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2.4 Symbols for Designating Objects and their Properties in Acts of Reflection and Functioning.

Methods of designating static characteristics of patterns and original patterns. 

If we are to further discuss various aspects of the problem of reflection, (which imples the obligatory presence of a reflecting object and reflected objects) then let us agree to use one word, interpretor, for the reflecting object. Then we shall usually be able to call reflected objects quite simply objects, acknowledging the ambiguity. Objects will be denoted by the large letters A, B, C, etc.

Any components, or component parts, of objects will also be designated by letters, for example, X, Y, P, and we shall reflect the fact that they are components of some object or other, for example. A, with the aid of the logical inclusion sign Н , reminding us of the arithmetical sign "less than or equal to". For example, the expression X Н A will be taken as confirmation that X has been included in A includes X.

Since in acts of reflection it is not the reflected objects nor their parts (for example, active parts), which are important for us, but the properties of these objects and their parts to the extent that the imposition of the reflected objects' properties on the reflecting object (the interpretor is the result of reflection), let us decide not to draw a distinction between properties and bears of properties when designating them with letters. For example, A is the object and the sum total of properties of this object; X is both a part of the object A, and part of the sum total of properties of this object; X is both a part of the object A, and part of the sum total of the object A's properties. In this case the expression X Н A can be taken as confirmation of the fact that X is a certain property (or properties) which become part of that sum total of properties inherent in object A.

Let us note one difficulty: X Н Z will be sued to assert 1/ that part X is included in object A; 2/ that property X (or sum total X) is included in object A's properties.

In all other cases it is the same. For example, if x X, this means that x is included in X, i.e. either part x is included in part X of object A, or property x is included among the properties X of the full combination of object A's properties as a component part.

Naturally in this sense the transitivity of the inclusion relationship is preserved, i.e. if x Н X, and X Н A, then x Н A.

The division of an object into parts and the breaking down of properties into groups can be effected by various methods, among which two types will interest us above all: "those with intersection" and "those without".

For example, if part X of object A is its active part in one interaction with the interpreter, and part Y is the active part in another interaction, then a position is possible where X and Y overlap, i.e. there is some part of these parts, (let us say, part p ) where p Н  X and p Н  Y.

In symbols of logical rotation this could be designated as follows: X.Y = p (where the "point" is the conjunction sign).

If there is no such overlap between X and Y this would be written in logical symbols X.Y = Ж.

But here, naturally, not only X Н A and Y Н  A but also the disjunction of these parts is included in A, i.e. (X + Y) Н A (where the "plus" is the disjunction sign).

Let us agree to designate the imprint as a result of primary deformation, imposed by the reflected object's active part on the interpreter, i.e. the direct imprint, where possible with the same letter as for the active part itself; to distinguish the symbol of the active part from the imprint of its activity let us add two strokes to the symbol of the direct imprint. For example if part X of object A leaves a direct imprint on which the properties X of the active part X have been imposed we shall designate such an imprint as X".

Since we consider primary imprints to be the result of the imposition of the properties of the active part on the interpreter (by the reflected object's active part). primary imprints, like the active parts themselves, can have general components. For example, if P Н  X and p Н Y and these two active parts of object A leave direct imprints in the interpreter, i.e. imprint X and imprint Y, then in each of these imprints a p”—component (where p” Н  X” and P” Н Y”) is represented.

Here we have to turn our attention to one important detail. If imprint X" is left on the interpretor by the object A's active part X, and the imprint Y" has been left by object A's active part Y, then part p of Part X and part p of part Y is one and the same part of object A, although it is observed in two acts of influence on the interpretor. However, as far as the component of imprint X" and component p" of imprint Y" is concerned, then insofar as these are independent imprints. Independent deformations, existing separately on the body of the interpreter, then the components p" in these Imprints are not the same, but are similar; they have a "common antecedent" - Part of object A, but they exist independently. Therefore it would be more accurate to write that P_x Н  X" and P_y Н  Y" which reflects component p" belonging to a certain direct imprint. But in those cases where this fact is obvious it is not obligatory to add an index to the symbol of the imprint's components in order to give a reminder of the symbol of the whole which this component is part of.

Naturally two independent objects can also be encountered which do not have the same general part belonging to them both, but they do have a similar part. If necessary, a correlation between objects of this nature can also be accurately reflected in symbols.

For example, we have object A and object B and in each of them is part C, the same as in the "partner" but not belonging at the same time to object A and object B. In this case we must also write C_a Н A; C_b Н B. However if the context is sufficiently clear then we can simplify the notation: C Н A and C Н B where C is a similar, but not one and the same, part of the objects.

By introducing the concept of the receptor as a certain part of the reflecting object having a heightened (greater) sensitivity to certain characteristics (properties) of the reflected object we have essentially acknowledged the possibility of the fact that one and the same reflected object or one and the same active part of a reflected object can leave various imprints on the interpretor's body (the reflecting object's); this depends, though, through exactly which receptors' mediation the-reflected object's (or active part's) interaction with the interpretor was effected. But this means that the imprint of the Interpretor's interaction with one and the same object can be varied if this object is in various reception zones of the interpretor. When this difference has to be reflected symbolically, let us introduce a reception zones' numeration and put the corresponding figure next to the imprint symbol in the form of an index (before the symbol and high up: a sort of super six). For example, the Imprint of part X of object A which is situated in reception zone 3 will be designated as ³X". The imprint of this part X of object A situated in reception zone No.1 will be accordingly designated as ¹X" etc.

Another case can occur. Various objects were situated in one and the same reception zone and therefore imprints of the interpreter's interaction with these objects are also varied. However, it is an important fact that these various Imprints have a certain common origin, namely, that they have been formed on the basis of signals from the same receptors, i.e. organs of "feelings". Let us call such imprints or forms izaesthetic, emphasising by the choice of this Greek term ("iz" the same, "aestheticos" - sensitive) the single sensitive source of such imprints.

The "a priori gestalt", as far as it exists in the interpretor as ready and farmed, and therefore not requiring an interaction of the Interpretor with real external objects in a certain reception zone, will be designated as corresponding to a "zero zone", e.g. as ⁰X (or ⁰Y etc).

However, the correspondence of a priori gestalt with specific receptors is all the same a fact, since in the evolutionary process of the type, i.e. philogenesis, it formed under the influence of signals of fully determined receptors. If this is for example a sense of smell and the small reception zone is given a certain number, say No.2, then when a certain reflective situation is described, the a priori smell gestalt can be signified as ⁰²X". The concept of the "izaestheticness" of a certain form to an a priori gestalt has accordingly a very clearly defined sense.

Naturally the a priori gestalt, representing the reflective experience of the type in the individual, does not have an original pattern in the shape of a specific object, i.e. of a unique object in unique circumstances: let us call such objects more concisely occasional objects, from the Latin "oc/casio" - an event, a happening, a coincidence of specific circumstances. Being generalised and not arising, but only being reproduced for a certain utilitarain function, the a priori gestalt must be related to a number of usual forms (from the Latin "usus" - usage, normal use). However, among occasional imprints (i.e. imprints of occasional objects), and also generalised imprints, which have become usual patterns produced in the workings of the Interpretor itself and which therefore are no longer a priori but a posteriori, a priori gestalts become members with full rights in all respects.

It is necessary for us to contrast the concept of "occasionalness" with the concept of usualness. We have already spoken of the adaptive object being able in certain cases to change its states not only locally, under the influence of the reflected object which is affecting it, but also integrally, by transferring from one state to another, changing the co-relationships between many or all of its components.

It is clear that functionally important reconstructions of this sort can also be reflected by the receptors, but the Imprints of these receptors' indications can be varied. Some of them reflect only the interpreter's inner state without any reference to what sort of interaction the interpretor has with the external environment. But other imprints reflect those Internal reconstructions of the interpreter which are conditioned by the interpreter's current interaction with the external object, and accordingly represent the components of a single integral event of a higher level. Such imprints (together with an object's imprints) will be named concasional, as will the interpretor's internal and external states corresponding to them.

Resemblance and Continguity Relationships and Methods of Designating them. Let us agree to name any two objects resembling objects, or objects that have a resemblance relationship, if in a particular aspect of their examination the presence in them of the same part or similar parts has to be taken into account. We shall call a similar part or the same part of these two objects the basis of the resemblance and we shall indicate the presence of a resemblance relationship between objects, e.g. A and B, in symbolical terms in the following way: A-pp-B, where the symbol p is repeated in the case of both A and B and must indicate the presence of a p basis of resemblance in both A and B.

If this is necessary we can also show in symbols the case where the basis for the resemblance relationship is the presence of just that similar (though not the same) part in objects A and B: A-p_ap_b-B.

However a definition of this sort will only be used in rare circumstances where the context does not exclude ambiguity.

In so far as the imprints on the interpreter have an independent existence, the concept of the resemblance relationship broadens to include them as well.

Let part X and part Y of object A include the same component p. Therefore they are in the resemblance relationship X-p p-Y. In this case as we have already said, imprint X" of part X and imprint Y" of part Y, if they are situated in the same reception zone, have a similar component LC, and this allows us to exactly describe the type of resemblance relationship between such imprints: X"-p" xP" y-Y".

But let us agree, if the concept allows it, to state the presence of a resemblance between the imprints also without indications of the basis's association with this or that imprint, i.e. in the form X"-LC LC-Y".

Moreover we shall not feel bound to include strokes with the symbol for the basis of the imprint resemblance, i.e. we shall, where it is permissible, also regard this notation for the resemblance relationship between imprints (X"-p p-Y") as equal to what has been given, where the symbol p only reminds us of the "genesis" of the resemblance relationship between Imprints - the presence of a resemblance relationship between active parts which have imposed the imprints under review on the interpreter.

Let us now move on to define what exactly we shall understand by Contiguity Relationship beginning once more with the relationship of inclusion, i.e. the relationship between the part and the whole.

A part of any whole can be composed of properties, where there are very few properties resembling properties of other parts. In this case we cannot consider that parts of the whole are found in a resemblance relationship as we have determined it. But in return they are inter-linked in the links structure of the whole, and can sometimes even be in direct contact with each other in space or if they are events, displace each other in time, in that they also represent aspects of one integral whole, its components. Let us say that such objects or events are in a continguity relationship.

It follows from this definition that if two objects, for example, two imprints, imprint X" and imprint Y", existed independently in the interpreter, and then a link developed between them (let us name it link LC), for example in the form of a "crosspiece" or contact, we are then justified in regarding imprints X" and Y" as parts of one single whole, including, apart from these imprints, link LC as well.

It now remains for us to decide on methods of designating a contiguity relationship.

Let us first of all examine the "pure" case of contiguity when correlating objects do not have a resemblance basis within them. For example part X and part Y of object A do not overlap, i.e. X.Y = Ж, or, in the case of imprints, in imprint X" there are also no components the same, and X".Y" = Ж.

In spite of the polarity of the resemblance relationships and contiguity relationships, they have channels for changing into one another. We shall make use of this circumstance when selecting methods of designating a contiguity relationship which accord with methods of designating a resemblance relationship.

If we compare objects in a contiguity relationship, e.g. imprint X" and imprint Y", link LC (in the form of a cross-piece or contact between objects) proves to be common and moreover the very same part of each object. Therefore it can be regarded as something specific, but at the same time as a resemblance basis between objects. And we can show this fact with the symbols already introduced :X"-LC_x„ LC_y,,-Y".

But since link LC, being an external component with regard to both X" and Y"_Ж in particular, can correspond in general to a simple contact, to the touching of X" and Y", let us agree to designate (when designating the contiguity relationship through the resemblance relationship) not the intermediary contact, not link LC, but only the symbols of the linked objects in contact. Then the contiguity relationship between X" and Y" will be shown as existing in this way: X"-x" y"-Y". If in the given case we omit the strokes in designating this relationship, the contiguity formula between X" and Y" will look like this: X" -xy-Y", which is different from the resemblance formula (for example, on the basis of p): X"-pp-Y".

In this particular case when one of the objects, (for example, imprints), is either fully included in another or coincides (is similar) as a part of the other, the resemblance relationship will be noted thus : X"-xy-Y" (if X" Y"), while a contiguity relationship will not change in the notation: X" -xy- Y". The simultaneous presence of both these types of relationships can be shown thus: X"-(xy, xx)-Y".

With this we conclude our account of methods of designating objects, their properties, their relationships and their properties, their relationships and their reflections in an interpreter, seen as invariable, static characteristics of the components of reflection situations; these interest us in connection with the problem of reflection and its cybernetic Interpretation, and also because of the need to have some convenient means of describing these characteristics. Let us now turn to the dynamic aspects of reflection processes, beginning first with a description of the simplest emelemtary acts.

Naturally we cannot, and should not, examine specific physical and chemical processes occurring in the reflecting object¹⁾: we must concern ourselves with the moment of the start and finish of these processes, and of the appearance of results and, when the links structures of elementary acts in an integrally whole complex event (which is interesting from the point of view of the formation of reflection mechanisms) are farmed: it is preferable to present all these in the form of descriptions based extensively on symbols, if their content is sufficiently stable and can be stipulated.

Let us introduce some new symbols for the elementary acts in reflection processes.

Footnote

1) K.H. Pribram attahces much significance to specific mechanisms for the memorisation patterns, their comparison and stimulation, in his book recently translated into Russian [147]. In particular he considers that the patterns of objects of external reality, revealed through receptors, are not flat pictures, but are fixed in the 3-dimensional space of the memory by holographic means. This hypothesis is becoming more and more accepted these days.

Instead of the words "the object A appears" (or object A's appearance") let us write !!A. remembering that it is a question of the appearance of object A in a certain reception zone of the interpretor. If necessary we can indicate the number of the reception zone as well, for example: !!³A. However when it is a question of izaesthetic reflection, we can also speak of the appearance of object A's active part X, and of the appearance of the direct imprint X" of this part X in the interpretor, and thus the expressions !!X, or !!X", do have some sense in our symbols system. In particular a direct imprint of just a component of object A's part X can appear, for example: !!p", where p" Н X". In exactly the same way the appearance of another component of this particular imprint can be noted, for example !!x", where x" Н X", as a result of the fact that x Н X.

Then we introduced the concept of the intential imprint we had to distinguish the fact of the rise, the formation, of this imprint from the fact of stimulation after it had already formed.

Naturally, until the intential imprint has developed it doesn't exist; and when it arose, it appeared. Therefore for the intentials imprint's act of arising we can use the same sign as for the appearance of the direct imprint, i.e. the sign !! But the act of stimulation in reflection mechanisms plays a special role, and it has to be designated with a separate symbol. Let us agree to write !X" instead of the words "intential imprint X" has been stimulated" (or "the stimulation of intential imprint X"). Then the formula !⁰X" must be seen as a description of the fact of the stimulation of an a priori gestalt.

When examining specific isolated acts of reflection, it might be necessary to distinguish them from each other. The most simple of the distinctions is the indication of the event's ordinal number. Far example we can speak of object A's first, second, etc. appearance in the interpretor's reception zone under examination. A brief notation for distinguishing one appearance from another can be this : !!₁A; !!₂A; ...; !!_kA. We can show this information even more briefly in this way: !!₁ -_kA. 

It is accordingly possible to differentiate an imprint'sacts of appearance, for example: !!₁ X" etc, or an imprint's stimulation: !₁X" ; !₂X",---;!_kX" etc or in the shortest form: !_1-kX". Sometimes it is not the act's ordinal number and not the number of acts which is important, but an emphasis that has been repeatedly accomplished. Let us agree to use dots for this purpose. For example, the expression ! ...X" indicates that X" is repeatedly stimulated, while the expression !! A indicates that object A appears repeatedly. Accordingly !! X" shows the repeated appearance of imprint X". The event !!°y" and, even more so, !!°Y" is impossible, as the a priori gestalt cannot appear; it is given in a completed form, a priori.

And, finally, it is sometimes important to emphasise that a similar, though not the same, phenomenon is being examined i.e. only a variant of the phenomenon of the same class. For example, if in respect of the interpretor the reflected object appears in the same reception zone in not absolutely equal perspective or these are in fact various examples of objects of the one class, we shall when necessary indicate the fact of the object's variation with letter or number indices next to the symbol of the object. For example, A₁; A₂; A₃ or !!A₁ - !!A₂ - !!A₃ . This can be written even more briefly: for various examples A_1-3 and, for their appearance, !!A_1-3. There are also obvious methods within our symbols system for indicating that the same object comes into various reception zones and is for this reason reflected in "various perspectives", i.e. in the form of imprints which are different from each other. The formula ²A"₁ - !!³A"₁ --!!³ A"₁ --!!⁴A"₁ shows that object A₁ has entered reception zone with the numbers 2,3,4, and that corresponding imprints have appeared in the interpreter. A briefer form of notation for this sequence of events can be this: !!^2-4A"₁.

As we shall have to frequently emphasise that in spite of the differences in receptors, i.e. in spite of the non-izaestheticness, various imprints have a common character, which is expressed in the identity or equality of original patterns and in this sense they can also be regarded as the same in "origin", let us agree to name such forms "izogenic" (from the Greek "IZO" - equal, the same, and "gen" - species, origin). We can then speak of the degree of izogeneity. depending on what basis we consider original patterns to be the same: they might be the same state of a particular example or various aspects of its state, various examples of a particular aspect, or various aspects of a type etc.

And finally, let us agree on the methods of designating the correlating events and phenomena.

They can be correlated by various methods and if necessary some of these differences will be reflected in symbols. So the fact that an event, a phenomenon, or a result has as its cause a different event, phenomenon, or result, will be designated by a "thick arrow", Э For example, !!A Э !!¹X" shows that the appearance of imprint X" has as its cause (being a consequence) the appearance of object A in the interpretor's first reception zone.

With the aid of a "thin arrow", an arrow of implication, we shall indicate a gnostic ("logical") sequence, which reflects the fact that from a knowledge of the one phenomenon we come to a conclusion about the existence of another. For example, we conclude from the fact that object A appeared in a certain reception zone that there is in this zone another part, for example, part X, although A is not the cause of X. The gnostic sequence will be shown in this case thus: !! A ® iiX.

The direction of the arrow of a gnostic sequence can either coincide or not coincide with the direction of the cause-and-effect arrow. For example, if on the basis of our knowledge of the cause we make a conclusion about the existence of an effect, then the directions coincide, but if, when we have revealed an effect, we make a conclusion that there was or there is present a cause, the arrows will not coincide. In other words if Ю !!X", then both !!A ® !!X" and !! X" ®!! A are possible.

When we examine complex events it is important to take into account their temporal correlations: preceding and following in time. In order to designate this relationship we shall use as a representation of the sequence of events an analogous sequence of symbols of these events in the text, and between these symbols we shall put a hyphen. For example, !!A - !!X" signifies that first of all object A appeared, and then its part X".

Let us introduce one more eventuality; we shall replace both the cause-and-effect signs, and gnostic signs of sequence by the sign for sequence in time anywhere where this does not lead to ambiguity, even if certain events have other temporal correlation; for example, they might appear simultaneously. So the chain !!A - !!X - ! X" could also be shown with arrows !! A®!!X Ю!X", since from the fact of the appearance of object A the fact of the appearance of object A's properties X follows only logically (though in time these events are not conveyed) while the appearance of properties X serves as a cause for the appearance of the imprint X". In this case the cause-and-effect arrow does not contradict the direction of the sequence of events in time. However, given that all this is obvious, we are able to describe the complex event which is under examination with a simplified formula: !!A - !! X - !!X".

As we established when examining various reflection processes the principal role is taken by events such as when the repeated recurrence of the same process leads to a gradual deep reconstruction of the reflecting object's (the interpretor's) substance, and over a certain amount of time the interpretor starts to react in a qualitatively different way towards the same influences. In this case we can speak, albeit with certain reservations, of threshold events which come after certain events have crossed a certain critical threshold - in the number of their repetitions - which we shall indicate with the letter П with some index or other: П, П₂ etc. The notation ((!!_1-k²A₃ -!!_1-k²X") (П₁ L.C) will always be read thus: the third example of object A appeared LC times in the second reception zone, and each time its ²X"₃ form appeared accordingly; here the number of appearances (the number LC) crossed the threshold П₁.

The semi-colon signifies here the conjunction "and" , "moreover", "here" etc.

It is the same for stimulation. For example the formula ((!_1-kX" - !_1-kX"); (П₂ Н k)) indicates form X" has been stimulated LC times and each time as a result of this form X" has been stimulated; here the number of such events has exceeded the threshold value П₂.

In this way we can also reflect the fact that the next single event occurred after a certain threshold process had already occurred. For example, the expression (!!²_kA; П₁ Н K) tells us that object A's appearance in the second reception zone occurred after the number of preceding appearances had crossed threshold П₁.

Types and Methods of designating Associations 

Let us now decide on methods of designating specifically reflective acts, that is stimulation interlinking acts between direct and indirect imprints in interpretors taking into account that these imprints can be in a resemblance or contiguity relationship.

Let us start with the contiguity relationship. Since the link C.L between two imprints, for example, imprint X" and imprint Y", is also a deformation an the body of the interpretor, it can, like any other information, simply appear for the first time or exist in the form of an intential deformation and then only be stimulated in some particular circumstances. The act of appearance or stimulation itself can however serve as a cause of stimulation of some other imprint, linked with this link L.C. All this enables us to use appearance, stimulation and sequence signs not only for symbols of imprints but also for symbols of the link L.C. between them.

For example, the formula ! X" ! xy - !Y" must be read as a brief notation of the fact that after imprint X" has been stimulated its link LC with imprint Y" is stimulated, which leads to the stimulation of imprint Y", where link LC is the basis of the contiguity relationship between these two imprints.

The formula ! X" - !! xy - ! Y" shows a similar chain of events but with the difference that link LC, serving as the basis for the contguity relationship, is not stimulated, but arises and appears, i.e. it had not yet occured in the form of an intential crosspiece.

We can also imagine in principle the position when an intential imprint Y" existed but there had not yet been an imprint X", and only when it appeared in the form of a primary deformation did this fact lead to the appearance of a link between the new extential imprint and the already present intential imprint. As a result of this the intential imprint Y" was stimulated: !! X" - !! xy - !Y".

We have to deploy many words to explain the contents of a formula containing a small number of agreed symbols and therefore the use of such symbols is justified, even essential.

If two imprints are in a resemblance relationship, i.e. they contain in their composition the same components, it is this sameness of components which plays a decisive role when there is a resonance interaction of imprints, in stimulating one imprint a stimulation occurring in another imprint. Therefore we can show symbolically not only the fact that imprint Y", for example, was stimulated after imprint X" was stimulated, i.e. ! X" - ! Y", but also that the cause of the relay of the stimulation was the resemblance relationship, which is expressed In the presence of a certain common component p in imprints X" and Y".

And so, if X" - pp 1 Y", and the stimulation of imprint X" on the basis of a resemblance relationship led to the stimulation of imprint Y", it is possible to show this chain of events thus: !X" - pp - !Y". we can emphasise, if necessary, whether this chain of stimulations arose for the first time, as we did for the contiguity relationship, and then the formula will be thus: !X" - !! pp - !Y", or whether this resonance cause of the influence of one imprint on another is reproduced each time, and will not appear anew, i.e. !X" - ! pp - ! Y". The possibility of one imprint being stimulated by another as a result of the presence between them of a resemblance relationship will be regarded as the presence of a resemblance association between these imprints. If however the stimulation of one imprint can lead to the stimulation of another as a result of the presence of a contiguity relationship between them (as a result of the presence of the link LC) we shall say that these Imprints enter into a contiguity association.

Let us now examine formulae which show associations of imprints, taking into account that these imprints are the result of the interpreter's interaction with the object, situated in certain reception zones and that consequently these imprints are izogenic.

The formula !!²X" - ²x¹x - !¹X" shows that after imprint X" has appeared as a result of the situation of the original pattern of this Imprint in the second reception zone this new imprint has entered a contiguity association with the imprint of this same object, which was left when that original pattern was situated in the first reception zone.

The formula !!²X" - xx - !⁰²X" indicates the association of the same imprint with the izaesthetic a priori gestalt, i.e. the gestalt of its reception zone, also association by resemblance.

The case when the object transverses the interpretor's reception zone sequentially (as a result of the object coming up to the interpretor or the interpreter to the object) presents special interest, in that it crosses, for example, the sight, sound, smell, touch, and taste zones. Such an object is reflected by the interpretor in the form of a sequence of izogenic izaesthetic imprints which will in fact overlap to some particular extent in time and have certain resemblance features, in spite of the fact that they are picked up by various different receptors. But in simplified terms we can consider that these are "sequences" or zones, adjacent at the time of appearance, of an integrally whole imprint of the same original pattern (zone imprints) which is scrutinised when there is a sequential change of "focus distance" of the instrument through which the object is examined by the interpreter.

In the cinema and television such a method of scrutinising (and demonstrating) an object is called transfocation, and therefore the succession of zone imprints of a particular occasional object transversing contiguous reception zones, can be called a transfocal imprint. We can protray a situation of the rise of a transfocal imprint, for example, thus (!!⁴A - !!³A - !!²A - !!A - !!¹A) - (!!⁴X" - !!³X - !!²X" - !!¹X ). But this natation can be simplified as well, by noting the initial and final transfocal zones. (!!⁴A ... !!A¹) - (!!⁴X" ... !!¹X"). This method can be kept only on the level of indices of transfocal zones, corresponding to the reception zones which the object transverses:!!^4-1A - !!^4-1X.

 If necessary the transfocal imprint can also reflect specific types of association between compositional zone imprints. We have already used such notation; for example, a double zone transfocal imprint with a reflection of the fact of association between zone imprints:!!²X" - ²x¹x - !¹X". If it is important to reflect the fact of "associatedness" of izogenic non-izaesthetic zone imprints in a single transfocal imprint, when this associatedness is caused precisely by the tontiguity of the reception zones, let us simplify this notation. It can be simplified in that in the association symbol there can be left only the numbers of the corresponding reception zones. Then the formula being examined will look thus: !!²X" - 21 - !¹X".

Like any imprints transfocal imprints can serve after a particular repeated occasional appearance as a basis for the formation of an intential pattern having a certain particular function so that the interpretor can carry out its general function in the meta-meta-system, A transfocal imprint can consequently change into a transfocal pattern which no longer appears occasionally but is stimulated usually.

The Objectivity and Subjectivity of Association 

It is clear from all that has been said above that the concept of association retains meaning only in respect of imprints, patterns, and the results of reflection. We cannot say that original patterns i.e. reflected objects, if they are not themselves imprints, are in any particular association. But nevertheless it does sometimes make a difference what the original patterns themselves or the relationships between an original patter's states are, if it is a question of the types of association between the patterns of these original patterns. For example, if the original patterns have even the same components, and the characteristics of these components are reflected in the interpretor in the form of the presence of the same components in imprints or in the patterns of these original patterns, it is obvious that the cause of the resemblance association between the results of reflection, i.e. between imprints or patterns, is the presence of a resemblance relationship between the original patterns of these reflections. In this sense association between patterns is objective.

In exactly this way original patterns can have not only resemblance but also a link (crosspiece or contact). And if this link is reflected in the form of a link between imprints or patterns of the original patterns (as a link or reflection contacts) such reflections will, firstly, are in contiguity association and, secondly, the cause of the appearance of this association will be the presence of a contiguity relationship between the original patterns. This means that such as association between patterns does not contradict our beliefs about the objectivity of reflection. We observe a somewhat more removed but nevertheless natural and therefore objective dependence between relationship and association when a transfocal pattern is developed. A spatial contiguous association between a transfocal pattern's zone patterns reflects the fact of a preceding temporal association of an original pattern's states, revealed in the varied relationship of the original pattern to the interpreter's reception zones.

But the result of all this is that the parallelism between the relationships of original patterns and the associations of their patterns does not always occur. For example, if the reflecting object, i.e. the interpretor, has not reflected a link which exists between the original patterns, the contiguity relationships between the original patterns does not disappear because of this, but there will not be contiguity association between their patterns - which means it would not find an objective reflection.

The same applies for a resemblance relationship.

Both for resemblance and contiguity a position is possible where there is an association of patterns but one which is brought about by internal causes of the interpretor's work, and not by a reflection of corresponding relationships between original patterns.

In this sense such ah association is not objective and we can call it (conditionally) a subjective association.

 And finally other types of subjectivity are also possible, i.e. of non-correspondence between the relationships of reflected original pattern objects and associations between the reflections of these objects, i.e. between imprints and patterns. For example, contiguity association between imprints can arise as a result of there being a resemblance relationship between the original pattern of these imprints. We still have to examine such cases when analysing complex reflection acts, and so we once again emphasise that all the non-correspondences and parallelisms named and mentioned above are a genetic prerequisite for the development of the distinction between subjective and objective reflection of reality.

It is easy to comprehend the correlation between the subjective and objective when comparing usual and occasional reflections. Usual units, for example intential patterns, can be regarded as more objective on the basis that they reflect only the generalised, the most frequent, and therefore the most stable features of objects of a certain class. The LC, the fortuitous, the non-typical has no chance of being consolidated in a usual form, and therefore usual units can more naturally be the most objective, more fully reflecting an original pattern's essence.

However, if we take into account that in a generalised usual pattern's formation process only that which is functionally significant for the interpretor is fixed, then a conclusion about the objectivity of usual units will no longer seem so obvious. An occasional Imprint of an occasional object can determine in certain cases a larger number of essential properties of this object than will be reflected in the object's usual generalised pattern. So from this point of view usual units seem to be more subjective than occasional units, being more "egocentric", utilitarian, and reflecting the essence not so much of these units' original patterns, as of the interpretor itself.

However, the contradiction we have shown does not invalidate the results we have obtained. Generalised, abstract usual units represent objective patterns of original patterns scrutinised in a subjective perspective. In other words, these are utilitarian projections of the essences of original patterns, i.e. the result of refraction of the essence of objective reality through the subject's essence.

The concepts of Hobbes and Descartes, already noted, concerning methods of fixing reflections of the sequence laws of actual phenomena related above all to the development of a contiguity association. But concepts concerning the possibility of a resemblance association developing, based on distance resonance influences of one Imprint on another have also long been familiar to scientists. The English Doctor Hartley in the middle of the eighteenth century advanced his vibration theory of the interaction of psychically fixed impressions from external influences. This theory has not, however, found general recognition. It would appear this can be explained first by Harley interpreting the vibrations and resonances themselves purely accoustically and, second, by his reducing all forms of associations to vibrationary ones. [201, p.132-133].

We have already noted that at the moment there is in vogue a particularly cogent hypothesis to the effect that an operative comparison of patterns and the disclosure of similar and varied components within them can be based on the comparison of hologramms of the signals coming from the receptors.[147]. If the processes of memorisation and comparison of patterns are such, this means that both simultaneous resonance mechanisms and spatial contiguous mechanisms of associations play a uniquely important role in higher forms of reflection and are constantly changing into one another. we shall indeed come to this conclusion later on - but without examining the physical bases of associations. At the moment it is important that we turn our attention to the fact that the reflection of links of (particular) phenomena in time sequences in the form of spatial associations of patterns does not mean that, if the process of timespace transformations does not prove to be uncontrolled, the reflection is not objective.

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