Tuesday, March 08, 2005

 

The "modeling" spectrum

William Tozier at Notional Slurry mentioned two of my posts on a to-blog list (Flotsam Nexus) with the following comment:
David Goldberg on blogging in Corporate vs. academic blogging; and also about the utility of models in Models live in the error-cost plane. In the latter case, I think there’s more to the word “model” than he’s caught yet, but that he’s on the right track….
I'll return to corporate vs. academic blogging later, but I hope my notion of a model is big enough to capture what the Slurrier has in mind. Let me draw a picture:


The modeling spectrum goes from unarticulated knowledge to equations of motion. Posted by Hello

On the right we have the usual sort of post-Baconian model, an equation of motion such as Newton's second law or a Markov chain, something with some red mathematical meat on it. What we 21st century modeling brats take for granted as a "model." On the left, we have a thought, a feeling, an intuition, a knowing that we have some trouble talking about. Polanyi called this sort of thing tacit knowledge, and Sowell called it unarticulated knowledge, and the error-cost plane applies to the whole lot.

I'm particularly interested in the modeling middle, especially the transition point when we move from articulated qualitative models (verbal or graphical representations) and we cross over to those models that are barely quantitative (simple measurements and dimensional reasoning), and I'll talk more about those in other posts, but I wanted to clarify that the project of The Design of Innovation is deceptively larger than might be inferred from the term "model."


Comments:
I like "The Slurrier." Henceforth let it be added to the Big List of Euphemistic Aliases, just after "Oh No Not Tozier Again."

I think in the forced brevity of my link list I came across sounding somewhat critical. Not so. But the brevity restriction still applies, and so let me jot a couple of notes for now and fill in as time allows. I apologize in advance if this seems cryptic or more addled than usual.

Models really only have meaning in the context of the research program or project in which they're developed and applied. As such, I like to think of them as the product of a design process -- with the word "design" here taken so generally that it can include the "design" of hypotheses and experiments in the natural sciences (which are more typically called "analysis" or research).

A phrase that you haven't used here yet (do you use it in DoI? I'll have to look it up): Cost of Change, from project management parlance. That phrase captures one of the crucial differences between traditional and agile project management methodologies -- and, I think, one of the crucial differences between scientific and engineering modeling. It's not orthogonal to your error and cost, but it's not entirely subsumed by them either.

Indeed, it seems a lot of interesting and useful analogies for talking about modeling (under the aegis of "design" and analysis) can be mined from the more philosophical software development literature, especially from the OO and Extreme Programming folks.

Surely there are design patterns for modeling (or something like Fowler's phrase: analysis patterns). When we're developing a complex model, I bet its organizational structure plays a big role in the costs and risks of the modeling project -- just as complex software developed without using familiar design patterns will be more convoluted and take longer to develop, a scientific or engineering model that's developed with unfamiliar patterns will be hard to think and talk about.

Come to think of it, if we think of modeling as a kind of project, your notion of error might usefully be called "risk", and thought of in terms of its various components: risk of error (statistical or symbolic), risk of failure, risk of changing goals, &c. All the risks associated with project management.

I'd also like to riff, when time permits, about the openness of modeling efforts: say (in our bailiwick) the difference between a GA fitting parameters to a particular equation structure, and GP searching among equation structures. In that light, there seems to be another aspect of the modeling process unaccounted for in error and cost: requirements. Strangely enough... another word from project management.
 
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