name.
When in a conversation the concept of the random number is invoked, it evokes for me a complex. I can sense within a *single complex: *frequentist randomness and Chaitin randomness and even an ephemeral feeling/non-symbolic experience. Comparison of these complexes with others provides the opportunity for new pivots and jumping-off points, for the serendipity of missed connections and false juxtapositions. There was something of this in my experience listening to the podcasters. At times I thought that one had completely missed the other's *point*, but really *I had missed the point*, namely that the discussion was *not about a point*. They were in play, constructing common complexes and variations which they could share. When I compare or attempt to describe my sense of this in terms of varieties and free module constructions, I am not saying that concepts *are* these things. I am appealing to varieties (say) in terms of its *conceptual* content. If we found that the language was flexible enough to do calculations, well that would be a pleasant though unintentional corollary. Jon
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