Basically this question stems from trying to answer yet another question that I have:
How does one analyse emergent properties that are not quantifiable, to allow for discrete mathematical probing?
Or in other words:
How does one go about building models for emergent properties that reject notions of simple counting?
Take the example of an emergent action: walking. By studying a single leg, you obtain no information about its purpose. But in the context of an entire human being as a system,
interdependence of two legs on each other with
coordination to put one leg ahead of the other and then repeat gives us a novel process we call "walking". I call this process novel because an alien philosopher with no knowledge of legs couldn't deduce its function by observing just a single leg. What changed was from understanding the leg as as
singular closed system we changed our context to understanding it as an
Now the leg, in order to explain itself, has to necessarily be regarded in the correct context. Also such a procedure introduces downward causation: a motivation in the environment that is causing the human to walk. This is already hinting to me, that when we are talking about strong emergence, one must necessarily take in the context as metadata/prerequisite in order to analyse effectively. This would not be the case with reducible entities like atoms for example, which may still be effectively studied without needing this metadata about its environment. Once we understand all the four forces it can interact with, we can at best hope to extrapolate into weakly emergent properties.
Another instance of necessary contextual information comes from the idea of quantum entanglement. In quantum entanglement, the polarization or spin of a particle are such properties that depend upon the orientation of the measurement apparatus. This already introduces
context as a factor in our study, namely, the
orientation of our apparatus. Once this particle splits into entangled pairs, the resulting daughter particles may give us individual measurements, which when looked without seeing the other sister, give us an impression of randomness, but when both sisters are taken together, the whole is such that the spin or polarization always adds up to that of the parent particle, as measured in the pre-split orientation. The weird thing however is that this parent particle seemingly acts as a multipartite system after the split and as an individual before the split. Again the context proves to be an important deciding factor when talking about the knowledge we gain from this entity. In a nutshell, the original polarization, with regards to the original measurement, if it has to be considered as a strongly emergent property, must necessarily also include the context information. Without this additional piece, looking at the sister particles individually cannot reconstruct this information unless taken together and then extrapolated backwards as to make a guess. Would a characteristic such as polarization even have
absolute observer independent meaning?
So off the top of my head, all the instances that I can think of involving (strongly) emergent properties, necessarily rely on the context of observation. In
strong emergence one expects to obtain properties that are in no way deducible from a single or even a group of constituent parts. Consciousness seems to be the strongest emergent phenomenon in which, I use a lot of layers of abstractions to just look at a group of water molecules and predict a weakly emergent property of "fluidity". The same knowledge, in order to be derived from computation would require a lot of computing, at least of the order of
O(N^2) for N molecules. Clearly, having such higher abstractions is vastly efficient, might not be solid, but for practical purposes, it is solid enough. In my opinion, this is the only roadblock towards a model strongly emergent phenomena. After all, how many functions/forces could an emergent property have after it has exhausted its intended environment? Would it be possible to obtain a class of strongly emergent phenomena that can be considered as inert/not relating to the environment in any shape or form whatsoever?