Template:Conway and complexity
The JC has encountered reductionists who see complexity as an emergent property of even a simple algorithm of Turing Machine.
On this view, fractals, polynomial mapping, even something as simple as Conway’s Game of Life is, if you let it go long enough, complex, as it spawns sub-systems, gliders, glider guns, and these interact with each other in marvellous and unpredictable ways. There is a tacit assumption here that real life — you know, the offworld — is really just a scaled-up version of the Game of Life, itself being just an implementation of Darwin’s Dangerous Idea, after all.
This is reductionism, only viewed from the wrong end of the telescope. Rather than taking the rich tapestry of modern life and boiling it down to basic rules of cause and effect, as reductionists normally do, this gambit starts with those basic rules, and scales them up. What prevents us from getting from one end of this spectrum to the other, say the reductionists, is only an absence of sufficient data to reverse engineer the algorithm (from the rich tapestry end) and a want of processing power to generate modern life (from the basic algorithm end). The universe is nonetheless fully determined at all levels of abstraction.
Hmm. So however long you run Conway’s life game, it does not seem to arrive at rice pudding and income tax. Reductionists say “Ah, but that is just because the rules aren’t quite right, or we haven’t quite got the right initial configuration”. But then, they would say that.
Complexity as an emergent property of algorithm?
The idea that complexity is merely an emergent probability of a simple algorithm is quite the piece of eliminative reductionism. Eliminative in that it eliminates complexity as discrete state. It converts all complex systems to no more than insufficiently-mapped, not-yet-properly-understood simple systems.
This is like saying — maybe it is saying — an analog signal is no more than an insufficiently granular digital signal. That binary code isn't just a neat way of representing the (apparently richer and subtler) analog universe but that, if you dig deep enough, analog signal reduces to binary code. That binary code is all there is.
If this is right — Spartan if, that — it has deep implications. For it means when we model the universe in binary code we are not just placing a convenient, subjective, all-too-human narrative on a hubbub of white noise — telling ourselves imaginative stories designed to help us get by, but whose “truth” value is beside the point — but that we are getting somehow converging upon the fundamental, transcendent essence of the universe.
Remember, we are so far away from having enough data, information and processing capacity as for the practical difference between these dispositions to be, for all time, nil — but the theoretical distinction between them is fundamental nonetheless.
In both cases, complex systems present us with unpredictable, non-linear outcomes in edge cases. All that differs is why they appear that way. (One is “because they are”, the other “because we have no way to better calculate them”.
But in the first case, any heuristic that helps us make sense of the system ISAs good as any other. There is no “epistemic priority” between competing heuristics: all that matters is what works best, judged by whatever criteria you happen to bring to the table. Beauty is in the eye of the beholder. In the other, there is such an epistemic priority. The most granular binary code is the closest to the truth. This gives the holders of that view grounds for insisting it is preferred, by everyone, over every other heuristic.
If algorithms are complex, everything is complex — or nothing is
Conflating simple algorithms with complex systems undermines the explanatory power of complexity theory. The distinction between simple, complicated and complex systems is meaningful. They are now just points along a continuum, without hard boundaries between them. It is really just saying, “well, in this complex system, something will happen; we don’t know what, but as and when it does we will be able to rationalise it as a function of our rules, by deducing what the missing data must have been.”
Ex-post facto rationalisation to comply with your rules is rather like the work normal scientists do in a research programme, of course. It is a form of narratisation.