network theory .. framework .. the blueprint of reality ..

network theory .. explaining .. it goes beyond ..explaining .. the framework .. upon which .. all systems possible .. existing (past and present worlds) .. or destined to exist (possible and plausible future worlds) .. the origins of all systems .. their evolution ..

a framework .. that acts as a blueprint .. systems' evolving nature .. self-similarity availed .. bestowed upon ..

a powerful tool ..


5.6
For all of the initial intuitive appeal network theory ran into two problems. First it was too complex for 1970s computer technology to manage. (Anyone who has tried to construct even a simple neural-net model of a social process has similar complaints about 1990s computer technology).

..the initial intuitive appeal .. being described as such .. of network theory

initial .. to begin with .. at an early stage .. still to be revealed in its ..all-surpassing overwhelming dimensions .. dimensions that .. cover, have the capacity to include ..the reality itself .. all realities the human individual grapples with .. hidden within an immense potential .. near infinite in its boundaries ..

..intuitive .. comes from within .. intrinsic .. inherent .. the source of all spontaneous .. ground-breaking notions, ideas, conceptualisations ..

..appeal .. its attractive power emanating from deep in the very being of the human individual .. expressing fundamental primordial elements .. vibrate .. hit chords that 'dance' to the same tunes .. in ---

.. network theory .. providing the explanations required .. the blueprint nature organised its fabric .. to be used as the tool to discover .. literally un-cover the nature of all things ..

5.7
Connectionism arose in the field of computer science as a way of deal with parallel processes. Connectionist systems not only have rich interconnections (as all networks do) but the capacity to carry on more than one operation or set of instructions at a time (ie. in parallel). In connectionist systems the various processes are not only carried out simultaneously but often without reference to one-another. Another feature of connectionist systems is the tendency to regard 'information' not simply as whether a particular bit is on or off, but also as the pattern of network activation. In this second sense information can be understood as the pathway along which a signal flows.

..connectionism .. parallel processes .. abiding to connections .. connectedness .. self-evident in nature .. describing conciousness itself .. nature's ..nature ..an ever-evolving loop .. endless loops that generate connections .. makes nature .. nature exists by virtue of the connections .. nature can never be thought as anything else .. but an immense network of connected elements .. connecting the multitude of parallel processes undergoing in its entirety ..

..parallel processes ..envisaged .. nature networked to its core .. processes ongoing .. never cease to be .. in mind of what is called .. Conway's automaton .. the essence of ..emergence .. out of nature' state space .. in its entirety .. defined .. trodden by any process .. that comes to be .. and out of them .. selected few .. connect to build networks .. to present the information .. network building information .. fractally rendered ..

..connectionist systems .. systems .. what nature consists of .. nature is comprised upon .. the conceptualisation of 'system' itself .. can never be thought as anything else but .. as connectionist system .. any other conceptualisation severely lacking in definition .. ignores vital properties .. conceptualised notion rendered useless .. system thus conceptualised .. a useless tool in probing nature .. 'brings fruits' .. with no-avail ..

.. connectionist systems .. bear .. bring along two important attributes ..

.. the attribute referred in - connectionist systems not only have rich interconnections but the capacity to carry on more than one operation or set of instructions at a time -,

.. reminiscent of ..quantum computation itself .. envisaged and sparked the search towards materialising ..quantum computers ..as such .. the parallel processes .. at its heart .. availed by quantum superposition .. the ultimate expression of the afore-mentioned attribute of connectionist systems .. nature at its very core .. its quantum realm .. abides to that property ..

..and the attribute referred in - connectionist systems regard 'information' not simply as whether a particular bit is on or off, but also as the pattern of network activation,

.. the pattern of network activation .. bits .. what digital computers rely upon .. the pattern of network activation .. a network made out of bits, of positions .. in ..on and off states .. the patterns of .. the on/off states of all the positions/bits .. the elements that make up the network .. regarded as being ..activated .. active .. in action .. not in stasis .. not static ..but dynamic .. the flow .. the sequence of presented states .. by all the bits ..otherwise known as being positions ..otherwise known as being elements .. the elements visited .. once the including network is activated .. and their states (on or off) .. being recorded .. are taken into consideration .. provide the content of the information .. taking part in the flow .. along the sequential series of presented states .. run along .. recording the signal .. the numerous combinations between the included elements .. different flows .. with the potential to give rise to different signals .. but only a few(?) are selected which provide .. sense(?) information .. represent information

according to .. 'a whole that is more than the sum of its parts' principle .. the information .. that suits ..its environment .. suits its neighbouring elements .. the tendency .. towards it .. what drives 'wholeness' .. 'wholeness' achieved ..out of .. 'whole being more than the sum of its parts' .. actions ..

these 'wholeness' .. enabling actions .. overwhelming .. information rendered .. through such manner .. reality building .. continuous reality .. continuity .. measurable .. appearing in the form of ..measurable variables .. determine the conditions .. prevailing .. the use of formulas depicting laws of nature ..

the signal flows .. the signal .. the 'process' materialising .. flowing .. coherent .. information discernible .. compact .. made possible by the architecture of the lattice .. architecture established .. architecture enabling the flux pattern ..



activated .. collectively





5.8
A connectionist model allows two kinds of patterns to be studied. The first is the pattern of the signals, communications or other influences which flow through the lattice. This shall be referred to as the flux pattern. The Lorenz Attractor (Figure 4) has, for example, been used symbolically in clinical psychological practices to describe what might be happening in the brain of a person with a bi-polar disorder such as manic-depression. The two attractor foci represent the two mood-poles and the trajectory around these two poles is chaotic in two ways: first because the precise symptomatology from one episode to another is similar yet different since no point on the trajectory is encountered twice; second: because even though the transition from one mood-state to another is predetermined by the initial conditions the prediction of when these transitions will take place cannot be made with any accuracy.

.. flux pattern .. flowing pattern ..

.. attractor foci .. trajectory around these two poles is chaotic .. no point on the trajectory is encountered twice .. and .. mood-state .. predetermined by initial conditions ... prediction of when these transitions will take place cannot be made with any accuracy

..and in this sense human nature is chaotic ..

chaotic .. outwards .. but .. equivalently .. chaotic .. inwards .. flux pattern .. becomes ..rigid .. as the ..architecture lattice ..

architecture lattice ..pre-existing nodes .. lasts longer .. than .. flux pattern ..

5.9
The second kind of pattern which can be studied is defined by the architecture of the lattice itself: the pattern of connections among the various elements of the lattice and through which the signals propagate. This is known as the architecture, the matrix, or the lattice. The lattice places, for practical purposes, limits on what flux patterns are possible. The architecture allows us to differentiate plausible futures from implausible futures and, perhaps, from impossible futures.[13]

..limits on what flux patterns are possible .. limits .. constraints .. which they may not be infinite .. in expanding ..outwards .. in its outward expansion .. but there is infinity ..inwards .. fractality's essence ..

Archimedes .. infinities in-between real numbers.. irrational numbers ..

more discreet .. discreet-isation .. discreet ..concepts .. to its ..lower limit .. to quantum ..elements .. realm ..

5.10
Using a connectionist model of a process (eg. Eiser, 1993) requires that we treat the phase-state as the current network location of the influence under study. The propagation pathway is not infinite but confined to orbits which follow the pre-existing pathways between various elements.[14]

..propagation pathway .. not infinite .. orbits follow ..pre-existing pathways ..

5.11
The simplest kind of model allows only one kind of influence with one direction of flow. Each neuron in the human brain is susceptible to between 100 and 200 neurotransmitters, has multiple outputs and inputs, can create new connections, lose old ones, change their resistance to certain pathways, and die. The complexity of the human brain is significant (Harth, 1991) and one should at least be prepared to believe that human society is at least of equal complexity.

5.12
It is therefore the flux pattern chaos theorists explicitly study and it is in these patterns chaos theorists will ultimately be compelled to define their own notions of structures.

5.13
In other words they do not study structures qua structures themselves but their study of structures is geared to understanding the implications of the 'structures' which in the connectionist paradigm be understood as the flux patterns called social interactions.

5.14
Initially it is useful to draw a distinction between the connectivity pattern of the lattice (the architecture) and the communications which may or may not flow through this lattice. The lattice constrains what flow patterns might exist but does not require that they do. This constraining influences not only what channels and nodes but also what dimensions may be followed.

5.15
Using a more sociological description of these terms: the lattice may be likened to the actors, actresses, props and stage where a play is to be given. The flux or flow pattern is to be compared to the actual performance itself. Traditional uses of the term 'social structure' have - by paying insufficient attention to the time dimensions - made it rather more difficult than necessary to tell the difference between props and people.

5.16
The criticism Homans made can be seen not just as the requirement that sociological laws be rooted in physiological laws but that our conceptual paradigms should allow us to understand or express one set of abstractions in terms of another.[15]

5.17
Connectionism however allows a different approach to theorising. Because connected networks can exhibit chaos the roles of individual elements cannot be discounted in advance. Because some networks can, under other conditions, exhibit highly predictable patterns, macro level analysis can be carried out and meaningful macro level generalities sought. Connectionist models lead us to consider the 'structure' of the architecture, the 'structure' of the flux, the temporal permanence of both. At this point we can join the debate over reductionism.

Ideas, fledglings of properties with the potential to expand into networks.

Wolfram, computable document format and what brought into my mind ..

.. what attracted 'me' .. on the cdf .. the computable document format .. Wolfram ..initiative .. and their ..network ..work .. and into what it developed .. this search ..of 'mine' ..

the search .. that goes into acquiring the 'right' expressions .. for the ..'my' ..ideas that keep popping up .. expressions that I need .. in order to give shape ..the oncoming ideas .. dress them up .. with words .. conceptualise the ideas .. into manageable, for my mind concepts .. the culmination of ..attractors' activity and action ..

the ideas .. spawning of .. grappled concepts properties .. seeds ..of properties .. new 'paths' of my brain's neural circuitry .. reverberated cell assemblies .. a new synapse .. the initialization of a neural network .. initialized ..neural network a result of ..bridging .. unabridged, already existing neural networks .. into a ..practically .. and virtually ..new network ..

the new word ..the missed link .. the newly-found expression .. developing into a bridge that connects .. enables the flow of information .. between the previously ..separated networks ..from the virtually near to even disparate regions of my brain's ..neural space

practically ..as already held ..knowledge .. is constantly re-arranged .. from .. slight to larger modifications .. a gradient-like increase .. to accommodate ..newly arrived knowledge ..

towards a full-fledged ..overall ..over-surpassing ..ever-including .. and inclusive ... super- .. or hyper- .. network


Syllabus
This basic course is organized into five segments.
Introduction:
Overview of neural network history and types of problems: function approximation, classification, data clustering, time series, and dynamic systems
Feedforward Neural Networks and Radial Basis Function
Learning, overlearning, and initialization of neural networks
Theory and Background of Neural Networks
Description of the inherited problems when functions are fitted to data, possibilities for handling these problems using neural networks, and practical aspects
Nonlinear Dynamic Black-Box Modeling
Modeling of time series and dynamic systems using linear and nonlinear models
Classification and Clustering with Neural Networks
Two classes, many classes, neural network classifiers and relations to other classifiers, the perceptron as classifier, nearest-neighbor classification, vector quantization, unsupervised methods, self-organizing maps, and the Hopfield network

Impossible futures

In Smith, R. D. (1998) 'Social Structures and Chaos Theory', ..

"5.9
The second kind of pattern which can be studied is defined by the architecture of the lattice itself: the pattern of connections among the various elements of the lattice and through which the signals propagate. This is known as the architecture, the matrix, or the lattice. The lattice places, for practical purposes, limits on what flux patterns are possible. The architecture allows us to differentiate plausible futures from implausible futures and, perhaps, from impossible futures."

The transition from level-to-level

In Smith, R. D. (1998) 'Social Structures and Chaos Theory', ..

the clue, or indication, or proof, or evidence ..

"5.7
Connectionism arose in the field of computer science as a way of deal with parallel processes. Connectionist systems not only have rich interconnections (as all networks do) but the capacity to carry on more than one operation or set of instructions at a time (ie. in parallel). In connectionist systems the various processes are not only carried out simultaneously but often without reference to one-another. Another feature of connectionist systems is the tendency to regard 'information' not simply as whether a particular bit is on or off, but also as the pattern of network activation. In this second sense information can be understood as the pathway along which a signal flows."

evident ..to the point of beiing ..self-evident .. self-evidence established as a notion of .. being a single pathway .. of paving the route for all thought processes to follow .. irrespective of ..vessel supporting them .. by any individual .. at any time or place

the process by which establishes itself as a single pathway .. a result of attractors being built .. over time .. in a manner according to what is referred to in ..

"5.9
The second kind of pattern which can be studied is defined by the architecture of the lattice itself: the pattern of connections among the various elements of the lattice and through which the signals propagate. This is known as the architecture, the matrix, or the lattice. The lattice places, for practical purposes, limits on what flux patterns are possible. The architecture allows us to differentiate plausible futures from implausible futures and, perhaps, from impossible futures."

"Another feature of connectionist systems is the tendency to regard 'information' not simply as whether a particular bit is on or off, but also as the pattern of network activation."

.. what is regarded as 'information' .. it is not just ..whether a particular bit ..is on or off .. but also .. the pattern of network activation ..

the pattern of network activation .. a network in itself .. with its very own ..particular nodes, entities .. its very own ..bits .. which presents itself ..as a pattern .. even taken as a bit .. by itself .. a bit that is ..on

a bit that is ..on .. its presence established.. being unequivocal .. its ..off .. position .. eliminated .. extricated into the realm of ..the impossible ..does not belong in the ..phase space .. of that process .. not just ..un-charted territory .. but never visited

-----------------------------------------
if ever .. can it be .. my thoughts ..organised .. self-organised .. without ..a plan .. out of no-where.. un-announced .. the ..'best-fit' approach .. it could be ..or .. the path .. has already being ..woven .. wound .. by attractors being brought into existence ..unobtrusively

-----------------------------------------

the transition from level-to-level .. equivalent to ..from system to system including ..and ..to systems included .. each system by itself is included .. it is the part of another system .. that lies above .. an upper level .. another step of a scale .. subordinate to(?) .. a super-system(?) .. a higher system(?) .. properties .. that emphasize attributes .. alien(?) to .. the overriding principle ..of a .. 'whole more than the sum of its parts' .. the unique combination ..of all-attributes .. offered .. presented .. available .. by all the parts .. systems as .. 'wholes more than the sum of their parts' .. combinations .. for which clues are given out .. collectively .. by the formulas that create .. Mandelbrot worlds .. all possible combinations

how the whole is organised .. out of its parts ..fractal ..whooole .. well that came without being expected .. but isn't obvious ..that such a whole .. can not be anything but ..fractally organised ..

is it the mind that it is concerned in the above ..assumption

or the mind's ability to emulate ..nature's way of ..processing ..which again it is not anything but .. the self-similarity attribute .. it is coming out .. directly out of the self-similar feature .. of the organised world ..

within one .. the arbiter ..and the creator ..

within one .. the arbiter ..and the creator .. a complete unit .. feedback personified .. self-sufficient ..

the myth that people need other people .. a fallacy .. people can do ..without other people ..

it is not a need .. it's something that is grown into us .. a courtesy ..

even .. somehow .. emerges out .. of the principle .. whatever stands still .. decays ..

that idea .. that keeps coming into my mind ..

that idea .. that keeps coming into my mind .. minds deal with matters .. as if matters being absolutes .. dealing with absolutes .. as the way to provide solutions to the problems they face ..

it brought into my mind .. the idea that .. yes..

it means nothing for the products and services .. the salary .. the compensation .. detached from the processes of life .. the money one needs to preserve self .. away from the products and services that one uses ..

creating a whole new world of its own .. that has nothing to do with the needs and wants of people .. growth unprecedented .. unbecoming .. excessive .. more than it needs to be ..

Systems built out of incompatible entities last longer.

Just came to me, of all the time I had in my hand, hours ago, just at the time I was ready to go and attend other daily matters, the idea or more likely the notion of incompatibility.

Systems instantiate selves, by virtue of incompatibility. Incompatible states the essence in every system's existence, of ever to be. Incompatible states retain their identity, what makes them unique, and out of, and despite of, their incompatibility, the ties that hold them together, are as strong, and stronger than what pushes them apart. What tries to separate them.

The essence of the existence of opposite forces in reality, like the positive and negative charge, the south and north poles in electromagnetic forces, and even to the core of the atom itself, the strong nuclear force that keeps protons and neutrons together, even down to the quarks within each proton and neutron, and why not down to the strings suggested in whatever way, their interaction is interpreted.

How come I have connected such a notion of incompatibility, with the existence of inertia itself. Inertial forces out of the necessity to hold the structures brought into existence, intact (..and not falling apart)? Counteracting the forces unleashed by each of the incompatible partners, as they are unwilling to co-operate with each other, each one of the participant states, fighting hard to rid self of, from the embrace of the other, assert their uniqueness, but if they meet with success, the structure built out of such (reluctant) co-operation, collapses, cease to be, and all the structures built upon it, collapse, cease to be. Reality evaporates into nothingness. All that is ever be, ceases to be.

And the forces developed, that keep structures intact, the very existence of the objects, as such, are immensely stronger as they descent to the deepest level of reality, to the atom, to the baryons of these world. And it weakens as it goes up the ladder of existence, systems pulled apart, collapsing with the mere push the weak human individual, can afford.

Joining together incompatible states, what brings a system to be, and the more incompatible being, the stronger the hold.

Past, present and future concurring? Nonlinear time

Mind-boggling ideas. Nonlinear time? Playing havoc with your mind. The musings I found in Chris Opperman's CD Baby website were far far interesting. That beats any bed time conversation by far

"Non-linear time is the theory that states that time doesn't REALLY occur in a linear fashion, but instead is more of a constant. However, we as human beings can only perceive time in chronological order. Some scientists theorize that the reality of time is that the past, present, and future have already occurred," said Linda."

I just liked this initial fervour and before I check this out further I want to put it into my mind and see what will bring out. Some scientists theorize that the reality of time is that past, ..... What reality is that? What realm past, present and future events are, or more precisely took place? And are taking place? Unfold? Since they are events they involve objects, objects that take up space. Time needs space. Space and time go together. Incompatibles? Anyway, leave that.

If the passage of time, the arrow of time can be imagined as vertical, now we have to think that the arrow of time is horizontal, extends horizontally? Bubbles? Bubbles of space? Time creates space and space creates time? The expansion of the universe looked at as the composite effect of time and space? Chaotic composition(?), spawning emergence as a result of time and space being incompatible (again), and by being incompatible means that they are not loosing their identity or integrity at any time but they continue to interact and by this continual interaction bring about the creation of ..., the world, universe, reality, the physical realm itself.

Time will create space? Create space where there is no space? A bubble of space? But space on its own accord can create time. Freshly-made space creates time? A bubble of time? Bubbles within bubbles? Co-existing? Concurring? Events within a bubble unfold in a linear fashion? Corresponded time and space, in each bubble a whole universe, and all the bubbles a multiverse? Space-driven universe and time-driven universe?

Past, present and future happening at the same time? Concurrently unfolding? How can this justify the nonlinear time notion? As a whole, as a multiverse time progresses as spikes, fragments of arrows? Broken into pieces? Constant? As regards, if looked as an aggregate quantity? Of the multiverse? That it could not surpass a defined pre-determined value? Which means that the values in each component universe fluctuate? Universes that exist in the future compensate against universes that exist in the past? Bringing up a multiverse overall aggregate value for time that remains constant? Be that zero? The present?

Or is it not time that is constant, but instead an aggregate value for time and space. Spacetime? A critical value(?), which if it is exceeded the bubble bursts?
The universe bursts? A way to eliminate universes that do not abide with the rule(?)? The rule being that overall, for the multiverse, time or spacetime is constant? To bring along the idea of the parallel universes in countless millions? Each time a decision is made and the world bifurcates? Chaotic bifurcations?

And to bring forth the anthropic principle and account for premonition as Linda mentions

"Well, that would explain why some people experience psychic phenomena or have premonitions, wouldn't it?" continued Linda. "The only way that someone could see into the future would be if the future has already happened."

any human individual or other living thing that acts as an observer or an agent, instantiates(?) a universe, becomes its centre, its very own parallel world, co-existing parallel worlds, mixtures of worlds as we come across each other? Or, our world and all others as objects within it. Explaining ego? How would that account for premonition? May be not. But premonition could only be imagined if we were somehow responsible for the splitting into parallel worlds. Which, by virtue of the decisions we make, we are. Decisions that have to do with

"It's your own life you make, based on your choices and the risks you take."

and

"Our future will always be based on our choices and the risks we take, since we can only perceive the future on a linear basis anyhow."

the choices and risks we take, and the critical value, coming out of time or spacetime being constant determines whether newly formed bubble, cum universe, cum parallel world would burst or not? Premonition being built out of our feel for time and space intrinsic in our consciousness by being the agents responsible for its creation?

Time? what is time?

Disparate notions striking my mind .. it feels like assembling pieces in a puzzle .. congruency foreseen .. applying it

time .. have been spun in its entirety .. universe effectively frozen .. the arrow of time .. its passage already set .. time, ticking clocks ... an illusion?

universe .. inflation .. the instantaneous jump .. in its evolution .. happened for its entirety ... the universe full to its brims ... time arbitrary .. chunks thrown here and there .. apparent, its passage, only for the objects within a chunk ..

pockets of time continuum

I read there "..after or simultaneously with any other event in the universe." .. it stopped in my tracks .. seen it as unfamiliar .. strange .. though .. something that is taken for granted .. and as such familiar .. solely .. on the basis of the notion of time .. held in our minds .. but is that so?

why .. we are so certain .. that such simultaneity exists .. it sounds as, that such claim is based .. on arbitrary grounds ..

time and space .. incompatible(!) .. I must have pondered on that notion .. and forgot ..

Quantum mechanics unpalatable?

"Some physicists still find quantum mechanics unpalatable, if not unbelievable, because of what it implies about the world beyond our senses."

.. the world beyond our senses .. if not unbelievable .. belief and senses hand-in-hand? .. quantum mechanics unpalatable?

"The theory’s mathematics is simple enough to be taught to undergraduates, but the physical implications of that mathematics give rise to deep philosophical questions that remain unresolved."

.. mathematics .. enduring factor .. spurs imagination .. new vistas unfold .. surpasses the boundaries human senses have drawn .. unpalatable .. the taste revealed .. discovered .. does not go down smoothly .. no mystery there .. it is expected as human individuals are foremost creatures of habits .. their lives must go on .. should feel cosy and secure within .. can not do anything else but avert from the physical implications brought forth .. need time to adjust .. to get familiar with what it is asked by them .. there will be the time that the newly-found perspectives would become deep-seated within the mind .. and define their lives along these lines .. and together embark on the journey to resolve the philosophical questions arising

Ontology. For a common language? Discerning between context-tied and context-free.

In John Holland's book of 'emergence, from chaos to order' there is something that fits my current streak of thoughts, and though haphazard I feel compelled in contemplating about it, in fear I would loose sight of the track it opens up.

In page 241-242, is mentioned

"In modifying the starting conditions, and in deciding which phenomena are critical or characteristic, insight and taste are indispensable. In the study of emergence, interdisciplinary comparisons are a critical aid in developing these two traits. As I 've emphasized in several places, interdisciplinary comparisons allow us to differentiate the incidental from the essential. When we look for the same phenomena in different contexts, we can separate features that always present from features that are tied to context. Moreover, what is hidden in one context may be obvious in another. Both aspects offer great help in the construction of models of emergence."

The incidental which is context-tied and do not confer any weight in elucidating the rules applied for every phenomenon under the emergence regime and the essential, which is context-free and bears relevance to universal laws emergence adheres to. The constant attempt to discern from all the information phenomena provide to the essential and steer away from the information that its presence appears trivial and it is not crucial in our understanding of the phenomenon itself. Emergence governs every phenomenon and its deeper understanding leads to worthwhile applications in explaining any phenomenon to ourselves.

Without this knowledge we feel lost, overwhelmed unable to function in an appropriate manner.



systems .. agents ... units ... variables and parameters ... environment ... self-organising ... emergent. The systems created by systems ... evolving .. self-organised. Agent based systems, become the agents of other systems, expanding in space. Agents of systems, are systems themselves.

Human individuals agents of societies. Human individuals systems themselves. Poly-systemic as comprised of many systems.

system-subsystem-instance separation

Experimental techniques in low-temperature physics By Guy Kendall White, Philip J. Meeson

"Most properties of materials are categorised in terms of the phonon system, the electron system and the spin system (i.e. the nuclear or electronic magnetic moments). Since spin and magnetic moment are closely related in quantum mechanics, we will use the terms interchangeably.
These different subsystems, although intimately mixed together in any one material, can be separated in the imagination and analysed as independent systems."

"Consider for example the separation of the phonon system from the electron system in a metal. This proceeds from the knowledge that the phonon system is 'heavy' arising from the motion of ions in the lattice whilst electrons are light. The mass difference (and differing statistics) influences the available energy levels in each system and ultimately limits the flow of momentum and energy between the two systems. This 'adiabatic' or Born-Oppenheimer approximation regards the two subsystems as separate but interacting via an electron-phonon interaction. In this particular case of a metal, for instance, phonons dominate the high-temperature heat capacity whilst electrons dominate the low-temperature heat capacity; however the electron-phonon interaction ensures that the electrons and phonons are in good thermal equilibrium at all temperatures for most practical purposes. This is because the coupling is in fact relatively strong, and at low or high temperature one or the other system has a relatively small heat capacity. In the intermediate regime thermal contact is still good, but subtle effects due to non-equilibrium may be discerned."

This paper describes a mechanism for defining ontologies that are portable over representation systems.


In that context, an ontology is a specification used for making ontological commitments.
"The formal definition of ontological commitment is given below. For pragmetic reasons, we choose to write an ontology as a set of definitions of formal vocabulary. Although this isn't the only way to specify a conceptualization, it has some nice properties for knowledge sharing among AI software (e.g., semantics independent of reader and context). Practically, an ontological commitment is an agreement to use a vocabulary (i.e., ask queries and make assertions) in a way that is consistent (but not complete) with respect to the theory specified by an ontology. We build agents that commit to ontologies. We design ontologies so we can share knowledge with and among these agents."

Space the final frontier. Is it?

The human mind to get to grips with the concept of space.

...inter-dimensional, dream-scape, inner-space

...from the 11 dimensions postulated in string theory, the notion of phase space introduced by chaos theory, the branes of quantum cosmology ..

..acquire a firm hold, add-on to the concepts arsenal to fire, kickstart, spark people's intuition

nooks and crannies ..

nooks and crannies ..

"All other colors will have wavelengths that are not exact multiples of the oil-slick thickness at that location, and they will not add up constructively. This familiar phenomenon is termed "interference" and is a signature property of waves."

the deluge of thoughts that came into mind while reading these two pages, p.24-25 out of the book of James Kakalios "The Amazing Story of Quantum Mechanics"

.. is inconceivable which at first glance it shouts out that it should not merit a further look, should be dismissed as incoherent blurting out of a play of connecting disparate and distant thoughts that barely have a common ground, lacking the obvious commonsensical approach.

Jumping back and forth, from so disparate and distant concepts. Each one on its own merit.

Wavelength, where waves meet up with ..distance? Length? Position? Matter? Objects? Attribute depth, height, width to our world ..distance is assumed by the speed the wave travels, firms up in our mind the sense of distance and by that the depth of our world from familiar, our immediate surroundings to the out-worldly distant, to the edge of the universe as is surmised by the cosmic microwave background radiation.

The universe itself is played out in the minds of people like a child's toy which despite its correctness or not, forces the mind to adjust its outlook to what it sees. And the mind sees, what the eyes see, the 'constructive' quality, out of the interference of waves, the essence. What underpins how the world appears to us.

Merely based on the fact, of the way enters into the minds of people, the perception apparent, forces the mind to make sense accordingly. Constructed out, of in-phase waves, that denotes existence, and when waves do not interfere constructively, that includes all other parts within their total spectrum of their phase, non-existent. A digital approach in the way we observe the universe. The 0 and 1, existence and non-existence, played out by waves. De Broglie waves.

Our notions of volume, dimensions, space 'constructed' out of the wave interference. Re-arrange the concepts associated with the previous outlook to accommodate the newly found notions. Notions of branes, our entire universe contained in paper-thin sheets, planes cross-interacting with one another.

.. an incomprehensible task, formidable

.. tries and tests the mind, goes beyond the wildest imagination

... seeing our surroundings under a new light

Frozen Universe. Time traversed in a similar manner as space is.

"This means that the future can never be predicted in all its details, and that the future of the Universe is not irredeemably fixed."

The thought just crossed my mind, at what advantage point can a human individual assert such notion. Whether the notion 'future' bears any relevance, assists in fathoming 'Universe' and Nature as such.

Why not, since its inception the Universe expanded, not only by its space-like components but, its time-like components also. The idea of a frozen universe brought forth as human individuals started contemplating on it. And time as such, only traversed in the same way as space is traversed from one end to the other.

Time a continuum not different than space. Future, present and past merely a human condition.

While these thoughts brought to bear in this haphazard post, a lapse of concentration, one way to call such act, led me in. As if my search to know, the closure required by the thoughts on this subject, drove me in a furtive look on something I pondered in the past, and got me hooked. Supplement, originary lack and invagination. Is it what it goes around here? Supplementation involved in the notion of time the human mind has in store?

Supplement, the ".. inessential extra added to something complete in itself." The notion of time, the 'inessential extra', its past, future, present attributes stripped out completely, leaving out time bare to stand on its ..own feet, then what is left? What time stand-out as different than space? Then why not being traversed in a similar manner as space is?

Dimensionality? The familiar of space, attributed in a similar manner for time? And the familiar time attributes of future, present and past be looked at from the viewpoint of the dimensionality attributes of space. And the space orthogonal perspective being carried on, on time. To make sense out of the notion of past, future and present as orthogonal to each other. And even further, whatever applies for the attributes of time to be carried over and be applied for the attributes of space. The arrow of time device revised? Attributed with the orthogonality apparent to space dimensions.

Space and time separate, and time not seen as another dimension added to space. The notion of spacetime ..un-manageable? Nonsensical?

An image of a frozen universe?



Taken from space.com post, depicting the entire history of the universe. The mind enters anywhere in that vast expanse, narrowed down to the few centimetres it occupies on the screen. Plays out all sorts of stories as it traverses time.

A playground for the mind to delve. Consciousness fulfilled.

Cosmic calculator. Irrational numbers, precision faulters, spawn chaos.

"It is impossible for nature herself to 'know' the state of the Universe to the required precision."

In John Gribbin's "Q is for Quantum, Particle Physics from A to Z", entry for 'Chaos'

Precision and predictability. Predicting the outcome a certain behaviour in a system would lead to, branding a behaviour as unpredictable or not. Leading to chaos or order, the eternal conundrum. Precise calculations required of the state in a system, the parametric descriptors of the state, the system is, that define the conditions prevailing in the system. Parameters as quantities to be measured, assigned to be completed by a number-crunching entity, a calculator, hand-held or not, which its operators employ to produce a value which would feed into their formulas describing functions defining future states of systems under observation.

Nature herself employs a similar, but attuned to its overwhelming size, cosmic calculator. Its role to achieve a similar feat, that the human individual counterparts attempt to elucidate observed systems states, discerning their lapse into chaos or not.

Cosmic calculator, emphasized entity to produce the numbers at a cosmic scale dealing with infinities that will be fed into the laws of nature to determine the fate of the universe in every time scale possible, envisaged, imagined.

A tool employed in understanding the workings of nature, the notion of position the meaning conferred and the devise of numbers to ascertain such meaning, the relationships existing between quantities expressed as parameters as if nature herself relies upon the notions human individuals invented to make meaningful nature to themselves.

Human individuals in their efforts to understand nature, their methods employed mirroring nature's own workings, out of the same blueprint according to the law of self-similarity. Nature herself is unable to confer the precision required, amenable to predictability, predictability the essence of evolution in a cosmic scale. Nature attempts to predict the outcome of the laws is endowed with, predictability determines the very structures favoured by the laws themselves. And nature runs into trouble as she is faced with a daunting task even for an entity as mighty as her. Precision evades her in the face of irrational numbers.

"To take just one simple example, known to the Ancient Greeks, the very concept of labelling the points on a straight line is an approximation to the truth. To label every point on a line (no matter how short the line is) you would need an infinite number of numbers. In the interval from 0 to 1, many of the points can be expressed in terms of the familiar fractions, such as 1/2 or 1/4 (or by less familiar fractions, such as 137/731). But some of the points can only be represented by 'irrational' numbers which cannot be expressed as the ratio of two integers in a fraction, and which require an infinite number of digits after the decimal point in order to be described fully."

An infinite number of digits, precision evaded, predictability un-achievable, unpredictable behaviour, chaos itself prevailing. In essence systems at that breakpoint separate into chaotic and non-chaotic behaviour. For what a position stabilises into a halt, a stop, a whole fraction, such a point provides an anchor for the state of the system to materialise. Its linear evolution becomes possible, a discernible pattern emerges. For any other position where its precision is impossible due to the appearance of irrational numbers in the presented 'solutions', confers unpredictability, system prevailing behaviour chaotic.

Fibonacci numbers, their implication in chaos, their involvement in the make-up of the irrational solutions might raise notions about their implied involvement.

Critical values of defining parameters in a system, the points where parameter relationships are defined by solutions running into the realm of irrational numbers. Precision affected, predictability compromised, chaotic behaviour ensues.

Chaotic behaviour ends, as the device of cosmic calculator, in running through the irrational number calculated provides a solution amenable to states involved, order emerges.