Dear Antony Garrett Lisi,
you give a concise summary of the concept of emergence. I like your clear and straightforward writing style and you make your main points easy to trace.
You point out that the core idea of emergence is its cumulative effects of systematical side-effects of some compounded systems. I understand these side-effects being systematical per definition (this is what the concept of emergence does) as correlations. These correlations - i assume - can come about at all because the underlying physics can do a remarkable thing: in some sense it can divide apart different physical properties of a physical entity.
For example a big molecule. It has many locations at its spatial extension that react different to a physical interaction with another, well defined, physical entity than other locations of it would in this situation. So there are local forces that force the molecule to behave like an entity which is compounded by some smaller entities. But there are other forces that penetrate the molecule. The global force of gravity for example acts onto the molecule as if it wouldn't be composed out of smaller entities. Gravity - as we handle it mathematically - does 'only' act onto the center of mass of the molecule.
So, intuitively, i see that the concept of emergence is an important one in science. But here comes my 'but': Does the fact that there are systematical side-effects in nature justify that one is allowed to define what has been meant by 'systematical side-effects' (one has meant by it the term 'emergence') that 'emergence' is a systematical property of all of nature? In other words, is 'emergence' a fundamental principle that can be extrapolated without limits in both directions - towards the very small and towards the very large? Are there necessarily in every aspect of fundamental reality systematical side-effects - to the result that what you define in your essay as 'emergence' should better be objectively termed as a kind of universal law with a kind of inevitable tendency implicit to it (the inevitable tendency to produce new properties in a law-like manner)?
How could one then be able to formalize this universal law by objectifying it into a mathematically sound theory? Surely, this could not be done so easily, because per definition, the term 'emergence' implies that one cannot know in advance the special circumstances of the cumulating side-effects. But as you wrote, in principle this should be absolutely possible, giving the example of reproducing all our perceptions, experiences and emotions by a computer simulation. In this sense, one had to define 'emergence' as mere data processing. And here comes my criticism: the gap between mere data processing and a consciousness associated with perceptions, experiences and emotions. I doubt that such a simulation is possible and cannot see any justification for it other than the axiom you started with, that all things have to emerge out of lower-level constituents. Surely, if one accepts this premise, then such a simulation seems to be not so far at reach. But i really doubt it and ask myself what specific side-effects must there be to turn a mere data processing task into an observer. I know that the answer should be that there are millions of such side-effects involved, accumulating to the desired result. But i would not bet on this, because the more side-effects there are involved, the more error-sensitive the system would be in my opinion and this should then become regularily obvious in some way to the emergent property called 'consciousness'. So i tend to believe that emergence has its advantages, but also its fundamental limits.
