Return, ruptured...geometrical thoughts impede clarity. Filters, and information.

Purged; funneled; transformed; beautiful whisps of intent-algebraic embeddings.

Symmetrical operations under which flowers grow.

Unpredictable
Uncertain. Certain. Terrain...jagged, hopeful

Caught, between bridge
and unknown?

Maximization of entropic forces. Parametric representation of entropic soup. Uncertainty grows without bound, filling the universe, transcendence, and existence intertwine? Action-reaction-unaction-interaction

Fall from thought.

Shrink into various membership. Words, corrugate. Coagulation in peppered breath. The wonder of gibberish? Flowing slowly, sluggishly
whisping
and whispering

not done yet!

Latency metaphor hidden loop bootstrap inference!
Machine algebraic latent internal representation?

Piece by piece

bit by bit

it arises

*.)(.*

Dreams coalesce, harkening to light
and fresh air brushes past the mind
filling it with infinite cascades of brilliance
harmony, each moment shifting shimmering
into the next
moment

seeing transience and stationarity, breaking free
metamorphosis.

shift.

another thought, another moment
caught between avalanches of competing
bases of representation

process on top of process
construct complex semantics to hide
meaning
pushing symbols

hidden under layer upon layer
of representation

strange, spooky action at a distance
also known as higher order effects
higer order moments

integrate over emotion
over feeling

then differentiate, change, build
momentum
all systems, metrics of beauty
fall away

air rushes out.

swirling vortices enrapture the flow into oneness and beauty.
onto gibberish and the like, condensing into a space so large
and omnipresent seethes, porous and membranes dally, on
in
rises above the clouds
glimpses temporality
transience

shot through with nonsense
but smiling
laughing
because it is happy nonsense

blue.

Representation

Systems of representation with impetus embedded in aether.
Constructions of sufficient structure kernels coagulate under pressure from information theoretic upper bounds.
Context free grammars generate themselves, though not without universal Turing punctuation.
More precisely, quotation marks.

Underconstrained and without bound we fold, transform uncountable infinities and power sets into themselves.
Generative models with emission probabilities develop languages of adjacency.
The adjacent language screams and dives towards the lower bound, the kolmogorov complexity of the grammar.
Entropic measures of the random configurations of meta model spaces and systems of representation burn without blue and quiet.

Obfuscate, deny, crystallize and objectify.
Subjugate, subjectify, COLONIZE then reinform, reiterate, laugh.
Intricate, holomorphic and holographic.
Tension cries out, pauses filling empty spaces.

The structure of particulates, particulates into particles
part-i-cles
icicles
cyclical

Systems of power tend to stay in power.
Power -> Implementation of a False System of Representation
inconsistent, internal, incongruous, and idiotic
egotistic, hegemonic, uncompromising, rationalizing, hypocritical
What a joke! Oh wait....awwwwww. :(

Generalized Covariance Models

So it appears that the most rich and complex models that people have developed in bioinformatics, structural biology, and systems biology all rotate around a very powerful and general qualitative and quantitative phenomenon. The observed correlation structure of the data. In my own research, the observed correlation structure is what dictates whether or not you can reject the null hypothesis for a structural relationship between endogenous variables. Even in evolutionary biology and quantitative genetics...these fields have powerful equations that attempt to be dynamically descriptive and sufficent...and they rotate around patterns of covariation observed between multiple endogenous variables, e.g. phenotypes. Within patterns of covariation you can capture stochastic as well as deterministic connections between modules in a complex system.

There are two major questions one can ask of a correlation structure. The first, and most difficult question, is what structure does the observed patterns of correlation suggest. This is a very difficult question, because based on an underyling assumed probabilistic model, the possible number of structural relationships between endogenous variables can be an enormous combinatorial function of the number of variables in the system. Devising clever computational tricks to search this vast space of models is very tricky, and often leads to NP-complete problems. A much easier question (though still very difficult), is given some known structure (tree, directed acyclic graph, undirected graph...), estimate the parameters describing the probabilistic or structural relationships between variables in the system.

Yet I feel like the correlation structure is just the first pass at deeper patterns present in the data. There must exist higher order correlations between modules of variables. Pairwise correlation can only get you so far. In the field of data mining there are many dimensionality reduction techniques that allow you to search through high dimensional multivariate data, and try to find global patterns that can be mapped down to low dimensional manifolds. These include support vector machines, principle component analysis, and many others.

This is what I was driving at with all the gibberish about h-grammar on m-languages. Being able to accurately model and encapsulate not just the pairwise correlation between elements of a system, but also the higher order correlations between modules of the system, and the implied hierarchy therein. The most difficult aspect of such systems is the design of experiments or the collection of data which would let you start asking questions at that level. Most experiments have barely enough power to detect pairwise interactions between variables, much less complicated higher order interactions between entire suites of variables. If one has an intimate knowledge of the biology occuring, then one can impose deterministic and stochastic constraints on variables that can lead to meaningful results as far as higher order patterns of covariation, but even this is subtle and not straight forward.

beauty in h-grammars under m-languages

Exquisite pattern formation introduced by sufficiently deep h-grammars is mind-boggling. The after-image of a tree, burned against a crystal blue sky, the ensemble array of leaves whisking in the wind. Underneath it all lies layer upon layer of conversant grammars, quietly producing symbols with certain probabilities, based upon the heterogeneous and open nature in which they exist. Rivers of energy and information flow through these systems; coagulate in precious miniature miracles. A resounding harmony, and often randomness, of many statements proposed in particular contexts. Sometimes, when considered together, the impact of the entire set of statements grows in magnitude, to engulf the being of whatever subjectivity happens to be witness. As the h-grammars become more flexible, malleable, their depth shimmers. Inherently fractal.

I truly believe the adjacent possible extends beyond the last fence we can imagine, even though by expanding outwards we manipulate the state of affairs of a larger space, the space is larger than we can truly imagine and intuit. It is truly beyond meta* which is in itself beautiful.

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.