Near Decomposability

Written by  on September 6, 2017 

In reading Machine Experiments and Theoretical Modelling: from Cybernetic Methodology to Neuro-Robotics, they rely to some extent on the concept of “near decomposability” and cite The Sciences of the Artificial, Third Edition as a motivation.

However, this raises the same problem I continually have with any discussion of hierarchical systems. I try/fail to point out my problem to people at conferences, in my own writing, in the papers I review, etc. But the point never lands. It is (of course) similar to the previous post on layers vs. levels. Here we can use Simon’s presentation to make the case, though.

Therein, Simon uses the example of a building with perfectly insulating walls to the outside world and imperfectly insulating walls between rooms, and then badly insulating cubicles within rooms. He then goes on to talk about the diffusion of heat through the building. At least I assume he’s only talking about diffusion because the matrix he arranges into nearly decomposable units contains the diffusion coefficients, but nothing about any advection. So, in this idealized example, the inter-room interactions are clearly weaker than the inter-cubicle interactions.

However, what if we add another MODE of interaction like, say, forced air HVAC? It strikes me that inter-room interactions will be stronger than inter-cubicle interactions under both advection and diffusion. Imagine the continually cold person sitting in the cubicle nearest the vent in your office.

So, the point being made is that some variables can be idealized as an aggregate, somewhat isolable from other aggregated variable sets. But if this is the purpose of the “nearly decomposable” concept, it’s at high risk of inscription error. Any system with a huge number of modes of interaction, over and above any number of variables within each mode, will force you to idealize down to particular modes. And, thereby, you’ve inscribed the aggregation rather than discovered it. And any predictions you may make off your near decomposition will have that choice programmed in.

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  1. […] who know me will expect this to devolve into an unread screed about unitarity and closure(s). But I just posted something about that. So, I can bail this […]

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