*Vela Velupillai, Madras School of Economics*

“Herb had it all put together at least 40 years ago – and I’ve known him only for 35.” Alan Newell, 1989.

And so it was, with* Hierarchy *in 1950, *Near-Decomposability* from about 1949, and *Causality*, underpinning the reasonably rapid evolution of dynamical systems into a series of stable complex structures. Almost all of these pioneering articles are reprinted in Simon’s 1977 collection and, moreover, the hierarchy and near-decomposability classics appear in section 4 with the heading “Complexity”. The cybernetic vision became the fully-fledged digital computer basis of boundedly rational human problem solvers implementing heuristic search procedures to prove, for example, axiomatic mathematical theorems (in the monumental *Principia Mathematica* of Russell & Whitehead) substantiating Alan Newell’s entirely reasonable claim quoted above.

In defining the notion of complexity in *The Architecture of Complexity* (*AoC*), Simon eschews formalisms and relies on a rough, working, concept of complex systems that would help identify examples of observable structures – predominantly in the behavioural sciences – that could lead to theories and, hence, theorems, of evolving dynamical systems that exhibit properties that are amenable to design and prediction with the help of hierarchy, near-decomposability and causality. Thus, the *almost* informal definition is (italics added): “*Roughly*, by *a complex system* I mean one made up of a large number of parts that interact in a *nonsimple* way. In such systems, the whole is more than the sum of the parts … in the … *pragmatic* sense that, given the properties of the parts and the laws of their interaction, it is not a trivial matter to *infer* the properties of the whole. In the face of *complexity*, an in-principle reductionist may be at the same time a *pragmatic holist*.”

Simon was always a pragmatic holist, even while attempting the reduction of the behaviour of complex entities to parsimonious processes that would exhibit the properties of “wholes”, based on nonsimply interacting “parts”, that may themselves be simple. He summarised the way this approach could apply to economics in a letter to Professor Axel Leijonhufvud and me after reading my book *Computable Economics*. (You can see the letter here.) Simon argued that:

“Finally, we get to the empirical boundary … of the level of complexity that humans actually can handle, with and without their computers, and – perhaps more important – what they actually do to solve problems that lie beyond this strict boundary even though they are within some of the broader limits.

The latter is an important point for economics, because we humans spend most of our lives making decisions that are far beyond any of the levels of complexity we can handle exactly; and this is where satisficing, floating aspiration levels, recognition and heuristic search, and similar devices for arriving at good-enough decisions take over. [The term ‘satisfice’, which appears in the *Oxford English Dictionary* as a Northumbrian synonym for ‘satisfy’, was borrowed by Simon (1956) in ‘Rational Choice and the Structure of the Environment’ to describe a strategy for reaching a decision the decider finds adequate, even if it’s not optimal in theory.] A parsimonious economic theory, and an empirically verifiable one, shows how human beings, using very simple procedures, reach decisions that lie far beyond their capacity for finding exact solutions by the usual maximizing criteria.”

In many ways, AoC summarised Simon’s evolving (sic!) visions of a quantitative behavioural science, which provided the foundations of administering complex, hierarchically structured, causal organisations, by boundedly rational agents implanting – with the help of digital computers – procedures that were, in turn, reflections of human problem solving processes. But it also presaged the increasing precision of predictable reality – not amounting to non-pragmatic, non-empirical phenomena – requiring an operational description of complex systems that were the observable in nature, resulting from the evolutionary dynamics of hierarchical structures. Thus, the final – fourth – section of AoC “examines the relation between complex systems and their descriptions” – for which Simon returned to Solomonoff’s pioneering definition of algorithmic information theory.

*AoC* was equally expository on the many issues with which we have come to associate Simon’s boundedly rational agents (and Institutions) *satisficing* – instead of optimising, again for pragmatic, historically observable, realistic reasons – using heuristic search processes in Human Problem Solving contexts of behavioural decisions. The famous distinction between substantive and procedural rationality arose from the dichotomy of a state vs process description of a world “as sensed and … as acted upon”.

Essentially *AoC* is suffused with pragmatic definitions and human procedures of realistic implementations, even in the utilising of digital computers. Computability theory assumes the Church-Turing Thesis in defining algorithms. The notion of computational complexity is predicated upon the assumption of the validity of the Church-Turing Thesis. Simon’s algorithms for human problem solvers are heuristic search processes, where no such assumption is made. Hence the feeling that engulfed him in his later years is not surprising (italics added):

“The field of computer science has been much occupied with questions of *computational complexity*, the obverse of computational simplicity. But in the literature of the field, ‘complexity’ usually means something quite different from my meaning of it in the present context. Largely for reasons of mathematical attainability, and *at the expense of relevance*, theorems of computational complexity have mainly addressed worst-case behaviour of computational algorithms as the size of the data set grows larger. In the limit, they have even focused on computability in the sense of Gödel, and Turing and the *halting problem*. I must confess that these concerns *produce in me a great feeling of ennui*.”

**Useful links**

*A version of this article with added commentary and references is available here.*

As mentioned above, Herbert Simon wrote to Professors Axel Leijonhufvud and Kumaraswamy Velupillai after reading Pr Velupillai’s *Computable Economics*. You can see the letter here.

The OECD organised a Workshop on Complexity and Policy, 29-30 September, OECD HQ, Paris, along with the European Commission and INET. Watch the webcast: 29/09 morning; 29/09 afternoon; 30/09 morning

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