I very much agree that questions of a formality-informality spectrum will weaveitself throughout the work. It seems to me that the informality ought to provide aplace for birds to make a nest, a bellybutton for lint to collect, and a place forrust 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.
I am brought to think of mechanical tolerancing in juxtaposition to precise machining. The latter yields better performance (e.g. in a high performance internal combustion engine) initially but the former provides for better interchangeability of parts, especially for example, replacing worn parts along the way, and as I understand the principle, better performance (including reduced further wear) than putting in a "perfect as when new" part which would at least *accelerate* wear and *reduce* performance (think of replacing one ring or one main bearing in an engine after the rest had "worn in significantly")
As I understand it,
traditional gunsmiths and early ICE mechanics had to *add* wear
to a replacement part to match (not always in an obvious way)
the wear amongst the existing parts.
In this *analogy*,
a formal description of a system is like the precision machined
parts which all function together well on assembly and all wear
in together in-balance; a *less* formal description might be
like a machined part with deliberate tolerance built in which
does not require as much "wear in" to reach a dynamic balance
and when a replacement (unworn) part is introduced the whole
system is more able to accept it in with it's pre-created
"slop". I am suggesting that a more informal (is
formal->informal a spectrum or a step-function?) description
of a system leaves room for the "moving parts" to operate even
if they do so sloppily where if you "tightened up" those
elements with (overly in this context) formalisms they would
bind against one another? Can an informal system be a
precursor to a formal system? Or must a formal system be
constructed by composing *smaller* formal components? Some of
the early attempts at powered, manned flight seemed to fail
because of their lack of precision while the Wright Bros
succeeded *because* they composed a series of more
precise/formal elements?
Following my line of thinking above, the contemporary penchant for developing software/systems as "soft assemblages" of existing allows for what seems like this "combinatorial explosion" what with "soft assemblage" leaving the "slop" to allow the components to work together in spite of not being designed to (humans in the loop often make up for the slop?). It also limits the combinatorics somewhat by allowing/selecting for larger components. Bolting a grappling hook onto an offroad vehicle with acrylic window-coverings and sheet steel-armor on the sides to make a storm-chaser vehicle (with only hundreds of variants) rather than building one of 10,000 variations from wheels, engines, nuts, bolts, etc. Spot welders and epoxy glue and self-tapping screws and duct tape and bailing wire and bungee cords make for "soft assemblage" .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.
I like this apprehension, which also evokes in me a sense of abstract classes in OO... the creation and manipulation of a meta-thing that captures the essence(s) of the myriad things that can be made more concrete and/or instantiated from the abstraction.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 Chaitinrandomness and even an ephemeral feeling/non-symbolic experience. Comparison ofthese complexes with others provides the opportunity for new pivots and jumping-offpoints, for the serendipity of missed connections and false juxtapositions. There wassomething of this in my experience listening to the podcasters. At times I thoughtthat 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, constructingcommon complexes and variations which they could share.
Interesting. I'll have to listen more (and more carefully) as this unfolds.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 apleasant though unintentional corollary.
- Steve
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