Incompleteness

2008-08-26T17:33:00.001-07:00

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

*.)(.*

2008-02-21T08:57:00.001-08:00

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.

2008-02-13T17:56:00.001-08:00

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

2007-11-09T06:24:00.000-08:00

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

2007-10-23T08:05:00.000-07:00

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

2007-09-22T12:12:00.000-07:00

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

2007-09-21T17:05:00.000-07:00

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.

Meta-meta-meta-meta....language

2007-09-17T20:23:00.000-07:00

It is interesting how functional constraints imposed by the mere form of objects of interest can give rise to novel characteristics. Yet, language sets the upper bound on what one can communicate about novel characteristics. And what makes a characteristic novel anyway? If I flip a quarter a million times, any particular outcome (when considering the entire string of flips) will be highly unlikely to observe. But we could care less if the information encoded by the string of 1's and 0's is truly random. What we truly care about is if there is some deeper pattern or organization to the string of 1's and 0's. But given an apparently random string of 1's and 0's how can we tell if it is truly random? What is randomness? This is a deep question in computer science relating to the most efficient algorithm to produce a particular output (e.g. a string of "random" 1's and 0's).

It seems likely that in the space of possible string's of 1's and 0's representations of ourselves and our reality(ies) exist in an infinite multitude of forms. This is both terrifying and awe-inspiring. In fact I would argue that if power-sets of infinities (ad nauseum) exist, then reality is much weirder than we could even begin to imagine, i.e. the holes and bridges that actually exist across all relations and non-relations are infinitely more complex than we can even begin to begin to...understand.

How does one go about constructing increasingly powerful languages, that can identify all (or at least most) salient characteristics of objects which they operate on? There is an upper bound on how powerful a language can be (i.e. it can't evaluate the truth of its own statements in finite time). But that doesn't mean we can't build languages that more accurately mirror the form of the objects they operate on. Say we have some complicated web of causal interactions with noise (protein folding, gene networks, membrane dynamics, any complicated ensemble process...). We want to talk in meaningful ways about the system. All we have to do is identify all conditional independencies in state-space, then all meta-conditional independencies (e.g. conditional independencies between groups of variables), then all meta-meta...(groups of groups), etc... These may also be multilinear groups of conditional independencies, (i.e. we may have hyper-(n)-graphs). This will parse the system into the relevant hierarchies. From this highly complex hyper-graph, we can develop qualitative state-space analysis techniques, essentially cutting up the state space based on the structure of conditional independence. Every level of conditional independency corresponds to some higher order structure we cannot see merely at the bottom level, but which may play an important role in the dynamics/behavior of the system. The most interesting cases will be where the meta-* conditional independencies end up feeding back down to the bottom of the hierarchy (and vice versa), thereby partitioning state-space in increasingly complex ways. (Feedback can be used to break symmetries in state space, including symmetries on higher order structures.) We can then assign probability to entire chunks of state space based on the inferred global structure of the system in question. This probability assignment will allow us to make statements about the current and future state of the system, couched in the noisy nature of our understanding of the system in question. We can then operate on this hypergraph embedded in some nonlinear manifold. We can ask questions like, if I couple these subsystems, what will happen to the global dynamics of my system? Since we know all the conditional independencies, we can immediately identify which structures any operations will affect, and then it should be possible to focus on just those structures to elaborate what the effects will be.

To make each level of meta-conditional independency tractable, there will need be clever notational and semantic rules. A language constructed in this framework would have the advantage of being both general and specific, which means that one could taylor the language well for multiple systems, then compare each of these specific languages to look for isomorphism. More on this when I'm not crunched for time...

Jorval and brey

2007-09-02T19:29:00.000-07:00

Quix core, cithe
Chart en racheq
Deaor brithel danr the
Nor falk and corl

Quarl, cae jalp
Pose sh., (<
Org and ynor
Wre colp ja mor ral tanta
o mley un-d a breol

Mae, moorsh laeon grysh
Youel, woer lofeirl
em
Ne
doorway

Wonderology (cont.)

2007-08-29T06:46:00.000-07:00

Though I did delete the asinine introduction on the last post, I suppose I'll reintroduce the idea slightly. Wonderology is a half-jokingly generative philosophy that pursues the question of relation and non-relation with respect to the apparent existence of subjectivity. It is both skeptical and positivist.

Yet, it drives at a space where philosophy, mathematics, and complexity intersect. The problem with most other philosophies is they do not take into account the true depth and complexity of the issues of subjectivity, relation, and non-relation. Especially with respect to the underlying forms driving these ideas (i.e. the physical realizations that for whatever reason make us think these bizarre and often ridiculous thoughts). Many simplifying assumptions are made at the grossly macroscopic level (i.e. the internal monologue, and maybe a few layers of subconscious underneath), without taking into account the structure, relation, and non-relation of the entire hierarchy of processes lying beneath the surface of the apparent phenomena of subjectivity. Hence, these philosophies restrict the space of possible interpretations and only scratch the surface of a much larger space hiding beneath the abstract symbol manipulations we perform daily.

As the human race hurtles into an increasingly strange reality these deeper questions beg to be answered, lest we perpetuate mistakes we made before. This will likely be a painful and arduous process, since it will require us to question the most deep-seated truths we hold to be self-evident. Hopefully, this will lead to an increasingly peaceful and wondrous reality for all subjectivities.

The next phase of this philosophy will be to generate a proposition for what systems can attain a state of wonder. I'm not sure the best way to go about this, since I'm not even sure if a system has to be subjective to wonder or not. Maybe.

Wonderology

2007-08-25T13:40:00.001-07:00

Preliminaries
Define phenomena as any realization of a well-defined process. A well-defined process being a process that does not suffer the agonizing (or not) state of being internally inconsistent. For example, a machine that runs under the assumption 1+1 = 3 (keep in mind inconsistencies can be much much more subtle).

Define inconsistent as being in a state of (human) logical fallacy. It may not necessarily be true that human logic is the end all when it comes to understanding all possible phenomena, but it is the best we've got so far when trying to construct systems for evaluating truth. (Though one could argue against this too...)

Define process as any system of rules that takes input (including no input) and produces output (including no output). Examples: computers, systems of differential equations, cellular automata, random number generators, etc...

Define rule as any well-defined relation between objects or processes.

Define relation as the state of not being in non-relation. Relations are a subset of objects. This is tricky, because all of our thoughts are set in a backdrop of relation, so we have to be wary of what non-relation does to what we think, since we can't think it.

Define object as anything that is not in non-relation.

Define non-relation as any object (which includes processes) which cannot be represented.

Define representation as any formalism for encoding relations.

Define primitive as any object that can not be described in more basic terms (e.g. anything below is in non-relation).

Reduct!
Proposition: One can construct new processes from other processes. As long as one maintains the ephemeral quality of internal consistency, any new object pieced together from other processes is a new process itself.

Corollary: Any process can be broken down into sub-processes if and only if the process is not primitive.

Note: The rules for breaking and constructing are non-trivial. Suffice to say, they exist, but may not be obvious for any particular process. Science is often concerned with the breaking of processes down into simpler processes. Engineering is often concerned with constructing new processes from pieces.

Holify!
Proposition: Certain process constructions produce phenomena that do not apply for any particular sub-process. This occurs whenever global and local qualities of a system cannot be transformed into one another. This is a type of symmetry breaking.

Define transformation as any map of one set to another.

Define set as any collection of objects (which is also an object).

Define symmetry as any property of an object that is invariant under a certain class of transformations (e.g. it doesn't change when transformed in certain ways).

Lemma: Symmetry breaking is the destruction of isomorphism.

Define isomorphism as any relation that implies sameness.

Wonder?!
Define wonder as any state of being that acknowledges and desires to reconcile phenomena, processes and sub-processes. In general this will include special attention to production of non-trivial global phenomena, symmetries, and symmetry breaking. A broad synthesis of reduction and holification. This will in general engender the creation of "meta" concepts. Beware the meta...it is a useful tool, but it can lead one to fixate on certain convincing illusions, and to become so captivated by these illusions that one is blinded to essential relationships hidden behind the meta.

Proposition: A state of wonder is a state of maximal (local or global) relation with other objects.

Note: This does not explicitly state the value of maximal relation. This is an open-ended moral question that may be context dependent (which would be a kind of symmetry breaking). It may also be that one must be in non-relation as well to attain a true state of wonder.

Statistical Methods for Dynamical Systems

2007-07-14T17:46:00.000-07:00

I just returned from a conference in Montreal on statistical methods for dynamical systems. It was absolutely amazing! I'm starting to get the feeling that people are just beginning to recognize the vast potential waiting around the corner for modeling complex high dimensional temporally and spatially dynamic systems while dealing with the tricky issues of appropriate model selection and statistical inference for parameters. There are of course a myriad of tricky issues and problems that need to be solved, but fortunately there are some powerful brute force methods that may usurp elegant computational and mathematical tricks as raw computing power becomes increasingly cheap and ubiquitous.

I envision a point where we have complicated hierarchies of spatiotemporal models that use dynamic models as building blocks. A sort of object oriented approach to modeling function spaces, where one can swap out various model types and parameterizations to best capture the essence of the observed process. Of course, a lot of this is data driven, in that these models will require vast quantities of data to validate or falsify, but as technology continues to improve this will not be a limiting factor. I think the largest limiting factor is going to be our ability to intuitively manipulate and understand these complicated models, though this may not be a huge problem as they become increasingly autonomous in their design and implementation.

We're definitely going to need these models if we're going to answer the question, "What is life?" I think this is one of the biggest and most important questions all of humanity is faced with. If we could elucidate the true nature of the autocatalytic process that is biology we would have a deep insight into not only ourselves, but also the complex web of relationships between all organisms and their environments/contexts. I imagine that truly internalizing the full magnitude of the complexity and subtlety that it is to be a living organism would be somewhat akin to a spiritual experience.

Of course, there may be reasons not to suffer such an understanding. We may swoon in despair, or annihilate ourselves and our environment out of fear and rage. It also may be impossible for us in our current state to ever truly model such complex processes...yet I find this argument incredibly weak and close minded. The most concerning and most likely possibility is that a relative few rich and powerful gain control of this knowledge, and use it for their own self interests. That is why I suggest in general all research towards understanding this question should be available in the public domain. Also, active outreach programs promoting the involvement of many people and organizations in policy making decisions concerning the ethical and moral implications of such knowledge would be absolutely essential for careful and responsible investigation. Ideally, we could use this knowledge and understanding to bootstrap ourselves out of many ills, while minimizing further risk.

I know that I'm going to continue to not only think about exciting new ways to build more powerful models, but the long term moral implications of understanding the systems I'm modeling.

Buddhism?

2007-04-12T15:51:00.000-07:00

I was thinking about Buddhism the other day. I wondered if maybe meditation is a form of redistributing the em-PHA-sis of "I" Imagine this...imagine that "I" arises because of a myriad of sufficiently flexible and powerful pattern identifying algorithms apply their said skills to themselves, and lo-and behold, a wondrous and resonant new pattern appears, magically out of nowhere. (It may be more of a progression...but that's not vital to the point I'm attempting to make). This new pattern (it's a pattern like any other pattern though, nothing makes it more than a pattern), appears to suddenly have an influence on everything we say and do, because no longer are the pattern recognizers mere cold and empty machines, they are machines with internal, or subjective, qualia (experiences). The qualia arise merely because of the context of the new pattern of patterns, since the pattern of "I" couches all other patterns and pattern recognizing algorithms in a very particular way, where self-monitoring is possible (and the pattern recognizers are sufficiently powerful and universal).

But since "I" is merely a pattern, and not some fundamental indescribable aspect of a person/thing, it can be manipulated and reorganized; just like more mundane patterns like the schedule for an upcoming conference (change key note speakers), the distribution of particles in a box (add a barrier), or how one organizes their desk (papers randomly distributed on top, or randomly distributed in a drawer). Perhaps when one meditates, one redistributes self such that it no longer permeates every conscious thought; it is no longer the nexus of the internal world. Instead, the nexus of the internal world diffuses out into one's surroundings, or the rate of one's breathing, or one's heart beat. This shift in the focus of the mind and the body breaks away from the all-mighty symbol of self and the pattern recognizers get a break from constantly being harassed by a bossy and needy ephemeral pattern of "I"

More to come later...

I am a Strange Loop

2007-04-07T15:28:00.000-07:00

I just finished reading Hofstadter's newest book, I am a Strange Loop. Though most of the book was an elegant and analogy filled redux of Gödel, Escher, Bach, there was one incredibly powerful and resonant extension on the loopiness of self. Basically, the thesis of his book is that "I" is a strange loop where "I" is essentially a pattern finding, approximating, and generalizing soup of particles that applies those respective procedures to itself. A "hallucination hallucinated by a hallucination," as Hofstadter so eloquently puts it. This strange feedback relationship leads to an upside-down sort of causality, where by looking back on oneself, an incredibly powerful and resonant symbol is created...the symbol of "self". Once this symbol is established, it has an effect on everything else we as human beings say, do, think, and dream.

But this is not quite everything that is going on...he extends this idea such that these subtle and fragile strange loops are not forced to be contained in a single container, and there is some gray area, or bleed-over. The work of Chopin is in some sense a highly focused view into Chopin's soul, and by listening, performing, and experiencing his music, we are in some way privy to the strange loopiness that was Chopin. In some small way his essence also resides in us for a brief time. I find this idea of multiple strange loops passing through a person very uplifting, since it means that as humans we can hopefully to some degree know what it is like to be another person, or subjectivity. It is also uplifting because it often seems like the volume is cranked up on the "I" part of many individuals...including myself. But the idea that many "I's" can potentially pass through a person, and have an effect on their own "I" is a beautiful and evocative contrasting thought.

Though everything that goes on in each and everyone of us can in theory be explained by the deterministic and often cold and indifferent laws of physics...Hofstadter shows us the most truthful and consistent position on where "I" arises from, without resorting to a Dualist point of view that requires the existence of some magic substance that imbues it's owner with consciousness. Though this means giving up on thinking there is something special about being conscious, in the sense of a soul existing independently of the substrate it resides within...it puts that much more weight and beauty on the upside down causal creature, "I". These Gödelian swirls in our minds build the visceral and resonant experience that is subjectivity. And since our minds are practically infinitely flexible, this leads to a wondrous cascade of experiences as well as languages and semantics in which to couch the multitude of ways in which it is to be.

I am a Strange Loop.

Original Symmetry Breaking

2007-03-08T05:38:00.000-08:00

Indexicality conceals underlying invariance

Dynamically sufficient manifolds
map themselves:
recursing into existence

there exists a dual space C
of the dynamically sufficient manifold M
such that C is the space which it is
to be M

forced by indexicality to C
I can only see other M
but no other C

A symphony of cacophony

2007-02-12T19:22:00.000-08:00

Interweaving melodies and membranes arc over metric spaces
Spontaneity and causality recombine across a frothing bath of correlated non-spontaneous processes, overwhelmed by random instantiations; forward and backward
Flux through phase space increases exponentially, and boundaries are forever fuzzy and frantic
How adjacent is the adjacent possible?
Is it right next to the subjective?
Or is it inside a broken objectivity whose shards glisten iridescent in the sun?

Or, a void, pregnant with potential.

A gathering wave of potential reverberates through weakened entropic soup
It builds and branches out in blazing fractals of brilliant luminescence
The fractal, whose non-linear irreducible self folds forever: irreversible and shattered
But whole.
The potential grows; the single note breaks unity/symmetry and enters basins of attraction, a chord harmonious but different
As the splitting occurs again, and again, and again the basins drift farther away
The cacophony swells, and the forms fade into disorder.
From this entropic chorus, cohesive pieces can coalesce, constellating in cue to coarse-graining;
it burns, abrasive and billowing through a body.

Uncertainty and subjectivity fold unto cyclical time; killing causality.
From the death of causality arises harmony: oneness.
And next door, the adjacency encompasses all unspoken and unspeakable complements of reality.
Waiting to be brought out of disorder and potential into actuality
By quiet and causal agency

Decentralization

2007-01-23T19:11:00.000-08:00

The decentralization of the production and distribution of energy will lead to a watershed in the existing social, political and economic power structure. There is a tremendous inertia behind the current production and distribution of energy because it maintains a self perpetuating hegemony where a very small group of people (relative to the entire population of the earth) control the means of production of energy. Energy makes all human endeavors possible, since all human endeavors are far from "thermodynamic equilibrium." In other words, practically nothing anyone is able to do in this modern age would be possible without utilizing energy resources. Because of this fact, people who control the energy have an undue influence on the way in which any particular subjectivity can participate in making a living. The decentralization of energy production and distribution will illuminate cracks in this hegemony that will lead to greater freedom among all humanity to participate in endeavors of their choosing. This will occur along social, economic and political dimensions. Anyone will be able to produce enough energy to engage in most activities of their choosing, with the ability to sell that energy to other people who need it or want it for other purposes. From a social perspective, this means that people will be able to be more self-sufficient, and hence class lines will be diminished because people will not be constrained to choose a particular lifestyle because of constraints on their energy usage. From an economic perspective, the greater independence will allow people to get more in return on almost all of their activities and aspirations, since decentralization will decrease dramatically the cost of all human endeavors. From a political perspective, the decentralization will be a stake in the heart of an antiquated idea of a rigid and controlling power structure that determines the production and distribution of energy resources. There will probably be a strong backlash, but this will not be able to forestall the march of progress towards a more robust and egalitarian political dimension for the utilization of energy.

Decentralization will not stop merely at energy production and distribution. Knowledge (as shown by the internet...and such phenomena as wikipedia) will also become decentralized to a greater and greater degree, which will also have a profound influence on the way in which people can make a living, since the current economic system is set up in a way such that specialists can perform a service or function that is a benefit to someone else. By having specialized knowledge and performing a service specialists make a living (e.g. doctors, lawyers, mechanical engineers, etc...). If this specialized knowledge is available to everyone, there will be pressure towards a greater human dimension (e.g. the quality of human interaction for any particular specialist) and the production of new fields in which to specialize (e.g. computational biology).

Eventually the means of production will become completely decentralized as molecular manufacturing becomes a reality. This will have a similar effect as the decentralization of energy production and distribution, except to a much larger degree. By decentralizing the means of production, every individual will be able to make a living in practically whatever way they choose, as all personal economic and social constraints (as we know them now) will be effectively lifted. Along with the decentralization of the means of production, there will be a revolution in medicine, with the advent of completely personalized medicine (along genomic, proteomic, molecular, metabolic, etc... dimensions) as well as personalized education.

I am fairly confident that new constraints will be developed, but these constraints will very likely be of a very different nature than the constraints people face today, such as not having enough food to eat or being stricken by horrible sickness. I am cautiously optimistic that most ills we face, along both personal and social lines, will be solved to some degree though I am sure that new problems will be generated. I am hopeful that we as a human race will be able to engage in a deep and introspective dialogue as to the profound moral and ethical implications of this continually cascading wave of change, and be able to anticipate and prevent the greatest falls into whatever abyss we teeter over along the way outward into the adjacent possible.

Local minima

2007-01-13T14:40:00.000-08:00

Consider that the space in which the mechanistic basis (purely psychological, not phenomenological) for the mind resides could be described by an energy landscape. Any particular thought, and more importantly any particular combination of thoughts would have associated with it a particular energy. This energy would be proportional to the amount of "mental work" associated with that particular combination of thoughts.

For example, if one does not know how to play the piano, one can learn how to do so, but in doing so one has to expend mental work to learn that skill, and actually go through the appropriate motions. By learning that skill a person is changing the energy landscape, by lowering the energy of a particular coordinated series of actions. Mental work can actually be quantified by the degree in which it affects the measurable behavior of a system.

This energy landscape dictates the way in which a mind can influence the behavior of the body in which it resides. One of the major problems for a mind trying to have an effect on the way in which the body behaves is that it can get stuck in local minima. This means that the mind can not overcome a previous series of thoughts that lead to a series of actions which the mind does not believe is as important as an alternative series of thoughts that lead to an alternative series of actions. Hence, why it is so hard for people to change once their energy landscapes have conformed to a particular configuration whose central structure is very rigid, with only slight gray areas on the fringe.

There really is no objective goodness inherent in any of these processes...or in other words, associated with any particular thought-action coupling there is no value. We assign value to the couplings based upon the phenomenological experience we have while going through the process of traversing the energy landscape and acting upon the traverse of the energy landscape. What causes this phenomenological experience is a mystery, all we can say is that as an individual traversing an energy landscape we not only think and do things, we also have subjective experiences associated with thinking and doing things. This subjective experience is probably by definition not reductively explainable.

Pragmatism

2007-01-07T01:12:00.000-08:00

Are "abstract" ideas like truth or justice any more significant than apparently mundane objects like a fork or a spoon? Truths and spoons serve their own respective purposes that only really matter when something is done with them or someone or something uses them. There seems to be an arbitrary and false hierarchy that assigns greater significance to certain ideas because of their purported significance to the human condition. Yet any particular idea can not be any more powerful than how useful it is to what happens in the moment. An idea or thought that does not somehow influence some one's or some thing's actual day to day experience of life has no power.

This makes intuitive sense from a Darwinian perspective. Neutral variations (or variations that have no effect on the fitness of an organism) have no power in determining what happens to an organism in two distinctive ways. First, they have no power to determine an organism's purpose (way of making a living/experience) in whatever context it exists within. Second, neutral variations have no power to change the entire purpose/structure (ways in which to make a living) of the context itself. In any particular context there are many ways of making a living. One could view a multicellular organism as a society of many different cell types, where each cell ends up making a living in a certain way by being one cell type or another based upon its neighbors as well as its overall position in the organism, and its developmental history (or a history of salient variations that had power in determining the way in which the cells develop). Yet variations can also affect the entire context...which in turn could conceivably flip good and bad for any particular organism in an environment. For example, if a meteor hits the earth, large organisms will suddenly find it very hard to make a living.

One consequence of only being concerned about variations that have an effect on the way in which life exists is that there are no absolutes. This may be a disquieting thought at first, but this appears the most internally consistent view of any "belief" structure. Ideas only exist so long as they are useful in perpetuating any particular mode of existence. Obviously such a philosophy can not answer questions such as how does one define the purpose of a particular mode of existence independently from experience (which is what a lot of philosophy tries to do). But it does not restrict the modes of existence and ways in which to make a living into an artificially superimposed hierarchy based upon rules or beliefs that may or may not be actually true. In essence, the philosophy of pragmatism allows for a infinite multitude of possible variations which have an effect on the way in which humans and other organisms make a living. The definition of pragmatism is somewhat circular (since it assigns meaning to ideas that affect the way in which one makes a living, and the way in which one makes a living affects the ideas one assigns meaning to), but this circular nature can be found in many physical systems, such as natural selection's "survival of the fittest" (who else would survive?) Within the context of any particular system there is no way to define a true golden standard (generalization) about what is good or best without imposing an artificial human value system. Since we'll never know what is actually true or best, or if either of those two ideas have any meaning whatsoever, it seems senseless to impose artificial rigid belief systems, and more internally consistent to allow for a more pragmatic and plastic belief systems.

This is of great importance to every living organism right now, because the world (the environment and ourselves) change whether we like it or not, and unless we recognize that fact and embrace it we will be forever fighting demons we do not even understand.

And now, for the Finale

2006-12-06T14:40:00.000-08:00

Once the elucidation of the geometry of multiple convolved correlation structures has been obtained and assigned either a universality class or underlying reduced or coarse-grained models, flow through phase-space will be reduced to common attractors (e.g. multiple convolved correlation structures). These common attractors will define new convolutions, that will in turn create larger and more complicated multiple convolved correlation structures. Possibly through a self-adjoint (or Hermitian) process, constraints can be generated and placed on these structures, such that new metrics can be defined and characterized for arbitrary combinations of convolutions of these multiple convolved correlations structures.

This process, coupled with an environment, will be able to generate arbitrarily complex partitions of phase space such that maximally explanatory interpretations of environment can be generated.

Relation and Non-Relation

2006-11-11T09:01:00.000-08:00

From one point of view it seems that there are only two fundamental bases for coming up with models of reality:

1) Everything is connected
2) Everything is disconnected

Every particular model of reality takes these two bases and combines them in various ways that can range from very simple to incredibly complicated. For example: probabilistic and statistical models quantify basis two, by introducing the idea of uncertainty, which is very closely related to non-relation (e.g. how do the ways in which things are not connected or non-related matter). Deterministic models quantify basis one, because they indicate the way in which objects are related to one another (or are connected).

The problem is that in reality the number of ways in which things are (1) or (2) is an unmeasurable quantity, so any particular model will be an imperfect realization of what is actually going on. This leads me to wonder if there is not an additional "orthogonal" basis that is independent of relation or non-relation that also describes reality in a completely consistent sense. Something that is neither connectedness or disconnectedness. What if we define this third basis as all aspects of a system that are not quantifiable from within a subjectivity?

Could we treat this third component of model building as the unknown unknowns (meta-unknowns)? These unknown unknowns could be incorporated in a Bayesian framework as the joint uncertainty in the model and the uncertainty itself. Or in this case, the joint distribution of parameters and the residual of the model. This joint distribution would give us an idea about how much information (connectedness and disconnectedness) our model is missing as a whole, and could provide a natural metric for testing model level hypothesis, such as how good is our model doing.

This could also lead to a series of Meta-Bayesian questions about uncertainty in model modeling.

"Black then white are all i see in my infancy.
red and yellow then came to be, reaching out to me.
lets me see.
as below, so above and beyond, I imagine
drawn beyond the lines of reason.
Push the envelope. Watch it bend.

Over thinking, over analyzing separates the body from the mind.
Withering my intuition, missing opportunities and I must
Feed my will to feel my moment drawing way outside the lines.

Black then white are all i see in my infancy.
red and yellow then came to be, reaching out to me.
lets me see there is so much more and
beckons me to look thru to these infinite possibilities.
as below, so above and beyond, I imagine
drawn outside the lines of reason.
Push the envelope. Watch it bend.

over thinking, over analyzing separates the body from the mind.
Withering my intuition leaving opportunities behind.
Feed my will to feel this moment urging me to cross the line.
Reaching out to embrace the random.
Reaching out to embrace whatever may come.

I embrace my desire to
I embrace my desire to
feel the rhythm, to feel connected enough to step aside and weep like a widow
to feel inspired to fathom the power, to witness the beauty,
to bathe in the fountain,
to swing on the spiral
to swing on the spiral
to swing on the spiral of our divinity and still be a human.

With my feet upon the ground I move myeslf between the sounds and open wide to suck it in.
I feel it move across my skin.
I'm reaching up and reaching out. I'm reaching for the random or what ever will bewilder me.
what ever will bewilder me.
And following our will and wind we may just go where no one's been.
We'll ride the spiral to the end and may just go where no one's been.
Spiral out. Keep going.
Spiral out. Keep going.
Spiral out. Keep going.
Spiral out. Keep going.
Spiral out. Keep going."

-Lateralus, by Tool

Everything is connected. Except when it is not.

To Grok (...or a post scriptum on the previous post)

2006-11-01T07:56:00.000-08:00

Once a person internalizes a unifying theme (symbol, idea, connection, pattern, symmetry, invariance, isomorphism, etc...) underlying a set of objects, or an ensemble of objects, the self of that person molds itself into the unifying theme. But, that is an incomplete picture. For there is also randomness or variation that is always outside of any particular internalization's ability to also internalize. Even if there were a theme that could explain all observed variation in existence, as soon as a person internalized it, there would exist variation that could not be explained by the internalization, merely because there was an agent that was internalizing it. Or in other words, as soon as a self attaches itself to a model of reality, from its subjective point of view new variation comes into existence, even though from an external observer there would not exist any new variation. What is this new variation?

One word: choice

Meaningful Interpretations of Reality

2006-10-18T01:42:00.000-07:00

Language allows us to express "meaningful" interpretations of reality. Unfortunately reality, and more important what is "meaningful" about reality are not necessarily conducive to being expressed given the inherent structure of language. Language is an emergent phenomenon critically organized around a few principles. These principles include, but are not limited to:

1) A language must be dynamic (e.g. it can change over time given various factors such as isolation of a sub-population, mixing of cultures, discovery of new information, etc...)

2) A language must have context depedencies and generalizations (e.g. for a language to make any meaningful statements about anything it must have words that are heavily context dependent...such as "red," "door," "hammer, " "Eiffel tower," as well as words that are capable of connecting apparently disparate objects...such as "metaphor," "freedom," "purpose," "justice," etc...)

3) A language must be subjective in practice (e.g. all interpretations of a language are made by sentient beings, and by necessity these interpretations must be subjective...hence no single idea can mean the exact same thing between two people, because the internal context in which the idea is represented, or given meaning, will be different)

I propose that all emergent phenomenon (in the framework of understanding them from a subjective point of view) are merely meaningful interpretations of an ensemble of objects with a particular set of rules or interactions in a paricular context.

Math:
Rules/Interactions => Axioms
Emergent Behavior => Theorems, Lemmas, Corollaries...

Physics
Rules => Quantum Mechanics
Emergent Behavior => Classical Mechanics

Biology
Rules => Laws of Chemistry
Emergent Behavior => Life

etc...

The problem is that in many horrendously complex systems our ability to intuit the connection between the interactions or rules and the meaningful interpretations of the system decreases exponentially as the complexity grows. Yet it is in these systems in particular that we need to understand the emergent behaviors, given the underlying interactions, to the absolute utmost, because these systems are the most interesting around us. For example, how a cancer develops (or any disease for that matter), how proteins fold, how signals are transmitted between cells, etc...

Therefore I also propose the development of a language that is designed to deal with making meaningful interpretations of horrendously complicated systems. Or, better yet, a way of translating the "meaningful" constraints or correlations in the phase space of a particular model into a short and compact description that captures the very essence of the emergence.

By "meaningful" I mean that the constraints and correlations are distinguishable in some way from noise.

This language, or metalanguage, or meta-meta-(*uncountable metas*)-meta-language would conform itself to any particular rule/interaction set, then take on a life of it's own, and given a particular context (or initial conditions), it would flourish...finding new meaningful interpretations of itself, and expressing them in such a way as to be understood by us.

Metalanguage

2006-09-27T07:57:00.000-07:00

Most sufficiently complicated non-linear systems can be sufficiently described by a few handy rules of thumb. In the case of the way light interacts with groups of atoms we have color. For the change in the number of ways in which atoms can be organized given a change in the energy of any particular arrangement we have temperature. For organic chemistry there are a certain number of rules of thumb that allows an organic chemist to design and implement reactions in which they know how the chemicals will change given the pKa's, Gibbs free energy, proposed reaction mechanism, and other salient aspects of the reaction (these being a finite list).

What if the way in which our "rules of thumb" are generated could be generalized for any sufficiently complicated non-linear system. In other words, what if the constraints in the possible outcomes given any input could be formalized?

In more explicit terms, what if it was possible to generate a language which would create contraints given a particular input (or environment), which in turn would create unforseen constraints, which could then change the original constraints as well as the environment. In other words, a system which given a continual input of environmental variation produces both order (predictable or individually defined constraints) as well as unintended constraints (e.g. ensemble defined constraints, or the sum total of unexpected by-products from each individual constraint) which lead to greater environmental variation. This in turn leads to the creation of different predictable constraints which also creates more unintended constraints, which in turn continues to increase environmental variation. In nature the envirnoment is very rich and diverse (highly variable), which can be viewed as coming from the earth being an open system as well as the fact that life (the sum total of unexpected by-products of chemical reactions) arises from the laws of chemistry (predictable, individually defined constraints).

Such a language could be considered a metalanguage since it would be constantly bootstrapping its own meaning. Or in other words, if one thinks of the ensemble constraints as being a meaningful interpretation of the sum total of individual constraints between elements of the system, the system would be constantly producing meaningful and new interpretations of itself as it expanded outwards into greater and greater diversified forms. A language which writes itself.

Do You Realize?

2006-09-12T21:01:00.000-07:00

What is life?

This question is a horribly difficult question to answer in a universal way. A friend recently brought to my knowledge the word "holon." A "holon" is a system that fails to be adequately described by either a top-down or a bottom-up perspective (for example a liver, or a heart, or a cell, or a brain, or an ecosystem). Life appears to be composed of many interacting holons composed of holons embedded within holons. This makes it seem like an impenetrable mess that cannot be understood completely from any perspective. One can describe aspects of a system (such as the DNA sequence of an organism, or the number of individuals in a population, or the behavior of an organism in a particular environment), but to get the whole framework with every level, layer, and permutation of significant information is for all practical purposes impossible. This is because the sheer volume of information appears to be prohibitively enormous...and how much of that information is actually useful is and more importantly how confident are we that we know how to define usefulness is anybody's guess. It seems ridiculous to try to describe the behavior of a human being based upon the solution to the Hamiltonian that gives the wavefunction which describes a person.

A subset of what you would need to know (obviously a very incomplete list):
Given any DNA sequence,type of organism, probability distribution of suite of molecules in any and all cells be able to predict:
Protein Structure
RNA Structure
Active sites in catalytic entities (proteins, RNA, protein-RNA complexes, others...)
Kinetics of all catalytic entities (diffusion limited, Michaelis-Menten, other approximations...)
Protein interaction sites on any proteins or protein complexes
Allosteric sites on proteins and protein complexes
Protein networks formed
Metabolome (-all metabolites in a cell)
Post-Transcriptional modifications
(alternate splicing, introns, exons, etc...)
Post-Translational modifications
(Methylation,Amination,Acetylation,etc...)
Lipid catabolism and anabolism
Protein catabolism and anabolism
Carbohydrate catabolism and anabolism
*Other molecule* catabolism and anabolism
Formation of higher order structures (e.g. organelles) and how that affects all other activities in the cell.
Physical model of the cell
Energy transduction pathways
Signal transduction pathways
Information flow within a cell represented as:
Be able to define all steady-states of the system given ANY perturbation at ANY level of information
Gene networks
Protein networks
Time resolved evolution of all components of the cell and hence:
Cell cycle
Cell apoptosis
All salient reactions in a cell given its steady-state

With previous set of information extending upwards...
Be able to define all cell types as different steady-states of the same model
All interactions between all groups of cells
Developmental interactions between cells (time-resolved evolution of groups of cells)
Higher-order pattern formation (e.g. spiral waves in heart, zebra stripes, leopard spots)
Complete physical model of groups of cells scaling all the way up to entire organisms
How this higher order information (organ level/organism level) changes the particular steady-state of any cell (e.g. going from starvation mode to energy storage mode, or a rest state to an active state)
Homeostasis
Cell differentiation
Morphology of organisms

Extending upwards...
Given a population of organsims be able to predict:
Response to any form of selection at any level of information and how it changes all levels of information
Mutation accumulation
Changes in all moments of distribution of phenotypes
Evolution of higher order structure in information structures composing organisms (e.g. how evolutionary forces affect and produce gene regulation, signal transduction pathways, higher order steady-states for more complicated functions of information arising in organisms)
Complete ecologies and ecosystems given a known physical/chemical environment

And that will get you one millionth of the way there.

The idea of steady-states and perturbations from steady-states is very important, and if one could understand the appropriate geometry of the interactions between all elements of the system, one could know exactly the paths between steady-states given a particular parameterization, intial condition, and perturbation. The question becomes if there are any universal features of the geometry of interactions between elements in the system, and more specifically how do the higher order structures created by underlying variables (e.g. organs/groups of cells performing one function created by proteins, DNA, RNA, etc...) in turn affect their own synthesis and function and the synthesis and function of other groups of cells. This is where the geometry becomes very warped and self-referential. On a simple level, DNA -> mRNA -> proteins which then can go back to DNA and can change which genes are being transcribed. But say one's liver is trying to detoxify a thousand different chemicals in varying concentrations (not an unreasonable assumption)... The presence of any one chemical, or in this case an ensemble of chemicals can have a different effect on the states of the cells. Say in the case of a 1000 chemicals of varying concentrations the liver decides to allocate the most toxic chemicals the most energy (e.g. makes an effort to divert as much precious cellular energy as possible) to degrade that chemical, and the least toxi chemicals the least energy. Or, if concentration was a more important factor, the liver could decide to degrade the most abundant chemical (e.g. ethanol after a night of binge drinking) as opposed to a more toxic chemical in lower concentration (e.g. ammonia). Each of these scenarios could lead to radically different spatiotemporal distributions of underlying molecular species in any particular cell in the liver, and potentially the entire organism (e.g. if one gets alcohol poisoning)

Stars, or why god exists(/doesn't exist)

2006-09-05T21:03:00.000-07:00

Each progressive symbol builds on previous symbols. Each symbol builds on itself causing stars (symbols) to burst outwards in a cacophony of constellations. These constellations constantly coalesce into greater galaxies (meta-symbols). Not linearly, but broken; jagged. Hidden relationships revealed, with vast expanses of nothingness in

-

between. But what, nothingness? Hardly. No symbol can capture nothingness, just like no symbol can capture itself. HA! Fooled you, because you can capture yourself...or can you? But what are you doing right now?

Galaxies grow without bound into universes. The universe, is not singular (uni-). The multiverse falls plague to the same paradox. How can there be many everythings? Infinity plus one. But why must there be a symbol that encaptures everything, including itself?

An infinitely recursive worm ouroboros expanding outwards in every conceivable and inconcevable direction, swallowing its own tail. Hidden meta-ouroboroses cause god to trip and fall. (How heavy was that stone?) But, a god, the god, only god, un-god, is beyond the constellation, beyond the confines of the symbols. God gOd goD is hidden in the nothingness and the infinities that lie in the blind spot of the mind's eye.

But...what happens, when the galaxies themselves wake up. What happens when the universe wakes up? All symbols (stars) coalesce into a singular point, that reverberates across the cosmos, faster than the speed of light, infusing all existence with...essence

What happens when nothingness wakes up? What happens when the wall comes crumbling, exploding, disintegrated...until symbols fill existence with pure...........................

The Singularity

2006-08-23T16:47:00.000-07:00

The world and universe are flooded with patterns. Patterns are hidden all around us, from the lowest level of reality to the utmost outer reaches of space. Patterns are also right in front of our faces. Our minds are only equipped to handle certain types of problems and patterns...mainly problems and patterns where we can encode the pattern/problem and come up with an internal representation of it that seems to match with the observed phenomenon in the real world. In many cases there could exist and I believe does exist significant patterns that our minds are not equipped to handle, or perhaps we can sense the pattern, but we can not grasp the pattern's full meaning and implications. For example, we can function on a day to day basis without understanding how our own minds work on every level. We can also function without understanding all of the billions of patterns that exist in the biological world around us, as well as the billions and billions of patterns in the abiotic world/universe as well.

But this disparity between the existence of patterns and our ability to fully grasp their meaning may be shrinking. At the moment the disparity is still very large in some cases (e.g. what makes things alive as opposed to being just a random collection of molecules). It seems entirely possible that we may be reaching a huge watershed in the way we view systems that appear to be irreducibly complicated...at least to our minds. I am of the belief that even the most complicated system can be made elementary if approached from the correct perspective and with the appropriate contextual framework, as well as with the appropriate resources. This is because it appears that most complex dynamic systems end up with some sort of emergent phenomenon that is produced from the underlying set of interactions, and if one can understand the relations between the interactions and the emergent phenomenon, then one could quite possibly break the system down into an easily digestible framework without having to understand every causality or specific relationship. One of the huge disadvantages of the current state of our brains is that, while incredibly adaptable and amazing in their own right, they still are fundamentally very limited in the way in which they can both modify their own architecture as well as the physical limitations of the speed at which neurons fire, and the information density that can be retained per volume of gray matter. Plus, our minds never evolved to deal with decomposing complex dynamic systems that may have many hidden patterns between the underlying set of interactions and any emergent phenomenon. Our minds evolved for many reasons, and understanding complex relationships does appear to be one of the abilities we attained...but only certain types of relationships and abstractions. Other types (such as a system of 1000 coupled ODE's with high degrees of non-linearity) are not as tractable to our minds but could be very useful when describing a neuronal circuit itself, or the complicated signaling transduction pathway between a set of cells.

But I believe that we are reaching a point where we are developing the tools to begin to understand the subtle patterns and relationships that have been hidden from us so far. The incredibly exciting product of this increased understanding is that it will build on itself in a nonlinear fashion...or in other words it will have a snow-balling effect. As our ability to understand and model the subtle and complicated pattern that are all around us increases, the rate at which we understand these systems will also increase. I believe this will occur because of the universality of some of these patterns. For example, if we could fully understand how a gene network would behave for every possible perturbation to its structure, then we would probably be able to extend this knowledge to neuronal networks, signaling transduction pathways, and all other sorts of systems where connectivity between elements and interactions between elements is isomorphic to that of a gene network. Another reason why this understanding will increase exponentially is because new tools and techniques in different and related fields will feed off each other. A good example of this is systems biology, where data and models from many different levels of information of an organism are integrated to produce a more holistic picture of the organism. An example would be looking at how the variation in a phenotype of an organism for some complex trait (e.g. how long a disease lasts) was related to genetic variation in a population (from the genome), the gene expression data (transcriptome), what proteins had the highest concentrations in what cells (proteome), as well as what metabolic pathways were activated (metabolome), and variation in the immune response (e.g. what kinds of immune cells were activated, and what salient structural features about them were correlated with how long the disease lasted). All of these different levels of information use different techniques (e.g. genotyping, microarrays, 2D-SDS Page, protein assays, NMR perhaps...), but when synthesized into an entire model with appropriate considerations for the assumptions that are necessary, it produces a better and better picture of the organism as a whole. This can be said for any complex dynamical system, where the techniques for observing information about the system are improving for many different aspects of the system all the time, as well as our ability to model the increasing quantity of information, and place it in the appropriate context.

What does this all mean in the long run? Well it could mean some pretty amazing things. It could also mean some pretty horrible things. It all depends on how we as a society and world decide to use this knowledge. Here's what I imagine could possibly happen:

As the connectivity and types of interactions evolve over time between models of reality (e.g. the models between gene networks, social networks, neuronal networks, etc...) the way in which we as human beings understand not only reality but ourselves will go through amazing changes. Just like the changes it went through after the theory of evolution, the theory of gravity, the theory of special and general relativity, etc... Except this time these changes will be to an even larger degree, because we will be driving right towards that point that we have never been able to look directly at before...the idea or reason behind what makes life live and what lets us go around having thoughts recognizing that they are thoughts. As we get closer and closer to these points our ability to not only understand but change ourselves on a much more fundamental level will become possible. This is an exciting but scary time. There will be a period of time where we will be on the edge of a precipice, and the slightest gust of wind could send us into an abyss of darkness so bleak it chills me just thinking about it. Yet if we can survive that incredibly precarious period, the possibilities are so amazing I can't even begin to describe them. One image that comes to mind is that of all symbols and internal models that describe reality that are contained in every mind in the world coalescing into a singular symbol which describes not only reality but itself as well. Sort of like a super-consciousness.

These are possibilities and concerns that we need to keep in mind in the coming years as we make what only appears to be incremental progress towards these amazing and frightening events. Because they will happen faster than we could ever believe.

Dreaming of New ?Dreams?

2006-08-02T23:55:00.000-07:00

Every thought and emotion can be assigned/is a symbol. Symbols affect one another in often mysterious ways. Many symbols can not be expressed adequately with language, because every time one tries to capture the essence of the symbol, the meaning diffuses away, leaving an empty shell of a thought or idea. This happens to me with the most meaningful symbols. I find that communicating a symbol that describes the why of what I'm interested in and what I want to do on a very basic level is impossible. Instead I'm stuck with the bulky and often unwieldy apparatus of language, whose inherent impetus towards obfuscating meaning gets in the way of the ideas I would like to share with others.

Language hides meaning because it imposes constraints that are merely a subset of the possible constraints that are working in my brain. This is an important distinction to make. Whereas there are many many constraints in my brain, keeping it from either falling apart physically or mentally, the number of possible constraints in the mind is much greater than those provided for by the mere syntactical structure of language. There are only about 171,000 words that are in current use according to the Oxford English Dictionary. This is compared to the billions of neurons and trillions of connections that exist in the human brain. Hence the inherent complexity that is possible in the mind is much greater than what can be adequately conveyed with words...at least for now. It is true that one can string many words together to try to capture the essence of a single thought, but in many cases this fails to do justice to the thought or symbol, whose inherent structure in one's mind is so crystal clear. And there is also a much larger set of unknowns which is even more mysterious. The following diagram illustrates these relationships:
This diagram shows how the constraints on the set of possible thoughts are organized into categories. The unknown constraints rule overall, with reality, my mind, and language all being subsets of the largest possible set of constraints.

But of course nothing is ever this simple...sometimes language breaks out of the system and tries to define itself. A computer program is merely a language that is implemented with some sort of processing unit that records operations and instructions and takes input and gives output. Some could argue that language is then inherent in our own brains, because each neuron is talking in it's own language to other neurons (like little processors), and the total sum of their interactions produces a new higher level language (there are probably many levels involved here) that is conscious thought. But then language then is able to start talking about itself, since a conscious mind can come up with ideas like language...so where does language come from? Is language then all there is to reality? Or is there something more fundamental going on here? And what about the unknowns?

I have no idea what the answer to these questions are, or if they are even meaningful questions. I feel like maybe I have succumbed to the very weakness I spoke of earlier...that of not being able to adequately convey the meaning of an idea...yet when that idea is "not being able to convey the meaning of idea" things start to get very tangled and confused. And this is where language starts to get very confusing...whenever it starts referring to itself, language does some pretty bizarre things that our minds can not handle. We can of course "jump out of the system" for many of these silly paradoxes (e.g. "this statement is a lie") but in some cases we can't jump out of the system and we are stuck in some bizarre loop, going round and round and round and never knowing it, or knowing that we are even in the loop.

It's kind of like being stuck in a dream within a dream. Even if you do wake up there will always be some other dream you are stuck in...

Variations on a Theme

2006-07-05T23:50:00.000-07:00

In the Jorge Luis Borge's library of Babel there is a book describing me sitting at my computer typing the words that are printed on the screen. Except there are a huge number of variations on that book in the library, where I do everything from get up and eat a bagel halfway through typing, to flying through the roof and meeting with the mad hatter for tea in an Alice in Wonderland setting. The library is a very difficult idea to consider. The number of books in the library is on the order of ~ 10^1,826,000, which is an incomprehensiblely large number. But the library contains every book of length 410 with all 22 Hebrew characters along with the space, the period, and the comma. Most of the books in the library are complete gibberish:

...fsadianbiaspaosj fdsaighdsam vcixhzzzzziudwwwprorlek cjvhybhdusoaposodiekknfdnsavhyhbuids...

you get the idea.

But among the gibberish, hidden like diamonds in a chunk of coal, are books that are meaningful. Every book that was ever written or will ever be written is in the library. The biographies of every human alive are in the library, along with every human who could ever exist. But there are some things that are not in the library. The question of what is not in the library is a very subtle one, because one could argue that a story that takes longer than 410 pages to tell could not be in the library, but it could in multiple books. Yet because the books are all different one cannot store a string of characters that has the same periodicity as the number of characters in a book. This seems like a trivial constraint, but it is actually fairly mind-boggling, if one considers the opposite extreme where one has a one page library of Babel, or a one character library of Babel. Obviously, as one shrinks the size of each book, the total amount of possible information stored also shrinks. The reason for this is that the periodicities that are ruled out are smaller and smaller. E.g. for one character you'd only have 25 books, each with one character. You couldn't construct anything much more complicated by linking books together because the periodicty is just one character. A two character library of Babel would have 625 books, but the periodicity of two characters still greatly restricts the higher order structures (e.g. words, paragraphs one can represent). Once one gets up to a single page, the maximum periodicity of characters one can represent is much much higher, and you could encode a small subset of the library in it (~10^4500), which is still many many many orders of magnitude greater than the supposed number of particles in the universe (~10^80).

The library gives one the vaguest inkling of the enormity of design space, the adjacent possible, or whatever you want to call it. The weirdest aspect is that there are books in the library that refer to the library and themselves. On one level this is not weird at all, because if you consider all the possibilities there will be every conceivable combination of characters. Yet on another level it is totally bizarre that in an abstract space there would exist ideas that refer to the abstract space itself. It's like the monkeys on the typewriters, instead of writing the works of William Shakespeare, wrote about how they were monkeys writing on typewriters. Total mind trip.

Of course, the symbols are only meaningful in the appropriate context, and this is where the whole system comes full circle. The works of Herman Melville and the output from a random number generator have approximately the same meaning to an entity with no understanding of language, and on a deeper level, ideas, meaning, and all of that philosophical stuff.

Another even weirder thought, is that in the library of Babel there might exist an algorithm, which if given to a compiler and run would think/act exactly like me (or like anyone in particular). Say this algorithm was generated by some random process (though very unlikely, still possible)...would it be me? Am I encoded in the library of Babel? Or is there some part of me that is not encodable, at least in the given dimensions...

Let's take this idea and stretch it a little bit farther. What if not only my mind, but my entire perception of reality was also encoded in the library of Babel. If that is the case, how do I know I am not merely an algorithm that was generated in the bowels of some cosmic infinity (or something I do not know how/can not describe) where all things possible can occur...including the coupling of information generated randomly to some sort of randomly generated compiler. Would it be possible to generate a system from complete randomness that could view itself and consider itself internally-consistent?

How fast can those monkeys type...

Update

2006-06-21T23:28:00.000-07:00

The project to construct an automated pattern generator and recognizer is coming in fits and starts. I finally got my sweet Octave code to work (Octave is like MATLAB, but free), only to find out that I have serious memory leak problems. This sets me way back, and makes me think that I should go back to my original idea of developing C++ code, and just use Octave as an algorithmic development tool.

Some other major issues include:
Numerical integrators. I only have a very basic working knowledge of numerical integrators, and at the moment the 4th order Runge-Kutta solver I am using in Octave appears to give good enough answers (at least when the solutions don't go shooting off to infinity). The question now becomes if it is worth it to try and develop my own numerical solver (probably using Numerical Recipes in C as a major resource) as well as an automated equation generator in C++? The nice thing about Octave/MATLAB is that data is much easier to manipulate than in C++.

But the biggest problem is the following: how does one quantify and qualify patterns in an automated fashion? Generating random non-linear differential equations is all well and good, but the whole point of this exercise is to basically find emergent phenomenon and characterize them. Then use what is learned by discovering emergent phenomenon to predict the existence of other emergent phenomenon in higher level structures.

The following is a very short summary of what I currently know about non-linear differential equations:
-Whenever nullclines (a nullcline is a line where the value of one of the time derivative is always zero) cross, there is a fixed point.
-Fixed points come in various flavors, from stable to unstable, and spirals, nodes and saddles. There are also other fixed points that are harder to examine (degenerate nodes, stars, centers, and some others...)
-To get chaos you have to have at least three dimensions
-Linear stability analysis at certain types of nodes (saddle, spiral, and stable) can use the Jacobian to determine the stability of a node in a nonlinear system.
-There are different types of bifurcations that can occur (where a fixed point undergoes some sort of transformation). These include saddle-node bifurcations, Hopf bifurcations, pitchfork bifurcations, and others.

Say you want to generate arbitrary emergent phenomenon for N "agents." What kind of system of equations would you use? Say the agents are homogenous (they all have the same set of interactions, but distributed amongst themselves in different ways). How does one characterize said emergent phenomenon? I guess the simplest way would be to start out with very simple equations (e.g. equations with only one or two terms), and see what the behavior is. Then bump up the complexity by adding new terms. So, for example, each individual would be represented by a single variable (this variable could be extended to any number of variables later on...). This variable would dictate something (such as position, hunger, velocity, size, concentration, or any other metric one wished to develop an interaction (and hopefully emergence) framework for). Then, the variables between individuals would be coupled, such that the concentration value (for example) of one agent has an effect on the rate of change of the concentration value for another agent. Then one could add environmental factors as well into some or all of the equations. This could be a natural decay rate of concentration, or influx rate. Environmental variables in themselves that change over time (e.g. spatial food/energy concentration function) could be incorporated.

Some other points to cover on these ideas in the next post:
Importance of connectivity between agents (random, uniform, higher order structure (which probably means higher order information)
Importance of correlations between agents
Importance of nonlinearity between agents
Defining emergent behavior with:
1) Correlation Functions (e.g. given I know that agent 1 is doing action x, what can I say about what agent 2)
2) Spatio-Temporal Distributions (how random/non-random is the distribution of agents in space-time)
3a) Information (e.g. given a set of inputs, what does the set of outputs look like (how discriminating/robust is the system between certain inputs)
3b) Does the system destroy, create, or merely transform information?
3c) Can we find symbols in the information patterns created by the system?
Other random thoughts with respect to making this project easier and more importantly, fruitful...

Hello!? Is anyone there?

2006-06-18T21:49:00.000-07:00

The strange thing about emergent phenomenon is that it can often seem like magic to even the most scientifically inclined person. I think it is largely because our minds evolved to be able to recognize and characterize certain kinds of patterns. Enormously complicated interconnected nonlinear systems were not one of the things our minds are naturally built to deal with. We like to understand systems as a series of rules where every action has a cause and effect. The problem with emergent systems is that they are often composed of many heterogeneous parts that act in nonlinear ways. This means that dissecting the tangent of causality in such systems is practically impossible, because it gets lost in a sea of other interactions that are affecting the system in often unpredictable ways.

I read somewhere that the butterfly effect really is not as significant as it would seem. In essence a butterfly could flap its wings and cause a storm halfway across the world, assuming the weather patterns are chaotic or highly sensitive to initial conditions. Yet to trace the line of causality to that specific butterfly would be impossible. The problem is that there are so many other variables in the system (other butterflies to start with) that are doing things to change the system, just like the hypothetical storm-causing butterfly. These lines of causality become completely tangled within this system and we lose our ability to say that a single butterfly at a specific point in space-time caused a horrific storm. Instead, all we are left with is the knowledge that, yes it could have been the butterfly, but it could have more likely been any number of other factors.

Complications in causality factors into many other complex dynamical systems. That's one of the reasons why fighting cancer is so hard. Cancer does not have a simple on-off switch. It is a complicated set of malfunctions and conditions that can change a cell from its normal healthy cell-type (or personality, say) into an unhealthy, voracious cell-type (or a psychopathic maniac). It is hard to trace the causes to a single gene or environmental factor. We do know that there are things that can tend to cause cancer, and there are many genes that have been identified as increasing the chance of getting cancer, but there is still no comprehensive understanding of the full set of underlying mechanisms and how different contributing factors have different causes and effects that lead up to cancer.

Other systems where lines of causality become tangled range from ecosystems, to economics, to the weather, and to biology in general. I wonder if it would be possible to develop a general framework to deal with these kinds of systems. It may be necessary to throw out a lot of our preconceptions about how to look at these kinds of systems. Science, for example, is very good at breaking up a system into pieces, examining the pieces, and seeing how they fit back together. The problem with this reductionist method is that it can miss out on higher level phenomenon that is only present when the system is functioning as a whole. Another example of this is in complicated signaling transduction pathways or gene networks, scientists often can not analyze the system as a whole, so they look at pieces of the system, and then try to put it together and reproduce the dynamics of the whole system.

I wonder if it is possible to come up with an evolving classification system for emergent phenomenon that would be able to recognize certain types of phenomenon and be able to predict the set of interactions underlying the phenomenon. If it could find an appropriate set of interactions, model, or even a suite of possible models, then it could be possible to be able to know the complicated lines of causality, or at least what the probable lines of causality were. The reason why the classification scheme of emergent phenomenon would have to be evolving in itself is because if it couldn't evolve there is no way it could deal with novel and unpredicted dynamics.

There is at least one huge potential problem with this classification scheme idea (and there are probably more). I've mentioned in my previous post The Adjacent Possible that there are an essentially infinite number of possible interactions, and therefore it is impossible to predict all possible configurations between objects in phase space. Hence, trying to catalog all emergent phenomenon may seem like a silly and useless idea. Yet, I have a hunch that there are certain types of interactions that are more likely to occur between objects than others, and that though there may be a large number of possible interactions and also a large number of potential objects, the distribution of objects and interaction is not uniform. There may be a few incredibly wacky interactions and even wackier objects (a conscious entity is a pretty wacky object in my opinion), but the majority of objects and interactions of interest fall into a relatively small number of classification schemes (at least in comparison to infinity). My justification for this hunch is largely based on the feeling that if the distribution of objects and interactions in the universe was entirely uniform, it would be impossible for complicated systems to develop.

The reasoning goes as follows: Stuart Kauffman discusses a hypothetical situation where all the biochemicals in all of biology were combined into a single vat. In the first few instants there would be an untold number of interactions between these biochemical objects. This would be similar to the case where the distribution of interactions and objects was made uniform from its natural non-uniform shape. Yet after a few instants this bubbling froth of biology would eventually create molecules that would hijack the entire system, poisoning most other molecules, until it finally reached a state where there were only a relatively small set of interactions occurring. Hence, biology has generated ways to keep the distribution of objects and interactions between objects very non-uniform...because if it ever approached uniformity everything would fall apart.

This seems to suggest to me that most emergent systems will not have a uniform distribution of underlying objects and interactions. In fact, the distribution of interactions and objects must be skewed in such a way as to give the system some sort of useful higher level property. Any sort of non-uniformity in the distribution of objects and interactions on any and all levels of an emergent system seems to suggest that though the number of possible interactions and objects is essentially infinite there is a much smaller number of interactions and objects that are actually implemented in reality.

More on this later...

Nonlinear Differential Equations...

2006-06-17T00:09:00.000-07:00

I stumbled upon a very useful program today called Octave. It is a high-level numerical oriented programming language that is somewhat similar to MATLAB. After many hours of tweaking the settings, downloading files, and writing some functions that write other functions, I've stumbled upon some interesting preliminary findings. Basically, I wrote a program that generates systems of nonlinear ordinary differential equations randomly. Then I used the built-in numerical integrator to see what the behavior of these functions looks like. In this first graph, lines 1-3 are the time solutions of the variables x,y, and z with the initial conditions (0,0.3,0.1). I checked for longer times of integration and it appears that the system eventually converges on a fixed point. The initial behavior of the system is very interesting, because it acts very similarly to a damped oscillator. Yet another interesting aspect is we can see that the variables x and z are out of sync up until around 5000 time units, and then they suddenly come right into harmony. If this is not order for free I do not know what is!

The next image is the phase space of the x and y dimensions. This is a very interesting pattern, it looks sort of like a wing or a leaf. The magnitude of the time solution of the y variable is very small compared to that of the x and z variables, but it still has interesting behavior.

This image demonstrates the phase space of the solution along the x-z plane. It looks like there are two basins of attraction, and eventually the basin on the right determines the long term behavior of the system. The point at which the x and z variables come into sync is probably when the function reaches an "event horizon" where it is forced to enter the basin of attraction on the right.

Finally, this last image is the phase space in the y- z plane. This is a totally different pattern, that brings to mind a cell under going mitosis. The dynamics of this system of non-linear differential equations is obviously very complicated, but there do seem to be some underlying patterns that govern the entire system. Hopefully I will be able to develop a more systematic system for identifying these underlying patterns as well as finding that elusive beast of emergence.

Symbols and topology

2006-06-14T21:27:00.000-07:00

In Douglas Hofstadter's book, Gödel Escher Bach an Eternal Golden Braid he goes into great detail on how inanimate matter can become conscious without the coexistence of some higher metaphysical entity such as the soul. His argument boils down to a relatively simple, if highly non-intuitive concept. It goes as follows: given a set of objects (say, for example, ants, or birds, or slime mold cells, or neuron cells, you get the picture...) there exists a set of interactions between the objects that allows them to organize themselves spontaneously. This is similar to some of the arguments presented by Steven Strogatz in his popular novel Sync, and I sort of eluded to it earlier in the post Order for Free. Once these objects organize spontaneously symbols can be encoded in patterns within these objects. These symbols are usually higher order phenomenon that are represented in the way in which the objects orient themselves in space and time. Hofstadter writes a clever interlude about a bunch of ants, where each ant is mindlessly going about its business, but the collective of ants is able to perform complicated interactions at a different level than the individual ants. A symbol is a tough object to define because it is highly dependent upon the context in which it resides. Random noise could be described as a pattern of sorts, but random noise does not have a few essential features that makes it symbol-like. A symbol has to be robust, insomuch as that it can have a variable response to similar inputs or parameters in its environment, but the variable response can not exceed a critical threshold such that the behavior of the system can not be distinguished from random behavior. This is very likely a very subtle point which may take some serious further investigation.

What do symbols do? Well that is a very good question. In my last post (The Adjacent Possible) I talked about the extra flaps of skin on the squirrel from Kauffman's book. This is a symbol of sorts, because it is a pattern among the spatio-temporal distribution of squirrel cells. The devil is in the details of course, because there are any number of other "patterns" in the spatio-temporal distribution of squirrel cells, but the key question is what patterns are important and which ones exist but do not serve any purpose. This begins to border on philosphical (and therefore there could be less opportunity to dissect analytically) for a few reasons. First of all, the idea of purpose is a little strange here, because the flaps of skin do not know anything about their greater purpose. Very likely they are the result of some random mutation or series of random mutation in a growth plan of the skin along the sides of the squirrel. There is probably a complicated network or series of networks of cellular signaling that determines the orientation, density, and type of epidermal cells that span this extra flap of skin. It seems unlikely but not necessarily impossible that a single mutation could produce such a pattern, but the point is that because of some change in the overall system of the squirrel, a new robust phenomenon has arisen. This new pattern, or symbol as it were, leads to a whole new functionality, which opens up an entire new region in the phase space of possible "spatio-temporal orientations" for not only the skin cells in the flaps of the flying squirrel, but also for future generations of squirrels. Yet this new functionality could quite possibly never be discovered without the occurence of a totally different event (the hawk!). And this is where the layers of stochasticity become coupled to the symbol (pattern). Mutation initially creates this pattern by feeding variation into the bottom of the system. This variation percolates up through the layers of organization and through some very likely complicated series of causes and effects (that probably are impossible to predict ab initio) which produces the new pattern or symbol. Yet at the top layer, the hawk has to come swooping in so that the squirrel can jump out of the tree and fly. If the squirrel never deviates from its normal behavior than it will never discover the greater functionality, or new region of phase-space that has opened up, and future generations of squirrels will be less likely to benefit from this beneficial pattern.

Symbols are usually used in a more abstract way than flaps of skin on a small furry mammal. Yet, this circles back to the original idea. The squirrel example adds a lot of added complexity, what with selection, additional stochastic processes, the the phenomenon of skin flaps being at such a high level in organization that the transition between the very basic level (say the genes) and the phenotype (the flaps) is anything but transparent. Yet going back to Hofstadter's ants, or an even more general example, with some even more boring agents, it seems possible that there exists any number of interesting behavior or symbols given the right rule set between the ants. The question becomes, can such rule sets be found such that the behavior of the ants (or agents) is something both interesting and useful in some manner? And by interesting I mean that it is robust, it responds to various inputs or initial conditions in dynamic and sometimes unpredictable ways, and that there is also something novel about the behavior.

This is a very hard idea to explain, but here it is worded differently: how does one distinguish mutliple levels in the system of ants. Obviously there is the base level, where the ants (or agents or whatever) go about mindlessly, doing whatever they do, not really thinking on a higher level. Then above the ants, because of their interactions is a much more subtle phenomenon. In Hofstadter's example, the patterns that the ants produce enable it to hold a conversation with other fictious characters. The patterns are having the conversation though, not the ants. Its as if by magic because of the interactions between the ants an entirely new level of organization and "symbols" is created. Within this higher level of organization there are new rules, new capabilities, and new constraints. The new capabilities come from the opening up of phase space that the interactions produce. This means that the ants, who as a disconnected uncoordinated mob, would not be able to accomplish much of anything (such as gather resources, create a suitable living environment, protect themselves) with any great success, are able to accomplish both new and greater things. For example, a single ant could never build a complicated colony in which to live, work, and propogate. But a colony of ants can. Also, a single ant could not protect itself from certain predators, but a colony of ants just by virtue of it being composed of many ants has a natural buffer against predation, because a predator would have to wipe out the entire colony...and the analogies go on. Colonies of ants can cover more distance, forage more efficiently, etc...But there is also more constraints for this higher level of organization. The colony can only grow so big, based upon the available resources and the environment in general. The colony is more adaptable than a single ant...it can respond almost like a super organism, if say a predator destroyed part of the ant mound, the ants could work in concert to repair the broken area, but there are limits to this adaptability. Also, ants who live by the colony, die by the colony.

Anyway, the whole point of this long rambling, is that interactions between agents in a system can produce very interesting behavior...behavior that can be described as being a symbol even. Now, the natural extension of this that Hofstadter goes into in great detail, is that the mind is essentially many many levels of these kinds of symbols, chugging along doing their thing, whether programmed in from birth, or whether acquired through interactions with the environment. Here is the key idea: the patterns created by the interactions between the base units (or the symbols on the first level above the bottom) can also interact with one another to produce higher level patterns above them. In terms of programming language this is sort of like the jump from machine language to assembly language, and then from assembly language to a higher level language like C++.

There is something very important to notice about the mind though. This is the fact that these levels of symbols can talk to one another. It is not like they are completely seperated from each other, not affecting the behavior of each other running like they are completely independent of one another. No, it is in fact very important to recognize the recursive relationsip between the levels of the system. Hofstadter's most controversial and contentious point is the idea that consciousness is the highest level symbol the mind has. He argues this because when someone become conscious, they become more aware of themself. In terms of the symbol analogy, all the different symbols that make up you, from every purely physical experience you have had, to every emotional experience you have had, to every thought and internal model you have built to try and reconcile the world in your head to the world outside of you starts to realize something. What all these symbols start to realize is that they exist. Whereas most other things that we know of, from the simplest to the most complex organisms, go about doing things for whatever reason, we are one of the only entities that we know of that can look aback upon ourselves and say AHA! I am a thing that thinks about other things, that feels things, and that has symbols for other things. It is as if all the symbols that flow through your mind do a doubletake, and realize that they are there in the first place. Hofstadter describes this as the top level of the mind looking down at the layers beneath it. This is one of the most amazing occurences in the history of life on earth, because by gaining the power to look down upon the symbols that make up ourselves we essentially bootstrap ourselves into consciousness and all the wonders of being conscious entities...(e.g. complex emotions, from love to hate, a sense of humor, the appreciation of beauty, and perhaps even a soul).

Now what I want to know is why isn't there a way to be able to both create such systems that build layer after layer of symbols on top of each other, each new layer adding some sort of new phenomenon or ability to the system. I have a hunch that there are a variety of factors that are very important in generating such systems. One such factor is the topology both within and between levels. The topology, or connectivity between both the base units or agents, as well as the symbols in each level above the base level, is probably highly correlated with the corresponding functionality. Also, I am pretty sure that the cross-talk between levels is also very important in gaining certain higher level functionality that is beyond the scope of isolated levels of symbols working independently of one another. Finally, the biggest mystery is the types of interactions between elements that are necessary to construct such elaborate systems of symbols and patterns.

These ideas drive to the very core of what I believe are some of the most interesting questions out there at the moment. I truly hope to develop a general framework for creating such systems of multiple levels of symbols, and maybe even developing an entirely new language or something! to deal with such systems.

I sincerely hope to write that C++ program ASAP so I can start posting actual results including graphical representations of some interesting systems.

The Adjacent Possible

2006-06-13T22:31:00.000-07:00

One of the most interesting aspects of the creation of new patterns and "stories" is that there are always aspects of a system that are beyond the capability to know ab initio. Stuart Kauffman discusses this issue in great detail in his book Investigations. He claims that the phase space for biology can never be completely defined, because the order of possible interactions is so large that it is essentially infinite and that in a way, there are always aspects of a system that are beyond our knowledge until they actually occur.

This makes me wonder if there is a way to shortcut the "innovation" process. Say, for example, one has two widgets. These widgets would have a fantastical, magical behavior, if they were able to enter into a specific configuration with respect to one another (e.g. a rule set) at the right place in space and time. In Stuart's book, he references the flying squirrel, whose abnormality in skin proves to be incredibly useful in the right context, when a hawk attempts to swoop down and eat the poor little animal (e.g. some aspect that seems apparently random or even a hindrance, ends up being very useful). Now in this case, it seems that there is no way of knowing ahead of time the usefulness of extra skin flaps when presented with an unbelivable number of possible circumstances that any object can enter in the course of its existence.

But, on the other hand, what if there was a way to create some sort of function, or program that searches specifically for new and innovative tools. Say, for example, this function was recursive, insomuch as it would use new tools (or patterns) to improve itself and its searching ability. This function would grow and morph into something more complicated as time went on. It would need a substrate on which to grow, and a plethora of information and constraints to establish incentives for it to innovate. Patterns in a vaccuum are relatively useless, but patterns that serve a purpose are infinitely more interesting and meaningful.

And here is where the tough questions begin to arise. Can such a function define its own purpose? Or does said purpose have to be constructed artificially ahead of time? These are difficult questions that may take some serious investigation to answer. It seems possible that such a program could start out with a very simple purpose, which as a by product of its activities would change in some way, and in turn would cause the function to change as well. A simple purpose would be an optimization problem...to see if the function could find a solution to the problem. But as the function analyzed and searched for a solution, it would change the landscape of the problem space, causing it to have to develop further more complicated techniques to search for a solution. The question becomes, how does one couple the search for a solution to the solution itself, and how can one incoporate the necessary freedom to allow for unpredictable but interesting behavior.

There is much to think about and elaborate on in the coming weeks and months.

Quick thought...

2006-06-12T23:34:00.000-07:00

...a simple c++ program that given a system of ordinary differential equations does the following:
a) Finds all fixed points and steady-states
b) Classifies stability and type of steady-state
c) Gives a plot of the phase-space given different initial conditions with..
d) ...the possibility of a uncertainity (or a distribution) of initial conditions, and the corresponding effect on the trajectories through phase space

This information will then be used to further develop a theory as to the genesis of patterns based upon interactions between elements, as well as, perhaps, information storage, transformation, and encoding within dynamical systems.

Order for Free?

2006-06-12T18:41:00.000-07:00

Assuming any complicated system of interconnected parts can be broken down into both deterministic and stochastic interactions, is there a way to quantify and qualify all salient aspects of the system? Salient is a tricky word, because it implies some sort of functionality or significance, which are only meaningful in the context of a human defined ontology. It seems that there should a way to define such systems, and search for patterns in the genesis of other patterns.

For example, consider the following system of ODE's:

x' = x^2 - y^2
y' = x^2-x+xy

where x' and y' are dx/dt and dy/dt respectively. The Jacobian matrix of this system looks as follows:

A =[ (2x) (-2y)
(2x-1 +y) (x) ]

The fixed points in this system occur where the nullclines intersect, or in other words where

0 = x^2-y^2
0 = x^2-x+ xy

intersect. This occurs at the points (1/2,1/2) and (-1/2,-1/2) in the x,y plane. The Jacobian evaluated at these points is A(1/2,1/2) = [1,-1;1/2,1/2] and A(-1/2,-1/2) = [-1,1;-5/2,-1/2]. For (1/2,1/2) the trace is 3/2 and the determinant is 1. For (-1/2,-1/2) the trace is -3/2 and the determinant is 3. This suggests that the first fixed point is unstable and the second is stable, with the dynamics of the two points being spirals (since the discriminant is negative in both cases). Hence the long-term behavior of the system will eventually approach (-1/2,-1/2) as long as it does not start exactly at (1/2,1/2) with no noise.

This tends to suggest that such a system would destroy information over time. In other words, if the initial conditions contain important information (say, the position in two dimensional space of some particle whose time evolution of its x and y coordinates is dictated by the previous system of equations) that information is eventually transformed into (1/2,1/2) after a long enough period of time. The system might transition through some interesting intermediate locations in phase space, but it will eventually end up at the stable fixed point.

Could this be an example of order for free? It is hard to say. It all comes down to what order means. If in this case order means a reduction in information, then yes, this system definitely reduces the information encoded in the initial conditions into the fixed point. But it also transforms that information into a trajectory through space-time that asymptotically reaches the fixed point, and different initial conditions could have wildly different trajectories. It would be interesting to see if the distribution of trajectories given some uncertainty in initial conditions adds any more information to the system...e.g. nearby trajectories tend to be like one another, or, on the other hand, are radically different.

Plus, adding uncertainty to the equations themselves could present some interesting results. In that case the system would never reach a total equilbrium, but would probably oscillate around a stochastic equilibrium.

Hopefully in my next posts I will have some more interesting thoughts with respect to more complicated structures...here are some rough ideas:
-multiple fixed points (or steady-states)
-how to perturb a system to transfer between fixed points (or steady-states)
-in the case of polynomial ODE's, the importance of the order of the equations
-connectivity (for systems with greater number of nodes)
-systems where each element has multiple dimensions (e.g. interactions between particles in space, each particle has three dimensions which describe its position)
-the importance of stochasticity and types of stochasticity (PDE, Monte Carlo, etc...)
-how does information (and perhaps entropy) play a role...and most importantly...
-how can a computer recognize a novel and useful phenomenon and classify it as something new and significant?
-and then, how can that computer take that information and apply it to both information it already has available as well as new information presented to it?