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## The information and its observer: external and internal information processes, information cooperation, and the origin of the observer intellect

**Vladimir S. Lerner, USA, lernervs@gmail.com**

We examine information nature of observing interactive processes during conversion of observed uncertainty to observer certainty, considering interaction as natural fundamental phenomenon creating Yes-No actions of information Bit and its information observer. The information observer emerges from interacting random field of Kolmogorov probabilities, which link Kolmogorov 0-1 law’s probabilities and Bayesian probabilities observing Markov diffusion process by its probabilistic 0-1 impulses. Each such No-0 action cuts maximum of minimal entropy of the impulse correlation, while following Yes-1 action transfers this maxim between the impulse performing the dual principle of converting the process entropy to information. Merging Yes-No actions generate microprocess within the bordered impulse, producing information Bit with free information when the microprocess probability approaches 1. The free information follows from the cutting correlation connecting the Markov process impulses. Each impulse’ free information attracts the interacting bits. The borderer impulse’ attracting interaction captures energy of the interactive action which memorizes the Bit. The multiple Bits, connected by the free information, move a macroprocess which self-joins its bits in triplet macrounits. Each memorized information binds the reversible microprocess within impulse with the irreversible information macroprocess along the multi-dimensional process. The observation automatically converts cutting entropy to information. Consecutively and automatically converts the cutting entropy to information conveying the process information causality, certain logic, and complexity. The macrounits logically self-organize information networks (IN) encoding the units in information geometrical structures enclosing triplet’s code, which selects objective or subjective information observer depending on the encoded units. The IN geometry self-forms the observer dynamical and geometrical hierarchical structures with a limited boundary. The IN time-space distributed structure self-renews and cooperates information, decreasing the IN complexity. The triplet units, built through attraction and resonance, have a limited stability, leading to a finite triplet structure which each IN ending triplet bit encloses. The observing process self-builds multiple IN with finite triplet number by the IN-ending bit free information. After each IN potentially loses stability, evolving in a chaos, it possesses ability of self-restoration by a cooperating triplet. Multiple IN binds their ending triplets, which encloses the subjective observer information cognition and intelligence. The observer’s cognition assembles the common units through the multiple attraction and resonances at forming the IN-triplet hierarchy, which accept only units that concentrates and recognizes each IN node. The ended triplet of observer hierarchical informational networks measures level of the observer intelligence. Maximal number of the accepted triplet levels in a multiple IN measures the observer maximum information intelligence comparative to other intelligent observers. The intelligent observer recognizes and encodes digital images in message transmission, being self-reflective enables understanding the message meaning. The variation problem for the integral measures of observing process’ entropy functional and the bits’ information path integral formalizes the minimax law, which describes all regularities of the processes. Solving the problem, mathematically defines the micro-macro processes, the IN, selective objective and subjective information observers, and invariant conditions of observer’s self-organization and self-replication. The observation process carries wave function, both probabilistic and certain as attribute of the variation problem, which self-organizes the hierarchical structures. These functional regularities create united information mechanism, whose integral logic self-operates this mechanism, transforming multiple interacting uncertainties to physical reality-matter, human information and cognition, self-originate the observer information intellect. The minimax information law creates invariant information and physical regularities.The applications and practical implementations confirm the formalism theoretical concepts and results.

*Keywords: impulse probabilistic observation; cutting correlation; minimax information law; wave function; micro-macro processes, integral information measure; causal logic; cooperative information dynamics; hierarchical network; objective and subjective observers; self-forming intellect; designing AI observer; applications; implementations.*

## Introduction

Revealing information nature of various interactive processes, including multiple physical interactions, human observations, Human-machine communications, biological, social, economic, other interactive systems, integrated in information observer, becomes important scientific task.

Physical approach to an observer, developed in Copenhagen interpretation of quantum mechanics [1-5], requires an act of observation, as a physical carrier of the observer knowledge. But this observer’ role not describes the formalism of quantum mechanics.

According to D. Bohm ontological interpretation of quantum physics [6-8]: physical processes are determined by information, which “is a difference of form that makes a difference of content, i.e., meaning”, while “meaning unfolds in intention, intention into actions”; and “intention arises from previous perception of meaning or significance of a certain total situation.” That observer entails mental processes.

J.C. Eccles’s quantum approach [9] “is to find a way for the “self” to control its brain”.

A. Wheeler’s physical theory [10-14] of information-theoretic origin of an observer, introduces doctrine "It from Bit". Wheeler hypothesized that the Bit participates in creating the origin of all physical processes. However, Wheeler’s theory remained unproven, and the theory does not include how the Bit self-creates itself.

Before existence of J.A. Wheeler’s theory, many physical scientists [1-14], including Einstein [15], Penrose [16], other, define the observer only physical origin.

S. Weinberg, focusing on probability on quantum mechanics [17], gets the trouble from this probability natural origin.

As it follows from physical quantum field [18], with vacuum quantum fluctuations, a natural probability of this fluctuation originates physical particles.

J.A. Weller has included the observer in wave function [14] according to standard paradigm: Quantum Mechanics is Natural. Nonetheless, "Quantum Bayesianism" [19], which combines quantum theory with probability theory, states: ‘the wave function does not exists in the world - rather it merely reflects an individual’s mental state.’ Since information initially originates in quantum process with conjugated probabilities, its study should focus not on physics of observing process’ interacting particles but on its information-theoretical essence.

A Kolmogorov [20] establishes probability theory as foundation of information theory and logics.

C.E. Shannon’s information [21] measures relative entropy, which applies to random states of information process.

Kullback–Leibler’s divergence [22] between the probabilities distributions measures relative information connections the states of the observed process.

E.T. Jaynes [23] applies Bayesian probabilities to propose a plausible reasoning mechanism [24] whose rules of deductive logic connect maximum Bayes information (entropy) to a human's mental activities, as a subjective observer.

These references, along with many others, studying information mechanisms in an intelligence, explain these through various physical phenomena, whose specifics are still mostly unknown.

Science knows that interactions have built structure of Universe as its fundamental phenomena.

There have been many studies these interactions specifics; however, no one approach has unified the study of all their common information origins, regularities, and differentiation.

The first approach unifying these studies is published in [26, 27], and extends results in [28-34] which we review.

The approach focuses on observations as interactions producing the observer itself.

This unified approach shows how an information observer emerges from the observing a random interactive process.

During the observation, the uncertainty of the random interactive process converts into certainty. This certainty is information. Any single certain inter-action is a “Yes-No” action known as a Bit, the elementary unit of information. Multiple observations generate the Bit dynamics, or informational dynamics.

The Bits organize themselves in triplets, which logically self-organize and assemble an informational network.

In the process of network assembling, the triplets merge and interact with each other. Each interaction gets memorized and becomes a node of the informational network. The nodes also logically organize themselves. A sequence of the logically organized nodes defines a code of the network. The code encloses all the information about the network.

This code integrates and carries all prior observations and *is* an immerged information observer.

The informational observer emerges from probabilistic observation without any preexisting physical law.

Even unknown particles, planets could be revealed from and *after* their probable or real interactions occur.

This identifies interactions as a primary indicator of a potential probabilistic object during an observation.

The introduced approach is based on the informational origin of the observer, and explains how an observer emerges from the random observations themselves.

The well-known Shannon approach defines entropy as probability measures of the uncertainty of the observation.

If the entropy is erased, uncertainty disappears, instead appearing as an equal certainty.

Uncovering certainty from uncertainty is a scientific path to determine facts of reality.

When the entropy is erased, the physical energy is exerted, which is converted enclosing the certainty.

This certainty is information, which in turn is a physical entity that contains physical energy equal to the energy spent to erase entropy. In this process, the elementary unit of information a Bit is created.

To summarize, a physical Bit is evolved from removing uncertainty from the observation. Or, a Bit evolves from the abstract probability of the observation and is an elementary observer itself.

Since information initially originates in quantum process with conjugated probabilities, its study should focus not on physics of observing process’ interacting particles but on its information-theoretical essence.

The approach substantiates every step of the origin through the unified formalism of mathematics and logic.

Such formalism allows understand and describe the regularity (law) of these informational processes.

Preexisting physical law is irrelevant to the emerging regularities in this approach.

The approach initial points are:

1. Interaction of the objects or particles is primary indicator of its the origin. The field of probability is source of information and physics. The interactions are abstract “Yes-No” actions of an impulse, probabilistic or real.

2. Multiple interactions create random process whose interactions model Markov diffusion process. The process observes the objective probabilities linking the Kolmogorov law’s axiomatic probabilities with Bayesian probabilities of the Markov process which correlates. Particular probability observes specific set of events which entropy of correlation holds.

3. Removing the entropy of this correlation or uncertainty produces certainty originating information which emerges from particular set of the observing probabilistic events that create specific information observer.

These points we describe below in more details.

The observing objective Yes‐No probabilities measure the idealized (virtual) impulses as a *virtual observer.*

Such an observer, processing random interactions, generates its virtual probability measurement of the random process uncertainty in an observable process of the virtual observer.

With growing probabilities of virtual impulses, the process’ correlations increase, and real impulses emerge.

The impulses, cutting (removing) entropy of the correlations, create real observing information, which moves and self-organizes the information process, creating information structure of the information observer.

The observing information and its observer generate the integration of multiple random specific interactions.

The integral measure of Kolmogorov-Bayes objective probabilities [31], transformed by the interactive observations, can evolve from an objective interaction to a subjective observer, uniting the observer information and its structure. It starts from a virtual probabilistic observation and virtual observer, connecting the interacting impulses, enable self -observation.

Merging Yes-No actions of the Markov probabilistic impulse generate microprocess within the bordered impulse. It produces information Bit with free information when the microprocess probability approaches 1. The free information follows from the cutting correlation connecting the Markov process impulses. Each impulse’ free information attracts the interacting bits. The borderer impulse’ attracting interaction captures energy of the interactive action which memorizes the Bit. The multiple Bits, connected by the free information, move a macroprocess.

The macroprocess bits continue attracting other creates a resonance. The resonance process links bits in duplets.

Free information from one bit out of the pair gets spent on the assembling the duplet. Free information from the duplet bits attracts a third forming bit, assembling and memorizing all three in a triplet-a basic macro unit.

The triplet third bit’s free information, attracting another duplet of bits, creates two bound triplets, which self-join and enclose another triplet, and so on. This continuing process creates the enclosed-nested levels of the bound triplets which self-organize an informational network with the levels of hierarchical structure. The last-ending triplet in the information network (IN) collects and encloses the entire network’s information.

Each bit’s memorized information binds the reversible microprocess within each impulse with the irreversible information macroprocess along the multi-dimensional process. The observation consecutively and automatically converts cutting entropy to information conveying the process information causality, certain logic, and complexity.

Each triplet unit generates three symbols from three segments of information dynamics and one impulse-code from the control, composing a minimal *logical code* that encodes this elementary physical information process.

The IN time-space logic encodes in double spiral space (DSS) triple code that rotates, encircling the conic structures, which the multiple triplet logic extends.

The macrounits logically self-organize information networks (IN) encoding the units in the information geometrical structures enclosing triplet’s code, which select objective or subjective information observer depending on encoding units.

The IN geometry self-forms the observer dynamical and geometrical hierarchical structures with a limited boundary.

The IN time-space distributed structure self-renews and cooperates information, decreasing the IN complexity through the attraction of their triplets. The IN ended triplet contains maximum amount of free information, which enables self-built other INs through the attraction, creating the multiple networks (domain).

The informational networks cannot connect to each other when free information of the third bit in a triplet is not sufficient to attract another bound duplet. This triplet becomes the ended triplet, and the network completes as a finite network.

The process of self-building network stops, the IN loses stability creating chaos of bits.

(In a DNA, the ended triplet’s code forms telomerase which controls the DNA life cycle).

However, in the chaos, there could be a pair of bits that bind creating a duplet, having enough of free information to attract another bit. Then the attracting bits create a triplet, and building the network may continue. Hence, the finite IN chaotic process could self-restore the bound triplets creating next generation of the informational networks.

Building the triplets, networks, and domains requires the observers’ cognition and intelligence. Every observer has different amount of the observed information needed for specific and individual cognition logic and intelligence code.

Each attracting bit, while forming a triplet, selects the bits with equal speed creating a resonance. The bits, cohering in the resonance, become common and recognize each other, which assemble and bind only theses bits.

Cognition is ability of recognizing and binding bits in a resonance process.

Each observer’ cognitive action equalizes the bit’s speeds, initiating the resonance where the bits become common, cohere, and recognize each other, and then bind by memorizing. These cognitive actions perform the bits free information.

If the free information is not sufficient for performing the cognitive actions, cognition does not emerge. It cannot build any duplets and triplets. The observer’s cognition assembles the common units through the multiple resonances at forming the IN-triplet hierarchy, which accepts only units that each IN node concentrates and recognizes.

At the enough observed information, cognition arises at all levels of the informational networks.

But each cognitive action requires different amount of information to perform the cognition.

(This process is analogous to human brain cognition through the neuron yes-no actions modeling a bit. Moreover, all described self-creation of the duplet-triplets, finite informational networks, multiple networks, as well as self-restoration, performs the human brain’ information machine in the process of probabilistic observation.)

The intelligence is an ability of the observer to build the informational networks and domains, which includes the cognitions. The ended triplet of observer hierarchical informational networks and domains measures level of the observer intelligence. (It brings the objective information measure of intelligence as a difference of currently used empirical IQ).

All observers have different level of intelligence which classified observer by these levels information measure.

Maximal number of the accepted triplet levels in a multiple IN measures the amount of the observer maximum information intelligence comparative to other intelligent observers.

That observer or observers builds maximum number of the hierarchical informational networks and domains with maximal cognition. These observers have an imbedded ability to control other observers.

The observation process carries wave functions, probabilistic and real—certain as attribute of the mimiax variation problem, whose solution brings the spinning space –time trajectory with increasing speed around its cross-section and decreasing rotation space speed along the trajectory which indicates its finite end.

The wave function frequencies self-organize the observer hierarchical structures during movement along this trajectory.

The approach results describe the emerging the observer’s information regularities and intelligence, satisfying a simple natural law during conversion uncertainty to certainty in the observer interactive probabilistic observation of environment.

Natural (real) interactions converts this entropy to information as the interactions’ phenomena.

The approach formalism comes from Feynman concepts [24A] that a variation principle for the process integral with the problem solution mathematically formulates the physical law regularities for this process.

The variation problem for the integral measures of observing process’ entropy functional and the bits’ information path integral [29-30] formalizes the minimax law, which describes all regularities of the observing processes.

Solving the problem [26,27,33,34], mathematically defines the micro-macro processes, the IN, selective objective and subjective information observers, and invariant conditions of observer’s self-organization and self-replication.

These functional regularities create united information mechanism, whose integral logic self-operates this mechanism, transforming the multiple interacting uncertainties to physical reality-matter, human information and cognition, self- originating the observer information intellect.

This logic holds invariance of information and physical regularities, following from the minimax information law.

The approach focuses on formal information mechanisms in an observer, without reference to the specific physical processes which could originate these mechanisms. The formally described information regularities contribute to basic theory of brain function and information mechanisms of Human-Machine interactions.

The information formalism describes a self -building information machine which creates Humans and Nature.

**Essence of the approach main stages. How the approach works.**

*Forewords .*

Interactions are natural fundamental phenomena of multiple events in common environment of Universe.

Interactions have built Nature.

Elementary natural interaction consists of action and reaction, which represents abstract symbols: Yes-No or[illustration not visible in this excerpt] actions of an impulse modeling a Bit.

In physical examples, a sequence of opposite interactive actions models rubber ball hitting ground, the reversible micro-fluctuations, produced within irreversible macroprocess in physical and biological processes.

Here the Yes-No physical actions are connected naturally.

How does the bit and their logical sequence originate?

The information structure of such logic is a basis of DNA, brain information mechanism, and forms many other physical micro and macro-processes.

We show that probabilistic interactions, instead of interacting particles, create information, physical processes, and an observer of this information.

Probability measures only multiple events. Therefore, the probability measures the interacting event-interactions.

The probability of interactive actions can predict both real interaction and the particles.

Interaction of the objects or particles is primary indicator of their origin, which measure probabilities.

The field of probability is source of information and physics.

The approach aim is the formal principles and methodology explaining the procedure of emerging interacting observer, self-creating information. The aim derives from unifying the different interactions independent of origin, and focusing on observation as the interactive observer.

The objective Yes‐No probabilities measure the idealized (virtual) impulses in observation in a *virtual observation.*

The observation correlates random interactive action. The observing interactive random process of multiple interactions evaluates probabilities, measured by equivalent entropy of the correlation.

Cutting correlation in the impulse observation removes entropy or uncertainty producing certainty (information).

Integrating the cutting correlations finally produce the information observer.

Natural (real) interactions innately convert this entropy to information and the information observer.

Information observers may reproduce a brain as its memorized copy- image.

1. Starting points

Multiple interactive actions are random events in a surrounding random field.

The interacting random events formally describe probabilities in Kolmogorov Theory of Probabilities [35]. The probability field defines mathematical triple: [illustration not visible in this excerpt], where [illustration not visible in this excerpt] is sets of all possible events [illustration not visible in this excerpt], [illustration not visible in this excerpt]is Borel’s [illustration not visible in this excerpt]-algebra subsets from sets [illustration not visible in this excerpt], and probability [illustration not visible in this excerpt] is a non-negative function of the sets, defined on [illustration not visible in this excerpt]at condition [illustration not visible in this excerpt].This triple formally connects the sets of possible events, the sets of actual events, and their probability function.

Each abstract axiomatic Kolmogorov probability predicts probability measurement on the experiment whose probability distributions, tested by relative frequencies of occurrences of events, satisfy condition of *symmetry* of the equal probable events. Some of them form a multiple infinite sequence of independent events satisfying Kolmogorov 0-1 law.

In the random field, sequence random events, collected in independent series, forms a random process, including Markov diffusion process [36] modeling multiple interactions.

The Markov diffusion process describes multi-dimensional probability distributions in the random field.

The events satisfying the Kolmogorov law with 0-1 probability affect a Markov diffusion process’ probabilities, distributed in this field, via its transitional probabilities, which randomly switch the drifts (speeds) of the Markov process.

The switching Markov speeds sequentially change the process current a priori-a posteriori Bayes probabilities, whose ratio determines probability density of random No-Yes impulses 0-1 or 1-0, as a part of the Markov process. That links the Kolmogorov’s 0-1 probabilities, the Markov process’ Bayes probabilities, and the Markov No-Yes impulses in common Markov diffusion process. Within this process, the Markov probabilities densities randomly observe the process, composing the observing process of a virtual observation. The Kolmogorov law probabilities do not observe, but initiate discrete probabilities actions on Bayes probabilities which do observe. Thus the observing Markov probability No-Yes impulses are different from former. The observing process holds random impulse of 0-1, or 1-0 actions having probability 0-1, or 1-0 accordingly. The multiple random actions describe some probability distributions on the observing sequence of specific set of events, which formally define the observing triple above in the probability field.

In natural fluctuations of elementary events, such a random probabilistic impulse (a virtual observation) represents an immanent randomness moving in a stochastic process with some time arrow-random in a surrounding random field.

So, how do the observing random probabilistic interactions become a logical sequence encoding the bits?

2. Observation. Virtual observer. Uncertainty, Information, Certainty

This objective 0-1 probabilities quantify idealized (virtual) impulses whose Yes-No actions represent an act of a virtual observation where each observation measures a probability of the possible events for a potential observer.

Multiple virtual observations transit these probabilities along an interactive random process, generated by a virtual probability measurement, which models an observable process of a potential (virtual) observer.

In the impulse’s virtual Yes-No reversible actions, each second (No) through recursion [37] affects the predecessor (Yes) connecting them in a weak correlation, if there was not any of that.

The arising correlation connection memorizes this action, indicating start of observation with following No-Yes impulse.

The correlation encloses a mean time interval [36] which begins a time of observation. The observing Bayes a priori-a posteriori probabilities determine arrow of the time course of an observation process with continuous correlations.

Uncertainty of observation measures conditional entropy of Bayesian a priori—a posteriori probabilities.

Maximal uncertainty measures non-correlating a priori-a posteriori probabilities, when their connection approaches zero.

Such theoretical uncertainty has infinite entropy measures, whose conditional entropy and time do not exist.

The finite uncertainty measure has a nonzero correlating finite a priori – a posteriori probability of the interactive events with a finite time interval and following finite conditional entropy.

Example of such finite uncertainty’ process is “white noise”.

That allows measuring the observable process’ uncertainty relative to uncertainty-entropy of the white noise.

The most common formal model of a natural random non-stationary process is Markov diffusion process which includes the interactive observable process.

If an elementary Dirac’ delta-impulse increases each Bayes a posteriori probability, it concurrently increases probability of such virtual impulse (up to real impulse with probability 1), and decreases the related uncertainty.

Information, as notion of certainty–opposed to uncertainty, measures a reduction of uncertainty to maximal posteriori probability 1, which, we assume, evaluates an observing probabilistic fact.

Actually, it’s shown [30,32], that each of the delta-impulse No-0 action cuts maximum of impulse minimal entropy, while following Yes-1 action transfers this maxmin between the impulses, decreasing the following entropy of the process.

Thus, the impulse interactive actions express the impulse minimax principle.

And the impulse observation imposes the minimax principle increasing each posteriori probability.

Simple example. When a rubber ball hits ground, energy of this interaction partially dissipates that increases entropy of the interaction, while the ball’s following reverse movement holds less entropy (as a part of the dissipated), leading to max-min entropy of the bouncing ball. Adding periodically small energy, compensating for the interactive dissipation, supports the continuing bouncing.

The observation under Kronicker’ [0-1] impulse-discrete analog of Dirac’ delta-function,-also formally imposes the minimax principle automatically.

The impulse minimax principle, imposed on the sequential Bayesian probabilities, grows each posteriori probability, correlations, and reduces the process’ entropy along the observing process. The correlation freezes entropy and Bayes probability hidden within correlation, which, connecting the hidden process correlations, conveys probabilistic causality along the process. The particular probability observes specific set of events which entropy of correlation holds.

The correlation connects the Bayesian a priori-a posteriori probabilities in a temporal memory that does not store virtual connection, but renews, where any other virtual events (actions) are observed.

If the observing process is self–supporting through automatic renewal virtual inter-actions, it calls a Virtual Observer, which acts until these actions resume.

Such virtual observer belongs to a self–observing process, whose Yes-action virtually starts next impulse No- action, and so on, sending the self-observing probing impulses. Both process and observer are temporal, ending with stopping the observation. Starting of virtual self-observation limits the identified threshold [33].

Each new virtually observing event–action temporary memorizes whole pre-history events from the starting observation, including the summarized (integrated) maxmin-minimax entropy of virtually cutting correlations. The memory of a last of the current correlation connection automatically holds the integrated entropy of the correlations.

The memory temporary holds the difference of the probabilities actions, as a virtual measure of a distance between the impulses’ No-Yes actions and a probabilistic accuracy of measuring correlation.

The measuring, beginning from the starting observation, identifies an interval from the start, which is also virtual, disappearing with each new connection that identifies a next interval memorized in that connection.

The random process’ impulses hold virtually observing random time intervals with the hidden entropy and the events.

Collecting and measuring the uncertainty along the random process integrate entropy functional (EF) [31].

The minimax of all process’ interacting impulses carries the minimax variation principle (VP) imposed on the EF, which brings invariant measure for the running time intervals.

The correlation indicates appearance of an invariant time interval of the impulse–observation.

The difference of the probabilities actions that temporary holds memory of the correlation identifies a virtual measure of an *adjacent distance* between the impulse No-Yes actions. That originates a space shift, quantified by the curved time.

The space displacement shifts the virtual observation from the source of random field to a self-observing space –time process, initiating the probabilistic emergence of *time-space coordinate system* and gradient of entropy-an entropy force depending on the entropy density and space coordinates.

The displaced self-observing process with the space-time priori-posteriori actions continues requesting virtual observation with time-space probing impulses, which intends to preserve both these probabilities and invariant impulses.

The observations under these impulses enclose reducing entropy of the space-time movement forming the volume. That initiates the observer’s space–time entropy’s and correlation connections, starting self-collecting virtual space-time observation in a *shape* of space-time correlation of the *virtual Observer volume.*

The space-time entropy’ force rotates the curved time-space coordinate system (within the volume) developing the rotating Coriolis force and a moment. Both are moving a space trajectory along the coordinate system, which depends on the gradient and velocity of running movement.

The gradient entropy along the rotating interval of the trajectory could engage each next impulse in rotating action, which increases the correlation, temporally memorizing the time-space observation.

The memory temporary holds a difference of the starting space-time correlation as accuracy of its closeness, which determines the time-space observer location with its shape. The evolving shape gradually confines the running rotating movement which *self-supports* formation of both the shape and Observer.

The virtual observer, being displaced from the initial virtual process, sends the discrete time-space impulses as virtual probes to test the preservation of Kolmogorov probability measure of the observer process with probes’ frequencies.

Such test checks the abstract probability via a symmetry condition indicating both the probability correctness and the observing time-space structural location of the Observer.

The increasing frequencies of the observer’s self-supporting probes check the growing probabilities and their symmetry.

The virtual observer self-develops its space-time virtual geometrical structure during virtual observation, which gains its real form with transforming the integrated entropy of the correlated events to equivalent specific information observer.

With no real physics affecting the virtual observation, the virtual probing impulses replicate the information impulses and start a probabilistic path from maximal entropy (uncertainty) implement -as a maximal real certainty.

2. The cutting entropy functions within Markov process, the related impulse, and the cutting EF satisfying the VP.

Microprocess within the impulse. Information Observer.

Since the Yes-No discrete actions, forming virtual or real controls, cut the EF within the Markov process, they should preserve its additive and multiplicative properties.

That requirement limits the admissible controls’ class by two real and two complex functions.

Applying these control functions identify the cutting invariant impulse.

The VP extreme, imposed on the process’ impulse cutting by the EF, proves that each three invariant virtual impulses of the process time intervals enable generating a single invariant information impulse. So, instead of these three emerges last.

Information delivered by the impulse step-up control, being transferred to the nearest impulse, keeps information connection between the impulses, providing persistence of the impulse sequence.

This condenses each two of the previous impulses intervals and entropies in the following information impulse interval.

It also proves that action, starting the information impulse, captures the Markov multiplicative entropy increments.

Such impulse includes three parts:

1-delivered by multiplicative action by capturing entropy of random process;

2-delivered by the impulse step-down cut of the process entropy;

3-information delivered by the impulse step-up control, and then transferred to nearest impulse; it keeps information connection between the impulses and provides persistence continuation of the impulse sequence during the process time.

Each of the three parts holds its invariant portion within the impulse measure.

Since each cutting impulse preserves it invariant information measure, each third of the sequential cutting impulses triples condensed information density. It implies that a final IPF impulse condenses all previous IPF impulses, while the final time interval is limited, depending on process time course. Because the final time interval evaluates the density of this impulse information or entropy, both are also limited, as well as total IPF.

Conclusively, the IPF finite maximal information density limits a finite minimal physical time interval in accessible time course. The finite three times intervals within the invariant impulse parts allow identifying the related discreet correlation functions and its cutting increments. The results [33] verify the estimated entropy contributions in all parts of the impulse and the following information increments. The increment measures the memorized correlation of the impulse *probability* events in the impulse *time interval’s invariant measure* **[illustration not visible in this excerpt]**,[34]. With growing probability and correlations, the intensity of entropy per the interval (as entropy density) increases on each following interval, indicating a shift between virtual actions, measured in the time interval’ unit **[illustration not visible in this excerpt]**. With growing the density of the opposite actions, they *merge* in a jumping impulse whose cutting action *curves* an emerging ½ time units of the starting impulse time interval, while a following rotating curved time-jump action initiates a *displacement* within the impulse opposite rotating Yes-No actions.

The rotating displacement’s space shift quantifies the curved time. When the displacement shift of two space units replaces the curved ½ time units, a transitional impulse within the same impulses **[illustration not visible in this excerpt]** rises.

The *transitional* time-space impulse preserves probability measure [illustration not visible in this excerpt] of the initial time impulse, holding the impulse probability for two space units (as a counterpart to the curved time, Fig.1) **.**

illustration not visible in this excerpt

**(** Author’s own work.)

**Fig.1. Illustration of origin the impulse space coordinate measure [illustration not visible in this excerpt]at curving time** [illustration not visible in this excerpt] **coordinate measure [illustration not visible in this excerpt] in transitional movement. On the right is an initial impulse with step-down (SP1) and step-up (SP2) actions before the jump at SP1 locality.**

From obvious relation [illustration not visible in this excerpt], their coordinate/time ratio [illustration not visible in this excerpt]leads to the ratio of measuring units:[illustration not visible in this excerpt]with elementary space curvature [illustration not visible in this excerpt]equals to inverse radius: [illustration not visible in this excerpt].

Thus, the transitional time-space has probability equal of related time interval impulse, and vice versa. That allows appearance of both transitional time–space interval simultaneously in random observation.

The merging impulse-jump on the impulse border, cutting the curving time, spots a “needle curve pleat” at transition from the cutting time to a finite space unit.

Thus, the growing Bayes a posteriori probability, along observations merges neighbor impulses, generating interactive jump on each on the impulse border.

The jump brings the extreme discrete displacement, which rotates the jump opposite actions in the anti-symmetric entropy increments, the starting *microprocess* within the bordering impulse [34].

The merging anti-symmetric entropy increments relate to the impulse’ actions superposition.

The jump initiates the inner transitional “mini” impulse within the microprocess.

The jump-wise displacement preserves the Yes-No probabilities of transitional impulse, and the emerging time-space movement conserves these probability’s measures in *discrete time-space form of the impulse* between the probabilities. The time interval the interactive jump-curving impulse estimates both the impulse curvature’ entropy measure and the time-space invariant measure equal to π [34].

At satisfaction of the symmetry condition, the impulses’ axiomatic probability begins transforming to the microprocess ‘quantum’ probability with pairs of conjugated entropies and their correlated movements.

The rotating conjugate movement starts *discrete time-space* micro-intervals forming the transitional impulse at rotating angle [illustration not visible in this excerpt]. That makes symmetrical mirror copies of the observation, holding within the transitional impulse. A maximal correlation adjoins the conjugated symmetric entropy fractions, uniting their entropies into a running pair *entanglement,* which confines an entropy volume of the pair superposition in the transitional impulse at angle of rotation [illustration not visible in this excerpt].

The entangled pair of anti-symmetric entropy fractions appears simultaneously with the starting space interval. The correlation, binging this couple with a maximal probability, is extremely tangible.

The pair of correlated conjugated entropies of the *virtual* impulse are not separable with no *real* action *between* them.

The entangled increments, captured in rotation with forming volumes, adjoin the entropy volumes in a stable entanglement, when the conjugated entropies reach equalization and anti-symmetric correlations cohere. Arising correlated entanglement of the opposite rotating conjugated entropy increments condenses the correlating entropies in the entropy *volumes* of the microprocess *.*

The stable entanglement *minimizes* a quantum uncertainty of the entangled virtual impulses and increases their Bayes probability. As maximal a priori probability approaches[illustration not visible in this excerpt], both the entropy volume and rotating moment grow. Still, between the maximal a priori probability of virtual process [illustration not visible in this excerpt] and a posteriori probability of real process [illustration not visible in this excerpt] is a small microprocess’ gap, associated with time-space probabilistic transitive movement, separating the entropy and appearance of its information.

The gap implies a distinction of statistical possibilities with the entropies of uncertain reality from the information-certainty of reality. The Bayes probabilities measure may overcome this transitive gap.

The gap holds a hidden real locality within the hidden correlation.

The rotating momentum, growing with increased volume, intensifies the time–space volume transition over the gap, acquiring physical property near the gap end at the rising probability.

When a last posterior probability, approaching [illustration not visible in this excerpt], overcomes a last prior virtual probability, the curving momentum may physically cut the transferred entropy volume.

Growing a posteriori probability of the virtual impulse successively brings a reality to its posteriori action, which injects energy, capturing through real interaction (like a bouncing ball) that cuts (erases) the entropy-uncertainty hidden in the correlations. When the conjugated pair of the correlated entropies is cut, this action transforms the adjoin entropy increments to real information which binds them in real Bit of the *entangled couple* where changing one acts to other.

The step-down (No) control’s cut *kills* a total entropy’ volume during *finite* time-space rotation and *memorizes* dynamically this cutting entropy as the *equivalent information with its asymmetric geometry.*

Ability of an observer to overcome its gap depends on the amount of entropy volume, enclosing the observed events collected during virtual probes. The probes entropy force and momentum spin the rotating momentum for transition over the gap, and the real control jump adds energy covering the transition. Cutting the curved volume places a real needle pleat with time–space interacting impulse.

The cutting action, killing the process entropy near[illustration not visible in this excerpt], produces an interactive impact between the impulse No and Yes actions, which *requires the impulse access of energy* to overcome the gap.

The impact emerges when virtual Yes-action, ending the preceding imaginary microprocess, follows real No-action which delivers equivalent information compensating for this impact, while the virtual cuts avoid it. Thus, the information impulse appears with energy within it.

Transition maximal probability of observation through the gap, up to killing the resulting entropy, runs a *physical* microprocess with both local and nonlocal entangled information units and real time-space, which preempt memorizing information.

When the posteriori probability is closed to reality, the impulse positive curvature of step-up action, interacting with an external impulse’ negative curvatures of step-down action, transits a real interactive energy, which the opposite asymmetrical curvatures actions cover.

During the curved interaction, the asymmetrical curvature of step-up action compensates the asymmetrical curvature of the step-down real impulse, and that real asymmetry is memorized through the erasure by the supplied external Landauer’s energy [38].

**A virtual impulse (Fig.2A) starts step-down action with probability 0 of its potential cutting part; the impulse middle part has a transitional impulse with transitive logical 0-1; the step-up action changes it to 1-0 holding by the end interacting part 0, which, after the inter-active step-down cut, transforms the impulse entropy to information bit.**

**In Fig. 2B, the impulse Fig. 2A, starting from instance 1 with probability 0, transits at instance 2 during interaction to the interacting impulse with negative curvature** [illustration not visible in this excerpt] **of this impulse step-down action, which is opposite to curvature** [illustration not visible in this excerpt] **of ending the step-up action (** [illustration not visible in this excerpt] ** is analogous to that at beginning the impulse Fig.2A).**

**The opposite curved interaction provides a time–space difference (a barrier) between 0 and 1 actions, necessary for creating the Bit.**

**The interactive impulse’ step-down ending state memorizes the Bit when the interactive process provides Landauer’s energy with maximal probability (certainty) 1.**

[illustration not visible in this excerpt] **[illustration not visible in this excerpt]**

**Fig. 2A Fig. 2B, (** Author’s own work.)

The step-up action of an external (natural) process’ curvature [illustration not visible in this excerpt] is equivalent of potential entropy [illustration not visible in this excerpt] which carries entropy [illustration not visible in this excerpt] of the impulse total entropy 1 Nat.

The interacting step-down part of internal process impulse’ invariant entropy 1 Nat has potential entropy [illustration not visible in this excerpt].

Here the interacting curvature, enclosing entropy density, lowers the initial energy and the related temperatures in the above ratio. From that follow *conditions creating a bit in interacting curved impulse* [34].

1. The opposite curving impulses in the interactive transition require keeping entropy ratio 1/ln2.

2. The interacting process should possess the Landauer energy by the moment ending the interaction.

3. The interacting impulse hold invariant measure M=[1] of entropy 1 Nat whose the topological metric preserves the impulse curvatures.

The last follows from the impulse’ max-min mini-max law under its step-down and step-up actions, which generate the invariant [1]-Nat time-space measure with topological metric π (1/2circle) preserving opposite curvatures.

Theoretically, a pure probability predictability in “idealized measurement” challenges Kolmogorov's probability measure at *quantum mechanics* ’ entanglement when both additive and symmetry probability for mutual exchangeable events vanish.

The observing Markov probabilities’ additive and multiplicative properties are changing within the microprocess. Specifically, the merging jump violates regular properties of Markov process leading to a sub-Markovian process [39].

From the starting jump-up to the following jump-down, launching space interval of transitional impulse, the microprocess holds additive properties for both probability and related conjugated entropy.

The transitional impulse, confining the entanglement, ends with jump-down, initiating only the multiplicative property for the entangled entropy and the probability.

The microprocess within the transitional impulse is reversible.

The microprocess within whole impulse is reversible until the impulse ending action cuts its entropy.

It concurs with property of quantum wave function before and after interactive measurement.

For each random impulse, proceeding between a temporary fixed the correlated random No-Yes actions, such microprocess is multiple whose manifold decreases with growing the probability measure. At a maximal probability, only a pair of additive entropy flows with symmetric probabilities, which contains symmetrical-exchangeable states advance in the superposition.

The multiple impulses initiate a manifold of virtual Observers with random space-time shape in a collective probabilistic movement.

With maximal observing probabilities, the manifold of the virtual observers also decreases.

The microprocess is different from that in quantum mechanics (QM), since it rises as a virtual inside probing impulse of growing probability under jumping action, and then evolves to the real under final physical No-actions. Its superposing rotating anti-symmetric entropy flows have additive time–space *complex amplitudes* correlated in time-space entanglement, which do not carry and bind energy, just connects the entropy in joint correlation, whose cuts models elementary interaction with no physics.

The QM probabilistic particles carry the analogous conjugated probability amplitudes correlated in time-space entanglement.

Virtual microprocess does not dissipate but its integral entropy decreases along No-Yes reversible probes in the observation.

The real microprocess builds each information unit-Bit within the cutting impulse in real time, becoming irreversible after the cut (erasure). These operations, creating Bit from the impulse, reveal structure of Weller Bit, which memorizes the Yes-No logic of virtual actions, while the Bit free information participates in getting the multiple Bits information.

Such Bit-Participator is primary information observer formed *without a priori physical law.*

Whereas *the observing probable triple in the field specifies each information observer.*

The information observer starts with real impulse cutting off the observing process and extracting hidden information Bit. That identifies the information observer as an extractor and holder this information emerging in observation. Killing physical action converts entropy of virtual Observer to equivalent information of real Information Observer.

Killing the distinct volumes densities converts them in the Bits distinguished by information density and curvature.

The curving impulse of each Bit accumulates the impulse complimentary–opposite actions carrying *free information*, which initiates the Bits’ attraction.

During the curved interaction, a primary virtual asymmetry, measured by equivalent entropy, compensates the asymmetrical curvature of a real external impulse. The real asymmetry is memorized as information through the entropy erasure by the supplied external Landauer’s energy.

The entropy’ cutting interaction, curving asymmetry and producing information, performs function of Maxwell demon, which emerges with the curving asymmetry.

Between different Bits rises information gradient of attraction minimizing the free information which finally binds Bits.

That connects the Observer’s collected information Bit in units of an information process, which finally *builds Observer information structure.*

The maxmin-minimax principle, rising in the impulse observation, leads to the following attributes of emerging information Bit:

-it information is delivered by capturing and cutting entropy of virtual observing correlated impulses;

-its free information is transferring to the nearest impulse that keeps persistence continuation of the impulse sequence via the attracting Bits;

-the persistent Bits sequentially and automatically convert entropy to information, holding the cutoff information of random process correlation, which connects the Bits sequences;

-the cutoff Bit holds time–space geometry following from the geometrical form of discrete entropy impulse;

-the information, memorized in the Bit, cuts the symmetry of virtual process;

-the free information *,* rising between the Bits cutting from random process, is spending on binding the attracted Bits;

-each three Bits’ free information allows binding the triple bits in a new bit, which is different from the primary Bit cutoff from random process;

-both primary and attracting Bits’ persistence continuation integrate the time-space real information process, which is composing the elementary information units in space-time information structure of Information Observer.

While the Bit preserves origin of its information, the growing information, condensed in the integrated Bit’s finite impulse size (limited by the speed of light), increases the Bit information density. The increasing density conserves growing energy being equivalent of interacting physical particles-objects.

The information microprocess’ formalism allows contribute in explanation of some known paradox and problems [34].

The optimal estimation of a lower limit on the increment of probability events evaluates the probabilities and limitations on process of observations [33]. Evaluation the information constraints, limitation on the microprocess, and conditions of the observer start predicts the probability path from virtual probes to the probability approaching a real cutoff.

On the path of observing uncertainty to certainty, emerge causality, information, and complexity, which the information Bit’s geometry encloses in the impulse time, curvature, and space coordinates.

An edge of reality, within the entropy-information gap, evaluates Plank’s fine structural constant in a sub-plank region of uncertainty [34]. A minimal displacement within this region estimates number of probing impulses to reach that region, which concurs with virtual probes approaching the real cutoff **.**

4.Information macroprocess.

The rotating movement (Fig.3) of the information Bits binds them in information macroprocess, which describes the extremals of the EF variation problem (VP) that was solved.

The macroprocess free information integrates the multiple Bits in information path functional (IPF) which encloses the Bits time-space geometry in the process’ information structure.

Estimation of extremal process shows that information, collected from the diffusion process by the IPF, approaches the EF entropy functional. The IPF formalizes the EF extreme integral for the cutting interactive impulse, whose information approaches EF at the bit number [illustration not visible in this excerpt], [32].

The IPF integrates flows of Bits units with finite distances and sizes.

The IPF maximum, integrating unlimited number of Bits, limits the total information that carries the process’ Bits and intensifies the Bit information density, running it to infinite process dimension.

At infinitive dimension of the macroprocess, it describes both the EF and IPF extremals.

The limited number of the process units, which free information assembles, leads to limited free information transforming the impulse microprocess to the macroprocess with a restricted dimension.

The randomly applied deterministic (real) impulses, cutting all process correlations, transforms the initial random process to a limited sequence of independent states.

. [illustration not visible in this excerpt] **(** Author’s own work.)

**Fig.3. Forming a space -time spiral trajectory with current radius [illustration not visible in this excerpt] on conic surface at points D, D1, D2, D3, D4 of spatial discrete interval DD1=[illustration not visible in this excerpt], which corresponds to angle [illustration not visible in this excerpt], [illustration not visible in this excerpt]of radius vector’s [illustration not visible in this excerpt] projection of on the cone’s base (O1, O2, O3, O4) with the vertex angle [illustration not visible in this excerpt].**

The ratio of primary a priori- a posteriori probabilities beginning the probabilistic observation identifies the initial conditions for the EF and its extremals. The initial conditions determine the entropy function starting virtual observations at a moment which depends on minimal entropy (uncertainty) arising in the observations.

This entropy allows finding unknown posteriori entropy starting virtual Observer.

The initial conditions bring complex (real and imaginary) entropies for starting conjugated processes in a virtual observer’ microprocess. This process’ minimal interactive entropy becomes threshold for starting information microprocess, beginning the real observation and information Observer.

Starting the extreme Hamiltonian processes evaluate two pairs of real states for the conjugated rotating dynamic process [27-31]. That allows finding the equations unifying description of virtual and real observation, microprocess, and the dynamic macroprocess.

Applying the macrodynamic equations [30, 34] to traditional form of dynamic model with unknown control function solves the initial VP which determines the optimal control for the traditional model. These controls, formed by feedback function of the macrostates, bring step-up and step-down actions which sequentially start and terminate the VP constraint, imposed on the model. That allows extracting the cutoff hidden information from the localities joining the extremal segments of the observing trajectory. The extracted information feeds the observer macrodynamics with the recent information from the current observations.

This feedback’ process concurrently renovates the observing Markov correlations connecting the macrostates and the controls The correlations identify the Markov drift function transferred to the equations of the information macrodynamics [29,34].

Within each extremal segment, the information dynamics is reversible; the irreversibility rises at termination of each VP constraint between the segments.

The feedback identifies cutting correlations and automatically transforms the EF to IPF. That reveals the integrated information hidden in the observing process randomness.

While the sum of cutting correlation functions identifies the IPF integrant.

The EF-IPF Lagrangian integrates both the impulses and constraint information on its time-space intervals.

The identified VP constraint leads to invariant relations for each impulse information, interval, and the intervals between information impulses holding three invariant entropies of virtual impulses, as well as invariant conjugate vector on the extremal. These invariants estimate each segment information on the macrotrajectory, the locality between segments, predicting where the potential feeding information should transfer the feedback or measuring.

The invariants allow encoding the *observing process* using Shannon’s formula for an average optimal code-word length of the code alphabet letters.

The information analog of Plank constant evaluates maximal information speed of the observing process, which estimates a time interval and entropy equivalent of the gap separating *the micro- and macroprocess.*

Shifting this time to real time course automatically converts its entropy to information, working as Maxwell’s Demon, which enables compensating for the transitive gap.

*The equations of observation finalize both math description of the micro-macro-processes and validate them numerically.*

4 a. The information process’ basic unit-triplet.

The cutoff attracting bits, start collecting each three of them in a primary basic triplet unit at equal information speeds, which resonates and coheres joining in triplet units **[illustration not visible in this excerpt]** of information process.

Specifically, each three bits, processing the joint attractive movement, cooperate in the created new attracting bit, which composes a primary basic triple unit and then composes secondary triple unit, and so on.

That cooperates a nested sequence of the enclosed triplet unit emerging during cooperative rotation, when each following triplet unit enfolds all information of th cooperating units in its composite final bit.

The **[illustration not visible in this excerpt]** size limits the unit starting maximal and ending minimal information speeds, attracting and forming new triplet unit by its free information along the macroprocess. The process movement selects automatically each **[illustration not visible in this excerpt] ** during the attracting minimax movement, by joining two cutoff Bits with a third Bit, which delivers free information to next cutting Bit, forming next cooperative triple unit [illustration not visible in this excerpt] (Figs.4,5). Forming the multiple triplet trajectory follows the same procedure, (Fig.5,6)

[illustration not visible in this excerpt] **(** Author’s own work.)

**Fig. 4. Time-space opposite directional-complimentary conjugated trajectories[illustration not visible in this excerpt] and[illustration not visible in this excerpt], form spirals located on conic surfaces (analogous to Fig.2). Trajectory connected bridges [illustration not visible in this excerpt] binds the contributions of process information unit[illustration not visible in this excerpt] through the impulse joint No-Yes actions, which model a line of switching controls.**

**Two opposite space helixes and middle curve are shown on the right.**

Each self-forming triplet joins two segments of the macro-trajectory with positive eigenvalues by reversing their unstable eigenvalues and attracting a third segment with negative eigenvalues. The third segment’ rotating trajectory moves the two opposite rotating eigenvectors and cooperates all three information segments in a triplet’s knot (Fig. 5).

Each triplet unit generates three symbols from three segments of information dynamics and one impulse-code from the control, composing a minimal *logical code* that encodes this elementary physical information process.

[illustration not visible in this excerpt] **(** Author’s own work.)

**Fig.5. Illustrative dynamics of assembling units [illustration not visible in this excerpt],[illustration not visible in this excerpt],[illustration not visible in this excerpt] on the space-time trajectory and adjoining them to [illustration not visible in this excerpt]knot along the sections of space-time trajectory [illustration not visible in this excerpt],[illustration not visible in this excerpt][illustration not visible in this excerpt] (Fig.4) at changing information speeds from[illustration not visible in this excerpt] , [illustration not visible in this excerpt],[illustration not visible in this excerpt] to [illustration not visible in this excerpt], [illustration not visible in this excerpt],[illustration not visible in this excerpt] accordingly; [illustration not visible in this excerpt]is dynamic information invariant of an impulse.**

Fig.5. shows how a minimum three self-connected Bits assemble optimal **[illustration not visible in this excerpt]** -basic *triplet* whose free information requests and binds new triplet, which joins and binds three basic triplets in the ending knot, accumulating and memorizing information of all trees.

Each current unit [illustration not visible in this excerpt] composes its bits in triplet code that encodes and connects the units.

[illustration not visible in this excerpt] **(** Author’s own work.)

**Fig. 6. Simulation of forming a triplet’s space structure on a knot node, composed from time-space spirals Fig.3 (according to Fig.4). The Fig.6 indicated time intervals measure real times[illustration not visible in this excerpt],[illustration not visible in this excerpt],[illustration not visible in this excerpt] during the simulation shown on cones diameters. **

The pair of opposite directional rotating units equalizes their eigenvalues with the rotating third one, attracts and binds them in the triple by the starting attracting force.

4b. Assembling the information network (IN).

During the macro-movement, the joint triple unit’ free information transfers the triple code to next forming triplet, which assembles a network that is building by the forming triplet’ code.

The multiple triples sequentially adjoin time-space hierarchical network (IN) whose free information requests from observation and attaches new triplet unit at its higher level of the knot-node, concurrently encoding the IN triple logic (Fig.7).

[illustration not visible in this excerpt] (Author’s own work.)

**Fig.7. The IN information geometrical structure of hierarchy of the spiral space-time dynamics (Figs.3-6) of the triplet nodes (tr1, tr2, tr3, ..); where [illustration not visible in this excerpt] are a ranged string of the initial eigenvalues, cooperating on[illustration not visible in this excerpt] locations of T-L time-space, where** [illustration not visible in this excerpt] **is number of a nearest IN triplets.**

Each triplet has unique space-time position in the IN hierarchy, which defines exact location of each code logical structure. The IN node hierarchical level classifies *quality* of assembled information.

The currently ending IN node integrates information enfolding all IN levels in this node knot (Fig.7).

The IN is automatically feeding novel information, which it concurrently requests by a deficit of needed information.

The deficit creates equal entropy-uncertainty, requesting new information, which initiates probing impulses and the frequency of the observing entropy impulses.

The information probing impulses interact with the observing cutting their entropy.

That provides the IN-feedback information, which verifies the IN’s nodes’ requesting information.

New information for the IN delivers the requested node interactive impulses, whose impact on the probing impulses, with observing frequency, through the cutoff, memorizes the entropy of observing data-events. Appearing new quality of the information triplet currently builds the IN temporary hierarchy, whose high level enfolds the information triplet logic that requests new information for the running observer’s IN, attaches it, and extends the logic code. The emergence of observer current IN level indicates observer’s information surprise measured by the attaching new information.

The IN time-space logic encodes in double spiral space (DSS) triple code that rotates, encircling the conic structures (Fig.3,4,7), which multiple INs logic extends.

[illustration not visible in this excerpt] (Author’s own work.)

**Fig.8. Simulation of forming double spiral cone’s structure ( DSS) with cells (c[l]), arising along switching control line hyperbola** [illustration not visible in this excerpt]

**(shown in (Fig.3)) and uncertainty zone (UR) geometry, surrounding the**[illustration not visible in this excerpt]

**.**

**The curved macro trajectory models line** [illustration not visible in this excerpt] **whose rotation around** [illustration not visible in this excerpt] ** forms UR, enfolding the geometry volume [illustration not visible in this excerpt] with space surface [illustration not visible in this excerpt] This space structure encloses each of the spiral models on Fig. 3, 5, 6.**

The ending knots of a higher IN’s level assemble its three units *[illustration not visible in this excerpt]* in the next IN level’s triplet which starts it, Fig.8.

**[illustration not visible in this excerpt]** (Author’s own work.)

**Fig.9.** A **ssembling three formed units** *[illustration not visible in this excerpt]* **at a higher triplet’s level connecting the units’ equal speeds (Fig.4)**

The attracting process of assembling knots forms a rotating loop shown on Fig.7 at forming each following cooperative triplet tr1, tr2,…. (The scales of the curves on Figs 8 distinct from the interacting knots’ curves on Fig. 7, since these units, at reaching equal speeds, resonates, which increases size of the curves on Fig. 9).

The rotating process in the loop of the harmonized speeds-information frequencies at different levels is analogous to the Efimoff scenario [40]. The loop could be temporal until the new formed IN triplet is memorized.

The loop includes Borromean knot and ring, which was early proposed in Borromean Universal three-body relation.

The multiple IN time-space information geometry shapes the Observer *asymmetrical structure* of cellular geometry (Fig. 10) of the DSS triple code, (Fig.9).

[illustration not visible in this excerpt](Author’s own work.)

**Fig. 10. Structure of the cellular geometry, formed by the cells of the DSS triplet’s code, with a portion of the surface cells (1-2-3), illustrating the space formation. This structure geometry integrates information contributions modelling on Figs.3, 7. **

The macroprocess integrates both imaginary e tropy of the merging impulses micro processes and the cutoff information of real impulses, which sequentially convert the collected entropy in information physical process during the macro-movement.

The observation process, its entropy-information, and micro-macro processes are Observer-dependent, information of one Observer distinct of the information of others Observers. However, the invariant information minimax law leads to the invariant information *regularities* for different Observers.

Observing the same process with different probability field triple, each Observer gets specific information. The information requests its current IN during its optimal time-space information dynamics. Optimal information process determines the extremal trajectories of the entropy functional, solving the minimax variation problem for the observing process.

The information macrodynamic equations [29-34] describe information macroprocess, which averages all observing microprocesses and holds regularity of observations under the maxmin-minimax impulses. These equations *predict optimal information path* from the starting virtual observation up to information process, and the physical macrodynamics.

5. Forming structure of information Observer and its regularities

The macro-movement in rotating time–space coordinate system forms Observer’s information structure confining its multiple INs that determine the *Observer time of inner communication* with *self –scaling* of both requesting and accumulating information. Each Observer *owns the inner time of information processing* and the time *scale* of the required information (on the micro and macrolevels) *,* depending on density of the IN nodes information.

(5a). The current information *cooperative force*, initiated by free information, evaluates the observer’s *selective* actions attracting new high-quality information. *S* uch quality delivers a high density-frequency of the related observing information through the IN selective mechanism of the requested information.

These actions engage acceleration of the observer’s information processing, coordinated with new selection, quick memorizing and encoding each IN node information with its logic and space-time structure, which minimizes the spending information. It determines observer’s self-organized feedback loop.

The optimal criterion is growing quality of the observing information, collected by the IN, which selects the needed information that the observer acquires.

(5b). The observer optimal *multiple choices limit and* implement the minimax self-directed strategy, which evaluates the amount of the information emanated from the IN integrated node *that identifies the attracting cooperative force*.

(5c). The IN nested structure holds cooperative complexity [41] measuring *origin* of complexity in the interactive dynamic *process* cooperating doublet-triplets. Their free information anticipates new information, requests it, and automatically builds hierarchical IN with the DSS that decreases complexity of not cooperating yet information units.

(5d). The information structure, self-built under the self-synchronized feedback, drives self-organization of the IN and the *evolution macrodynamics* with ability of its self-creation.

(5e). The observer cognition emerges from the evolution process, as evolving intentional ability of requesting, integrating, and predicting the observer needed information that builds the observer growing networks.

The evolving free information builds the Observer specific time–space information *logical* structure that conserves its “*cognition*”.

Such logical structure possesses both virtual probabilistic and real information causality and complexity, whose information measures the cognitive intentional actions.

The rotating cognitive movement connects the impulse microprocess with the bits in macroprocess, composing the elementary macrounit-triplet, and then, through the growing IN’s levels quality information, integrates multiple nested IN’s information logic in an information domains.

The observer’s cognition assembles the common units through the multiple resonances at forming the IN-triplet hierarchy, which accept only units that each IN node concentrates and recognizes.

The cognitive movement, at forming each nodes and level, processes a *temporary loop* (Fig.6) which might disappear after the new formed IN triplet is memorized.

The loop rotates the thermodynamic process (cognitive thermodynamics) with minimal Landauer energy, which performs natural memorizing of each bit on each evolution level.

The cognitive actions model the correlated inter-actions and feed-backs between the IN levels, which controls the highest domain level. Both cognitive process and cognitive actions emerge from the evolving observations, which maintain the cognitive functions’ emerging properties and encodes the cognitive logic information language.

6. The emerging information Intelligence.

The observer intelligence emerges on the path from staring observation, virtual observer, creation microprocess, bits, information macroprocesses, and nested networks (IN) with growing quality of information and the nested logic.

These self-generate the observer selective actions, ability of their prediction, the IN concurrent renovation, and extension to complex self-built IN domains enclosing maximal quality of condense information and its logic.

The self-built structure, under self-synchronized feed-backs, drives self-organization of the IN and evolution macrodynamics with ability of its self-creation.

Within the evolving processes, integrating by the IN space-time coherent structure, emerges the observer cognition, which starts with creation elementary units of virtual observer holding a memory at microlevel.

The coordinated selection, involving verification, synchronization, and concentration of the observed information, necessary to build its logical structure of growing maximum of accumulated information, unites the observer’s self-organized cognitive actions performing *functional organization.*

The functional organization of these intelligent actions spent on this action evaluate the memorized amount of quality information at each IN’ ending hierarchical level. This functional organization integrates the interacting observers’ IN levels and domains in the observer IN highest (ending) hierarchical level. Maximal level measures maximal cooperative complexity enfolding maximal number of the nested INs structures, which memorize the ending node of the highest IN.

The intelligence is an ability of the observer to build the informational networks and domains, which includes the cognitions. The ended triplet of observer hierarchical informational networks and domains measures level of the observer intelligence. All observers have different levels of intelligence which classify observer by these levels.

The quality of information *memorized in the ending node of each observer IN highest levels* measures the observer information Intelligence. The cognitive process at each triplet level preempts the memorizing.

An observer that builds maximum number of the hierarchical informational networks and domains has maximum intelligence. This observes have an imbedded ability to control other observers.

The *Observer Intelligence* holds ability to uncover causal relationships enclosed in evolving observer networks and self- extends the growing quality information and the cognitive logic on building *collective observer intellect.*

The intelligence of a multiple interactive observers integrates their joint IN’s ending node.

The Observer *Cognition* emerges in two forms: a virtual, rotating movement processing temporal memory, and the following real information mechanisms, rotating the double helix geometrical structure and memorizing it.

The DSS concurrently places and organizes the observing information bits in the IN nodes, whose sequential knots memorize information causality and logic.

The self-directed strategy develops multiple logical operations of a self-programming computation which enhances collective logic, knowledge, and organization of diverse intelligent observers.

The EF-IPF measure allows evaluating information necessary to build a minimal intelligent observer.

The increasing INs hierarchy enfolds rising information density which accelerates grow the intelligence that concurrently memorizes and transmits itself over the time course in an observing time scale.

The intelligence, growing with its time interval, increases the observer life span.

The self-organized evolving IN’s time-space distributed information structure models *artificial intellect.*

7. The Observer individuality determines:

-The probability field’ triple observing specific set of probabilistic events that arise in emerging particular information observer;

*-* Time of observation, measuring quantity and density of information of the delivered bits;

-Cooperation the observing information in a limited number of the IN-triplet nodes and limited number of the observer’s IN, which depends on individual observer selective actions [34].

*-* The selec *t* ive actions define the cooperative information forces, which depends on the number of the IN nodes. The minimal cooperative force, forming very first triplet, defines minimal selective observer.

The individual ability for selection classifies information observers by levels of the IN hierarchy, time-space geometrical structure, and inner time scale whose feedback holds *admissible* information spectrum of observation. The individual observers INs determine its explicit ability of self-creation.

-These specifics classify the observers also by level of cognition and intelligence.

The information mechanism of building all observers is invariant, which describes the invariant equation of information dynamics following from minimax variation principle.

8. Communication of intelligent observers with understanding the receiving message.

When an intelligent observer sends a message, containing its information, which emanates from this intelligent observer’s IN node, another intelligent observer, receiving that information, can recognize its meaning if its information is equivalent to this observer IN nodes information quality.

Since the DSS code is invariant for all information observers, each observer encodes its message in that coding language, whose logic and length depend on sending information, possibly collected from the observer–sender’s different INs nodes.

The observer request for growing quality of needed information measures the specific qualities of free information emanating from the IN distinctive node that need the compensation.

Recognition of the needed information initiates the observer request. The recognition involves copying and cooperation of the comparative qualities enclosed in the observer –receiver distinctive INs nodes.

(The copies can provide the temporary integral mirrors of the microprocess transitive impulses.)

The message acceptance includes cooperation of the message quality with the quality of an IN node enclosed in the observer –receiver IN structure.

If the cooperative information coheres in the cognitive loop, the message can be accepted and memorized in the receiver’s IN. That allows the intelligent observer to uncover a meaning of observing process using the common message information language and the cognitive acceptance, which are based on the qualities of observing information memorized in the IN hierarchy. The intelligent observer recognizes and encodes digital images in message transmission, being self-reflective enables understanding the message meaning.

Understanding the message describes the information formalism, which includes copying the accepted message on the cognitive moving helix which temporary memorizes it as triplets’ entropies in a virtual IN structure.

This converting mechanism includes a compression of observing image in virtual impulse ending the virtual IN.

The virtual impulse, holding the entropy equivalent of the image information, moves the cognition scanning helix along the observer’s INs until its negative curved step-up action, carrying the entropy equivalent of energy, will attract a positive curvature of the IN node bit’s step-down action. The forming Bit encloses the equivalent energy’s quality measured by its entropy value. When the IN bit’s step-down action interacts with the moving image’s step-up action, it injects energy capturing the entropy of impulse’ ending step-up action. This inter-action models 0-1 bit (Fig.2A, B). The opposite curved interaction provides a time–space difference (an asymmetrical barrier) between 0 and 1 actions, necessary for creating the Bit. The interactive impulse’ step-down ending state memorizes the Bit when the observer interactive process provides Landauer’s energy with maximal probability (up to a certainty). Such energy delivers the cognitive helix movement having maximal energy quality (minimal entropy production), which can be called “cognitive thermodynamic process”. It allows spending minimal cognitive quantity equal to triplet structure Landauer’s energy [illustration not visible in this excerpt] for erasure the observing bits and memorizes each bit by the equal neuron information bits. (This means, at forming a triplet, this energy can be spent on memorizing a third bit before it gets asymmetrical structure needed for memorizing.)

Therefore, the cognitive thermodynamic process practically has not thermodynamic cost, which models of a cognitive software with the minimal algorithmic complexity. The important coordination of an observer external time-space scale and its internal time-space scale happens when an external step-down jump action interacts with observer inner cognitive thermodynamics’ time-space interval, which, in the curved interaction measures the difference of these intervals [34].

Understanding the receiving information includes classifying and selecting such information that concurs with this observer’s memorized *meaning* of other comparative images. Thus, cognitive movement, beginning in virtual observation, holds its imaginary form, composing entropy microprocess, until the memorized IN bit transfers it to an information macro movement. That brings *two forms* for the cognitive helix process: *imaginary reversible with a temporal memory, and real-information moving by the irreversible cognitive thermodynamics memorizing incoming information.*

Multiple experimental studies [42-44] conclusively demonstrate that the large monopolar cell (LMC), the second-order retinal neuron, performs the cognitive model’s main actions.

The brain neurons communicate [44a] when presynaptic dopamine terminals demand neuronal activity for neurotransmission; in a response to depolarization, dopamine vesicles utilize a cascade of vesicular transporters to dynamically increase the vesicular pH gradient, thereby increasing dopamine vesicle content.

That confirms the communication of interacting bits modeling the neurons.

The intelligent observers interacting through communication enable the message recognition, which involves cognitive coherence with the reading information, it selection and acceptance.

The selective requirements and limitations on the acceptance are in [33,34].

Therefore, the intelligent observer can uncover a meaning of observing process, or a message, based on the sequential memorized its observing information, which, moving in the rotating cognitive mechanism, gives start to a succeeding IN level that this meaning accumulates.

The formal analysis shows that observer cognition and intelligence self –control the observer evolution [34].

The numerical analysis [34] evaluates the highest level of the observer intelligence by a maximal quantity of potential accumulated information, which estimates the intelligence threshold. The intelligent observer (humans or AI) may overcome the threshold requiring highest information up to all information in Universe. Such an observer that conquers the threshold possess a supper intellect, which can control not only own intellect, but control other intelligent observers.

9. The Mathematical Basic of observer formalism includes:

1.Probabilities and conditional entropies of random events.

2.The integral measure of the observing process trajectories formalizes Entropy Functional (EF), which is expressed through the regular and stochastic components of Markov diffusion process.

3.Cutting the EF by impulse delta-function determines the increments of information for each impulse.

4.Information path functional (IPF) unites the information cutoff contributions taking along n- dimensional Markov process’ impulses during its total time interval.

The Feynman path integral is quantum analog of *action principle* in physics, and EF expresses a probabilistic causally of the action principle, while the cutoff memorizes certain information casualty integrated in the IPF.

5.The equation of the EF for a microprocess under inverse actions of the interactive function, starting the impulse opposite time, measured in space rotating angle, which determine the solutions-conjugated entropies, entangling in rotation. The process conversion of entangled entropy in equivalent qubit and or bit.

6.The information macrodynamic equations whose information force is gradient of information path functional on a macroprocess’ trajectories and information flow is a speed of the macroprocess, following from the Markov drift being averaged along all microprocesses, as well as the averaged diffusion on the macroprocess, and information Hamiltonian.

These equations are information form of the equation of irreversible thermodynamics, which the information macrodynamic process generalizes and extends to observer relativity, connecting with the information curvature, differential of the Hamiltonian per volume, density of information mass, and cooperative complexity.

The approach formalism comes from Feynman concepts that physical law regularities mathematically formulate a variation principle for the process integral. The variation problem for the integral measures of observing process’ entropy functional and the bits’ information path integral formalizes the minimax law, which describes all regularities of the processes. The theoretical concepts, which scientifically proves the mathematical and logical formalism allows uncovering these regularities. The results simulate mathematical models, which various experimental studies and applications confirm.

The information observer with the regularities arises without any physical law.

10. About information structure of artificial designed observer: the basic stages toward artificial brain

Observers are everywhere, including people, animals, other species, multiple particles, and objects communicating and *interacting* between each other, accepting, transforming and exchanging information.

In physics, elementary particles interact, starting four known fundamental interactions in Nature, which form interacting atoms, molecules, different intermolecular forces, chemical interactive reactions up to biological interaction, building genetics of organisms. Biological interactions involve multilevel interspecies interactions in Ecology. Various interactive communications creates social interactions, mutual technological, economic and financial interactions. Interactive communication in different languages, computer interactive telecommunications, and Internet connect society, technology, business, science, education, and media.

Prospective artificial intelligence-human interactions would generate future technology and societies.

All these interactions simplify the example with a rubber ball hitting ground and bouncing, which consists of inter-active yes-no ([illustration not visible in this excerpt]) actions.

Term of information each of these observers understands differently. Whereas a single certain inter-action is a―Yes-No impulse known as a Bit, the elementary unit of information.

There have been many study each observer’s specific interactions; however, no one approach has ever unified the study of all their common information origins, regularities, and conditions of differentiation.

This is the first approach to unify these studies aiming to understand common notion of information.

Since multiple observer interacts through a manifold of such Yes-No actions, these interactive actions are random and their multiplicity generates a random process.

That’s why retrieving the information units from this random process requires its *observation*.

Searching information on Web, a potential observer of this information sends probing impulses and evaluates the needed result by its probability. More probable occurrence allows selecting the needed result estimating its certainty as observed information.

A simple example is observing some uncertain planet moving around a star. When probability of its observing increases, making the shot-a film brings the copy of that most probable observation. Such copy removed the observer uncertainty, while spending energy on the shot, which consumes a film. Now the film exposes a certain observation, which encloses the spending energy. It brings the current information of the observing planet.

Therefore, the observations are the multiple acting probabilities, which the observer generates while observing a random uncertainty searching a certainty as its information. Such observation is actual search of information, since the observer is interacting during the search until getting multiple Yes-No impulses of elementary bits.

**1. Probabilistic observation measured by discrete probabilistic impulses of the observing process**

Since the probabilistic observation runs the multiple interactive impulses, they are the probability impulses probing a random environment which formally describes a random field. The axiomatic probability field defines mathematical triad: the sets of possible events, the sets of actual events, and their probability function.

Each of this triad specifies the particular observer whose probability, belonging to the field, observes the current events.

Multiple triads extend observation toward artificial designing a brain during multiple observations.

According to formal theory of probabilities [19], the axiomatic probabilities are objective by definition, formalizing multiple experimental occurrences of each random event.

In artificial observation, the probabilistic impulses can produce a random generator.

Formally, a source of such discrete probabilistic impulses is Kolmogorov 0-1 law probabilities, which generates the sequence of *mutually independent* variables of the field events.

These probabilistic impulses interact with an observable random process in the field, which comprises the multiple yes-no impulses. The classical process of multiple interacting impulses is Markov diffusion process, widely used in many physical, chemical, biological and many other applications.

Under the sequence of probabilistic impulses of the random field, the Markov process’ probabilities sequentially change, providing virtual observation of this process through a priory probability (before yes-action) and a posteriori probability (after yes-action).

These axiomatic probabilities belong to the evolving Markov process, but have analogy with Bayes probabilities that evaluate the probability of a hypothesis by a priori probability, which is then updated through a posteriori probability of the evidence.

Both impulse probabilities and Markov process probabilities start within the random field’ specific triad at beginning of the observation. The observation, thereafter, provides the Markov process probabilities under impulse action of the random field, which carry the same initial field triad. Multiple-dimensions of observing Markov process start with multiple triads.

In this probabilistic model, a potential observer (obtaining hidden bits) is modeling by Markov process which is placed in the surrounded random field and therefore is affected by the field random impulses-frequencies.

Since our Universe build multiple interacting processes, their running multiplicity is actual source of random field.

The observing process, carrying hidden bits of the interactions, starts with observation the specific field triad which spots the current observing environment.

The artificial designed observer, generates the random impulses in that its current environment.

In the formal probabilistic model, the axiomatic artificial probabilities objectively measure the observation process.

In the artificial observer, designing during the observation, these probabilities identified through the multiple interacting events in the observable spot, measures the probability of revealing the bits.

During repetitively probing probabilistic (virtual) observations, these sequential probabilities with the concurrently observing events enable self-building the observing process, creating a virtual observer that sends the probes.

Thus, the artificial observer, designing during observation, self-creates the observable process of hidden bits. The uncovered bits provide a future code which generates that information observer.

**2. Reduction of the process entropy under probing impulse, and rising probabilistic logic**

Uncertainty of random events between the impulse yes-no probabilities identifies the relative probabilities’ logarithmic measure which is a relative entropy. This entropy is immanent to each observing impulse, which measures correlation connection between the impulses. Each No-probability of probing impulse virtually cut this entropy and correlation.

Within each interacting impulse, its step-down No-cutting action maximizes the cutting entropy, while its step-up Yes reaction, spending an entropy on this action’ creation, minimizes the cutting entropy. That provide max-min principle for each impulse, and minimax along the multiple observing impulses.

The impulse’ maximal cutting No action minimizes absolute entropy that conveys Yes action (rising its probability), which leads to a maxmin of relational entropy between the impulse actions transferring the probabilities.

In simple example with bouncing rubber ball, when the ball hits ground, the energy of this interaction partially dissipates that increases the interaction’s total entropy, while the ball’s following reverse movement holds less entropy (as a part of the dissipated), leading to max-min entropy of the bouncing ball. Adding periodically small energy, compensating for the interactive dissipation, supports the continuing bouncing.

As soon as the initial impulse 0-1 actions involve, the minimax principle is imposed along all impulse observation.

This leads to reduction the process entropy under probing impulse that increases each posterior probability.

The sequential a priori-a posteriori probabilities determine probabilistic causality along the observing process, which carries its probabilistic logic. The logarithmic ratio of these probabilities defines relational entropy which measures this logic for each impulse in the sequence. The process logic integrates entropy functional (EF) along trajectories of the observing Markov process, which measure the process integral entropy.

The minimax principle formalize its variation problem (VP), which, applying to the EF, allows analytically describe the observing process minimax trajectory as the extreme VP solution [32].

The solution brings invariant entropy increment for each discrete impulse preserving its probability measure and the impulse time interval measure [illustration not visible in this excerpt](as equivalent of Nat). The EF connects the entropy with the process total time, which synchronizes and adjoins the local impulse time measure along the process in an absolute time scale.

The impulse logical measure[illustration not visible in this excerpt] includes *logical bit*, which measures[illustration not visible in this excerpt], and difference[illustration not visible in this excerpt], which covers a wide of the impulse Yes action transferring [illustration not visible in this excerpt]to next impulse. That evaluates measure [illustration not visible in this excerpt]of the impulse *free logic*. Each of these logical measures have characterizes specific relational probability.

The reduction of the process entropy determines the growing logical dependency of the impulses during the observation, which involves virtual impulse’ attraction. Since free logic connects the impulses it measures the virtual attraction.

Until this probability less than one, the probabilistic logic, even with growing the probability, is still uncertain (virtual), while specific relational probability measures closeness this uncertainty to certainty with probability one.

**3. The emergence of space-time geometry in the impulse observing process. **

With growing correlations, the intensity of entropy per the interval (as entropy density) increases on each following interval, indicating a shift between virtual actions, measured in a time interval’s unit measure **[illustration not visible in this excerpt]**.

The shift merges the border impulse interactive action[illustration not visible in this excerpt], which generates an interactive jump with a high entropy density.

The jump cutting action [illustration not visible in this excerpt] of the growing density *curves* an emerging *½* time units of the border impulse’ time interval.

The jump, curving that time, initiates a *displacement* starting *rotation* the impulse opposite Yes-No actions. .

This originates the curved space shifts, quantified by the impulse [illustration not visible in this excerpt]invariant probability (1 or 0) measure [illustration not visible in this excerpt]on *two shifting space units* (as a counterpart to the primary curved time) (Fig.1).

The displacement within the impulse [illustration not visible in this excerpt] changes the impulse primary time to discrete space form while *preserving* its measure [illustration not visible in this excerpt] in the emerging time-space coordinate system.

The measure is conserved in following time-space correlated movement transferring the minimax.

The curved impulse is measured by its curvature.

The virtual observer, being displaced from the initial virtual process, sends the discrete *time-space* impulses as virtual probes to *self-testing* the preservation of axiomatic probability measure through the probes’ frequencies defined by the observing probabilities.

The Observer is *self-supporting* the probes increasing frequencies, which are checking the probability grow.

Such test checks this probability also via symmetry condition (imposed on the axiomatic probability) indicating the probability correctness and identifying time-space of the virtual observer’ location.

The temporary memorized correlation encloses a difference of the starting space-time correlation, identifying an accuracy of its sequential closeness. The memory of rising time-space correlations holds a time-space shape of the evolving observer.

The evolving shape gradually confines the running rotating movement, which *self-supports* developing both the curved shape and the Observer time space geometrical structure. The virtual Observer *self-develops* its space-time virtual geometrical structure during virtual observation, which gains its real form with sequential transforming the integrated entropy to equivalent information.

**4. The impulse transformation the observing process entropy to information**

The observation, reducing the uncertainty of the random interactive process, concurrently integrates it until the final uncertainty approach zero, or to its opposite notion-certainty. Then, the integrated uncertainty-entropy is removed by injecting energy equivalent to that which this entropy encloses. The erasure of the entropy–uncertainty brings information with certainty as the contrary equivalent of the minimal integrated entropy during the observation..

These transformations actually emerge during the interactive impulse observation, when a posteriori probability of a last probing No action of this impulse, cutting the final minimal entropy, follows the Yes action of that impulse, bringing posterior probability one, or certainty.

That indicates the certainty-reality of observing the previously hidden bit, which was carrying energy in real interactive process before had covered by the entropy of the multiple random interactions.

This is an information bit of the certain logic coming with the certain free information of the impulse logic which carries the certain logical attraction.

The certain the logical information bit become physical bit through erasure the entropy of this logic, which allows replacing the logic by memorizing its bit. The memory must be stored or placed in some physical entity, which performs encoding of the memorized bit. Encoding logical Bit extracts it initial position, which erases the logical bit information.

The physical reality of revealing the bit brings also its energy for potential erasing this entropy. However, acquiring certainty-information from the entropy, satisfying the second law in initial irreversible process, requires cost of the energy equivalent to that in Demon Maxwell, or Landaurer energy.

According to Landauer principle [6], any logically irreversible manipulation with information, such as encoding leads to erasure the information in a dissipative irreversible process. Erasure of information Bit requires spending minimal energy [illustration not visible in this excerpt] ([illustration not visible in this excerpt]is Boltzman constant, [illustration not visible in this excerpt] absolute temperature) which should be delivered outside by an environment.

Therefore, the transformation of observing impulse entropy to information includes: getting the certain information logic, its memorizing through erasure, and encoding the memorized bit by storing its position in some environmental process.

This process will also bring the energy for the process of memorizing ending with the encoding bit.

The observing virtual process ending with the minimal entropy is reversible and symmetrical, while physical bit is anti-symmetrical. Therefore , the logical entropy bit becomes information bit through an anti-symmetrical transformation.

The impulse interaction curves each impulse, and the virtual attracting connects the impulse ending Yes action with the

following opposite No action of the next interacting impulse. It brings opposite topological curvatures of these impulses: positive for the Yes action and negative for No action. The interaction of such impulses creates topological anti-symmetrical transitive transformation , which evaluates its logical entropy [illustration not visible in this excerpt].

With approaching the certainty, it brings asymmetry information[illustration not visible in this excerpt].

The opposite curving impulses in the interactive transition require keeping entropy ratio 1/ln2. The opposite curved interaction decreases difference of the entropies ratio of amount [illustration not visible in this excerpt]. During the process of interaction with external (environmental) impulse, by the moment [illustration not visible in this excerpt] of appearance of the interacting Bit, this ratio [illustration not visible in this excerpt]selects part of the information impulse [illustration not visible in this excerpt]which the curve interaction deducts from the external impulse measure I Nat. It evaluates the free logic in the curve interaction and moment [illustration not visible in this excerpt]relative to the impulse invariant measure **[illustration not visible in this excerpt]**. After that moment, during relative interval [illustration not visible in this excerpt] the bit appears.

The transitive transformation has no actual cost. That’s why the erasure of free logic entropy requires free information [illustration not visible in this excerpt] of the external impulse, which appears on relative time interval [illustration not visible in this excerpt].

So, from begging of the impulse, time interval [illustration not visible in this excerpt]appears. It deducts from the external impulse measure **[illustration not visible in this excerpt]** time interval [illustration not visible in this excerpt]which estimates time interval needed for encoding. Information logic covering time of encoding is[illustration not visible in this excerpt], where [illustration not visible in this excerpt]is transferred to next interacting impulse as the equivalent to entropy is[illustration not visible in this excerpt].

Both free information and the needed for encoding carry information logic., the last we call encoding logic.

Since Landaurer energy allows memorizing only 1 bit, the free information currying the attraction, and information cost of encoding are not becoming physical until additional to Landaurer energy the environmental impulse brings energy[illustration not visible in this excerpt]. It cost adding [illustration not visible in this excerpt]of Landaurer energy. The encoding cost [illustration not visible in this excerpt]with total additional cost [illustration not visible in this excerpt]at the same temperature.

This energy should be delivered on time interval [illustration not visible in this excerpt] whose start identifies the impulse interacting time transferring entropy[illustration not visible in this excerpt]. The moment [illustration not visible in this excerpt]ends the interval of the curved opposite interaction which adds interval~0.02 bringing total interval 0.19. Hence the moment of delivering total energy identifies potential encoding time interval ending the internal impulse which interacting with the external impulse through the opposite curvatures.

Since the external process’ movement within its impulse ends at the impulse step-up stopping states, the thermodynamic process delivering this energy should stop in that state.

Hence, the erased impulse entropy memorizes the equivalent physical information [illustration not visible in this excerpt]in the impulse ending state, where the encoding stores this information.

That can automatically produces the curving interaction of the observing impulse with real environmental process. Such interaction starts producing the physical bit after the moment ending transitive logic, and ends producing it by the moment ending delivering Landaurer energy. This time interval estimates ln2. The time intervals of memorizing free information and the encoding estimate accordingly [illustration not visible in this excerpt] and [illustration not visible in this excerpt].

From that follows necessity of proper concurrence of the time curse of the impulse inner and external impulse and coordination the sequence of the moment appearance bit, its memory, and encoding. .

Integration of the process entropy and its transformation to process information;

**5. Transformation of the integrated process entropy to the process integral information. Growing information density of the process impulses.**

The EF functional integrates all the observer process’ impulses which sequential Bayes probabilities virtually observe and cut. The EF measure total process entropy as the process potential information and the VP generates the minimax trajectory of the observing process.

After the impulses of the EF integrated multi-dimensional process reach certainty, the impulses were cut with maximal probabilities transforming each impulse entropy invariant measure to equivalent information invariant measure.

All these multiple impulses information integrate information path functional (IPF) passing through the discrete impulses’ time –space information measure.

The transformation converts the EF to the IPF and the virtual observing probabilistic multi-trajectories to the trajectory of information process. Each impulse invariant information includes the bit, free information, and information needed for encoding, and the IPF integrates the bits and the information logic between the bits sequence.

Since this logic has created Yes-No actions between a nearest impulse bits, which during the observation, reducing entropy, attract the nearest impulses, such logic is attractive, and the information logic attracts the nearest bits.

Along the minimax trajectory of the IPF information process, each following impulse encloses more information than the previous one, while the time interval of the invariant information impulses decreases proportionally. It sequentially condenses each of the following impulse’ increasing information in the decreasing time interval, growing density of the impulse information, including the information of attraction~1/3 bit. In that path, one bit information of each third impulse in the sequence increases on one more bit, or twice. Then growing information attraction in 2/3 bit increase the following third (six from the beginning) impulse on two bits. So such third bit, acquiring total 3 bits, increases its information in triple. Since growing impulse information proportionally decreases its time interval, the density of third impulse increases by 2/05=4 and the density of the six impulse increases by 3/025=12, or in triple, and so on. By the end of the IPF integration, all integrated information encloses a last impulse whose information density approach maximal limit.

Thus in the information processes emerge multiple bits with triple growing density, and raising the process information logic, while the IPF integral information with its logic enclose the last integrated impulse time –space interval or volume.

The multiple information impulses describe a frequency of their appearance in the information process, which grows with shortening the impulse discrete interval and the increasing density. That increase the impulse information speed. The impulses, located on the prolonging path, carry the increasing frequencies, shorted time with higher space interval, and growing speeds. So, the impulse time–space geometry encloses the impulse information, density, and frequency, concentrating information logic and information of all previous impulses along the path.

The EF-IPF space-time extremal trajectories form spirals located on conic surfaces Fig.3, which starts from virtual (entropy) process and continues as the information process. Since each bit of this trajectory creates the cutting entropy in the impulse observation, the trajectory consists of segments of information process dynamics and interval of delivering each following bit between the segments. On Fig.3 each segment starts on the cone vertex -point D and ends on the point D4 which connects to vertex of a following cone. The observing bit is delivering at each cone vertex. The segment presents the impulse process with its logical bit, logical free information and encoding logic-as the logical process.

The information dynamics describe the process of sequential logical interaction of such multiple impulses, rotating with information speed determined by the impulse density. The information dynamics between the cone vertexes is reversible and symmetrical as an analogy with Hamiltonian dynamics. The logical anti-symmetry brings the anti-symmetrical bit before the interaction with external impulse starts delivering the external energy. This bit is supplying at each cone vertex.

After the external energy generates physical bit, the physical information process of with such multiple bits starts.

Since moment of this process start identifies the time interval of the logical anti-symmetrical interaction, the frequency of such interactions [illustration not visible in this excerpt] determines time of starting supplying external energy which equals to time of it stopping. Between these moments of time locates time interval of memorizing the bit, which identifies the bit information measure[illustration not visible in this excerpt] equivalent to the part of invariant impulse. It determines frequency [illustration not visible in this excerpt] of spectrum [illustration not visible in this excerpt] necessary for delivering energy memorizing and encoding the bit.

After supplying the external energy during these time intervals, whose sum equals to the invariant impulse time interval, the whole impulse becomes the segment of physical information process. Therefore, physical dynamics describe the IPF extremal trajectory rotating on sequential cones (Fig.3). Each cone vertex encodes the bit memorized in a previous impulse with frequency[illustration not visible in this excerpt], each segment repeats with frequency[illustration not visible in this excerpt], and transfers to next cone vertex with frequency [illustration not visible in this excerpt]of encoding the current impulse bit. Hence, each physical information impulse carries spectrum[illustration not visible in this excerpt], while their sequence on the trajectory carries spectrum impulses[illustration not visible in this excerpt].where [illustration not visible in this excerpt]is the resonance frequency which connects the impulses.

**6. Self-forming triplet logical structures and their self-cooperation in information network (IN) hierarchical logic.**

The emerging logical bits start self-cooperation under the attracting free information. The bit’s attracting free information rotates with the speed holding its frequency toward a resonance with the frequency of next bit’s free information attracting two. This resonance process links these bits in duplets. Free information from one bit out of the pair gets spent on the binding of the duplet. Free information from the other bit attracts the third bit and binds all three in a knot bit creating in the triplet information structure. The knot bit still has free information and it is used to attract a different bound pair of bits, creating two bound triplets. This process continues creating nested layers of bound triplets, three triplets and more (Figs. 4-6). Hence the triplet information logical structure creates the resonance frequencies joining the triple bits. The trajectory of forming triplet describes the rotating segments of their cones (Fig.5), whose vertexes join the knot starting the base of the following cone. The knot frequency joins the cone vertexes in resonance along the cone base when the next spiral segment starts. It connects next triplet in the resonance and so on, creating the nested layers information network (IN), where the layers’ knots hierarchy identifies the nested nodes of the IN hierarchy.

Triplets are the basic elements that form a nested informational network with a hierarchical structure.

Each triplet unit generates three symbols from three segments of information dynamics and one when the segment attracting triple logic is binding in the logical triplet knot. These symbols can produce triplet code, while the knot logic symbol binds the triple code for potential encoding all triple. The encoding will release its free information logic which transfers this triple code to next triplet node. Thus, the nodes logically organize themselves in IN code.

The attracting free information in resonance of three bits frequencies creates the triplet information logical structure which carries the not bound free information logic including the encoding logic with related frequencies. The frequency of free information logic determines the moment of time when the external energy starts memorizing the bit. The frequency of the triple encoding logic determines the moment of time when the external energy starts encoding the knot triple code.

The IN emerging logical structure carries the triple code on each node hierarchy, and the last triplet in the network collects and encloses the entire network’s information. The network, built through the resonance, has limited stability and therefore each IN encloses a finite structure. That’s why the observing process self-builds multiple limited INs.

The final triplet in every network contains the maximum amount of free information.

Because of this, the networks are self-connected through the attraction of their *ended triplets.*

Even after each IN potentially loses stability evolving in a chaos, it possesses ability of self-restoration.

The multiple INs self-cooperate in hierarchical domain, starting with the cooperation of each tree ended triplets’ free information in a knot which joining this INs’ triple in resonance. This IN ending knot’s free information resonates with other three INs’ ending free information, joining these INs in a next IN of the domain hierarchy.

The hierarchical logical trajectory describes space-time spiral structure (Figs.7,9) which also presents trajectory of information process evolving in observations.

This hierarchy enables generating sequential triple code locating on the rotating trajectory of the cone vertexes, which are distributed at the different hierarchical levels of the multiple IN and the domain hierarchy.

Such space-time code integrates the observing process in space-time information geometry of self-organizing observer.

**7. Self-forming hierarchical distributed logical structure of cognition.**

The multiple moving INs, sequentially equalizing the speeds-frequencies of the nodes attracting information logic in resonance, assembles total observer logic. This logic consists of the mutual attracting free information, which, sequentially interacting, self-organizes the cooperative logical rotating spiral loops enclosing all observing information. We call it observer cognitive logic, which encloses both, probabilistic and information causalities distributed along all observer hierarchy. The logical functions of self-equalizing the free information in the resonance perform the cognitive functions, which are distributed along hierarchy of assembling units: triplets, IN nested nodes, and the IN ending nodes. These local functions self-organize the observer cognition. Assembling runs the resonance frequencies [illustration not visible in this excerpt]spreading along this hierarchy. Since each unit, ending high level structure encloses all its information logic, the unit’ impulse invariant time space interval containing this information increase more information density than the unit of lower level hierarchy. The resonance frequencies holding the cognitive logic loop-self creates the unit hierarchy.

**Proposition 1.**

*Let have the followings:*

The space-time spiral trajectory of the EF extremal describes sequence of curving rotating segments, representing interacting impulses of observing process, which integrates the observing process’ logic. Each segment’ impulse has invariant entropy measure [illustration not visible in this excerpt], moving along the trajectory with the curved impulse invariant measure [illustration not visible in this excerpt] which includes time coordinate measure [illustration not visible in this excerpt]and space coordinate measure [illustration not visible in this excerpt]; measure [illustration not visible in this excerpt] includes the impulse logical bit [illustration not visible in this excerpt]and free logic [illustration not visible in this excerpt]. The logic density per each third segment triples.

*Then*:

1.Along each [illustration not visible in this excerpt] segment moves *three dimensional space wave functions*, spinning like a top (Fig.A), with rotating [illustration not visible in this excerpt]speed along each spiral cross-section [illustration not visible in this excerpt] and orthogonal to it rotation with space speed[illustration not visible in this excerpt], which turning on space angle [illustration not visible in this excerpt]proceeds three single turns [illustration not visible in this excerpt] during the rotation that ends the cross-section. The wave repeats with period [illustration not visible in this excerpt]of each following impulse and carries its cross section frequency [illustration not visible in this excerpt]and the rotating space spiral trajectory frequency[illustration not visible in this excerpt], which the wave function distributes along the tree-dimensional rotation. Each third segment frequency triples.

2. Along each [illustration not visible in this excerpt]segment rotating cross-section’ speed is [illustration not visible in this excerpt] and orthogonal space speed [illustration not visible in this excerpt] with related frequencies [illustration not visible in this excerpt]and [illustration not visible in this excerpt].

Poof. 1.We apply equation of a wave [illustration not visible in this excerpt]depending on velocity of movement [illustration not visible in this excerpt] and distance[illustration not visible in this excerpt] to the moving segment on the spiral trajectory, considering both evolutions of the wave functions [illustration not visible in this excerpt]along its cross-section and along the rotating section-impulse length[illustration not visible in this excerpt].

Where [illustration not visible in this excerpt]and impulse cross-section square [illustration not visible in this excerpt] is analog of distance to reach with current speed [illustration not visible in this excerpt]during two-dimensional rotation of the trajectory on the cone basis along angle[illustration not visible in this excerpt], Fig.3.

It allows finding the length of rotation radius [illustration not visible in this excerpt]by its end of the impulse, which is equal to the impulse measure[illustration not visible in this excerpt]:[illustration not visible in this excerpt].By the end of rotation, increasing left multiplication in [illustration not visible in this excerpt]reaches distance[illustration not visible in this excerpt], and[illustration not visible in this excerpt].

Since the wave function argument[illustration not visible in this excerpt], decreasing along the segment, reaches [illustration not visible in this excerpt] by the end of each segment, with period equals impulse measure[illustration not visible in this excerpt], the wave function [illustration not visible in this excerpt]is periodical with period [illustration not visible in this excerpt].

Wave function [illustration not visible in this excerpt]moves along its cross section with entropy speed [illustration not visible in this excerpt] .

Wave function [illustration not visible in this excerpt] movement along impulse length [illustration not visible in this excerpt]with space rotating speed [illustration not visible in this excerpt]to reach the impulse volume [illustration not visible in this excerpt] describes Eq.

[illustration not visible in this excerpt],

where [illustration not visible in this excerpt] at reaching volume [illustration not visible in this excerpt]and[illustration not visible in this excerpt] with speed [illustration not visible in this excerpt].

Thus, the wave carries along the spiral trajectory information frequency [illustration not visible in this excerpt] and along its cross section frequency[illustration not visible in this excerpt]. Or rotation with frequency [illustration not visible in this excerpt] extends frequency [illustration not visible in this excerpt] approximately in three times. Each space angle [illustration not visible in this excerpt]is equivalent to tree intervals of rotation along the square cross section, while each such turn brings space angle[illustration not visible in this excerpt] .

2. Each third impulse density concentrates increasing invariant impulse measure [illustration not visible in this excerpt]in impulse density [illustration not visible in this excerpt] with volume [illustration not visible in this excerpt].

Each [illustration not visible in this excerpt] impulse has density [illustration not visible in this excerpt] which for each [illustration not visible in this excerpt] impulse density satisfies ratio[illustration not visible in this excerpt], or [illustration not visible in this excerpt], and [illustration not visible in this excerpt]. That brings [illustration not visible in this excerpt].

Assuming each impulse preserves ratio [illustration not visible in this excerpt] and relations [illustration not visible in this excerpt] , we find [illustration not visible in this excerpt]and [illustration not visible in this excerpt]from equality [illustration not visible in this excerpt]. It follows [illustration not visible in this excerpt],[illustration not visible in this excerpt]from which [illustration not visible in this excerpt],[illustration not visible in this excerpt], and[illustration not visible in this excerpt].

Relation [illustration not visible in this excerpt]brings [illustration not visible in this excerpt] and [illustration not visible in this excerpt]brings [illustration not visible in this excerpt]with related frequencies [illustration not visible in this excerpt]and[illustration not visible in this excerpt].

Finally the periodical wave function includes the sequence of repeating arguments along both orthogonal rotations:

[illustration not visible in this excerpt].[illustration not visible in this excerpt]

illustration not visible in this excerpt

Fig.A. Illustrative schematic of spinning top (from Google’ top trajectory).

**Corollaries**

1. The wave function with above speeds and frequencies emerges during the observation process when a space interval appears within the impulse microprocess during reversible time interval of [illustration not visible in this excerpt]of the impulse invariant measure [illustration not visible in this excerpt]equivalent to time interval[illustration not visible in this excerpt]. These space function parameters deliver the lowering down space speed.

Before that, the observing trajectory had described the probabilistic time function indicating appearance of a space time probabilistic wave with probability[illustration not visible in this excerpt]. During the probabilistic time observation, the entropy of Bayes priori-posteriori probabilities measures its probabilistic symmetric logic.

Thus, wave function initially emerges in probabilistic observation as a probability wave in probability field.

At beginning of the microprocess is only time measured probabilistic wave.

2. The asymmetrical logic emerges with appearance of free logic interval [illustration not visible in this excerpt] which indicates starting the interactive rotating asymmetry. From that, the observation logic becomes the asymmetric as part of total free logic [illustration not visible in this excerpt]. The asymmetric wave emerges.

The asymmetric logic appears with the certainty-reality of observing the previously hidden bit, which was carrying energy in real interactive process had covered by the entropy of the multiple random interactions. This is an information bit of the certain logic coming with the certain free information of the impulse logic which carries the certain logical attraction. Therefore, the wave function in the microprocess is probabilistic until the certain logical information bit appears.

The certain logical information bit become physical bit through erasure the entropy of this logic, which allows replacing the logic by memorizing its bit.

3. The wave function, both probabilistic and real—certain is attribute of the EF variation problem, whose solution brings minimax extremal trajectory carrying the wave function.

The spinning space –time trajectory describe the increasing speed around its cross-section and decreasing rotation space speed along the trajectory which indicates its finite end.[illustration not visible in this excerpt]

**Proposition 2.**

1).The hierarchy of self-cooperating triplet’s units emerges along the EF extremal trajectory, where each third impulse progressively increases the information density measure of its bit in triple.

The time-space hierarchy of the units starts with emerging the symmetrical logic at appearance of time interval in the microprocess. This logic self–forms a hierarchy of the logical unit structures by the impulse’ mutual attracting free information which sequentially equalizing the speeds-frequencies of the attracting information logic in resonance, assembles total observer logic.

2).The hierarchy of the logical cooperating units becomes asymmetrical with appearance of certain logical information bit on the extremal trajectory. It indicates the repeating free logic interval which the wave frequency[illustration not visible in this excerpt].

The EF rotating trajectory of three segments equalizes their information speeds joining in the resonance frequency during the space rotation on angle [illustration not visible in this excerpt]with frequency[illustration not visible in this excerpt]. That cooperates each third bit’s segment on the trajectory and logically cooperates each triplet structure in the unit hierarchy.

3).The appearance of the information bit on the trajectory indicates entrance the IPF information measure on its path from forming logical bit ln2. The IPF starts when logical asymmetry appears. This path indicates the end of the relative time interval[illustration not visible in this excerpt]. During the tree [illustration not visible in this excerpt]turns on space angle[illustration not visible in this excerpt], the third time interval [illustration not visible in this excerpt]2 indicates the end of the triple cooperative logic, which builds the triplet knot. Forming the cooperative knot in the triplet needs a time interval during which the triple free logic binds in the triplet bit. The time of creating the bit approaches [illustration not visible in this excerpt].The difference [illustration not visible in this excerpt]evaluates the time of binding. Thus, the wave space interval delivers the logical bit with wave frequency[illustration not visible in this excerpt], while the triplet knot appears with frequency[illustration not visible in this excerpt].

4). Start of delivering external energy for memorizing the logical bit identifies moment [illustration not visible in this excerpt]ending the interval creating the asymmetry. The asymmetrical logic of the resonance frequencies by this moment has already created. Along the IPF path, this moment starts after interval [illustration not visible in this excerpt] of creation logical bit ends, including the emergence of the knot binding the free logic. The interval of memorizing physical bit requires the same interval [illustration not visible in this excerpt] during which the entropy of logical bit erases. The external impulse, erasing asymmetric logical, starts with interval [illustration not visible in this excerpt] and ends with interval of encoding the bit[illustration not visible in this excerpt]. The external energy supplies on time interval [illustration not visible in this excerpt] including erasure the logical bit and its encoding, while interval of free logic [illustration not visible in this excerpt] is left for attracting a new bit, adding interval~0.02 of the opposite asymmetrical interaction. It brings total [illustration not visible in this excerpt] or the interval of external bit. When this bit’ free information starts encoding on interval[illustration not visible in this excerpt], interval 0.02 has been already spent. That now identifies its interval of encoding [illustration not visible in this excerpt]-the same as the external impulse interval of asymmetry, and therefore, the frequency, initiating the encoding, equals [illustration not visible in this excerpt]in sequence[illustration not visible in this excerpt].

Thus, the sequence of segments on the EF-IPF extremal trajectory carries its wave function’ frequencies self-structuring of the unit logical bit hierarchy that self-assembles total observer logic, which controls memorizing and encoding both physical bits and their unit hierarchical structure.

5).The segments’ impulses on the EF spiral trajectory sequentially interact through the above frequencies on the time–space locations connecting the segments in trajectory.

Hence, the sequence of segments assembles the resonance frequencies of the self –forming structural units.

Thus, the sequence of segments on the EF-IPF extremal trajectory carries its wave function’ frequencies self-structuring of the unit logical bit hierarchy that self-assembles total observer logic, which controls the memorizing and encoding both physical bits and their units’ hierarchical structure.[illustration not visible in this excerpt]

**Proposition 3.**

1). The observer logical structure represents the EF-IPF space-time trajectory (Figs.3, 4), where each of its sequential segments runs logic of the created structural triplet: the nineth segment integrates related IN node information, the 27-th segment integrates information of 27 nodes of higher level IN, and so on.

This logic consists of the mutual attracting free information, which, sequentially interacting, self-organizes the cooperative logical rotating spiral loops enclosing all observing information. This logic self –forms a hierarchy of the logical unit structures through the sequence of segments assembling by resonance frequencies.

Each triplet logical structure models Borromean ring consisting of three topological circles linking by Brunnian link-loop. The spinning top trajectory, FigB, as well as EF-IPF trajectory model a chain of Borromean rings.

2). The observer logical structure carries the logic of information frequencies {[illustration not visible in this excerpt][illustration not visible in this excerpt][illustration not visible in this excerpt],[illustration not visible in this excerpt][illustration not visible in this excerpt][illustration not visible in this excerpt]….}, where each wave of trajectory’ segment delivers sequence {[illustration not visible in this excerpt][illustration not visible in this excerpt][illustration not visible in this excerpt]}. Two sequential segments syncronozes at resonance frequency [illustration not visible in this excerpt], while the triplets synchronizes at resonance frequency [illustration not visible in this excerpt].Therefore to hold the observer minimal logical structure one bit, the observer logic should carry frequencies [illustration not visible in this excerpt], while to hold the triplet units logical structures, the observer should carry frequences [illustration not visible in this excerpt]. Each consecutive segment’ wave function along the EF-IPF trajectory will automatically deliver the needed frequencies [illustration not visible in this excerpt]and [illustration not visible in this excerpt]to hold a growing hierarchy of the cooperating logical units.

3). The logical loop wide determines the invariant impulse’ time interval[illustration not visible in this excerpt]. However, the growing density of consecutive impulses of the trajectory sequentially squeezes this interval within the invariant impulse. That squeezes the time-space sizes of the logical loop and increases frequencies [illustration not visible in this excerpt]and [illustration not visible in this excerpt]along the loop according to growing the triple density for each current trajectory impulse. To carry these synchronized frequencies, the logic loop rotation and movement require a small energy, whose minimum is equivalent of logical bit=ln2.

4). This observer logic loops synchronizes the triple rhythms along the EF-IPF trajectory in a melody, or melody of the rhythms of Borromean rings’ hierarchical chain. [illustration not visible in this excerpt]

Therefore, the wave function, initiating self-forming the observer cognition, emerges along the EF-IPF extremal trajectory, in form of probabilistic time wave in probability field, whose impulse observation starts the microprocess developing space and continues it form the rotating space-time probability wave.

Emergence the opposite asymmetrical interaction (Figs.2A,2B) forms the space–time wave function certain, as well as the observer’ cognitive logic.

The wave function is attribute of observing interactive process which describes the minimax EF-IPFextremal.

**5. The multi-level self-encoding the hierarchical cognitive logic in intelligence code enclosing the Observer information geometrical structure.**

Each assembling logical unit’ free logic, possessing the topological asymmetry, interacting through resonance frequency, can open a switch to an external impulse carrying the Landauer’s energy starting erasure entropy and memorizing the information up to its encoding the memorized bit.

The multiple local bits, encoding the self-organized cognitive logic at all hierarchical levels, self-organize the observer cooperative code up to the highest hierarchical level.

Since such code holds the external energy, it physically organizes the multiple structural units, the IN with their local codes in coding information structure of information Observer.

The code, self- organizing the multiple local codes, we call *observer intelligence.*

The logical switching of the free information at all level performs the *intelligence functions*, which generate each local code.

Therefore, these functions are also distributed hierarchically along the assembling logical units of the cognitive loop.

**Proposition 4.**

1).To memorize and encode the unit logical hierarchy in physical information structure, the observer logic provides the above sequence of frequencies [illustration not visible in this excerpt] and [illustration not visible in this excerpt] along the loop according to growing the triple density for each current trajectory impulse. That identifies the sequence of the moments for entrance external information with energy for both memorizing the units hierarchy and its physical encoding. This sequence of frequencies is the same that hold the observer logic which delivers the observer logic minimal energy.

The attracting free information of the memorized bit encodes the physical bits, connecting them, first, in the triplets, second, in the INs nested nodes, and then, in each IN ending triplet code.

Therefore, along the IPF trajectory emerges triplet code in the sequence of segments whose frequency sequentially brings logical triple following its physical encoding. The cognitive process at each triplet level preempts the memorizing.

2).The spinning three-dimensional space wave functions, synchronizing the segments, synchronize the triplet code in rotating spiral structure. The cooperative code which the switching time clock synchronizes has rhythmical sequence of time intervals (windows) where each observer logical structural unit gets the needed external energy. The clock time course assigns the frequency through the repeating time intervals, which determine each local resonance frequency of assembling the structural unit. These frequencies-local rhythms identify the moments of ending interval of the free information at each unit level, or the interacting cognitive and intelligence local actions.

Thus, cognitive logic logically encodes intelligence of this logic.

3).Each stable observer conserves its widows according to the variation law regularities.

4). Each bit, memorized in the conjugated interactive bridge (Fig.4, left), divides the trajectory on reversible process section, excluding the bit bridge, and the irreversible bridge between the reversible sections, on the triplet knot, located on the cone vertex. The information logical dynamics memorizes as *information physical dynamics*.

The EF-IPF optimal observing process and the information dynamics produce the observer double spiral structure (DSS), Fig.8, which encloses finally the predicting cooperative code. The observer logical structure self-connects the local codes in the observer cooperative code, which encodes all these structures in the space-time information structure of information observer. The observer triplet code memorizes the observer cooperative information structure and enhances multiple rhythms of the local structural units. The cooperative DSS coding structure memorizes total collected observer information quantity and quality, which determines the observer cooperative complexity. This coding structure, which self-organizes all assembled information, integrates function of cognition and intelligences.

The EF-IPF observing process and information dynamics artificially design the DSS.

5). Multiple observations build numerous of such DSS space-time structures which integrate in the information geometrical structure of Information Observer (Fig.10).

6).The quality of information, memorized in an ended triplet of the observer hierarchical informational networks and domains, measures level of the observer intelligence. Maximal level of emerging intelligence measures maximal cooperative complexity, which enfolds maximal number of the nested INs structures, memorized in the ending node of the highest IN. Number of level limits minimal space speed ending the wave function; its information-general limitation [34].

7).All information observers have different levels of intelligence which classify the observer by these levels.

8).The multiple levels of the observer interacting logical and intelligent functions develop self-programming and computation which enhance collective logic, knowledge, and organization of diverse intelligent observers. The intelligent actions and the intelligence of different observers connect their level of knowledge, build and organizes the observers IN’s information space-time logical structure. Increasing the INs enfolds growing information density that expands the intelligence, which concurrently memorizes and transmits itself over the time course in an observing time scale.

9).The intelligence, growing with its time-space region, increases the observer life span, which limits a memory of the multiple final IN ending node in the extended region.

10).Since whole multiple IN information is *limited*, as well as a total time of the IN existence, the IN self-replication arises, which enhances the collective's intelligence, extends and develops them, expanding the intellect's growth.

11).The self-organized trajectory with the wave functions, evolving IN’s time-space distributed information structure, models *artificial intellect.*

12).The invariance of information minimax law for any *information observer* preserves their common regularities of accepting, proceeding information and building its information structure.

That guarantees objectivity (identity) of basic observer’s individual actions with *common information mechanisms.*

The common mechanism enables creation of *specific* information structures for each particular observed information, with individual goal, preferences, energy, material carriers, and various implementations.

13).Multiple communications of numerous observers (by sending a message-demand, as quality messenger (qmess) [120], enfolding the sender IN's cooperative force, which requires access to other IN observers allowing the observer to increase the IN personal intelligence level and generate a collective IN's logic of the multiple observers.

This not only enhances the collective's intelligence but also extends and develops them, expanding the intellect's growth.

14).The artificial designed DSS information measures total IQ of this observer. The cooperative code information of each natural (individual) observer encodes its IQ. The difference of these IQs measures a distinctness of their intelligence.

The maximal information, obtained in the observation, allows designating the maximal achievable IQ measures to optimal AI observer DSS design by the EF-IPF’ VP. The space-time information structure, encoding all the EF-IPF integrating observed information (Fig.10), analytically designs the AI information observer. The observing information of a particular observer is limited by the considered constrains of this observation.

The constrains limit conversion of observing process in the information process.

The thresholds between the evolving stages of the observation limit the stages’ evolution.

All these limit the integral cognitive information and the following intellective actions, which also limit the amount of free information reducing ability of making intelligent IN’s connections. [illustration not visible in this excerpt].

We believe the observer current mind is integrated information of causal logic distributed at the observer hierarchical levels, or integral of cognitive logic; the memorized mind integrates the physical cooperative DSS code. That integral according to the VP enables prognosis new observation process which creates new logic and extended code intelligence that renews multiple observations developing evolving observer with its regularities and individuality.

The intelligent observer has two main attributes: multi-levels cognition and intelligence.

**6. The intelligence code self-controls the observer physical irreversible processes and evolution.**

The intelligence code, initiating each new observation, self-controls the observer evolution during multiple observations as the followings stages.

1. The observing inter-action of the impulses with the field’ energy, cutting the impulse entropy, develops its conversion to the emerging bit of information, which self-participates in evolving interactions reducing the observable uncertainty. These interactions, holding probabilistic and then information logic, evolve the stages and levels of evolution process.

2. The formal analysis the stages and levels of the evolution [34], starting from multiple interacting impulses of observable random field shows that each following level enables self–generate next level and self-form a nested time-space pyramidal evolution’ stages-an hierarchical network structure. The continued interaction delivers new level’s information through each level’s feedback with other levels along the hierarchy of levels and stages down to the field. Information attraction, which measures quantity of information requested by the IN stage, determines the evolution *potential* of this evolutionary stage.

Information complexity of evolution dynamics [124] measures density of collective information enfolded in the IN stage, which defines the information value of the stage’ potential of cooperation.

3. The specific constrains imposed on each level, stage, and domain limit each of IN of these structural units.

When the observer attempts to increase information quality by overcoming-destroying its specific constrain, the accidentally arising singularities enable renovating the observer constrain location, bringing new original (personal) level, or stage, and the domain quality distinctive from the evolution of information dynamics within the constrains.

Other non-cooperating singularities contribute the random field, which self-closes a current chain of the observer *personal* evolution. Interactive acquisition, bringing increasing quality information, allows automatically self–overcoming some thresholds decreasing the observer *diversity.*

4. Since acquisition information by its interactive binding increase the IN parameter of node hierarchy ([illustration not visible in this excerpt]), it decreases the frequency with tendency of growing information quality in evolving IN. That delivers information forces, which enable overcoming a threshold and transfer to next stage of the growing quality.

It allows self-adjusting the constraints and threshold during the evolving observation in a creative observer.

5. The observers, reaching potential threshold on the time-space locality along the process trajectory, but unable to overcome it, will settle between the thresholds and eventually disintegrate.

6. Evolution automatically selects the observer remaining on the trajectory and eliminates others by memorizing the threshold through its encoding. That performs the local intellectual functions emanates from the cooperative intellectual code which thereafter control each stage of evolution. It establishes the evolution *hierarchy* of the evolving nested hierarchical structure of the IN levels, stages and domains.

The evolution *stability* depends on ability of memorizing information of each evolving stage.

An observer, which unable to cross the threshold of the stage stays stable within its stage.

That memorizes *diversity of the selective and stable observers.*

7. Such evolution develops without any preexisting laws following each observer trajectory, which includes all its levels, stages and domains, and potential thresholds between them.

The observer regularity rises in impulse observation from the self-created virtual observer up to real observers, where each impulse is max-min action transferred to the following through mini-max action. This variation principle imposes information form of the law, which encloses the following regularities. The process extreme trajectory, implementing that law’s mathematical form, releases these regularities in most general information form. The physical process on this trajectory is information macrodynamics [27, 28,117] in form of irreversible thermodynamics [121,122,123].

The observer self-develop specific regularities in prolonging observation and self-evolution which self-creates a law with extending regularities.

These abilities initiate the chain of virtual, logical, and information causalities, which extreme trajectory includes.

8. Self-encoding information units in the IN code-logic and observer’s computation, using this code, serves for common external and internal communications, allowing encoding different interactions in universal information language and conduct cooperative operations both within and outside the domains and observer. That unites the observers.

9. The emergence of observer time, space, and information at multiple hierarchical levels follows the emerging evolution information dynamics creating multiple evolving observers with information mechanisms of cognition and .intelligence. The distributed intelligence coding actions at each hierarchical level control entrance the needed external physical processes. whereas DSS code carries the cognitive thermodynamics.

**7. The interacting intelligence observers enable understanding meaning in each communication (Sec.8).**

**8. The information observer self-develops converting mechanism [34] that coordinates connection of the observer inner and external time, allowing transform the observing wave function to the observer inner processes.**

**9. The stages of artificial designed information observer open path toward artificial brain.**

**[illustration not visible in this excerpt]**

(Author’s own work)

**Fig.11. Schematic of the main operations with the objective and subjective observers at acquisition information creating brain cognition, neurodynamics, memory and learning applying the approach formalism.**

The brain physical structure models the DSS coding space-time rotating structure (Figs.4, 8-10) materialized through an advanced technological computation.

Both logical and intelligence distributed functions, which carry the multiple frequencies, have analogy of nervous system, which can materialize an advance electrical conducting system.

Each material should satisfy optimal physical irreversible process trajectories integrating the reversible segments implementing the described observer functions in observation, getting information, memorizing, cognitive logic, encoding, and acceptance, moving, all others.

**Significance of main finding: The composite structure of observer’s generated information process, including: **

**1.** *Reduction the process entropy under probing impulse, observing by Bayesian probability’ links that increases each posterior correlation; the impulse cutoff correlation sequentially converts the cutting entropy to information that memorizes the probes logic in Bit, participating in next probe-conversions; creation wave function in the observations.*

*2* *. Identifying this process stages at the information micro-and macrolevels, which govern the minimax information law;*

*3* *. Finding self-organizing information triplet as a macrounit of self-forming information time-space cooperative distributed network enables self-scaling, self-renovation, adaptive self-organization, and cognitive and intelligent actions.*

*4*. *Finding information structure of artificial designed observer toward artificial brain.*

*The results’ analytical and computer simulations validate and illustrate the experimental applications*.

**Areas of Applications**

**I. The selected examples and reviews of the scientific investigations in different area of natural sciences illustrating the information regularities, and supporting the theoretical information results**

**1. General Physics **

1.The physicists [45] demonstrate a first direct observation of the so-called vacuum fluctuations by using short light pulses while employing highly precise optical measurement techniques, proving no the absolute nothingness. The positive (red) and negative (blue) regions are randomly distributed in space and they change constantly at high speed. Vacuum is filled with finite fluctuations of the electromagnetic field, representing the quantum ground state of light and radio waves in the quantum light field. The found access to elementary time scales is shorter than the investigated oscillation period of the light waves. It confirms the approach initial assumption of an initial random probability field, and an observer of this field should have a probabistic observation.

2. Gluons in Standard Model of Particle Physics exists only virtually mediating strong forces at interactions [46]; each carries combination of colors charges; whopping colors and holding two colors own at pair interactions; the increasing interaction forces conserve their shape like a string. Higgs particle also matched the probabilistic observation. The illustration [46] looks similar to our virtual processing.

3. In sub-Plank process [47], quantum sates, confined to phase space volume and characterized by `the classical action', develop sub-Plank structure on the scale of shifting-displacing the state positions to orthogonal, distinguishable from the unshifted original. The orthogonality factor moves classical Plank uncertainty in random direction, which reduces limit of a sensitivity to perturbations. It relates to origin of the structure of virtual observer (Sec. I).

4. Measurement the probability distributions for mapping quantum paths between the quantum states [48] “reveals the rich interplay between measurement dynamics, typically associated with wave function collapse, and unitary evolution of the quantum state as described by the Schrödinger equation”. The wave function collapse only in final measurement. The measurement starts with time distributed ensemble trajectories whose rotation in the waveguide cavity produces a space coordinate to the ensemble.

5. Study the non-equilibrium statistical mechanics of Hamiltonian systems under topological constraints [49] (in the form of adiabatic or Casimir invariants affecting canonical phase space) reveals the correct measure of entropy, built on the distorted invariant measure, which is consistent with the second law of thermodynamics. The decreasing entropy and negative entropy production arises in arbitrary a priori variables of the non-covariant nature of differential entropy, associated with time evolution of the uncertainty.

Applying Jaynes' entropy functional to invariant entropy measure requires Euler's rotation with angular momentum identifying appearance of the Cartesian coordinate which satisfies the topological invariant.

These results agree with the applied EF functional, invariant measures of impulse’s entropy, and appearance of space coordinate in the rotation preserving the impulse measure (Secs.I-II).

From [49a] it follows: “The Japan Sea wave statistics of the entropies has a more pronounced tail for *negative entropy* values, indicating a higher probability of rogue waves”.

**2. Neural Dynamics. Integrating an observing information in neurodynamics**

In [50] we have analyzed the selected multiple examples and reviews of different neurodynamic processes.

Here we add some recent results, studying the following publications.

1. According to [51], “Recent discussions in cognitive science and the philosophy of mind have defended a theory according to which we live in a virtual world .., generated by our brain…”; “this model is perceived as if it was external and perception independent, even though it is neither of the two. The view of the mind, brain, and world, entailed by this theory has some peculiar consequences”… up virtual brain thoughts. Experimental results [50] show that Bayesian probabilistic inference governs special attentional belief updating though trials, and that directional influence explains changes in cortical coupling connectivity of the frontal eye fields which modulate the “Bayes optimal updates”. The frequency of oscillations which "strongly modulated by attention" causes shifts attention between locations. Neurons increasingly discriminate task-relevant stimuli with learning, modify sensory and non-sensory representations and adjust its processing preferring the rewarded stimulus. This causal stimulus-response, reflecting anticipation choices, predicts the features of observer formalism. Brain learns distinction between what is important and what is not, discriminating between images and optimizing stimulus processing in anticipation of reward depending on its importance and relevance.

2. Existence of DSS' triple code confirms [52], uncovered that a neuron communicates by a trinary code, utilizing not only zeros and ones of the binary code but also minus ones. The experiment [53] provides “evidence for the analog magnitude code of the triple -code model not only for Arabic digits but represents “semantic knowledge for numerical quantities...” Results [54] demonstrate decreasing entropy in brain neurodynamic for measured frequency spectral densities with growing neurodynamic organization. Influence of rhythms on visual selection report results [55].

3. Importance of decisional uncertainty in learning focuses results [56], where stimulus-is an impulse, decision–getting information, greater distance-more probability-closer to information, comparing that to correct choice. Evidence from experiments [57] show that “specific region of the brain appears essential for resolving the uncertainty that can build up as we progress through an everyday sequence of tasks, a key node in a network preventing errors in keeping on track. Study [58] shows how learning enhances sensory and multiple non-sensory representations in primary visual cortex neuron.

4. Paper [59] describes how to build a mini-brain which is not performing any cogitation, but produces “electrical signals and forms own neural connections -- synapses -- making them readily producible test beds for neuroscience research”.

5. Author [60] proposes that all cells are comprised of series of highly sophisticated “little engines” or nanomachines carrying out life’s vital functions. The nanomachines have incorporated into a single complex cell, which is a descendant of a three-stage combination of earlier cells. The built complex signaling networks (Quorum Sensing) allowed one microbe to live inside and communicate with its host, forming a binary organism. Third entity, a bacterium that could photosynthesize, gained the ability to synchronize its mechanism with the binary organism. This “trinity organism” became the photosynthetic ancestor of every plant on earth that have driven life since its origin. "Resulting complex nanomachine forms a ‘Borromean photosynthetic triplet’.

6.Analysis of all selected multiple examples and reviews of different neurodynamic processes, substantiates that our approach’ functional regularities create united information mechanism, whose integral logic self-operates this mechanism, transforming multiple interacting uncertainties to physical reality-matter, human information and cognition, which originate the observer information intellect. The information mechanism enables specific predictions of individual and collective functional neuron information activities in time and space. Neurons’ microprocesses retrieve and external information, including spike actions, related to the impulses, which generate the inner macrodynamics. The identified cooperative communications among neurons assemble and integrate their logical information structures in the time-space hierarchy of information network (IN), revealing the dynamics of IN creation, its geometrical information structure, triplet code, and limitations.

The found information forces hold a neuron's communication, whose information is generated automatically in the neuronal interactions. Multiple cooperative networks assemble and integrate logical hierarchical structures, which model information brain processing in self-communications.

The information mechanism’s self-operating integral logic reveals: the information quantities required for attention, portioned extraction, its speed, including the needed internal information dynamics with the time intervals; the information quality for each observer's accumulated information by the specific location within the IN hierarchical logic; the information needed for the verification with the digital code, generated by the observer's neurons and their cooperative space logic; the internal cooperative dynamics build information network (IN) with hierarchical logic of information units, which integrates the observer required information in temporary build IN’s high level logic that requests new information enclosing in the running observer’s IN.

The IN nodes enfold and memorize its logic in self-forming cooperative information dynamical and geometrical structures with a limited boundary, shaped by the IN-information geometry; the IN hierarchical locations of the nodes provide measuring quality of information, while the IN-ending node memorizes whole IN information.

The IN operations with the sequentially enclosed and memorized information units perform logical computing using the doublet-triplet code; the cooperative force between the IN hierarchical levels selects the requested information as the observer’s dynamic efforts for multiple choices, needed to implement the minimax self-directed optimal strategy.

The information quantity and quality, required for sequential creation of the hierarchical INs values, self-organize brain cognitive and intelligence action, leading to multicooperative brain processing and extension of intelligence.

**3. Self-organizing dynamic motion of elementary micro- and macrosystems**

1. *The experiments and computer simulations of collective motion* exhibit systems ranging from flocks of animals to self-propelled microorganisms. The cell migration established similarities between these systems, which illustrates following specific results. The emergent correlations attribute to spontaneous cell-coupling, dynamic self-ordering, and self-assembling in the persistence coherent angular motion of collective rotation within circular areas [61]. The persistence of coherent angular motion increases with the cell number and exhibits a geometric rearrangement of cells to the configuration containing a central cell. Cell density is kept constant with increasing the cell number. The emerging collective rotational motion consists of two to eight cells confined in a circular micropatterns. The experimentally observed gradual transition with increasing system size from predominantly erratic motion of small cell groups to directionally persistent migration in larger assemblies, underlining the role of internal cell polarity in the emergence of collective behavior. For each nucleus, the angular position was evaluated respectively to the circle center, and angular velocity is normalized and averaged over the individual angular velocities of the N-cell system. Circle size increases in such a way that the average area per cell is constant at approximately 830 μm2. Probability distribution of the mean angular velocity for systems containing two to eight cells is fitted by a single Gaussian and their mixture is two Gaussians. For all N cells, the probability distribution displays symmetry breaking into clockwise and counterclockwise rotations. Both directionalities are almost equally represented, with a small bias towards clockwise rotation. Average mean squared displacement indicates ballistic angular motion for all cell numbers, while the averaged the displaced intervals of nucleus exhibited diffusive behavior.

Both experiments and simulations showed consistently that the persistence of the coherent state increases with the number of confined cells for small cell numbers but then drops abruptly in a system containing five cells. This is attributed to a geometric rearrangement of cells to a configuration with a central only weakly polarized cell.

It reveals the decisive role of the interplay between the local arrangement of neighboring cells and the internal cell polarization in collective migration. The similarities suggest universal principles underlying pattern formation, such as interactions rules [62-66], the systems’ generic symmetries [67-69].

2. Confinement stabilizes a bacterial suspension into a spiral vortex

1.‘Enhanced ordering of interacting filaments by molecular motors [70] demonstrate the emergence of collective motion in high-density concentrated filaments propelled by immobilized molecular motors in a planar geometry”. At a critical density, the filaments self-organize to form coherently moving structures with persistent density modulations. The experiment allows backtracking of the assembly and disassembly pathways to the underlying local interactions. The identified weak and local alignment interactions essential for the observed formation of patterns and their dynamics. The presented minimal polar-pattern-forming system provide new insight into emerging order in the broad class of bacteria and their colonies [71-74], and self-propelled particles [75-79].

2. Confining surfaces play crucial roles in dynamics, transport, and order in many physical systems [80-83]. Studying [84] the flow and orientation order within small droplets of a dense bacterial suspension reveals the influence of global confinement and surface curvature on collective motion. The observing competition between radial confinement, self-propulsion, interactions, other induces a steady single-vortex state, in which cells align in inward spiraling patterns accompanied by a thin counter rotating boundary layer.

3.The cited experiments validate: “spontaneous cell-coupling, dynamic self-ordering, self-assembling in the persistence coherent angular motion of collective rotation within circular areas”, the displacement in angular motion with diffusive behavior of displaced intervals, emergence of collective order confined on a curved surface, others.

4. According to recent discovery [85], “the protein stable shapes adopted by a few proteins contained some parts that were trapped in the act of changing shape,the changes relate to how proteins convert from one observable shape to another”. From the process of RNA translation of DNA triplets to enzymes and aminoacids, all proteins start as linear chains of building blocks and then quickly fold to their proper shape, going through many high-energy transitions to proteins multiple biological functions.

**4. Experimental results, encoding, and practical implementations.**

Last theoretical results [86-88] and many previous [30,31,33,34] confirm the following applications.

Natural increase of correlations demonstrates experimental results [89], [90].

Coding genetic information reveals multiple experiments in [91], [92].

Experimental coding by spiking neurons demonstrates [93].

Evolutions of the genetic code from a randomness reviews [94].

That supports natural encoding through the cutting correlations and physically verifies reliability of natural encoding information process. The impulse cut-off method was practically applied in different solidification processes with impulse controls’ automatic system [95]. This method reveals some unidentified phenomena-such as a compulsive appearance centers of crystallization indicators of generation of information code, integrated in the IPF during the impulse metal extraction (withdrawing). (In such metallic alloys, the “up-hill diffusion, creating density gradients, is often observed” [95]). The frequency of the impulse withdrawing computes and regulates the designed automatic system to reach a maximum of the IPF information indicators.

(The detailed experimental data of the industrial implemented system are in [95] and [96]).

The automatic control regulator in the impulse frequency cutting movement was implemented for different superimposing electro-technological processes [97] interacting naturally. The comparative experimental results [98] confirm that advanced chemical- thermodynamic description of casting process coincides with information description by the IMD. Moreover, the IMD solutions leads to the optimal casing process. [99]. The automatic computer system, controlling horizontal casting process, have been implemented in the casting factory [100]. Examples of the method applications in communications, biological and cognitive systems, others are in [101], [102] and [103]. Retinal Ganglion Cells are the Eyes discrete impulse receptors interacting with observations and generating information which transmission integrates [104].

Encoding through natural chemical reactions connecting chemical molecules are in [105]. Experiments [106] confirm encoding coherent qubits in spinning electron locked in attractive “hole spin”. Other examples are quantum solar dots of semiconducting particles using for the information coding, retrieving images and encoding quantum information [107-109]. Natural Encoding of Information through Interacting Impulses published in [110]. Applications in biology, medicine, and economics along with related theoretical results are in [111-119].

**I. The computer restoration and simulation of the information model**

**1. The structure of computer procedure**

The diagrams, implementing the procedures of the model restoration and simulation of its performance, are shown on Figs.12.1a,12.1b, and 12.1c.

On Fig.12.1a, the statistical data from the microlevel process **[illustration not visible in this excerpt]** are used to identify matrix *A* of the macrolevel equation by computation of the correlation function and its derivative during each discrete interval **[illustration not visible in this excerpt]**, which compose the computed invariant **a** [illustration not visible in this excerpt] **.**

[illustration not visible in this excerpt] (Author’s own work)

**Fig 12.1a. Diagram of computation of the optimal model's process [illustration not visible in this excerpt][illustration not visible in this excerpt], using the microlevel's random process [illustration not visible in this excerpt] by calculating the correlation function [illustration not visible in this excerpt] its derivative [illustration not visible in this excerpt]; the object macrooperator [illustration not visible in this excerpt], invariant a, discrete interval [illustration not visible in this excerpt]; these allow simulating the optimal macroprocess [illustration not visible in this excerpt], the inner [illustration not visible in this excerpt] and output [illustration not visible in this excerpt] optimal controls. the inner [illustration not visible in this excerpt] and output [illustration not visible in this excerpt] optimal controls.**

[illustration not visible in this excerpt]

(Author’s own work)

**Fig.12.1b illustrates the scheme of computation of the optimal model's process [illustration not visible in this excerpt][illustration not visible in this excerpt] , using a given space distributed information [illustration not visible in this excerpt] per cross-section [illustration not visible in this excerpt] , the model's invariants INVAR, the time [illustration not visible in this excerpt] and space [illustration not visible in this excerpt] discrete intervals, eigenvalues [illustration not visible in this excerpt] of the model differential operator, and simulates the inner [illustration not visible in this excerpt] and the output [illustration not visible in this excerpt] optimal controls.**

The methodology is based on the connection of the model macrodynamics with the corresponding information geometry [29,86,89,111-119].

In this case, the microlevel stochastics are not used for the macromodel’s restoration.

Instead, the restoration requires the computation of the model’s basic parameters: dimension **[illustration not visible in this excerpt]**, uncertainty **[illustration not visible in this excerpt]**, and the curvature’s indicator **[illustration not visible in this excerpt]**; which allow finding the model optimal macroprocess, the synthesized optimal control, as well as the model’s hierarchy. The computation uses the primary parameters of a basic model (*n* *[illustration not visible in this excerpt]* *,* *[illustration not visible in this excerpt][illustration not visible in this excerpt]* *,k* **[illustration not visible in this excerpt]**) and the known parameters of the object’s geometry.

[illustration not visible in this excerpt]Fig.12.1c.

(Author’s own work)

Diagram Fig.12.1c. presents the functional schema of the IMD software operations: computing invariants INVAR, discrete moments **[illustration not visible in this excerpt]**, space coordinates **[illustration not visible in this excerpt]**, increment of volume **[illustration not visible in this excerpt]**, MC-complexity function, speeds **[illustration not visible in this excerpt]** and their difference **[illustration not visible in this excerpt]**, the current space parameters **[illustration not visible in this excerpt]**, polar coordinates **[illustration not visible in this excerpt]**, and gradients GRAD **[illustration not visible in this excerpt]** for a given space distribution’s cross-section F*; with calculating its radius **[illustration not visible in this excerpt]**, coordinates of center ** O ** -

**[illustration not visible in this excerpt]**, and a square

**[illustration not visible in this excerpt]**, which are used to compute the object space model’s minimal (optimal) parameter

**[illustration not visible in this excerpt]**.

The output variables are: optimal dynamic process **[illustration not visible in this excerpt]**, optimal controls **[illustration not visible in this excerpt]**, eigenvalues **[illustration not visible in this excerpt]** of the model differential equation, distributed space-time process **[illustration not visible in this excerpt]**, space’s current speed **[illustration not visible in this excerpt]** (**[illustration not visible in this excerpt]**) with the intervals of moving **[illustration not visible in this excerpt]** and stopping **[illustration not visible in this excerpt]**, which are computed by averaging a speed **[illustration not visible in this excerpt]**.

An estimated time of computation for each of the diagrams is approximately 3-5 minutes on conventional PC.

The computation can be performed during a real–time movement of the object’s cross section (Fig.12.1b), or through an input of the calculated object’s current statistics (Fig.12.1a).

Solving the considered complex problem in a real-time by *traditional computation* methods requires the developing of mathematical methodology and the software, which are able to overcome the method’s high computational complexity. For solving even, a part of the problem, the existing techniques require many hours’ computation on the modern main frames.

**2. Structure of the IMD Software Package**

*The software package transfers the IMD analytical methodology into the numerical procedures, computer algorithms and programs.*

The packet (consisting of 35 programs) includes the following modules for computation of:

- the identification procedure for the restoration of the object's equations;

- the parameters of space–time transformations and a time-space movement;

- the OPMC parameters, processes, controls, and the IN structure;

- the function of macrosystemic complexity;

- the transformation of the informational macromodel's characteristics into the appropriate physical and technological variables (using the particular applied programs).

The *main software modules* compute:

- the basic optimal macromodel parameters (*n* **,** [illustration not visible in this excerpt], *k*);

- the spectrum of the model’s eigenvalues **[illustration not visible in this excerpt]**;

- the macromodel informational invariants **a** [illustration not visible in this excerpt] **, b** [illustration not visible in this excerpt][illustration not visible in this excerpt] **;**

- the time-space intervals **[illustration not visible in this excerpt]**);

- the distribution of the optimal eigenvalues **[illustration not visible in this excerpt]** and the optimal controls **[illustration not visible in this excerpt]**;

- the geometrical macromodel’s coordinates and the space distributed macroprocesses **[illustration not visible in this excerpt]**;

- the procedure of the macrocoordinates’ cooperation and aggregation;

- the IN hierarchical macromodel structure and its macrocomplexity.

The formulas, algorithms, complete software, and numerical computation’s equations are given in the program package [125] (not included in this description).

The IMD software programs have been used for the practical solutions of the different applied problems including [99,103, 111-116].

*These results formalize Observer’s regularities in a comprehensive information-physical theory, connecting the virtual quantum world with the physical classic and relativistic world.*

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- Quote paper
- Vladimir S. Lerner (Author), 2017, The observer information processes and origin of the observer cognition and intellect, Munich, GRIN Verlag, https://www.grin.com/document/379103

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