Holy Experience

The semantics of the language would have to be rooted in a strict but putatively dynamic framework. Ideally one would be able to incorporate as arbitrary of symbols as possible, to build complex underlying suites of hyper-relationships. I would argue that for most of these systems the underlying hypergrammar would not be as complex as it could possibly be. In fact, in the power set of possible relationships between the elements of the system, most of the elements would be conditionally independent of one another at some point. This sparsity of higher order structure would allow one to construct incredibly powerful models without having to have them be so intensely complex as to incomprehensible.

The trick would be to incorporate the necessary and sufficient nonlinearities on the hyper grammar that would allow for the partitions of the state space that were most intutitive and meaningful. This brings into quesiton what intutitve and meaningful mean in this context...I would argue that they mean that the partition would give insight into the relationship between the local and global behavior of all the elements of the system. This is where it is definitely necessary to include the higher order conditional independencies, since without those the higher order structure cannot feed down and change the structure of the local interactions in increasingly complex ways. I think that is why most computational experiments with autocatalytic sets or evolutionary algorithms eventually tap out, since they do not explicitly incorporate the effect of the entire set of interactions taken as a whole on the local interactions of each element in the system. This feedback between levels of the hierarchy is absolutely necessary to have a true understanding of any of these complex systems, since it is the feedback between the emergent whole and the local behavior that gives rise to all qualia and phenomenon that we as human beings find beautiful and awe-inspiring.

It would be amazing to synthesize all sorts of coupled systems in one realization of the process. This would allow one to partition phase space in elegant and beautiful ways. I have a feeling that music does this to one's mind. The patterns of neurons flicker and flare bursting out of nowhere and fading into blackness.

The trick for the m-language will be to develop the appropriate hyper-grammar. This h-grammar will have to be constructed in a very clever way, such as to make the large order conditional independencies and the local conditional independencies play off of one another in highly intuitive ways. This means that the effect of the suite of all genes on the interaction between any gene, or the effect of the ensemble structure of the protein on any particular van-der waals interaction will be framed in such a way as to capture as many of the dynamically sufficient characterizations of the system as possible. One way to do this would be to assign some sort of low dimensional manifold to the suite of all variables, then "integrate out" that manifold from all of the local conditional indendencies (like it was a nuisance parameter). For example, send the states of the entire system to a 2 dimensional sphere. This lower dimensional manifold would then represent the collective effect of the entire system, and wherever on the sphere the particular realization was sent would be integrated out of the conditional relationships for each of the variables. One could choose as arbitrary (and as high dimensional) a manifold as one wished that would hopefully reflect the ensemble (or sub-ensemble) behavior of the system on each of the local dependencies. An example of this with protein folding would be, if one broke the protein into a hierarchy of structures. There would be the fine scale structures (e.g. local interactions) and the large scale structures (e.g. secondary or tertiary structure interactions). To find the most parsimonious time course trajectory, would would assign some sort of mainfold to each of the levels of this system, and integrate out the effects of each level on the lower levels, until the true time course trajectory of each atom could be predicted based on the entire ensemble h-grammar, implemented in an m-language. One could also do this for gene networks, for the structure of membranes for the formation of any sort of higher order structure in biology or nature, as long as a well-defined mechanistic and stochastic process could be defined upon it. The key aspect of this process would be to optimize for large ensembles of heterogenous objects, hence the local and global interactions would not be obvious, but these systems are the most interesting systems we encounter in nature.

Another incredibly exciting possibility would be to have self-optimizing substrates, that would take the form of the h-grammar they were operating on. The problem with many computational problems is that we have to restrict ourselves to a very specific physical computational architecture. Yet this is not the end all when it comes to computation (or directed realization of various states based upon some suite of criteria). We could optimize various computational questions (such as large scale modeling and optimization of heterogenous h-grammars) much more efficiently by having computational substrates that mirror the structure of the grammars themselves.

Essentially, human beings are hyper-grammars implemented in a particular meta-language. Yet there are also a myriad of h-grammars surrounding humanity, and flowing in and out of everyone of us. If the code of the m-language is broken so as to better understand the h-grammar, there will be a meta(infinity symbol) experience. A realization of a rosetta stone of the adjacent possible leading deeper down the rabbit hole. Leading beyond all thought, and beyond all possible comprehension. Weird how god sneaks in, in the strangest places.