We’ve talked about the nature of the Multicomputational Paradigm, and about its application in physics. But where else can it be applied?
Already in the short time I’ve been thinking directly about this, I’ve identified a remarkable range of fields that seem to have great potential for the multicomputational paradigm, and where in fact it seems quite conceivable that by using the paradigm one might be able to successfully unlock what have been long-unresolved foundational problems. Beginning a few decades ago, the computational paradigm also helped shed new light on the foundations of all sorts of fields. But typically its most important message has been: “Great and irreducible complexity arises here—and limits what we can expect to predict or describe”. But what’s particularly exciting about the multicomputational paradigm is that it potentially delivers a quite different message. It says that even though the underlying behavior of a system may be mired in irreducible complexity, it’s still the case that those aspects of the system perceived by an observer can show predictable and reducible behavior. Or, in other words, that at the level of what the observer perceives, the system will seem to follow definite and understandable laws. But that’s not all. As soon as one assumes that the observer in a multicomputational system is enough “like us” to be computationally bounded and to “sequentialize time” then it follows that the laws they will perceive will inevitably be some kind of translated version of the laws we’ve already identified in fundamental physics. Physics has always been a standout field in its ability to deliver laws that have a rich (typically mathematical) structure that we can readily work with. But with the multicomputational paradigm there’s now the remarkable possibility that this feature of physics could be transported to many other fields—and could deliver there what’s in many cases been seen as a “holy grail” of finding “physics-like” laws. One might have thought that what would be required most would be to do a successful “reduction” to an accurate model of the primitive parts of the system. But actually what the multicomputational paradigm indicates is that there’s a certain inexorability to what happens, independent of those details. The challenge, though, is to figure out what an “observer” of a certain kind of system will actually perceive. In other words, successfully finding overall laws isn’t so much about applying reductionism to the system; it’s more about understanding how observers fit together the details of the system to synthesize their perception of it. So what kinds of systems can we expect to describe in multicomputational terms? Basically any kind of system where there are many component parts that somehow “operate independently in parallel”—interacting only through certain “events”. And the key idea is that there are many possible detailed histories for the system—but in the multicomputational paradigm we look at all of them together, thereby building up a structure with inexorable properties, at least as perceived by certain general kinds of observers. In areas like statistical physics it’s been common for a century to think about “ensembles of possible states” for a system. But what’s different about the multicomputational paradigm is that it’s not just looking “statically” at “possible states”; instead it’s “taking a bigger gulp”, and looking at all possible whole histories for the system, essentially developing through time. And, yes, a slice at a particular time will show some ensemble of possible states—but they’re states generated by the entangled possible histories of the system, not just states “statically” and combinatorially generated from the possible configurations of the system. OK, so what are some areas to which the multicomputational paradigm can potentially be applied? There are many. But among the examples I’ve at least begun to investigate are metamathematics, molecular biology, evolutionary biology, molecular computing, neuroscience, machine learning, immunology, linguistics, economics and distributed computing. So how can one start developing a multicomputational model in a particular area? Ultimately one wants to see how the structure and behavior of the system can be broken down into elementary “tokens” and “events”. The network of events will define some way in which the histories of tokens are entangled, and in which the tokens are effectively “knitted together” to define something that in some limiting sense can be interpreted as some kind of space. Often it’ll at first seem quite unclear that anything significant can be built up from the things one identifies as tokens and events—and the emergent space may seem more familiar, as it does in the case of physical space in our model of physics. OK, so what might the tokens and events be in particular areas? I’m not yet sure about most of these. But here are a few preliminary thoughts:
It’s important to emphasize that the multicomputational paradigm is at its core not about particular histories (say particular interactions between organisms or particular words spoken) but about the evolution of all possible histories. And in most cases it won’t have things to say about particular histories. But instead what it will describe is what an observer sampling the whole multicomputational process will perceive.
**And in a sense the nub of the effort of using the multicomputational paradigm to find new laws in new fields is to identify just what it is that one should be looking at, or in effect what one would think an observer should do.**
Imagine one’s looking at the behavior of a gas. Underneath there’s all sorts of irreducible complexity in the particular motions of the molecules. But if we consider the “correct” kind of observer, we’ll just sample the gas at a level where they’ll perceive overall laws like the diffusion equation or the gas laws. And in the case of a gas we’re immediately led to that “correct” kind of observer, because it’s what we get with our usual human sensory perception.
But the question is what the appropriate “observer” for the analog of molecules in metamathematics or linguistics might be. And if we can figure that out, we’ll potentially have overall laws—like diffusion or fluid dynamics—that apply in these quite different fields.