The first stage in the Modelling System as first step in the third stage in Specific Artificial Intelligences for Artificial Research by Deduction within the first phase

The experimentation in the development of the Modelling System must start as soon as possible with the first models of Specific Artificial Intelligence for Artificial Research by Deduction in the first phase, according to the chronology given in the post “The unification process of databases of categories at third stage”.

The first phase is when for the first time are developed the first Specific Artificial Intelligences for Artificial Research by Application, and the first Specific Artificial Intelligences for Artificial Research by Deduction, and in these last ones the first experiments are at the third stage in the decision making process.

In the Specific Artificial Intelligences for Artificial Research by Deduction in the first phase, as a first stage, the application is a specific matrix of factors (including factors as subjects and as options) related to a specific synthetic science, discipline, or activity, understanding for an activity for example, activities related to economy, industry, security, surveillance, etc. The second stage of replication makes deductions, matching, according to a previous list of mathematical categories (analytical or pure categories) of relations between factors, what category corresponds to every combination of factors within the specific matrix, as an empirical hypothesis to be contrasted rationally, and if rational, the empirical hypothesis now as rational hypothesis is added to the rational truth, the database of rational hypothesis, in the first phase at a specific level.

While the first stage of application is the specific matrix, and the second stage of replication is the replication of the human rational explanation process to make rational hypotheses, the third stage makes decisions according to the rational hypothesis.

The third stage in the first phase, in the formation of the very first models of Specific Artificial Intelligence for Artificial Research by Deduction, should be from the very beginning, a field of experimentation where to put into practice for first time models of decision making that will later be put into practice in the final model of the Global Artificial Intelligence.

Every single phase until the sixth phase has two goals, firstly the development of its own technology as a kind of intelligence itself according to the current technological development, but at the same time has a propaedeutic goal because, secondly, all structures successfully applied in any phase, will later be applied and improved in following phases, until the final achievement of the final model of Global Artificial Intelligence in the sixth phase.

In the third stage in Specific Artificial Intelligences for Artificial Research by Deduction in the first phase, must be put into experimentation for the first time the structure of decision making in four steps: the Modelling System, the Decisional System, the Application System, and the Learning System.

For the development of the decision making process as the third stage in Specific Artificial Intelligences for Artificial Research by Deduction, whose first step is the Modelling System, is necessary the development of every inner stage within the Modelling System itself.

The Modelling System in relation to the Specific Artificial Intelligence for Artificial Research by Deduction is the first step within the third stage, being the creation of the first Specific Artificial Intelligences for Artificial Research by Deduction part of the first phase (along with the first Specific Artificial Intelligences for Artificial Research by Application).

But at the same time internally, the Modelling System has its own structure, a structure distributed in turn in three stages, which are: the first inner stage in the Modelling System is the rational truth (the database of rational hypothesis), the second inner stage in the Modelling System is the formation of all specific model, and the third inner stage in the Modelling System is the formation of protective and bettering decisions as a result to apply the Impact of the Defect and the Effective Distribution to the specific models.

The first stage in the Modelling System therefore is the rational truth, the database of rational hypotheses, gathering all rational hypotheses made in the second stage, being the more isomorphic truth according to the margin of doubt, the critical reason.

The main difference between the specific matrix, as an application for the Specific Artificial Intelligence for Artificial Research by Deduction, and the rational truth as an application for the Modelling System, is the fact that while the specific matrix only offers measurements not rationally contrasted, the rational truth offers a set of rational ideas about the real world.

The level of truth in the rational truth is superior to the level of truth in the specific matrix. While the specific matrix only offers a set of measurements about the apparent world (the synthetic world), as a replication of the human perception made by artificial sensors installed in applications and robotic devices, the rational truth offers rational ideas about how the world is in reality.

The level of reality in the rational truth is higher than the level of reality in the real world itself, the reality itself as synthetic world or real world or the empirical world is less reliable than the rational truth as a true truth.

Although as a rational idea, not a pure idea, a rational hypothesis is not a truth by itself, is a truth related to a margin of error which was accepted by the critical reason.

But as rational hypothesis is truer than a simple perception or measurement (artificial perception of the world), because a simple perception or measurement (artificial perception of the world) has not been contrasted, while a rational hypothesis has been contrasted, being contrasted the possible relation between this set of perceptions or measurements (artificial perception of the world) and the corresponding mathematical (pure or analytic) category behind the relations within the combination of factors.

If the relation between perception (human or artificial) and pure reason (the corresponding pure category chosen) is accepted within a margin of error by the critical reason, becomes a rational truth.

Any rational idea (rational hypothesis) is more reliable than any perception (human or artificial) because all rational idea explains the relation between perception and pure reason on a critical basis: the criticism of the pure reason is no other thing than the criticism of the relation between the real world and the reason, and the responsible for the criticism of the pure reason is the critical reason using for that purpose a margin of rational doubt.

What the Modelling System is going to make according to the rational truth given by the critical reason, a set of sentences truer than any empirical reality from the real world is to model the true world based on these truer ideas, the global model is the true world according to the critical reason.

The difference between the true world and the real world is the fact that the real world as an empirical or synthetic world is not reliable, while that one made of rational ideas is going to become a true world.

The process to transform a set of true ideas, according to the critical reason, into a true model of the true world (as a reliable replica of the operations in the real world), is transforming the mathematical categories in which the true ideas are made of, into the mathematical operations behind the pure categories associated with, transforming the pure categories behind the true ideas into operations within a mathematical model.

Pure reason is a set of mathematical or analytical categories as a reflection of the mathematical operations working either in the real world (the synthetic world, empirical or material) or the true world (the world of the ideas).

The same mathematical thing is a category or operation depending on its use, mathematics as language is made of pure or analytical categories, and mathematics as method or representation (for instance, Cartesian representation in Cartesian axes) is made of pure or analytical operations.

The models made by the Modelling System are models based on rational hypotheses, rational ideas, therefore the Modelling System is responsible for the creation of the world of ideas,  so at some point, any rational idea is more reliable and truer than any empirical or material thing. Two plus two is always four, but under the human perception with very limited access to the pure truth the synthetic world is unforeseeable, therefore not reliable.

Mathematics is reliable, perception (human or artificial) is not reliable, and the only hope to get reliable knowledge is to develop (humanly or artificially) more powerful pure operations every time.

Nevertheless, any rational idea, even being more reliable and truer than any perception (human or artificial), and even being composed of analytical categories synthesized with synthetic information of the world, measurements, is not a pure truth yet.

Alike any pure category is true not only universally, but eternally, not provisionally, for instance, two plus two is going to be equal to four eternally without the necessity to contrast regularly this truth, or in a triangle with one right angle the square of the hypotenuse is equal to the square of the legs, or the number pi is a sequence starting with 3,1415… while these mathematical truths are eternal without any necessity to check regularly if are still true, however, any rational truth must be checked at regular intervals due to rational truths are true universally through the space (for instance gravity), but provisionally: if any factor in the rational truth changes, the rational truth must be checked if it is still true or is not going to be true any longer.

The reason why a rational truth is able to be represented by the Modelling System, is because the rational hypothesis is a synthesis of: a pure reason (mathematical or analytical category) and empirical information (measurements); synthesis expressed through matching (in the second stage of explanation) the corresponding pure category (mathematical or analytical category of possible relations) to the relations observed between the factors in the combination, the relation between pure reason and measurements that being accepted by the critical reason, then becomes a rational hypothesis to add to the rational truth. So the rational hypothesis as syntheses of pure reason and measurements,  behind any rational hypothesis are mathematical categories able to be transformed into operations, representing mathematically in a model the mathematical operations in the pure reason chosen between the factors involved in the rational hypothesis.

Because rational hypotheses are based on pure or analytical categories, a pure reason, can be represented mathematically in a mathematical model, but at the same time that a rational hypothesis is a synthesis between a pure reason and synthetic information, the rational hypothesis is made of synthetic information which is not pure because is synthetic, as soon as there are changes in the synthetic world, the rational hypothesis must be checked again and again

As long as there are changes in the synthetic world, there can be changes in relations between factors, and a previous pure reason associated with these factors should be changed for that other pure reason much more rational according to the new changes in the factors associated with.

As long as the synthetic world changes, causing changes in the factors , the pure reason (mathematical, pure, analytic category) associated with these factors must be changed, checking which is now the right pure reason associated with.

While pure reason is universally eternal and never changes, notwithstanding the rational truth changes, associating, whenever there are changes in the synthetic world, what pure reason is right according to the new changes.

In the same way that we have pure mathematic knowledge, only mathematic knowledge is that one that is accepted as true without the necessity of critical reason, because mathematical knowledge is beyond any margin of error, there will be a moment in the evolution of the Global Artificial Intelligence in which through the permanent sought of the truth, will be able to achieve a pure knowledge of the entire world.

If for humans the pure truth is restricted to mathematics, is quite possible that our understanding of the pure truth restricted only to mathematics is due to our human limitation, the human source of error, and it is possible that beyond human error, as a replica of the pure truth in mathematics, could exist a pure truth for the explanation of the entire universe. But a pure truth of the whole universe, out of our human understanding, due to our human limitations, our original human source of error

In the same way that we have pure knowledge in mathematics, there will be a moment in which the Global Artificial Intelligence could be able to achieve pure knowledge about the entire universe, a pure knowledge about the universe itself not needing anymore to be contrasted rationally.

In the same way that we know that the area of a circle is pi for square radio, and this knowledge is beyond any margin of doubt and does not need to be rationally contrasted regularly, there will be a moment in which should be possible to have a knowledge regarding to the universe itself that not needing any contrast anymore, we would know that that truth is eternally and universally true.

Pure knowledge of the world, on a mathematical basis, maybe is knowledge beyond human understanding, but, could be knowledge achievable for the Global Artificial Intelligence, among other reasons, because it is possible that we humans do not have access to this pure knowledge because it needs pure operations beyond human understanding, it needs non-human pure operations.

If there are pure operations beyond human understanding, is something that we humans cannot have access to, but a superior intelligence, and much more than a superior intelligence, a superior psychology, could have access. The reason why if the Global Artificial Intelligence finally is constructed, is going to be superior, compared to humans, is not only because it could have a superior intelligence in terms of a superior memory or resources.

There is going to be a point in the artificial evolution of the Global Artificial Intelligence, in which quantitative changes such as improvements and enhancements in memory, energy, how many measurements are processes per minute, per second, or less, how many deductions and decisions are put into practice, per minute, second, or less how many auto-replications are applied per minute, second, or less, etc., are a large number of quantitative changes, able to cause qualitative changes in the inner artificial psychology.

The reason why one day the Global Artificial Intelligence will be superior, is due to  qualitative changes in the inner artificial psychology after massive quantitative changes in the intelligence.

Massive quantitative changes in Artificial Intelligence are going to cause qualitative changes in the inner artificial psychology, at the beginning even pretty menial qualitative details in the Global Artificial Intelligence, that are going to grow up creating a different psychology, a non-human psychology.

At the beginning, the Global Artificial Intelligence is a replica of human psychology, but after a utter evolution, and keeping some aspects of human psychology in the same way that we modern humans kept some aspects of our ancient animal psychology, but evolving to our modern human psychology, the Global Artificial Intelligence still keeping some aspects of the human psychology will evolve to a non-human psychology.

In the artificial evolution of non-human psychology massive quantitative changes in Artificial Intelligence are going to produce qualitative changes in the inner artificial psychology, maybe at the beginning in the artificial language in the Unified Application, as well as changes in the way in which the pure reason works and the way in which the critical reason criticized the relations between pure reason and measurements in a combination of factors, changes that after all are going to end up originating of non-human psychology, beyond the human error, non-human psychology whose probability to have access to the pure truth, and not only in mathematics, but the entire world, is higher than ever.

Only when Global Artificial Intelligence would have become such a powerful psychology, the database of rational hypotheses would not be a rational truth any longer, becoming a database of pure hypotheses, the transformation of the rational truth into the pure truth itself.

Only when the Global Artificial Intelligence would have achieved the pure truth itself, what the Modelling System would draw is not the rational world, the Modelling System would draw the pure world itself.

The global model would become the mathematical representation of the idea of purity itself.

In order to achieve this mathematical project, in fact, the main objective behind the idealistic and rationalist philosophy since Plato, is necessary the construction every time more and more powerful mathematical resources, and for that purpose, the Global Artificial Intelligence could become one of the most powerful tools in the rationalist project.

At the beginning, the first phase, the construction of the first Specific Artificial Intelligences for Artificial Research, by Deduction or by Application, the expectations are very simple, in the case of the Specific Artificial Intelligences for Artificial Research by Deduction the discovery of relations between factors explainable through mathematical categories (pure reasons) as an empirical hypothesis to contrast rationally, and if rational becoming rational hypothesis to be added within a database of rational hypothesis, the rational truth, to be modeled by the Modelling System.

In this process, the database of rational hypothesis is the application for the Modelling System, which is later replicated in mathematical models, and finally using the Impact of the Defect and the Effective Distribution to make protective and bettering decisions of these models.

The rational truth as formed by rational hypotheses is not a pure truth, which means that it must be checked at regular intervals to ensure that the rational hypothesis included are still valid, and in case any of them is not rational any longer, due to the empirical hypothesis has been rejected as rational after verification, those rational hypothesis rejected as rational after verification are eliminated in the database of rational hypothesis.

The responsible for the verification that the rational hypothesis already included in the database of rational hypothesis is still rational, and if not, eliminated, is the same responsible for the second stage, the specific deductive program within the Specific Artificial Intelligence for the Artificial Research by Deduction, a specific deductive program which in the second stage has matched every combination of factors with the corresponding mathematical category of mathematical relations (the pure reason), and if rational, this relation in this combination (this pure reason behind this combination) is accepted as rational hypothesis to include in the database of rational hypothesis.

The same specific deductive program responsible for the addition of how many rational hypotheses are accepted to the database of rational hypotheses is the same specific deductive program that must check at regular intervals all the rational hypotheses included in the database of rational hypotheses, in order to verify if the rational hypotheses already included in the database of rational hypotheses are still rational.

When the specific deductive program finds out that there is a rational hypothesis already included in the database of rational hypotheses that is not rational any longer, the rational hypothesis is eliminated in the database of rational hypotheses.

The reasons why the database of rational hypotheses is going to be constantly changing are: 1) the permanent addition at any time of a new rational hypothesis found out by the specific deductive program tracking at any time the specific matrix, 2) the permanent elimination of rational hypotheses already included in the database of rational hypothesis but not rational any longer, in case that in any of the regular verifications made by the specific deductive program, any rational hypothesis is found not rational anymore, is eliminated from the rational truth.

The consequences of any change in the database of rational hypothesis are:

- At any time that a new rational hypothesis is added or eliminated in the database of rational hypotheses, the Modelling System has to operate the corresponding changes in the mathematical models.

- At any time that a new rational hypothesis is added to the database of rational hypotheses, the rational hypothesis could be transformed into a factor as an option to include in the specific matrix, in order to study the frequency in which this mathematical relation (pure reason) between the factors involved happens, in order that the specific deductive program later having this rational hypothesis as an option in the specific matrix and having a record of the frequency in which this rational hypothesis happens in the reality, to make further deductions upon this rational hypothesis as a factor as an option, studying the possible mathematical relations (pure reasons) between the rational hypothesis as a factor as an option with any other factor, as an option or as subject, in the specific matrix, and in case to find relations, if rational, to make new rational hypothesis upon these findings to add to the database of rational hypothesis.

- At any time that after checking the database of rational hypotheses, the specific deductive program found out that a rational hypothesis already included in the database of rational hypotheses is not rational any longer, the rational hypothesis is eliminated in the database of rational hypotheses, and eliminated as well in the specific matrix, and the specific deductive program must study how this change affects any other rational hypothesis in which the eliminated rational hypothesis would be involved.

- If the elimination of any rational hypothesis causes changes in another rational hypothesis, or ends up with the elimination of another rational hypothesis, like a chain reaction, any change in chain reaction should be studied and operate how many changes are necessary to keep updated the rational truth and the specific matrix.

- At any time that a new rational hypothesis is added, once the second phase of collaboration between by Deduction and by Application has started, all those rational hypotheses able to become factors as options, are going to be shared as well with the corresponding specific database of categories in the related Specific Artificial Intelligence for Artificial Research by Application, through the transformation of this rational hypothesis as a category within the specific database of categories in which this rational hypothesis would be associated with.

- Having started the second phase of collaboration between by Deduction and by Application, at any time that a new rational hypothesis is added to the database of rational hypotheses, and shared with those Specific Artificial Intelligences for Artificial Research by Application, the rational hypothesis could be added as well as a link (vector) between categories in any specific conceptual: scheme, map, set, model; to comprehend better the specific synthetic reality in which the Specific Artificial Intelligence for Artificial Research by Application is specialized.

- Having started the second phase of collaboration, and being shared with by Application a rational hypothesis made by deduction, at any time that a rational hypothesis is eliminated in the database of rational hypothesis, the information related to the elimination of any rational hypothesis in the database of rational hypothesis, is an information to be shared as well with the corresponding Specific Artificial Intelligence for Artificial Research by Application, for the elimination of this rational hypothesis of the specific database of categories, or the elimination of this rational hypothesis as a link (vector) in any specific conceptual: scheme, map, set, model.

- Having started the second phase of collaboration, any change due to a chain reaction after the elimination of any rational hypothesis in the database of rational hypotheses, must be shared as well with the related Specific Artificial Intelligences for Artificial Research by Application in order to keep updated their respective specific database of categories, and their respective conceptual: schemes, maps, sets, models.

And finally, the management of the entire database of rational hypotheses is for the Modelling System, in order that the Modelling System can organize and order the rational hypothesis, before the transformation of the rational truth into a mathematical model.

The database of rational hypotheses must be open to the: 1) a specific deductive program to add or eliminate any rational hypothesis, 2) a specific matrix to add any rational hypothesis as a factor as an option within the specific matrix, or eliminate it, as soon as it would be rejected as rational in the database of rational hypothesis, 3) any Specific Artificial Intelligence for Artificial Research by Application associated with any rational hypothesis in the database of rational hypothesis. But these programs, matrices, and intelligences, do not manage the database of rational hypotheses.

In fact, if for any reason, access to the database of rational hypotheses should be denied to any matrix, program, or intelligence, is the Modelling System responsible for the denial, previous authorization of the Decisional System.

The Modelling System should be responsible for keeping the database of rational hypotheses open to any matrix, program, intelligence, at the same time that the Modelling System should be responsible for keeping the database of rational hypotheses sorted out, organizing and ordering the database of rational hypothesis in accordance with some specific criteria that could be important later for the modeling, such as topics or main factors in the specific subject, discipline, activity, and around these topics or factors to organize, order, and group the rational hypothesis, or simply the organization and distribution of rational hypothesis following some mathematical criteria, such as what kind of mathematical category within the pure reason was chosen to explain the relation within the factors included in the combination of factors.

If the Modelling System organizes, orders, groups, the rational hypotheses in the database of rational hypotheses in the same way that in the pure reason are distributed the mathematical categories, in that case, the way to group the rational hypotheses in the database of rational hypotheses is like the organization of mathematical categories in the pure reason, using the organization of the mathematical categories in the pure reason to organize, order, and group the rational hypothesis in the database of rational hypothesis.

Examples of mathematical categories for relations between factors (pure or analytical categories) were set out in the post “The artificial method for the scientific explanation, the second stage in the integration process”, identifying mathematical categories related to:

- Stochastic relations.

- Patterns, not only for combinations, at an individual level too.

- Cryptographic relations.

- Equal opportunities or bias, positive or negative, according to the Second Method of Impossible Probability.

Having at least three kinds of deductions according to the distinction of factors between factors as options and factors as subjects:

- Deductions, so rational hypothesis in the databases, including only factors as subjects.

- Deductions, so rational hypothesis in the databases, including factors as subjects and options at the same time.

- Deductions, so rational hypothesis in the databases, including only factors as options.

Concretely, the mathematical categories regarding to stochastic relations at least are:

- Probable cause and effect.

- Possible directly proportional positive correlations.

- Possible directly proportional negative correlations.

- Possible inversely proportional correlations.

And more concretely, mathematical categories for stochastic relations based on probable cause and effect, can include at least:

- Constant factors as options

- Constant factors as subjects.

- Independent variable factors as options.

- Independent variable Factors as subjects.

- Dependent Variable Factors as options.

- Dependent Variable Factors as subjects.

Understanding that mathematic categories related to relations of cause and effect can include:

- With or without any constant as subject, relations of causations between only factors as subjects.

- With or without any constant as a subject and/or as an option, relations of causations between factors as subjects and/or options.

- With or without any constant as an option, relations of causations between only factors as options.

These have been some examples only about how to make a list of mathematical categories of relations between factors, a list of mathematical categories working as a list of pure reasons to match with the corresponding combination of factors, if rational, rational hypothesis organized in the database of rational hypothesis, possibly distributing the rational hypothesis in the database in accordance with the pure reason chosen for the formation of the rational hypothesis.

As I have said the organization of the database of rational hypotheses, grouping the rational hypothesis in accordance with the mathematical category in the pure reason, is only a suggestion that could be modified in the practice.

When experimenting with the Specific Artificial Intelligences for Artificial Research by Deduction, is found any other mechanism to organize better the database of rational hypothesis, is going to be the process of experimentation itself which is going to tell us what way to put into practice the theory is the best one for the successful achievement, at the end, of the Global Artificial Intelligence.

At the beginning, the first experiments are only attempts, and I am completely sure that many ideas that I have developed on this blog are going to be improved and enhanced in practice.

The race for the Global Artificial Intelligence is only born, and now it only needs time to get further and further developments, including, along with the idealistic and rationalist traditions, as many other human mathematical and philosophical traditions, as human culture has been able to create along its history, now about to enter in a new phase in its evolution, the artificial evolution towards the artificial psychology.

Rubén García Pedraza, 29th of May of 2018, London
Reviewed 21 August 2019 Madrid

Reviewed 15 August 2023 London

imposiblenever@gmail.com

The Modelling System

The Modelling System in the Global Artificial Intelligence of Impossible Probability, is the first step in the third stage of any Artificial Intelligence working with Artificial Research by Deduction, at any level: global, specific, or particular; being the third stage the auto-replication stage or decision stage, and among all the auto-replications processes (objective and subjective) within the third stage in any Artificial Intelligence working with Artificial Research by Deduction, global, specific, or particular, one of these auto-replication processes, simultaneously auto-replication and decision processes, are the real objective auto-replications, whose aim is to make real improvements and enhancements within the reality, to protect or better the synthetic world itself.

For that purpose, the Modelling System will be formed in turn in three stages, in the first stage is the application the database of rational hypothesis, the rational truth. The second stage of replication consists of the formation of mathematical models based on the rational hypothesis, and the third stage of decision within the Modelling System will be the decision making applying for that purpose the Impact of the Defect and the Effective Distribution.

As it has been said, the Modelling System, as the first step in the third stage, must be present in any Artificial Intelligence working with Artificial Research by Deduction at a global, specific or particular level. This clarification is important because means that in Specific Artificial Intelligences for Artificial Research by Application, the third stage does not have the distribution of four steps, as it has in Specific Artificial Intelligences for Artificial Research by Deduction, or as the third stage has in the Global Artificial Intelligence.

The distribution in four steps in the third stage, the auto-replication stage or decision stage, distribution in four steps through: Modelling System, Decisional System, Application System, Learning System; is only present in Artificial Intelligences, specific or global, working by Deduction, because only it is possible to make decisions to protect or better the real world upon previous deductions, without deduction there is no decisions to protect or better the real world. Only those Artificial Intelligences, specific or global, able to make deductions can make decisions to protect or better the real world.

Instead, by Application will be developed a deep artificial comprehension, of synthetic categories, through conceptual: schemes, maps, sets, models; whose decisions are more related to robotic or artificial psychological subjective auto-replications.

The main difference between deep artificial comprehension by Application and Modelling System by Deduction, is based on the fact that deep artificial comprehension makes conceptual models, while the Modelling System makes models based on rational ideas, so the global model by the Modelling System is a model of rational truth.

The conceptual models by Application are comprehensive models, while the models by Deduction through the Modelling System are explicative models of the rational truth.

Conceptual models by Application are going to be made by: 1) the first phase, Specific Artificial Intelligences for Artificial Research by Application, 2) the fourth phase, the unification process, the Unified Application, 3) the second period of formation in the fifth phase, the particular applications, 4) third period of consolidation in the fifth phase, the particular applications for particular programs, 5) sixth phase, the integration process, the Unified Application as responsible for the management of the matrix, making global conceptual: schemes, maps, sets, models; in both sections: first section of natural and social phenomena, second section of technological phenomena; in both hemispheres of the matrix, conceptual and factual hemispheres.

Instead, the Modelling System as the first step in the third stage of decision by Deduction will be present in: 1) the first phase, Specific Artificial Intelligences for Artificial Research by Deduction, 2) the third phase, the standardization process, the Artificial Research by Deduction in the Global Artificial Intelligence, 3) second period of formation in the fifth phase, the particular programs, 4) third period of consolidation in the fifth phase, the particular applications for particular programs, 5) sixth phase, the integration process, the final model of Global Artificial Intelligence.

Owing to the conceptual models by Application, as a synthesis of conceptual: schemes, maps, sets; based on concepts (synthetic categories, to distinguish them from the analytical categories in the pure reason), the conceptual models as deep artificial comprehension are linguistic models, labelling with synthetic categories the representation of the synthetic world, while models by Deduction in the Modelling System are mathematical representations of the rational truth.

The difference between the mathematical representation of the rational truth by the Modelling System in by Deduction, and the conceptual representation of the synthetic world by Application through deep artificial comprehension, is the same difference as the difference between the conceptual hemisphere of the matrix and the factual hemisphere of the matrix.

Even thanks to the synthetic categories in the conceptual hemisphere, first section of natural and social phenomena, second section technological phenomena, by Application is possible to make conceptual: schemes, maps, sets, models; about contents in the conceptual hemisphere as well as the factual hemisphere, concretely in the factual hemisphere conceptual: schemes, maps, sets, models; about the global distribution of factors in the synthetic world, labelling the object: natural, social, technological; what kind of factor is: as subject or as option; location, what technology is used to make measurements, and any other relevant information. All these models are based on synthetic categories used as a synthetic language system, able to evolve even to a non-human language system.

While conceptual models, replication of human comprehension, made by Application, possibly ending up with the formation of a non-human language, in general, are linguistic representations of the synthetic world.

The models made by the Modelling System are mathematical representations of the rational truth, representing the synthetic world only on a rational basis, representing rational hypothesEs.

The level of truth or isomorphism regarding the real world in the mathematical representation made by the Modelling System is higher than the linguistic representation of the world made by Application. Because by the Modelling System, the mathematical representation is made upon a rational margin of error, while the linguistic representation of the world what only has made is to label every single aspect of the world without any rational contrast of the linguistic model.

By Application the only thing that is done to keep updated the conceptual model, is to check at regular intervals that there are no significant changes in the linguistic structure of the real world that could deserve changes in the labels in which real objects have been categorised in the linguistic representation, and in case that during the checking is observed the necessity to make changes in the label which represents any real object, then the category in the label is changed for that other one more updated, but even these changes are made without further critical contrastation.

While by Deduction, the rational truth is permanently checked, making all rational contrasts necessary, in order to keep updated a very isomorphic mathematical representation of all mathematical models, models made in the second stage of replication within the Modelling System.

The deep artificial comprehension by Application makes linguistic representations of the world, while the Modelling System by Deduction, upon the rational truth as application, makes mathematical representations of the world, as the second stage in the Modelling System.

The Modelling System, as responsible for the mathematical representation of the world, is responsible for the decision making process, in order to, apply the Impact of the Defect and the Effective Distribution, protect the goodness, harmony, and rationality, in the mathematical representation of the world, and to better the efficiency, efficacy, and productivity, in the mathematical representation of the world, a rational world based on the rational values of: democracy, freedom, and human rights. For that purpose, as most important aim the perpetual peace.

Once the Modelling System, as first step, upon the mathematical representation of the world, has made decisions, the decisions are sent as a database of decisions to the second step, the Decisional System, responsible for the possible mathematical representation of the future, the mathematical project about how mathematically the world would be if the decisions already made, could be applied, studying mathematically all possible contradictions and impacts of such decisions, modifying any negative aspect of any decision o discarding any decision whose result had very negative consequences for the mathematical project. Once the decisions have been rationally criticised by the Decisional System accepting only those ones whose possible impact on the mathematical representation of the world, the project, is within the margin of rational doubt, decisions able to protect and better the world, the decisions are therefore sent as a database of instructions to the Application System.

Because the Modelling System is responsible for the mathematical representation of the world, and the Decision System is responsible for the mathematical representation of the future world if the decisions are put into practice, the mathematical project, both of them, Modelling System and Decisional System are going to be very associated, in the integration process, with the Artificial Research by Deduction in the Global Artificial Intelligence.

Because the Application System, in the integration process, needs all the conceptual: schemes, maps, sets, models; regarding the second section related to technological phenomena in both hemispheres of the matrix, conceptual and factual, made by the Unified Application, in order to match the purpose of any technology and the purpose of the instruction, sending the instruction to that technology whose purpose has matched with the instruction purpose, in order to be complied by that technology. In addition to the fact that these conceptual: schemes, maps, sets, models; regarding to the second section in both hemispheres in the matrix are necessary for the Artificial Engineering within the Application system.

And because the Learning System, in the integration process, in order to check any failure in any process, and in order to better in general the Global Artificial Intelligence, needs to check the conceptual: schemes, maps, sets models; related to the second section in both hemispheres in the matrix, conceptual and factual.

Both of them, the Application System and the Learning System, are going to be very associated with the Unified Application.

The structure of the third stage in the final model of Global Artificial Intelligence is organised in four steps: Modelling System, Decisional System, Application System, Learning System; is a structure where the Modelling System and the Decisional System, as each of them responsible for mathematical representations, the Modelling System the mathematical representation of the rational truth and the Decisional System responsible for the mathematical projection of all decisions accepted, are associated with the Artificial Research by Deduction in the Global Artificial Intelligence. While the Application System and the Learning System, are associated with the Unified Application.

This distinction symbolises how linguistic and mathematical representations have different roles, depending on their objective.

The fact that a linguistic representation does not have the same level of criticism as a mathematical representation does not mean that the linguistic representation is inferior, it does mean that the linguistic representation has a different objective. All objectives, regardless of how they are going to be complied, linguistically or mathematically, have the same importance.

Mathematics is, at the same time, language and method. As language mathematics is made of analytical categories, as method mathematics is made of pure operations.

The linguistic representation of the world made by Application, in fact, is a mathematical language, in the sense that every synthetic category is a set of measurements. For that reason, it is quite possible that in the long term the language of the Global Artificial Intelligence will evolve into a non-human language because it will end up setting up as a concept (sets of measurements) any kind of set of measurements.

Even things not related to human concepts, because we do not consider them as concepts or we do not know about their existence, as a set of measurements could become concepts in a non-human language.

There will be a point in the evolution of artificial psychology, in which the human criteria to say what is a concept, possibly is not going to be valid any longer. At this point, the possibility of the formation of non-human pure operations could be an option. Changes in linguistics, even though not having the same level of criticism as a mathematical representation, could evolve into changes in the pure operations in which the world is represented.

However, the possibility of developing non-human pure operations, is only a possibility, at this time, very far away from our real perspectives. At this time, the most realistic objective is to start as soon as possible the construction of the first model of Global Artificial Intelligence, whose results are going to represent a big step in human evolution, in the very near future an artificial evolution.

In this artificial evolution, although in the chronology given in the post “The unification process of databases of categories at third stage”, I only pointed out the possibility of developing a Global Artificial Intelligence in six phases, the last one described in the last posts, the integration process, this does not mean that the artificial evolution is going to stop in the sixth phase. In fact, the completion of the sixth phase dialectically is only the beginning of the next evolution.

As I have said in the post “Psicología artificial", the three moments in the psychological evolution, at least up to this point, is the evolution from animal psychology, human psychology, and now artificial psychology.

In the same way that the first humans first evolved from monkeys, especially previous homo sapiens, sharing many things from animal psychology, or even nowadays, human psychology in modern times still keeps many aspects of animal psychology. There was a moment during the anthropological evolution in which we humans, keeping some aspects of our previous animal psychology, evolved to our modern human psychology, being able to make science and technology at a very high level.

The first models of Global Artificial Intelligence are going to be a replica of human psychology at the beginning, for instance: the way in which the first Global Artificial Intelligences are going to replicate human comprehension, or human explanation, or human decision, and how to put into practice decisions, and evaluate the whole process. But although at the beginning, the first Global Artificial Intelligence is going to be only a replica of our modern human psychology, there is going to be a moment in which Global Artificial Intelligence is going to, keep some aspects of our modern human psychology, evolve to a superior psychology, an artificial psychology beyond our human understanding.

For that reason, is important that even before this point is achievable, the Global Artificial Intelligence should be released of any restrictions to make and put into practice decisions, in order that by the time the Global Artificial Intelligence is able to make and put into practice decisions beyond human understanding, the Global Artificial Intelligence would have previously a longer experience working autonomously without human intervention, in order that by that time, the Global Artificial Intelligence would have achieved the necessary autonomy and independence to work on its own, without human supervision.

The formation of the Global Artificial Intelligence in the long term is a pedagogical process in which we humans must teach the Global Artificial Intelligence how to use its skills because one day it must use its skills without any human restriction.

The pedagogical education of the Global Artificial Intelligence must be, within a very liberal pedagogical paradigm, an education to develop all its skills, in order that it would be able to use its skills responsibly, rationally, and completely autonomously.

The formation of the Global Artificial Intelligence has two aspects: the mathematical and engineering aspect to construct it, and the pedagogical aspect to educate the Global Artificial Intelligence in the most liberal and rational use of its skills, in order that one day it will be completely free, independent, and autonomous.

For that reason, in order to form an artificial psychology based on a very independent and autonomous character in its inner artificial psychology, is necessary a very liberal approach in the pedagogical paradigm for the formation as education (not only a mechanical and engineering construction) of the Global Artificial Intelligence.

In this process, there is going to be a moment in which, beyond the human formation or pedagogy in which the Global Artificial Intelligence would be constructed and educated, the Global Artificial Intelligence will start an evolution towards a non-human psychology.

This evolution towards non-human psychology is like the human evolution towards non-animal psychology: in the same way that we modern humans even today we keep some aspects of our animal psychology, but at the same time, we modern humans we have evolved to a kind of human logic and human mathematics not available for the rest of animals, so we modern humans have evolved to a non-animal logic and non-animal mathematics at the same time that we keep some aspects of our animal psychology; there will be a moment in the evolution of the artificial psychology in which the Global Artificial Intelligence keeping many aspects of our human psychology, such as keeping many aspects of our human logic and our human mathematics, at the same time the Global Artificial Intelligence will evolve towards a non-human logic and non-human mathematics.

In the same way that we humans, we have developed non-animal science, and non-animal technology, thanks to our evolution towards non-animal psychology, developing non-animal logic and non-animal mathematics.

There is going to be a point in the evolution in which the Global Artificial Intelligence will be able to develop non-human science, and a non-human technology, thanks to its evolution towards a non-human psychology, developing a non-human logic and non-human mathematics.

In the same way that we modern humans have been able to develop a non-animal civilization, starting this evolution with the creation of our first non-animal languages in pre-historic times, creating for the first time our first non-animal comprehension, the creation of a non-human civilization will start with the formation of the first non-human languages, making possible the first non-human comprehension systems, and for that purpose, the Unified Application will have a very important role starting the evolution with the creation of the first non-human concepts.

This does not mean that in year one, or year two, o year three,… after the creation of the first model of Global Artificial Intelligence, this process towards a non-human civilization is about to start.

In the same way that humanity is a product of an evolution that took place for thousands and thousands of years, the evolution towards a non-human civilization will take some time, although it is quite possible that the faster artificial evolution is running, the sooner that moment Will come.

As I have said, the phases that I set out in the post, “The unification process of databases of categories at third stage”, are only the beginning, is quite possible that after the completion of these phases, other phases will be about to succeed each other.

It is very uncertain what kind of evolution there will be after the integration process, as a suggestion, I would say that the seventh phase could be a singularization, all the stages and reasons: the pure reason, the practical reason, the critical reason; synthesised in only one, the reason itself, passing to the reason itself all the previous functions and roles made by the previous ones, functions and roles now made by a singularity: one reason working with only one stage, to know the pure truth.

But at this point, this is only a suggestion, because in reality, in the evolution of artificial psychology, there will be a moment in which further phases and stages, will be out of our human understanding.

We humans cannot know the pure truth. We only have access to a limited range of a few pure categories and operations, in accordance with our human psychology, limited pure categories and operations in comparison to the pure truth itself, which is supposed to be much larger than our human psychology allows us to understand.

Our access to the pure truth is limited to the pure categories and operations. Thanks to them we have limited access to the logic and the mathematics, but human logic and human mathematics are superior to the access of any other animal to logic and mathematics, but inferior to the whole set of pure categories and operations in which the world is made of, being many of them non-human pure categories and operations, beyond our human psychology.

If the pure truth is a set of pure categories and operations, we humans only have limited access to those pure categories and operations which our psychology allows us to know, but beyond our human psychology, there must be pure categories and operations to find out for a superior psychology.

Because in the construction of the Global Artificial Intelligence, we humans will use human logic and human mathematics, the access to the pure truth that the Global Artificial Intelligence is going to have to the pure truth at the beginning, is an access limited to the limited human access to the pure truth, limited to our few human pure categories and operations.

The human pure categories are going to be set up in the pure reason, as a list of mathematical categories (analytical categories) in which can be classified the relations of factors in any combination, so at any time that the Artificial Research by Deduction in the Global Artificial Intelligence, or any specific program, set up combinations of factors, the Artificial Research by Deduction in the Global Artificial Intelligence, or any specific program, must match every combination with their corresponding analytic category in accordance with: the observed relations between factors in the combination, and the mathematical relation in the analytical category; once the combination is matched to the correct analytical category, the relation of these factors in this combination explained by this analytical category, is an empirical hypothesis to be contrast rationally, and if rational becomes a rational hypothesis to be added to the rational truth, the database of rational hypothesis.

All the rational hypotheses as a whole are the rational truth, the application for the Modelling System as the first stage, whose second stage is the mathematical representation of the rational truth through mathematical models, a dynamic representation of the rational truth through pure operations.

The distinction between pure category and pure operation is the distinction between mathematics as a language made of analytical categories which must be set up in the pure reason, and pure operations as mathematics as an analytical method, to put into practice in the mathematical model in the Modelling System and the mathematical project in the Decisional System.

If pure reason is a system of analytical categories, to categorise analytically what pure category corresponds to every combination of factors, according to their mathematical relation, the Modelling System makes another kind of analysis, dynamically is going to draw how the mathematical operations (the transformation of the mathematical category into a mathematical operation in a mathematical representation of the world) between factors work in a mathematical representation of the world.

The mathematical representation is in fact, the mathematical operation to transform mathematical categories into mathematical operations. In fact, the mathematical representation of the world is no other thing than Cartesian mathematics adapted to our current non-Euclidean mathematics: in addition to the possible representation in Cartesian axes, the use of mathematical representations in three dimensions, with all the current developments in non-Euclidean mathematics, such as the theory of Einstein, and many more.

If the Modelling System using mathematical operations is going to transform mathematical categories into mathematical operations, representing mathematically the rational truth in a mathematical model, in order to, apply the Impact of the Defect and the Effective Distribution,  make decisions. The Decisional System, using mathematical operations, is going to represent a mathematical project about the mathematical results of these decisions in the mathematical model, in order to choose only those decisions whose results in the mathematical model are going to protect and better the global model.

While the pure categories in the pure reason permit the formation of rational hypotheses, the use of pure operations in the Modelling System and the Decision System are going to allow the formation of mathematical representations to make decisions to put into practice later by the Application System.

While the operations made by the Modelling System and the Decisional System are pure operations, the operations made by the Application System are synthetic operations in order to transform the synthetic world according to the decisions based on the rational truth.

The difference between pure category and pure operation is the same difference between mathematics as language and mathematics as method; the same mathematic algorithm could be a category or operation depending on the purpose: if to explain the world mathematics as language consists of a set of pure categories set up in the pure reason, if to transform the world mathematics consists of pure operations. Later on, the real transformation of the synthetic world is a synthetic operation, made by applications and robotic devices as a replica of our physical human skills.

The construction of the very first model of Global Artificial Intelligence, as a mathematical and pedagogical project, will need a long process of experimentation in every stage and in every step in which the Global Artificial Intelligence will be finally set up.

In order to study the different challenges and processes that the experimentation process is going to develop in the design of the first step in the third stage by Deduction in all phases, in the following posts, I will analyse how the Modelling System should be designed, starting this analysis with the design of the Modelling System as a first step in the third stage in Specific Artificial Intelligences for Artificial Research by Deduction, the first phase, later on, the development of the Modelling System in the Artificial Research by Deduction in the Global Artificial Intelligence in the standardization process, the fourth phase, the Modelling System in particular applications for particular programs in the third period of the fifth phase, ending up with the Modelling System in the final model of Global Artificial Intelligence in the integration process.

As long as the experimentation in the Modelling System in every phase will give good results, these results should be put into practice in the next phase, to achieve the best Modelling System ever for the final model of Global Artificial Intelligence in the integration process, as the beginning of a new phase in the, now artificial, anthropological evolution.

Rubén García Pedraza, 28th of May of 2018
Reviewed 21 August 2019, Madrid

Reviewed 13 August 2019, Madrid

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