An Algorithmic Model
There are profound reasons that the structure and growth of the economic web is not part of current economic theory: modern economic theory is deeply mathematical. What mathematical framework would allow us to say that the screw works complementarily with the screwdriver to create value? What algorithmic model can describe unforeseeable Darwinian preadaptations in the economy? There may be none.
The hope of finding a mathematics that could describe and predict how novel goods and services unfold as the economy evolves into its adjacent possible thus seems precluded, at least at present. But even if the growth of the economy is not algorithmic, an algorithmic approach may still be of use in finding statistical features of model economies for comparison to the real one. Crucial here is the enlargement of the current framework: a concept is needed to mathematically tame the "adjacent possible."
One such approach is a "grammar model" that represents goods and services with binary symbol strings, such as (000). Within our model, the number and diversity of the strings can stand for renewable resources, appearing each year. Symbol strings can act on one another to create new symbol strings. For example, a symbol string with a (000) in it can rewrite the (000) in a second string into a (1010). A "grammar table" lists all the pair rules for these transformations. This arrangement can simulate a simple economic production function.
Intuitively, one sees that if the starting (and renewable) number of strings is small, that their diversity is low and that the grammar table has few pair rules, symbol strings will probably not be able to act on one another and few novel symbol strings will be created. We call such behavior subcritical. A subcritical economy cannot generate a growing diversity of goods and services. On the other hand, studies show that as the number of pair rules, resource strings or both increases, the system can abruptly transit into a supercritical domain where a large—perhaps unending—diversity of symbols strings may be generated. We call this explosion of goods and services supracritical.
Networks of Productive Pairs
We have recently idealized the above model and have confirmed analytically and numerically the existence of the subcritical and supercritical phase transition. In this idealization we map the problem of interacting strings into the setting of the autocatalytic networks that describe how one good can act on another to produce some third good. We will call such pairs productive.
We can take a wheel and a rope, for instance, and combine them to form a tackle, or we can use the rope to secure a boat at the pier. So ropes can be used in various productive pairs, as in (rope, wheel) -> tackle. Obviously most pairs we form randomly will not be productive. There is no rule that would allow us to do something useful with a supernova and a fish (except possibly in some psychedelic science fiction novel).
Next, we can ask whether the underlying production network instantiates some good, beginning solely with a fraction of the available possible goods. In a way we mathematically benefit from our profound ignorance of the real economic web's detailed structure because it forces us to model the catalytic network as basically random.
The absence of any particular plan underlying some catalytic economic network allows us to see something fascinating. If a random catalytic economic network contains sufficiently many productive pairs, then below some critical number of initial goods there are insufficiently many productive pairs to sustain the invention of new goods. Above this critical number of initial goods, however, practically all possible goods arise within comparatively few generations of production.
Some real-world economies appear to be subcritical. Joseph E. Stiglitz of Columbia University describes one African nation whose major economy consists only of diamond and cattle exports. One of us (Kauffman) lives in Alberta, Canada, which exports shale oil, animal and forest products, and has an information technology industry correlated with the oil industry. These two economies appear to be subcritical: they do not seem to be creating an ever growing and changing diversity of goods and services complement and substitute for one another. By contrast, the U.S. economy, the European economy, the global economy and perhaps other national and regional economies appear to be supracritical, creating an ever changing spectrum of novel goods and services.