Let's keep our problem simple and bound our considerations at the earth's atmosphere, considering solar radiation as exogenous. Now, this is not an undifferentiated mass of disordered particles, but rather a hodge-podge of both order and disorder. At some points it is highly simple and at other highly complicated. In the midst of this system, a part of the system, is the human economy, and the behaviour of that system is of great interest to me. And, I think, to you.
On the other hand, consider our economy. It's a complex mess of stuff, inconceivably many products, technologies, informational signals, personal interactions, and so on. As messy and hard to quantify as it is I wonder how the number of teeming dimensions of economic configuration compare to those of a mole of ideal gas.
This minutely detail assemblage of human beings coupled to their own physical constrains and that of the environment, we hope to model this with some vastly lower dimensionality than a uniform phase space of all the particles that make it up. The question is, how can we do this usefully and come to an understanding of the regularities in our system?
The power set of all sets of matter in this is not the smallest dimensionality; rather we have many classes of statistically indistinguishable states that form the meaningfully distinguishable states of the system. We want to get at these to understand the dynamics of the system, its evolution and the potential trajectories. I'm especially interested in the information-processing function of the economy, the linkages to physical energy sources, and, probably the intersection of these, technology. How does innovation by our monkey minds come to change the shape of the world itself, the very composition of its atmosphere, and, how does it come to change out behaviours to unutterably? Why is there is trajectory towards increased innovation that some extrapolate into the singularity? Why are we richer now than before? How can a bad day on a stock market destroy wealth?
We have only bad models of technology, how it interacts with us and itself to produce strange emergent effects. I'd like better ones. The configuration space of innovations, the constraints thereupon. Obviously several things are happening here. Some types of innovation are contingent in their details, like the notorious QWERTY keyboard, and any industrial standard you care to name. Some are plausible on many possibly civilisations, even disregarding the constraints of earth itself - say, a parabolic antenna is good for any situation where you need to transmit a wave in a parallel beam. Some are generally plausible for many alternate histories of the earth (Say, the burning of fossil fuels, since they are a most stunningly easy and portable source of fuel). Some, that is, are tightly coupled to the history of the worldline they are part of. (HTTP as a communications standard is the most successful of a million standards, and no better than many, but is contingently highly successful for complicated reasons)
And somewhere along the line we get better, in the mean, at doing things with technology, sometimes getting more efficient at doing things with it, or at least creating more of it.
How do we quantify this? How do we come to understand how much of a difference we are making in technology by investing in its development? Is doing so just finding more ways to increase total entropy as per Howard T Odum? What is a viable substrate for innovation? What are the path dependencies? What are the existential risks? How would you simulate it in silico?
Note that I'm not asking if we can sit here and predict the direction of technology; that is a good idea for a science fiction story I should write one day, but is hardly plausible. What I am asking is if we can find a stochastic process whose dynamics are statistically similar enough to the course of technological development that it might serve as a component in a models which would explore the effects of that driver.
Intuitively, qualitatively, the answer is not necessarily ‘no’. We have some clear retrospective technological trajectories, towards faster diffusion and aggregation of information, profusion of standards and components, more miniaturisation, higher energy intensity, longer supply chains, greater specialisation in the work of those who create technology and so on. All these are by no means monotonic, or predictable, but, I think, in the mean, they hold. (Note about model of patent citation networks).
There is good precedent for modelling arbitrarily complex structure via symbol strings (Thing how language imposes arbitrarily complex structure, how gene expression encodes highly complex behaviour, and how genetic programming encodes high royalties for John Koza) That seems like a starter, but encoding technology as a string is non-trivial.
for one thing you'd want to do that neat trick that language and genes seem to do, and find referents for the symbols. The process whereby words come to mean things has confused the crap out of a lot of philosophers, and how gene expression encodes behaviour is complex. Hell, anyone in proteomics will tell you that how they encode proteins is computationally nightmarish. We don't get that for free. (Example of concrete gene expression problem here)
- although perhaps sufficiently good conditioning on environmental signals could explain how technology is created.
you'd still need to construct the linkages to physical reality. How much does a particular strategy cost? What are the constraints? Technology on earth is strongly conditioned by the abundance of fossil fuels, the abundance of water, the scarcity of uranium, and across the universe by things like conservation of momentum and energy. If you wanted to experiment with the evolution of technology strings, how could you possibly come up with a fitness landscape which was statistically like that encoded by gross reality?
See also Technium, Tainter, and probably even Prigogene, probably Wolpert and Bonabeau too.
Are there other structures better than discrete strings to encode what we need? Things less discrete? Would they able to cleave reality gracefully?