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2.2.2 The explanatory gap in the mind – body problem, as the impossibility to deduce from one representation the other, follows from the fact that the two different explanations are based on different basic concepts. Pain and nerve cells, heat and joules, light and photons are not qualitatively deduced from each other either; they are only compared to each other in experience. Pain is defined as a feeling, while the nerve cells that cause it are regarded as microorganisms, light is defined as a sensation, while photons – as physical objects. The explanatory gap occurs wherever different ontologies exist.

2.2.3 For example, sound. It can be generated by means of a circuit constructed by the interconnection of radio parts with a speaker. Sound definitely exists, and we can hear it, but this is a dynamic process that cannot be separated from the radio circuit. On the other hand, you will never find anything resembling sound in the radio circuit itself. There are transistors and capacitors there, but there is nothing that we define as sound. Even a speaker is just a coil and a cone. An explanatory gap exists wherever something is described by different models on different perceptual bases.

2.2.4. One can’t say that there is an objective, and one does not need to try to explain how the subjective is derived from objective. According to constructivism, everything is a representation. One should say that there is the subjective and should explain what we consider intersubjective in it, i.e. concerted and the same for all. For the first humans, the natural attitude meant that everything exists beyond them, and therefore, objectively, even their fantasies about dragons. It was only over time that human realized that dragons were his imagination. Now it is necessary to recognize that everything is our imagination controlled by perception, not just dragon images. And most people share common concepts, which are interpreted as intersubjective.

2.2.5. There is nothing objective, that is, nothing independent of the perceiver. Everything we know takes place in someone’s mind. Without an observer there is no representation. Without a representation, there is no knowledge. And if we agreed with someone to call something so-and-so, then when it happens, it is intersubjective (collective subjective) which is called “objective”. Even a blind man can agree with a sighted man on the color of things he has never seen. The world as implied by representations is an agreement with others about its existence. However, it must be remembered that it exists only in the representations of each. These representations are agreed through common practice. While, subjective is the representation, which is realized as belonging to me.

2.2.6. The objective is the collective subjective. It is given to us in no other way than through the belief that what I see can be seen by others. It is our accepted agreement that we are talking about the same thing. It is what others see and call the same thing. Here is a red apple in front of me. It is an objective image, on the one hand, it is seen by others, it can be eaten. But, on the other hand, there is no “red” in the world, it is a subjective representation. It follows that I see both subjective and objective at the same time. This is the paradox that creates dualism. Realism has no answer to this paradox.

2.2.7. Even in the nature of living there are different representations of the same thing. The senses cannot all be in the same modality because they cannot convey information simultaneously. These modalities complement each other – the sound of breaking branches in a forest tells us as much about danger as the sight of the large animal that caused these sound. With insufficient information we would lose a lot to prediction and confidence – when I can’t see, I can hear and predict the yet unseen. But that is why they are incompatible – one can’t convey sound with color so it doesn’t interfere with it. And signs of certain modality are related by certain pattern, such as color or tone. By means of speech we construct many more different representations and models, than nature does.

2.2.8 Objectivists agree that representations belong to us; however, their structure and meaning reflect the external world, as in the laws of physics. However, this is paradoxical thinking because the meanings of the numbers that make up the laws of physics do not exist in the world. You cannot point to them by finger.

2.2.9. The thesis that all our representations are subjective constructs can be substantiated by the following mental experiment. Imagine that my skull was opened and I was provided with a mirror to observe my own brain. The image of the brain scientists would consider objective. It’s what the doctors around me see as well. But let’s take an electrode and insert it into the area of the visual cortex which is responsible for color perception. I can see where it is stuck in my brain. And suppose the doctors hit just the red perception neuron in a certain visual field. What happens? A red spot will appear in front of my eyes, and I will be aware of the red qualia. This subjective redness will overlap the objective picture of the brain that caused it. However, doctors will not be able to discern this redness; however, they may possess their own “overlaps”. What inferences can be drawn from this phenomenon? This phenomenon signifies that the redness is primary in our perception. It is primary, which is only later related by us to what we call objective or subjective according to completely different criteria (belonging to everyone or belonging only to ourselves).

2.2.10. I see a picture in front of me, and I know how my eye is organized so that I can see it. However, the construction of the eye does not give the sensation of seeing. This is the difference between the process itself and a model of the process. One cannot get the vision in the model. From the vision one cannot see the process itself, which gives the effect of seeing. Therefore, one can feel and observe only by being part of the process, being within the process. One can study and analyze the process itself only from the outside. This is the only reason in differentiating between objective and subjective approaches. However, these are not different substances, these are different models of the same process with different data – how it is felt from the inside and how it is seen from the outside. And to know about the process from the inside allows only consciousness as a process carried out after the realized process, which will be written about further.

2.2.11. Anyone who has been fond of radio circuits knows that it is impossible to create a color music which would response in the tact of the melody we hear, because the radio circuit responses only to the frequency and amplitude of the flow of sound waves. The concept of “phrases” and “moves” in music, that is, musical patterns, is recognized by humans, rather than by radio circuitry. This is due to the human ability to recognize the correspondence of information to any of our subjective models, rather than input information.

2.3.1. There is an opinion that all information programs and devices are based on the processing of input information. However, this can also be interpreted as the transformation of an input signal into another signal. This transformation does not contain “information” in the sense of knowledge; rather, it is our interpretation of the transformation. For example, filtering can be seen as a form of the signal classification. If there is a classification, then the classifier must contain a model of the class, whether passive or constructive, such as a filter or resonator in a radio circuit. The input signal is merely an entity that undergoes selection in the classifier. If the signal “passes” the filter, it is interpreted as receiving “information”. This is just a signal processing as a series of transformations of the input signal. The information is actually contained within the filter or resonator as a model of what we call information. We only determine whether the input signal falls within this model or not.

2.3.2. How much information is in one megabyte? It’s a silly question because it could be one megabyte of noise. The amount of information we can obtain depends not on the source but on the models by which we perceive this megabyte as meaningful information. Reading a text requires not only the words in the book but also knowledge of their meaning.

2.3.3. Information theory is incorrect. What is information? From a constructivist standpoint, there is no flow of information from objects to subject. This notion is absurd because it assumes that knowledge depends only on the object and is outside the subject, and to see this, one has only to take a closer look. But how can one read without knowing the meaning of words? How can one learn about an object without first having a model to represent it? If we were to perceive the world directly as it is, education would not be necessary. For example, reading would not depend on knowledge of a primer. A text can be written in the sand, on a blackboard, or on a sheet of paper. This would be the same text, although the information is quite different. If all knowledge is contained in space, nature, or the book pages, why couldn’t we transform it into knowledge as early as in the times of ancient China? Still, it’s clear that in order to read a book, one must first learn letters and words, i.e., acquire a language model. The information flow carries something else, rather than information about the object itself. It carries changes that transform our internal model into one of its possible states. This process is called “information acquisition” and will be explained in the following chapters.

2.3.4. The information processing metaphor is incorrect. This metaphor originated with the transmission of a scroll containing text. We still believe that we obtain all information from objects that transmit the scroll to us in the form of photons and other physical impacts. But then people back in ancient Greece would have perceived all the knowledge about the stars and planets that we have only learned from Copernicus. In response, it is said that information from objects is processed, or encoded; that is, individual pieces of information are linked into images and concepts. Actually, we all know that to read books, the books themselves are not enough; one needs to know a primer and the meaning of words. But what is a primer? It’s not just individual letters; it’s a way of linking them into words so that we can read them. It is only because of this pattern that we can read a text. Therefore, it is logical to assume that new knowledge is not determined by the information flow from the subject, but rather by the schema itself, which determines the possible letter combinations in a text sequence.

2.3.5. The fewer letters are available, the fewer possible words there are. This does not depend on the object of perception, i.e. a book. If the words are written with letters you don’t know, you won’t be able to read them and won’t receive any information. In other words, the amount of information you can potentially obtain from an object depends solely on the schema of this object and its resolving power, which is determined by the number of possible combinations in the schema. Due to such potential combinations a schema as a model, contains all possible words in advance. This is a combinatorial set of m by n variants because the length of words is limited by our pronunciation and memory abilities.

2.3.6. When we transmit information through speech or text, we alter the state of interlocutor’s model. Each spoken word is a selection from among all possible word choices that the interlocutor can expect from us. We perceive the choice of a model variant as receiving information.

2.3.7. Traditional information theory is not a theory of value transfer; rather, it is a theory of the transfer of changes in the form of switches between model variants (their density, speed, and loss). Therefore, white noise is the most “informative” transmission because it does not fit any model and has the largest number of differences between pixels, even though it itself carries no information.

2.3.8. Is a bit a unit of information? No, a bit is merely a 0—1 trigger for anything. A bit itself does not carry information because it cannot be decoded without interpretation within a model. It could be information about an elephant or Mars.

2.3.9 The amount of information depends more on the discriminating power of the models the subject has than on the information flow from the object. We can increase the amount of information about an object simply by adjusting the resolution of the model as a device. It is the model that allows us to distinguish between different variants of an object. The name of an object is a generalization of its possible variants, some of which we have even not seen yet, as will be discussed later.

2.3.10. Systems built on the “information processing” paradigm which are completely dependent on input, cannot recognize noisy, distorted, or modified models, such as a syllogism. These systems have difficulty computing them from the interrelation of the seme input values. Constructivism, instead of a processing paradigm, involves finding a model or combination of models that fit a set of input features through similar semes. In fact, no information processing system can identify inputs without explicitly incorporating a model of what it is supposed to recognize into its design. This applies to everything, be it a radio receiver or a computer. Neural networks learn the models themselves, but only through large-scale simulation without the possibility of learning, that is, only by recognizing the input pattern without the possibility of creating new models during use. Therefore, such systems cannot recognize anything beyond what is embedded in them in advance. They can perform only minimal smoothing. Systems based on the constructive approach can create models and recognize a set of input features based on the principles described in this book.

2.3.11. According to information processing theory, information enters the brain and is encoded into sensations. However, this encoding poses a problem when trying to explain how objective information transforms into subjective sensation. This is an unsolvable mind – body problem in the information paradigm. A simpler explanation is that there is no recoding; rather, the brain generates sensations as prediction models, while perception serving only to confirm it.

2.3.12. Motion perception is also prediction rather than information processing. Otherwise, how could one fail to perceive an approaching car when input information is clearly present on the retina at every moment? A person cannot perceive motion in rare cases, such as when a car approaches him unexpectedly on the road. In other words, he does not expect to see the car in front of him the next moment after seeing it in the distance. A sense of motion is a time-based prediction of a new position at the next moment, verified through perception. When the prediction is incorrect, the change in position becomes unexpected.

2.3.13. Now, we know that color perception is not so much the processing of a wavelength, but the generation of a color of a point in relation to its surroundings on a color wheel. Information processing theory could not explain why despite different wavelengths illuminating and reflecting from different parts of the picture, we see colors as permanent. An explanation is possible only if we accept that color is a relationship between neighboring colors according to the schema of opponent colors. Without neighboring colors, any color strip under any illumination will appear gray to us.

2.4.1. The reference theory is incorrect. We are not comparing signs, meanings, and referents, but rather signs as pointers and nominations of subjects and meanings as the relations of these signs to other signs in the model of the subject in the same or another modality. There is nothing more here than the indicated relationship of signs in the model of the subject, because the subject is not a sign, but an interrelation of signs describing the subject in one way or another. The sign of the subject merely serves to concisely express it, but description as meaning is always implied when pronouncing the name of the subject.

2.4.2. When describing what we see or hear using words, we describe in the modality of words what we see in the modality of colors and lines. Colors are just as much “words” as regular words in the modality of speech. They make up the “text” of a picture. One can only talk about relating one description to another. Speech is universal as a way of description – it can be used to name and describe both color and sound, but not vice versa. It is this capability of speech that distinguishes people from those who do not command speech. One cannot separate a fact and its description as something objective that has happened from its explanation and description.

2.4.3. The notion of truth became obsolete. A sentence cannot always be true because its meaning lies in its interpretation, which can differ for different people, in different models, and thus cannot be unambiguous as truth is supposed to be. This is possible only in a strictly formalized system where the variables in formulas have an unambiguous interpretation. In this case, it is possible to have coherent truth within this formalism. In all other cases, it is impossible to speak of any truth as the “God’s viewpoint” seeing the only true state of affairs. All facts of the world are subjective because they constitute the content of our consciousness rather than objective reality.

2.5.1. What is constructivism in simple terms? It is the idea that we do not perceive the world as it is through our eyes and other senses, but rather, we actively construct it in our representations, which we then verify through experience. It is the concept that we cannot have direct access to the world without the mediation of our own representations of it. There is simple evidence for this: our eyes only give us a clear, colored picture in a small focal area. The rest of the picture is blurry and less colorful. Yet, we see everything in color. This is because our brain generates a full-color image so that we can see everything in color and make more informed decisions about how to proceed in a given situation.

2.5.2. Our perception of the world depends entirely on the schemas by which we construct our representation of it. This concept is well exemplified by the dual illusion. Depending on what you are willing to see, you will first notice one of the two images, even though only one image is in front of you. Furthermore, it may take you a very long time to see the second image. But it is worthwhile to give you a pointer of the schema, that is, to tell you what image is still there, and you will immediately notice what you did not see in the same image at point-blank range. The schema of representation will suddenly turn on like a light! This means that the schema completely determines what you see. This also applies to physics, which “sees” through the mathematical schemas. If you don’t have a schema for a process, you can’t build an experiment to measure a phenomenon. The schema defines only what you can observe rather than the object itself. The schema serves as the “optics” of our cognition.

2.5.3 Anyone who has seen a child who fears you as if you were a Barmaléan or an elephant cannot say that the child is merely processing information from the outside.

2.5.4 Even to find a red pencil, we must first visualize what it looks like and notice its distinguishing features, even if only a small part of it is sticking out from under the notebook.

2.5.5. In front of you is a chair. It is white. You can’t see the red chair because the model’s triggers (eyes) are active. Close your eyes and you will be able easily visualize a red chair because your triggers do not prevent you from changing the color of the chair in your representation through top-down activation. This is a straightforward argument for interactive constructivism.

2.5.6. The steady-state thermal problem (Fourier equation) and the electrostatic problem (Poisson equation) are mathematically equivalent. Although these two mathematical structures are identical, the physical phenomena they describe are entirely different. This suggests that we use the same constructs for different purposes. This means they are definitely not caused by something outside of us, but rather, are constructed by us.

2.5.7. There can be no truth as such in constructivism. If hypotheses about the same phenomenon can differ and change with new data, then true statements can also become false in a new model. This contradicts the very definition of correspondence truth. A statement can be called true only if it is not in contradiction with other statements in a given schema; this is coherent truth. However, the truth of such a statement loses all meaning when reviewing the hypothesis in which it is agreed upon.

2.5.8. We can create many models that seem to be about the same thing. For example, light can be represented as an illuminating ray, a wave, or a stream of photons. However, not all of these representations exist at the same time. Are we discussing a dualism of light’s properties, or the possibility of different theories of light? Adherents of objectivism are not helped even by apparent contradictions, such as the dualism of physical phenomena, in doubting their views.

2.5.9. What is knowledge from the perspective of constructivism? A model contains all possible variants of what it represents. However, knowledge is the selection of one variant from among all the possible variants in the model. For example, the sky is blue, but not green, although green is a possible color (as seen in the northern lights). That’s what knowledge or fact consists of: it consists of a constraint on the combinability of the variants in the predicate “the sky is blue”.

2.5.10. Constructivism reconciles empiricism and rationalism. It asserts that we generate rational ideas, which then undergo empirical testing to determine their validity. This is the only way of knowing. What is the reason for coming up with ideas, how variants arise, and how they are tested in experience? These questions will be addressed further.

2.5.11. We create a representation of the world not as a tracing of it, but according to our own maps, created by us for the convenience of distinguishing and harmonizing knowledge, for the convenience of operating it. These are not Plato’s shadows; these are just constructs of our minds, resting on the reality of the body, rather than the world. It is clear that the sense organs cannot convey the full richness of concepts, but only help to separate one concept from another, make it possible to distinguish between them. It seems to us that when we construct a sentence, we perceive and describe reality. But in reality, we build it in order to distinguish the perceived one from the same possible ones by finding a predicate for the distinction. It is an elephant, but not a gray elephant, but a blue one.

2.5.12. We create concepts to which nothing outside of us is comparable, but it is convenient for us to use them to construct schemas for our thinking. For example “zero”, “time”, and “infinity”, which some scientists even consider it to exist, although it is obvious that “zero” cannot be an entity, as well as any number, and time as such is just a function of memory and consciousness, and cannot be pointed at with a finger. But if we continue with such an analysis, it quickly becomes clear that nothing corresponds directly to our concepts “out there” beginning with color and sound, which are the primary sensations from which all our concepts are composed.

2.5.13. Why do we cognize by means of our constructs? To address this question, let us imagine a subject who possesses an internal structure yet remains unaware of the external environment. The question that must be addressed is how this subject can create an adequate “model” of that environment in order to be able to act in it. The imprint is not a model because it is static and cannot be used to organize action in a changing environment. All that such a structure has is the ability to act. In order to create a model of the environment, it is necessary to take discrete steps that can be mapped within oneself. In the event that one wall is situated three steps to the right and another wall is located two steps to the left, this will inherently generate a representation of the space between the walls equivalent to five steps. This model will serve as a representation of the environment in which one can navigate, with the ability to recognize when one will reach the wall. It is made up of the subject’s steps, not a measure of space. And it is only the model of the steps that creates space, not the other way around.

2.5.14. The nature of the representations generated and limited by the schema indicates that in the phenomenon of the world, only specific facets are perceived, i.e., only the relation of certain features emphasized by the schema, rather than the whole phenomenon. This can be attributed to the creation of new schemas regarding the same phenomenon, which in turn leads to the discovery of new facets. Consequently, the identification of novel characteristics within a phenomenon is dependent upon our existing schemas, rather than the inherent properties of the phenomenon itself. We can create different schemas for the same phenomena, and therefore the phenomenon has as many facets as we can create different models of it.

2.5.15. The nervous system is capable of predicting its own states, rather than the external world. The nervous system has the capacity to recode all impacts in receptors into its internal code, which does not correspond in any way in content to the external impact (neuron commissures are the same from all receptors). The modality of a receptor is defined as a distinct physical device that elicits a similar neural response as other receptors. All signals from different receptors are transmitted in the same way (through commissures). The nervous system has no goal to cognize, for example, a light wave, but it does have a goal to adapt to its changes by finding an acceptable variant of the possible states of its model in response to a change in the environment detected by the nervous system’s triggers; for example, to wake up in the morning when it becomes light.

2.5.16. One who moves and wants to survive must anticipate, that is, have a model of what will happen, rather than what has already happened. A model with memory came into being when movement came into being. The state had to be memorized so that what had occurred could be compared with what had been predicted, and proper adjustments to the model could be made.

2.5.17. Hypotheses about the world as a model require no proof of their correctness, except for internal consistency of statements and consistency with experience. The viability of any hypothesis is contingent upon its capacity to reflect relationships that are susceptible to empirical scrutiny. The hypothesis that aligns most closely with the observed changes in action is considered applicable. Competition in the application of hypotheses is better than any criterion of truth.

2.5.18. The world is organized according to our schemas. In order to cope with the chaos of the perceived, thinking constructs a world according to a structure that allows us to distinguish, compare, and, most importantly, to act in a schema-marked world. The act of thinking unfolds the world in space, while consciousness unfolds it in time. This temporal unfolding enables the return to the past for the self, thereby establishing a sequence order and cause.

2.5.19. But why, for all its obviousness, has constructivism not yet been accepted in the scientific community as the scientific paradigm that conditions all reasoning about cognition? Because until now there has been no convincing answer to the question of how in this case we cognize the new things around us, how our representations agree with experience, with the world, although everything is just our representation.

2.6.1. Constructivism is opposed to realism because in the old paradigm they are opposed. The author of the present study posits that interactive constructivism reconciles them. The latter argues that whenever we create a representation of “A” it is already one of the variants, because for us there is at least a variant of “not-A”. And such constructivism is no longer solipsistic, because there is a choice. And it is only from experience that one of the two possible variants is chosen, in interaction with the world through perception as a model trigger. That is why it is interactive.

2.6.2. We do not have direct access to the world; however, its existence is proved by the fact that we are not the ones who choose the possible variants in our models of the world. It is only in these choices that we come into contact with the world. Only this choice independent of our will is the proof of a world beyond our constructs. What is independent of us is really there.

2.6.3. No model can describe the world as it is. One can always ask the question “Why?” to any predicate and find one that has no answer. That is why new hypotheses are created; it is only worth looking closely at the predicates of a model and applying a different ruler to them. We are actively building the model. We are constantly seeking to improve it through the question and the experience gained from the answer.

2.6.4. All sensations are variative. We distinguish many colors, and seeing one color immediately implies the potential for distinguishing other colors. This is a perceptual model that acts as a trigger for the model variants we construct; for example, the colors of a car. The neurons from the auditory cochlea do not convey the character of the sound itself; they only convey changes in the sound, as do the neurons of the eyes and skin. The very character of sound and color is encoded in the cerebral cortex, rather than in the sense organ.