TOWARDS AN OBJECTIVELY COMPLETE LANGUAGE

An essay in Objective Description as applied to Scientific Procedure

J. G. Bennett, H. P. Bortoft and K. W. Pledge

SYSTEMATICS      Vol. 3 No. 3 DECEMBER 1965

NOTE: The DuVersity makes this article available for several reasons. The first and foremost of these is that this is the only place in which Bennett attempted any kind of rigorous use of his concept of three modes of inner togetherness - compatibility, compresence and coalescence. The distinguishing of modes of togetherness is crucial for any theory of systematics. Secondly, he and his colleagues make the concept of the present moment as defined in terms of will the primary starting point for their investigation of the structure of what a scientist does. Bennett's understanding of will and the present moment is, as far as we know, quite exceptional and unique. It is still the case that people seek to understand questions of reality in terms of consciousness and function alone, which means that they cannot understand!

We have preserved the mathematics mostly for the sake of the record. It is exceedingly clumsy and wearisome to follow. However, it does emphasise the hard work required to focus attention in precise ways on what it is we do, instead of thinking in terms of our habitual representations. Those who can struggle with the symbolic terminology may find some ultimate benefits.

Ken Pledge brought to the work his considerable experience in teaching experimental method to students. His 'Structured Process in Scientific Experiment' which appeared in the next issue of Systematics [it is presently included in the collection Enneagram Studies that is still in print] took up the themes introduced here to do with 'setting up' procedures in using scientific apparatus and showed how the inner lines of the enneagram precisely corresonded to such procedures. Pledge's paper remains perhaps the only one that gives evidence for the enneagram as a diagram of the present moment and applicable to concrete and precise combinations of actions.

Henri Bortoft went on to struggle with the formalised system in his own way, as in 'The Resolution by a Rigorous Descriptive Method of Some Dilemmas in Modern Physics' (Systematics Vol. 4 No.2) which he worked on while completing a PhD thesis under David Bohm. Eventually however he turned for his inspiration away from 'rigorous descriptive method' to Goethe. He has become known in recent years as a key expositor of Goethe's 'way of science' and has written an important book on The Wholeness of Nature.

ABSTRACT

A symbolic language is built up for the purpose of describing the structural features of operations such as characterise the procedure of scientific investigation. There are five sections: In Section I two key notions of Will and of the Present Moment are introduced as the foundation of the descriptive scheme. Section II develops and elaborates, with special reference to the scientific activity, a comprehensive symbolic model whose elements derive from the structuring discovered within the content of the present moment. Certain elements of the model are then applied in Section III to distinguish and specify six types of complex situations significantly exemplified in scientific work. In Section IV the descriptive symbolism and the complex situations thus defined are used to describe and clarify the operational procedure involved in the genesis and performance of a typical physical experiment. The description is carried only to the stage where the results of measurement are recorded. In the Conclusion, Section V, the scope and limitations of this description of an experiment are examined and possible extensions of the language, proposed for a later paper, are discussed.

I INTRODUCTION

Our languages of verbal signs and sentences have grown out of the need to communicate experiences and instructions. In relatively simple situations they are effective; but even so they require a community of memories and behaviour patterns to supplement the inadequacy of words to express the complexity of experience. In scientific discourse the community is that of specialists who can recognise one another's experiences and behaviour.

In modern times two difficulties have arisen in the use of language. One is connected with the increasing specialisation of the communities able to have shared experiences. The second is due to the changing requirements of communication in itself. In the present paper we shall be concerned only with the second type of difficulty and with an attempt to remove it by constructing a new kind of language rather than by supplementing the existing forms.

The requirements of communication have changed because it is no longer possible to have an effective community of knowledge and action. We know too much and we do too much to be able to convey what is required by means of words and sentences. The present trend is to think in terms of structures and organisations rather than elementary objects and actions that can be expressed by single words and verbal sequences.

Moreover there have been profound changes in our way of looking at the processes of nature. The traditional concepts of space, time and causality have been criticised and modified. Even the belief in universal "Laws of Nature" has given place to a tendency to regard successful description and action as more promising than the search for truth.

In keeping with these tendencies, we have undertaken to construct a descriptive scheme, using a formalised notation of symbols and signs, for the purpose of describing various features of scientific procedure. The basic signs and symbols can be arranged in formal expressions to provide models for procedure. For this reason we refer to the formal scheme as a "language".

Our natural language already provides us with models, but it is not without disadvantages. It is vague and imprecise, containing many elements whose meaning is not readily discernible. It is rich and diffuse and so does not lend itself easily to characterising the essential features of a situation. Through adhering to the language with which we are familiar we often incorporate elements which we do not intend along with elements which are quite unnecessary and whose effect is to hide what we are seeking to show.

An accurate description, which is also not misleading, is attainable so long as we are prepared to limit and discipline ourselves. For this we must agree to use only descriptive elements whose meanings are directly verifiable in experience and which are therefore unambiguous.

As an example, references to "the past" are inherently ambiguous for the simple reason that all meanings must be within the present moment. We cannot recognise "the past" and so we do not know what it could mean. That we can use "the past" effectively, that is in the construction of proper sentences, can hardly be taken as a guarantee that in doing so we know what we are talking about.

If a sign is to have meaning then it must point to an element of experience. When one sign is correlated with the recognition of a single recurrent element within experience, that is with a meaning, then that sign is a model of the meaning. Further, if the one-to-one correspondence of signs with meanings is rigorously adhered to then the meanings of expressions built up from such signs will be evident and can be communicated without ambiguity. Thus by imposing upon our scheme such limitations we can justifiably hope to convey what is intended and no more. For our present purposes many features of experience are irrelevant and consequently only a few basic elements are required.

We start with the one certainty of our experience: that there is a region of experience which for us is the present moment. All our certain experience is confined within this region. We start then with the axiom that if anything can be described at all, it can be described in terms of the content of the present moment.

The elements of the present moment are distinguishable from elements not present. Collectively they form a whole enclosed within boundaries that are never well-defined and usually not even recognisable. Moreover, there is a paradox of the present moment that is unique in our experience. This consists in the contradiction of our experience which is always and necessarily confined to the present moment and our conviction that the present moment is not all there is. We do not doubt, for example, that there are things we do not experience and never shall experience which yet exist. We do not doubt that there are other selves or other minds and that each of these has his or its own "present moment" that is different from ours.

In short, we have the paradox that the present moment is always single, unique and all that we can know; and that it is also multiple, indeterminate and capable of being enlarged to include what is outside it. The formal resolution of the paradox is given by the definition of Will as that which determines a present moment and is both unique and multiple; always the same in its nature and constantly changing in its power to act.

We start, therefore, with the notion of Will as having the special property of being non-numerical and non-extended, so that it is not legitimate to say that it is either one or many. We shall therefore speak indifferently of "the" Will, "a" Will and of a disjunction and coalescence of Will or Wills. When associated with the present moment, Will appears as a "self" or a "person". But it may also be the initiating factor for an act too restricted to merit the description of "person". Each differentiated part, or sub-region, of the present moment can be regarded as the domain of a "Will".

The Will of the present moment experiences, decides, initiates and terminates actions but it is not itself involved in action. This latter condition follows from the definition of Will as non-extended and non-numerical. It is not even necessary to resolve the question whether "Will" is a descriptive fiction, a substance or an independent mode of reality. We are concerned in this paper with the problem of complete, adequate and unambiguous description: not with any metaphysical questions of being and knowing.

Within the present moment, we can distinguish three main kinds of elements. These are:

1. "Goings-on" which range from a general flux that has no immediate significance, to meaningful transformations and purposive acts.

2. Recurrent features which include material structures both living and non-living, executives, observers and agents.

3. Modes of togetherness which can vary from mutual tolerance or compatibility, to a common presence, and ultimately to a fusion of elements into a whole that can exist and be acted upon and cognized as such. These descriptions are not definitions nor are they intended to identify precisely differentiated parts, or sub-regions of the present moment. If we can recognise what is referred to that is all that is necessary. In the present paper we shall construct a descriptive model based upon the formalisation of these distinctions within the present moment. This artificial language will then be utilised to construct a model of experimental procedure which is less cumbersome than the models provided by our customary language, and which can, therefore, more evidently demonstrate the major structural features which characterise experimental procedure.

II THE DESCRIPTIVE MODEL

1. That which uniquely exists is the Present Moment. There is only one present moment, namely, that which is here-and-now.

1.1. The present moment may be thought of as a region of experience which is diverse in content yet present as a whole. It embraces separate elements of experience in a whole which is the place of action and existence.

1.1.1. The present moment varies both in content and in range of embrace ("extent"). The power to focus or to extend attention determines factors of inclusion and exclusion. Thus, by the focusing of attention a subordinate present moment may be isolated.

1.1.2. The range of embrace of the present moment is the limit of immediate experience.

1.1.3. The present moment is not a point. If it were, it would be without action and awareness. A point present moment is without content and is thus equivalent to zero experience.

1.2. The present moment cannot be conceived, let alone defined, without reference to the centre of experience. There is such a centre S for whom the present moment Q is immediate experience. Q as such does not exist. All that S is, or can be, aware of is the content of Q. We write:

          P Q...................................................................................................................(1)

which reads "P is within the present moment Q of S". More simply, we can write:

          P S.....................................................................................................................(2)

which reads "P is within the experience of S". It follows from 1.1.2 and 1.2 that (2) implies (1), and the converse. The symbol always means "is included in".

1.2.1. The centre of experience is not a part of experience but "that" for which experience is present. Since "that" is active and effective we shall call it a will.

1.2.2. Every will determines the present moment.

1.2.2.1. Will is monadic, excluding all other will but itself; this is why the present moment is unique.

1.2.2.2. It is unique from the stand-point of the will 'for which' it is: but it is not unique for another will.

1.3. For every will S there is a present moment Q.

1.3.1. The present moment is different for different wills or centres of experience, such as selves or people.

1.4. The present moments of separate selves need not be isolated. They can be combined in different ways. For our purposes we distinguish three different modes of togetherness.

1.4.1. The present moments Q, Q, ... , Q are compatible. We write this

          (Q, Q, ... , Q) ................................................................................................(3)

To form a statement we write

          (Q, Q, ... , Q) (Q) ......................................................................................(4)

which reads " Q, Q, ... , Q are compatible within the comprehensive present moment (Q) ".

This statement cannot be doubted, for if there are n present moments, corresponding to n selves S, S,..., S, then they must be compatible. If we can generalise to

          (Q, Q, ... , Q, ...) (Q) ...................................................................................(5)

then this is equivalent to the presupposition of some universal order (in the sense that it is not restricted to a universe of n selves). Consequently (5) is the basic presupposition of order. If there is some present moment that is not within the universal present moment (Q), then it cannot be compatible with any or all of those present moments that are within (Q). This implies that it is beyond order in the sense that order may not be predicated of it. The introduction of (Q) and (Q) is a formal device which ensures meaningful usage of "compatibility".

1.4.2. The present moments Q, Q, ... , Q can be compresent. This is written

          [Q, Q, ... , Q] ................................................................................................(6)

Such a compresence unit is equivalent to a communal present moment, for which we write [Q]. Thus

          [Q, Q, ... , Q] [Q] .......................................................................................(7)

That there is such a communal present moment, formed by the compresence of separate present moments Q, Q, ... , Q is the basic condition for communication. Two selves S and S can only communicate if their present moments Q and Q are compresent. If there is no compresence then there is no "contact". Further, within such a compresence there can be changes which are meaningful; that is, there can be transformations. Communication is an example of meaningful change.

1.4.3. The present moments Q, Q, ... , Q can coalesce: that is they can fuse into one whole. We write this

          {Q, Q, ... , Q} .................................................................................................(8)

In the coalescence mode of togetherness integrality predominates over separateness. Consequently individual present moments can no longer be added or subtracted without detriment to the whole. Such a coalescence unit is equivalent to a super present moment {Q} thus:

          {Q, Q, ... , Q} {Q}.....................................................................................(9)

1.4.3.1. Such a super present moment is the condition and basic presupposition of unification of will, that is, a community of purpose.

1.4.3.2. A coalescence bracket defines the sphere of operation of a single will.

2. The present moment is a perpetual flux. Although it always is the present moment, it is constantly changing.

2.1. The flux which is the present moment is not homogeneous, continuous, or closed.

2.2. Within the present moment we can distinguish simple flux, meaningful flux and origination.

2.3. Because of its "openness" the present moment can carry meaning and significance over and above the flux itself.

2.3.1. Simple flux is taken to be that, more or less, continuous background of the present moment, taken without reference to meaning or significance. It is that which merely happens. Happening just goes on; it is without meaning or purpose. We refer to this simple flux as change and denote it by the symbol "'. The change symbol is the most general way, in our model, of referring to motions, transitions, modifications of state and configuration, etc., which are not particularly meaningful. Rules for the use of this symbol will be introduced later (props. 7.1 to 7.4.1).

2.3.2. Meaningful flux, or meaningful change, we refer to as transformation and denote by the symbol "". Transformation, since it is meaningful, is always a reciprocal relationship. We indicate this reciprocity by doubling the arrow. There can be transformation only if the transforming subject has the capacity for it. As an example, one can consider a seed which transforms into a plant, thus preserving the order inherent in its genetic constitution. This can occur only if the seed is healthy and if the environment is favourable. If this is not so, the seed will decompose with resulting loss of order. Thus, in this example, if the seed decomposes we write

          PP............................................................................................................. (10)

where P1 stands for a speck of humus. If the seed transforms into a plant we write

          PP ............................................................................................................(11)

where P stands for the plant. In both (10) and (11) P stands for the seed. Such formal expressions will be discussed later in greater detail (c.f. props. 8.1-8.4.1).

2.4. Because of its discontinuity the present moment permits beginnings and ends, that is, operations of the Will.

2.4.1. A beginning is not a beginning ex nihilo. A beginning is a discontinuity within experience. It marks a change of direction, the injection of novelty, and the presence of purpose. Simple change is without beginning or end.

2.4.2. Beginnings are intentional acts of the Will within its own present moment.

3. Transformation is originated. Change is not, it just happens as it may.

3.1. Origination is an act of Will. The act which originates is a decision. An act is represented by the symbol "".

3.1.1. A decision is a decision to do something and not to do something else. It is an act both of commitment and of sacrifice.

3.1.2. Decision is a necessary sacrifice. Without this act nothing can be realised.

3.2. Decision without choice is impossible and choice without decision is unreal. They supplement each other in one act which is the first step in the direction of realisation.

3.3. The act of decision is always willed for it cannot be reduced to a choice between a definite number of previously available alternative possibilities which are completely cognised. On the contrary, a decision is an opening out towards an indefinite number of possibilities the majority of which are unsuspected by the will that decides. Nevertheless the decision opens the will to them.

3.3.1. Mechanical "decision", after the fashion of switching-circuit and game theory models, would be a null act. It would make a change of direction, but there would be no opening for novelty. Such a mechanistic model is inadequate as a picture of the world of human purposes and endeavours.

4. An act of Will results in the partitioning of a field of compatible possibilities.

4.1. The executive act of Will partitions what is possible from what is not possible and so brings into operation factors of inclusion and exclusion. It provides, at the same time, a criterion of relevance. All that is compatible with the decision pertains to it; all that is not becomes irrelevant.

4.1.1. It would be too "strong" to say that when a scientist makes a decision he "creates" possibilities. It would be too "weak" to say that he "selects". "Partition" is intended to convey a notion intermediate between "creation" and "selection". Nevertheless, either extreme may be approached asymptotically.

4.2. The paradox of action is that while everything is possible nothing is possible and that for something to become possible nearly everything else must become impossible.

4.2.1. Possibilities only become "realistic" as possibilities when they are limited. It follows that there must also be impossibilities. A decision is the act which effects the partition possibility/impossibility.

4.3. When a decision is made there is then a potential for realisation through further acts involving choice and hence commitment of the will. Without a decision there is no such potential and the situation contains only change.

4.3.1. Consider a traveller who has a choice of several towns to visit the following day. Initially, within the field of activity partitioned by the decision "to visit towns" he has several possibilities open to him. But until he has further decided which town to visit he can do nothing. We could say that when all the possibilities are open to him he is severed from these possibilities. He is able to do something only by an act of decision which links him with one possibility and effectively removes the remaining possibilities out of reach. If he refuses to choose, there is no linkage and nothing purposive can come about. By refusing to exercise his will as an executive power the traveller sinks into the world of mere happenings and merges with the simple flux. In effect he is refusing to be real, giving himself up instead to simple change. On the other hand, when he does make this further decision he opens himself towards an indefinite number of further possibilities of action, cognition, etc., formed around his choice. Only a few of these will be realised but if they are compatible with his decision they will all be initially compatible.

5. The act of decision is represented:

         E(P, P, ... , P , ...) ..................................................................................(12)

which reads "the executive E makes a decision (an act) which results in the partitioning of an open-ended field of possibilities of action P, P, ... , P , ... which are compatible with respect to that decision.

5.0.1. The executive E is Will in action. Without decision Will remains in abeyance; but so long as there is a present moment the will is there as its principle of unity and potential realization.

5.0.2. The Will cannot act in a vacuum and the possibility of action is the content of the present moment.

5.1. An act of will cannot be separated from the actor or the acted upon. The expression (12) does not tell the whole story. It must be amplified to show how the executive and the content of his present moment are conjoined.

5.1.1. As it stands the expression seems to imply a definite separation and sequence. It looks as though the executive E "existed" before, and the compatibility unit after, the decision, while the act itself "exists" and is separable from its elements.

5.2. There is no reason for supposing that any of these elements have the same meaning, or indeed any meaning, outside of an action situation. The compatibility unit and the executive are present, not after and before, but, within the act. It is only within the reality of the act that these elements are separable; and if our scheme makes it look as though they may lead a separate existence of their own, then we must introduce a correction term.

5.2.1. For this purpose we use the coalescence bracket and write;

          {E (P, P, ... , P , ...)}..............................................................................(13)

This bracket is to represent "present as a whole" which is the mode of togetherness we have named "coalescence". The situation enclosed within such a unit is coalescent. It is wholly present as one, and can be thought of as such.

5.2.2. Coalescence is not structural dissolution.

5.3. There is an almost self-evident rule of interpretation to the effect that the coalescence bracket is primary over its contents in the sense that it signifies the wholeness of the situation which is primary to particulate features to which the attention may be directed by the will.

5.3.1. The particulate features are secondary for they presuppose the whole in relation to which they are aspects.

5.3.2. Aspects are aspects of some total situation and it is only inasmuch as they are such that they have meaning and so can be recognised and known.

5.3.3. Thus the very condition for particularisation is that a situation is primarily present together as a whole. Such a primary wholeness is always, and must always be, presupposed when reference is made to particulate aspects.

5.4. Referring now to expression (13) we see that it represents primarily a total action situation. Within this total situation, two poles which are linked emerge. The executive E is the "subject-pole"; the compatibility unit (P, P, ... , P , ...) is the "object-pole"; the act "" links the two poles.

5.4.1. These elements bear meaning individually only when they are taken together. To isolate any element and consider it without reference to the others collectively within the present moment is artificial. We can hardly avoid doing this for the purpose of explication, but we must not assume that the corresponding elements of experience are similarly separable. So, for example, we must not suppose that the executive exists apart from an act. His only reality is within an action situation.

5.4.2. Will is meaningless except in a present moment and a present moment is unspecifiable except by reference to a Will.

5.5. Expression (13) is an example of what we call in our scheme a descriptive simplex. Such simplexes are the minimal descriptive expressions which can be said to refer to an element of experience having independent reality. Neither the executive element by itself nor the compatibility unit by itself can be said to have independent reality when taken in isolation. They require to be connected by the linkage act and it is then the whole act itself, represented by {E (P, P, ... , P , ...)} which is the element of experience. This is not to say that the constitutive elements are no more than representational artifices. They stand in distinct relationships to the present moment within which they are contained.

5.5.1. Descriptive simplexes play the role of building blocks in the construction of more complex expressions representing realising situations.

5.5.2. Any simplex has the following formal characteristics:
      (i) A subject-pole.
      (ii) An object-pole.
      (iii) A linkage.
      (iv) A coalescence bracket.
(i), (ii) and (iii) may be simple or compound.

      In expression (13) above, the subject pole is simple and the object-pole compound.

5.5.3. An expression is well-formed if it contains only descriptive simplexes, and as a whole has the form of a descriptive simplex. This will be illustrated when we come to build complex expressions out of simplexes.

5.5.4. An expression is complete if it contains direct reference to the Will S, that is the centre of experience. Since, in this paper, we shall be concerned with features of scientific procedure, we shall refer to S as "the scientist". Expression (13) is well-formed but not complete. It is completed by writing

          {E (P, P, ... , P , ...)} S ........................................................................(14)

where S indicates "within the experience of the scientist" or "within the present moment of the scientist S", or, best of all, "within the sphere of possible action of the Will S".

5.5.5. The full constitution of S will be given (props. 12.4.1 to 12.4.6) when all the necessary elements of the scheme have been introduced. At this stage all we need to say is that the executive element E is a property (but not a part) of the scientist S, whereby he is able to act within his present moment.

5.5.6. When the descriptive simplex refers to an act the subject-pole is the executive, since he is the source of the act. The object-pole, in this case, is called the aim or the objective.

5.6. In (13) the object-pole is represented as open-ended. This is to indicate that the possibilities compatible with a decision cannot in principle be enumerated. This does not mean that they are infinite but that enumeration is not possible by the very nature of the situation. If the bracket were closed, then decision would be no different from selection. But it can never be closed, for our very experience, with its characteristics of uncertainty and hazard, tells us immediately that we do not inhabit a closed Universe. Only if we accept this can we entertain the possibility of a truly creative act, an act which results in something entirely new and unsuspected.

5.6.1. The entries in the compatibility unit, i.e. P, P, ... , P, ... , etc., are referred to as "passive elements" or just passives. This name is not meant to imply any distinction between animate and inanimate or inert, for it includes both of these categories. A passive is any recurrent element taken without regard for the power to act or cognize. Passives can transform, change and participate in operations.

5.6.2. In expression (14) the passive elements are the "objects of decision". The objects of decision are possibilities. Inasmuch as what is possible can be considered only with respect to what is impossible, possibilities must always be within a compatibility unit.

5.6.3. Let Pc be all possibilities compatible with (and relevant to) a decision; and let Pc* be all possibilities not compatible with that decision and therefore effectively impossible. We may formally write this

          N (Pc, Pc*) S ..................................................................................................(15)

Where Pc (P, P, ... , P, ...) and the sign "N" indicates "not", in the sense of "it is not the case that ..." This expression is indicative of a beginning.

5.6.4. To illustrate how what is possible can only be considered against a background of what is not possible we might suppose that we are tempted to ask "is the field of possibilities not compatible with a decision compatible with itself?" i.e. can we write (Pc*, Pc*)? The answer is that this question cannot be asked. The expression (Pc*, Pc*) is meaningless for there is no criterion of limitation by which the compatibility unit referred to could be defined.

5.6.5. The interpretation of the passives as, in this case, objects of decision, has the advantage of not implying that they can exist independently in isolation from an action situation. This is reinforced by, and reinforces, our use of the coalescence unit. The passives have meaning in this scheme only inasmuch as they are within the present moment of an active Will.

5.6.5.1. This is consistent with the definition of meaning as "the recognition of a recurrent element in experience".

5.6.5.2. For the purpose of a descriptive model, it is not necessary to "step outside of the present moment". Questions of isolated independent existence do not therefore arise.

6. Words used as symbols are treated as invariants that can be transferred from one situation to another without change of content. This eliminates the dynamism inherent in the present moment as immediate presentation.

6.0.1. Conceptual thinking which uses words as symbols is by nature static. It freezes into immobility that which is by nature mobile.

6.0.2. In consequence, verbal description of change, transformation and flux in general encounters difficulties that, being inherent in the linguistic form, cannot be removed by a linguistic device.

6.0.3. Nevertheless, such devices are employed-without recognition of their artificiality-and they usually consist in introducing further concepts to link together the supposedly static elements. The latter are usually regarded as "states" and the former as "relations".

6.0.4. "States" are spurious present moments that are no more than conceptually instantaneous cross-sections of the situation. "Relations" are spurious acts of will that are not true acts because they neither begin nor end a process. Description by states and relations is then no more than a representational device that could be justified only if it worked.

6.1. This representational device tends to squeeze out the very features of experience which one is trying to point to. By directing attention to the static it seems to deny the primacy of that dynamism which is so striking in the immediacy of experience. Indeed, in its crudest form it amounts to an attempt to constitute the dynamic from the static, and is often associated with the claim that we do not know change directly but only infer it from the cognition of different states. In our model we take flux to be a primary feature of experience.

6.2. This representational device is intimately connected with that view which sees time as a simple linear uni-directional progressive sequence of instants. But what is not seen is that this characterisation of time, arises of necessity from the way in which we try to grasp our experience by the method of conceptualisation to which we are accustomed. If we hypo-statise the experienced flux into separate states then we are forced to introduce a connecting link with linear characteristics. It is the "temporal sequence" with its distinctions of past, present and future which fulfils the role.

6.3. The picture of time as a linear sequence of instants is a mental construct within the present moment. It is not a directly perceived notion since, within the present moment, there is awareness of content and change but not of time.

6.4. The picture of the world as a series of moments in temporal succession breaks down entirely when we seek to find a place in it for organised complexity. A structure that is in process of organisation cannot be described by a sequence of steps without loss of the very features that make it a structure. The features referred to are expressed by such words as "organisation", "complexity", "wholeness", "integration", "structure", etc., which refer to integral rather than to particulate features of experience.

6.5. The present moment is such an organised complexity. Its embrace is variable as is its degree of organisation and structural articulation. But with all its variations of content and togetherness it is totally present as a whole.

6.6. There is succession within the present moment. This is not succession in the temporal sense of "before and after". The elements which are successive are yet together within the present moment.

7. Change is simple flux; that is, flux taken without regard for its purposiveness or even significance (cf. prop. 2.3.1).

7.1. If a passive P changes into a passive P we write

          {P P} ......................................................................................................(16)

which is a descriptive simplex. To complete this expression we must place it within the experience of some particular scientist, S. We write, therefore

          {P P} S ..................................................................................................(17)

7.1.1. Since the coalescence bracket is primary over its contents (c.f. prop. 5.2.), it stresses the wholeness of the change. This means that the change is present as one whole within which elements are distinguished. The sequential order which may be implied is within the present moment and so is not temporal in the sense of "before and after".

7.2. The subject pole of (16) is referred to as the "initial state", and the object pole the "final state". If we call P the changing subject then P is the object of change.

7.2.1. To speak of an object of change in this way, referring to the final state (and not the initial state as might be expected) is no different to speaking of "reaching an objective" implying the gain of an "object of purpose" or of an "object of endeavour".

7.2.2. Nowhere in our scheme is "object" equivalent to "thing". An object is always an "object of. . .".

7.3. The present moment is perpetually changing; but not all the elements change in the same way. Within a given moment, some elements change so little that they can be treated as non-varying. The same element when related to a more widely embracing will, i.e. a greater present that contains the first, may vary or even disappear. All change is within the present moment, but what is change for one, may be invariance for another.

7.3.1. Expression (16) describes non-invariance, i.e. the change of one passive into another which is different in identity. An example of this (c.f. prop. 2.3.2.) is the seed changing into humus.

7.3.2. The features of experience which we distinguish as relatively permanent or stable can be treated as if the particular passive is invariant, and we can write

          {P P} ......................................................................................................(18)

7.3.3. This expression appears to be tautologous and trivial. It is, however, the basic axiom of identity, put in a form that relates it directly to experience. It is significant and true only within the present moment defined by the coalescence bracket. If we were to write

          [P, P] .............................................................................................................(19)

i.e. P is compresent with P then, indeed it would be tautologous, but still not trivial for it tells us that there is an entity P that remains itself within a present moment. It is only when we write

          (P, P) .............................................................................................................(20)

i.e. P is compatible with itself, that the statement degenerates into triviality.

7.3.4. The invariant expression (18) is meaningful if P is in the company of other passives which are changing non-invariantly. This, of course, is the assumption which is always tacitly made, for invariance only has meaning within the context of non-invariance. In the extreme case, the contrary would also be true, for if there were total flux with no invariant features it would be impossible to entertain the concept of non-invariance.

7.4. There is the intermediate case of semi-invariance. Identity is conserved, so that the same passive occupies both poles of the descriptive simplex, but there is a distinction of state. This is indicated by a suffix, thus

          {P1 P2} .................................................................................................(21)

which reads "the passive P in state 1 changes into the same passive P in state 2". An example would be of the same liquid at two different temperatures.

7.4.1. In view of this, expression (18) should more properly be written

          {P1 P1} ..................................................................................................(22)

which appears to be an awkward way of saying that nothing has happened at all. Nevertheless, such a descriptive simplex finds frequent application in theoretical physics, particularly in the formulation of thermodynamics.

8. When change is meaningful, that is, when due regard is given to the significance of features of the flux, then it is called transformation (c.f. prop. 2.3.2.).

8.1. If a passive P transforms into a passive P, we write

          {P P} ...................................................................................................(23)

which is a descriptive simplex. To complete this expression, we must place it within the present moment of some particular scientist, S. We write

          {P P} S ..............................................................................................(24)

8.1.1. When there is a transformation the subject pole of the descriptive simplex contributes a significant element to the flux. We indicate this by doubling the arrow into .

8.1.2. Since the coalescence bracket is primary over its contents (c.f. props. 5.2., 7.1.1.) it stresses the wholeness of the transformation. The ransformation is present as one whole within which elements are distinguished. The sequential order which may be implied, need not be temporal in the sense of "before and after".

8.2. Because the subject-pole in (23) contributes a significant element to the transformation it is referred to as the originator. The object-pole is called the outcome.

8.2.1. Comparing "originator and outcome" with "initial and final state" it will be seen that the former carry implications of meaning and significance which are missing in the latter.

8.2.2. We can take, as an example, the transformation of a seed into a plant. This is described by expression (24). The originator is the seed and the plant is the outcome. It is clear that the seed contributes a significant element to the transformation.

8.2.3. If we call P the transforming subject, then P is the object of transformation.

8.3. Within the present moment a given passive may undergo meaningful change without loss of identity. This is transformation in the sense of development or degeneration by which a passive becomes more like or less like its own natural pattern.

8.3.1. When we write

           {P P} S...............................................................................................(25)

we are saying that the scientist S can observe a change in P that is meaningful without diminution of the identity of P.

8.3.2. The propositions of section 7 as applied to simple change can in most cases be transposed into propositions about transformation.

8.3.3. When a passive transforms according to (25) we describe the change as a "self-transformation" of P. We can also say  P is invariant for the transformation.

8.4. The simplex {P P} describes a happening, whereas the simplex {P P} describes an event.

8.4.1. Transformation, since it is meaningful, must be more closely bound to a centre of experience than in the case of change. Two centres of experience S and S may be in agreement that a change occurs, but for S it may be meaningful and significant whereas it may not be so for S. Thus we have

          {P P} S ............................................................................................(26)
          {P P} S

where both expressions make direct reference to the scientist for whom the change is or is not meaningful.

8.5. The notions of change and transformation which we have introduced are somewhat akin to the mathematical concept of transformation. For example, in a vector space there are matrix transformations of a vector. If the vector represents a particular state of some system, the matrix too will transform it into another vector representing a different state. This operation is analogous to the descriptive simplexes {P P} and {P P}. The analogy is more appropriate if we imagine a transformation matrix whose components are not constant.

8.5.1. Flux may perhaps be visualized as being rather like a rising and falling, something giving way and something coming into place, which when seen in a certain perspective presents the appearance of a sequential order moving on.

9. There is a special class of transformations which is particularly important. These are cognitions.

9.1. Since, by definition, the present moment is for a self, a centre of experience, S, the flux in Q is connected with S in a special way. This connection consists in S "cognising" what is going on. S does not necessarily cognise all the "content" of Q, for there is always the background flux which forms the context of the cognition. Part of this background may, in turn, become the foreground, i.e. may become a cognition.

9.1.1. It is important to note that cognitions are contained within the present moment: they are not apart from it. There is no separation of knower and known; but there is a distinction between cognitive and non-cognitive flux. 9.2. Cognitions are ipso facto meaningful.

9.2.1. Cognition is reciprocal. Meaning depends as much on the cognitive element which is the subject as it does upon the object of cognition. These two poles of a cognitive situation depend each upon the other.

9.2.2. Looking down a microscope to observe Brownian movement, observing the oil drops in Millikan's experiment to determine the electronic charge, seeing the interference fringes in Michelson's interferometer or visualizing a thought structure in theoretical physics; all of these examples demonstrate the point. More familiar examples are, reading a thermometer, a galvanometer, a computer programme, etc. Even more directly, a chair would not be cognised as "chair" by a member of a society whose members always seated themselves upon the floor.

9.2.3. Propositions 9.2. and 9.2.1. demonstrate that a cognition is a transformation within the present moment.

9.3. The introduction of a special symbol for cognition is fortunately unnecessary. We represent cognition by associating the transformation arrow with the sign "O", which stands for "cognitive element". Thus we write

          {O P} ....................................................................................................(27)

which reads "the cognitive element 0 cognises the passive P". Whenever we have the combination "O " then the transformation sign is referring to a cognition.

9.3.1. More completely we have

          {O P} S ...............................................................................................(28)

which stresses that the cognition is within the present moment of the scientist S. The cognitive element O is a property or member (but not a part) of the scientist S. (cf. props. 5.5.5., 12-12.5.3.)

9.3.2. The coalescence bracket indicates the immediacy and "wholeness" of cognition. The distinction between the cognitive element 0 and the object of cognition P, is secondary.

9.3.3. The descriptive notation does not take the object of cognition and the cognitive element as being capable of existing in isolation. However, we do not say that the passives do not exist unless perceived. To do so would be to make the passives dependent upon the cognitive element which would then be prior to and independent of the objects of cognition. But to give independent individuality to the cognitive element apart from the objects of cognition would be false for it would imply that a continuously present consciousness remains even when not cognitive.

9.3.4. The cognitive element and the object of cognition each depend upon the other. Their only independent reality is as they occur together within a cognition situation.

9.4. In pointing to the wholeness of cognition the traditional separation between "outside-world" and "inside-world" is seen to be secondary rather than primary. Both these worlds are contained within the present moment which is one whole.

9.4.1. Our experience does not disclose to us any distinction in kind between "outer" cognition, or what is usually called perception, and "inner" cognition such as thinking. Consequently, no notational distinction need be made and expressions (25) and (26) each describe the two cases which are usually distinguished.

9.4.2. The difficulty with "perception" is that its referend is unclear. Does a scientist perceive "something" in an "outer" world which is then interpreted in his "inner" world and presented to him as "thermometer", or does he perceive "thermometer" directly? In other words, what is a percept and when can it be said that we have perceived? For the purpose of description all this is unnecessary, and can be abolished if one is prepared to deny the distinction inner/outer as being primary.

9.5. It must be remembered that although cognitions are transformations not all transformations are cognitions. Thus, if we introduce a cognitive element into expressions (26) we have

                    {O {P P}} S ................................................................(29A)

and              {O {P P}} S ................................................................(29B)

In (29A), the first transformation symbol refers to cognition whereas the second belongs to the object of cognition which is the transformation of the passive.

9.5.1. It will be noted that, in (29A) and (29B), the object-pole itself is a descriptive simplex, and hence that the expression as a whole is formally correct, i.e. it is itself a descriptive simplex, (c.f. prop. 5.5.2.).

9.5.2. If the passive P referred to in (29B) is invariant, then we have

          {O {P P}} S ...........................................................................(30)

We take this to be equivalent to "no change" (c.f. prop. 7.4.1), thus

          {O P} S .............................................................................................(31)

We write

          {O {P P}} {O P} ........................................................(32)

which reads "the cognition of invariant change is equivalent to no change". The symbol "" reads: "describes the same situation as . . .".

9.5.3. Since transformations are meaningful an invariant transformation is not equivalent to no transformation. An invariant transformation is meaningful and hence is a transformation. Consequently there is no expression for transformation of the same form as (32).

9.5.4. The present moment is an indivisible whole and it is, therefore, never rigorously permissible to isolate a single act of cognition, change or transformation. Nevertheless, owing to the property of quasi-invariance possessed by the perceptual apparatus of the Will S and by the general physical environment, it is in practice possible to make statements as if there were single, isolable acts of cognition and decision within the totality. If this were not the case, there would be no order or organisation within the complexity of the present moment and there would be nothing to be communicated in our symbolic language or any other.

10. The will that determines the present moment can be associated with any of the modes of togetherness and can enter into any of the three types of linkage namely, change, transformation and decision. In nondegenerate states where there is effectual action the will to know and the will to act are distinct but complementary. Will without cognition is blindness, whereas cognition without the power to act is impotence.

10.1. In any real action situation we would not have expression (14) only, but

{{O N (P, P, ..., P)} {E (P, P, P, ... , P, ...)}} S ................(33)

which reads "O cognises that the possibilities P, P, ..., P are not compatible within the experience of the scientist S. This transforms into the act whereby the executive E decides upon one possibility P which results in the partitioning of an open-ended field of possibilities P, P, P,..., P,... which are compatible with respect to that dec'sion within the experience of the scientist S". When we add that the whole of this is within the present moment of S, it will be seen that expression (33) is both more concise and more informative than its English language equivalent.

10.1.1. If decision were merely selection we would have to write

{{O N (P, P, ..., P)} {E P}} S ...............................................(34)

and interpret the simplex {E P} as "the executive E selects P". If decision were only selection then it would be a "closing" operation. In our scheme decision is taken to be an "opening" operation and consequently the simplex {E P} is not admissible.

10.1.2. The cognitive situation transforms, not only changes, into the executive situation. This is clearly the case inasmuch as the change is meaningful and the two situations are reciprocally related (c.f. prop. 9.2.).

10.2. The subject-pole of (33) and (34) requires further discussion. The possibilities P, P, ..., P represent alternative courses of action. The bracket is closed because here the scientist is cognising alternatives prior [the temporal implications of "prior" belong, of course, to customary usage. There are no such implications in the formalised expression since the latter is constructed to avoid such usage.] to decision, and clearly he can only definitely cognise a few such alternatives. When a decision is taken then although only one of these alternatives is chosen (in this case P), nevertheless the act opens S to a non-enumerable totality of possibilities P, P, ... , P, ... focused around P.

10.2.1. In many cases, there will not be a finite number of alternatives which can be clearly cognised. Even so the will that makes the decision will be able to cognise only a definite number from among which he will make his choice.

10.2.2. It has previously been maintained (prop. 5.6.2.) that possibilities are the objects of decision. Yet in (33) and (34) we have possibilities which appear to be objects of cognition. The contradiction is only apparent. Firstly, decision is connected with a set of compatible possibilities, whereas in (33) and (34) the cognition is connected with a set of incompatible possibilities. When such a set is cognised, we refer to the possibilities as "alternatives". Secondly, the cognition of alternatives is clearly connected with a prior decision, namely, the decision to consider alternatives. Thus, our usage is consistent.

10.3. In (33) and (34), both subject-pole and object-pole are compound, though each in itself is a descriptive simplex. Thus we have coalescence brackets within coalescence brackets giving the expression the overall coalescence form of

          {{    } {    }} S ....................................................................................(35)

There are three coalescence brackets and we say that all that is within each of these is within the present moment of the scientist S. Thus the whole simplex, as well as each sub-simplex, is taken to be within the present moment.

10.3.1. This will appear strange, since we would certainly think of such a sequence as "occupying a stretch of time". We would then perhaps use a linear sequence for representation, such as

          {  } {  } ..................................................................................................(36)

The difficulty with this arrangement is that when the referent of the first bracket exists, the referent of the second bracket is not yet; and, when the second exists, the first is no longer. Yet both exist as traces together in the representation which is within the present moment. Are we to infer- from this that one present moment can be compared with another? Clearly this cannot be so, for there is only the present moment which is, not one which is past and another which is present.

10.3.2. The paradox of the present moment is that all present moments are within the unique present moment. This suggests that any adequate representation scheme should try to imply a nested rather than a sequential order. This may be strange, but it is certainly not absurd. If one reaches the conclusions that all acts, cognitions, operations, transformations, etc., are within the present moment then one may well be led to ask "why not strive to represent it so?"

11. Within the present moment of scientific activity there are "higher' cognitions or insights.

11.1 An insight is a cognition, but it is more than just meaningful.

11.2. An insight has the character of a beginning. From an insight new series of transformations originate. In this way an insight is purposive.

11.2.1. An insight has the quality of an act. It is a creative act.

11.3. Since insight involves both cognition and purpose, or intention, we coalesce the executive and cognitive element into {E, 0}.

If P is the object of insight, we write

          {{E,0} P} S ............................................................................................(37)

The arrow is intended to indicate that the link "insight" has the quality of transformation (and hence of cognition since there is a cognitive element O in the subject-pole) as well as the quality of an act.

11.3.1. As in the case of (ordinary) cognition (cf. prop. 9.4-9.4.2.) the traditional distinction between "outer" and "inner" is not implied. If P is "inner" we call it a "creative thought", whereas if P is "outer" we call it "invention".

11.4. Consider the case of a scientist S who has a set of scientific results, P, P, ..., P. which seem to be quite incompatible with the existing relevant theory T. He is troubled by this and ponders upon it. Suddenly, in a flash, he sees a new theory T which would "explain" these results, i.e. the results are compatible with T. The cognition of T is an insight which may be the origin of further experiments and theoretical enquiries. This can be written

{{O N (P, P, ..., P, T)} {{E, O}(P, P, ..., P, T)}} S.................(38)

(note that the passives P, P, ..., P are scientific results and not possibilities. Here they are not alternatives as discussed previously (prop.10.2.2.).)

11.4.1. If the scientist is not successful, that is, he does not have an insight, we would write

{{O N (P, P, ..., P, T)} N{{E, O}(P, P, ..., P, T)}} S..............(39)

12. Every real action situation must include decision, cognition, and operation.

12.0.1. There can be no successful outcome to action if any one of these linkages is either absent or too weak. Ideally they are coeval.

12.0.2. Operation reconciles decision and cognition; cognition reconciles decision and operation; decision reconciles cognition and operation. All these relationships are necessary for realisation.

12.1. The scientist operates, he performs operations.

12.1.1. Operating is intentional, it has the quality of an act of will.

12.1.2. An operation, if successful, results in a transformation.

12.1.3. Because of the intention, the transformation is directed. Directed transformation implies purpose, progress, and refinement.

12.1.4. There is always hazard and uncertainty. If an operation fails, then transformation degenerates into change and the action does not meaningfully proceed.

12.2. Every operation of the Will requires an operative element which must combine intention and agency.

12.2.1. The scientist's agent is his body. The scientist's body is his way of combining change, meaningful operations of cognition and action with the direct initiative and terminative power that resides in his Will. His body fills the present moment by its acts and cognitions actual and potential. We can say that by his body he is "at-the-world-from-within-it" [this suggestive phrase is borrowed from M. Merleau-Ponty].

12.2.2. The body is a passive among passives, but it is not inert. It can behave automatically, but it can also be directed.

12.3. An operation which results in the transformation of a passive P is written

          {{E, P} {P1 P2}} S ......................................................................(40)

This expression would describe, for example, the operation of connecting the power supply into an electrical circuit. The passive P may refer to the whole circuit, to some part of the circuit, or even just to the switch. Which is intended could be indicated by specifying the referent of P explicitly.

12.3.1. The operative element is written {E, P} to indicate that it is a coalescence of the executive element E and the agent P. The latter does not require any distinguishing mark for we take it that, whenever the element {E, P} occurs in the subject-pole of a descriptive simplex, then the passive referred to is the scientist's agent.

12.3.2. The symbol for operation, i.e. is in effect the symbol for decision, i.e. repeated twice. This is to indicate that operation is intentional and has the quality of a decision, but that it is more than a decision alone. An operation is a decision which is implemented.

12.3.3. If the operation fails and transformation degenerates into change, we could write

          {{E, P} {P1 P2}} S .....................................................................(41)

12.4. Expression (40) does not include the cognitive element which would be present in any real situation. This element is included by writing {E, O, P} and by adding an extra barb to the operation symbol so as to indicate cognition. (40) then becomes

          {{E, O, P} {P1 P2}} S .................................................................(42)

and (41) becomes

          {{E, O, P} {P1 P2}} S .................................................................(43)

12.4.1. The element {E, O, P} is equivalent to the scientist S, i.e.

          S {E, O, P} ....................................................................................................(44)

This defines S and we refer to {E, O, P} as a total element.

12.4.2. Thus far we have used {E, O, P}, {E, P}, {E, O}, E, O and P.
            Each of these elements must be "included" within the scientist S. But they are not components or constituents, for that would imply that S was in principle separable into isolable parts. They may be distinct elements, but they are not separable parts, since they are what they are only within the coalescence unit.

12.4.3. For descriptive purposes we refer to non-separable though distinct parts as "members", and to separable parts as "components". This distinction is discussed further when compresence is introduced (props. 13.1.4, 14.0.2-14.1.2.).

12.4.4. The scientist S is a total element who is prior to his members. The use of the coalescence unit reflects this. Consequently the terms {E, 0, P}, {E, P}, {E, O} etc. are each members of S.

12.4.5. We make the following rule, which is characteristic of the concept of coalescence:

If the coalescence bracket consists only of elements without linkages, then any element which is a member, or any coalescence subbracket with members numbering up to the total number of members involved, is considered to be capable of manifesting independently within the total bracket. Thus (44) is equivalent to

S = {{E,O,P}, {E,O}, {E,P}, {O,P},E,O,P} .............................................................(45)

The total bracket is always implied though not necessarily explicitly stated. For example, if we write

          {O P} S ..................................................................................................(46)

then it is implied, by virtue of the symbol " S" that 0 is a member of Q, the present moment of S, and that S is primary over 0.
12.4.6. We have not so far used the element {0, P} which appears in the total element. This element serves to stress that "seeing" is "looking by means of instruments". Thus if we wished to stress that seeing is looking through one's eyes, that it is instrumental, we would write

          {{O,P} P} S ........................................................................................... (47)

rather than simply

          {O P} S ................................................................................................(47a)

Thus (47) more properly describes looking down a microscope, etc. to observe Brownian movement (cf. prop. 9.2.2.) than does (47a). It is artificial to separate the "seeing eye" from any additional instruments which may be used. When a microscope is focused it becomes an extension of the eye, with which it optically coalesceses. Hence the element P in {O, P} may represent the eye together with a focused optical arrangement. In the case of observing Brownian movement it would be the eye together with the focused microscope, treated as optically one.

12.4.6.1. It will be noted that, since the element {O, P} is a coalescence unit and hence the wholeness is primary, the traditional Cartesian distinction between mind and body, thinking substance and extended substance, does not arise. To insist that the distinction is primary is to mistake {O, P} for [O, P]. The latter is inadmissible in our model since it would imply separability between O and P and this cannot be the case.

12.5. The elements E, O, P and their various combinations are, to some extent, present in any present moment Q. Consequently it would appear that the scheme could be simplified by writing "S" in any expression. This is true but it would descriptively weaken the scheme for it would fail to show clearly what was involved in each individual simplex.

12.5.1. In any present moment Q, we find E, O, and P to some extent. If there is one element which is dominant while the others are in abeyance then we use only the symbol for that one element. The symbol "S" is sometimes used in place of {E, O, P} when it is necessary to distinguish between different scientists.

12.5.2. We find in societies examples of other total elements which have the same type of members. For example,

(i) An insurance company which has executives, agents, and cognitive individuals. Yesterday, the cognitive individuals would be clerks with their records; today they are computers with programmers.

(ii) A government or industrial research unit, which has executives, scientists, and technical assistants.

(iii) An advertising agency, which has executives, "visualisers" and agents.

From the human point of view, the elements will be seen as quite separate in each of these three cases. But from the point of view of the total element, the working system, the member elements are not isolable parts.

12.5.3. As the executive element E, say, is what it is only inasmuch as it is within a coalescence unit with others, so each total element, in turn will only be what it is inasmuch as it is within such a unit. We cannot imagine an insurance company which was not within a society. Nor could we imagine a scientist apart from a scientific community. However, a total element is such that we can recognise it as a whole capable of relatively independent existence within experience. The scientist S is, in this sense, the first total element we have come to in the descriptive scheme.

13. All scientists are combined in a totality that we call the world of science or simply "Science". There is in mankind a common Will to know and operate upon Nature. This "Will to Naturalise" or to perform the operations performed by scientists determines a present moment Q which is the scientific activity of mankind within the greater totality of human history.

13.0.1. All scientists when "doing science" form part of Q.

13.0.2. All passives used by or investigated by scientists can be called scientific objects inasmuch as they are the object-pole of an intentional or directed activity. They have a family resemblance [the term "family rsemblance" is borrowed from Ludwig Wittgenstein] by virtue of their common relevance for Q.

13.1. The individual scientist, selects, assembles, arranges and connects scientific objects that are relevant to his own purpose, i.e. the Will that determines the present moment of a specific piece of research or a particular experiment.

13.1.1. The scientist establishes a group of mutually relevant objects by an act of Will that is his initiating decision to do a particular piece of work and not another.

13.1.2. The scientific objects when assembled and arranged are called "components".

13.1.3. The bringing together of scientific objects, the forming of components, introduces a degree of organisation characterised by a mode of togetherness which is more than simple compatibility. This further mode of togetherness is equivalent to our compresence.

13.1.4. Within a compresence unit the elements are distinct and there is a degree of separability inasmuch as adding or removing one component will not reduce the mode of togetherness.

13.1.5. The components of a compresence unit are not entirely separate; they are not distinct "things". They are related inasmuch as they are objects relevant to the particular purpose in hand. This relationship derives from the originating decision. Without that how could one say "this is relevant"? If one could not say "this is relevant" how could one construct a compresence unit?

13.1.6. From 13.1.5 it follows that the objects which form the components of a compresence unit are connected by mutual relevance. Inasmuch as 13.1.4. is the case, the relevance is extrinsic.

13.2. The setting up of a compresence unit constitutes a transformation in- the mode of togetherness. A set of elements which are compatible, (P, P, ... , P) is transformed by operation into a set, [P, P, ... , P] which are compresent. This operation is expressed

{{E, P} {(P, P, ... , P) [P, P, ... , P]}} S ........................................(48)

13.2.1. The operation described by (48) could be expressed more concisely by writing

{{E, P} [P, P, ... , P]} S .............................................................................(49)

and interpreting the symbol as "constructs". Then (49) reads "the operative element {E, P} constructs a compresence unit [P, P, ... , P]".

13.2.2. In the case where an operation results in the transformation of a mode of togetherness we can, if we choose, interpret the symbol to be equivalent to "constructs" and omit any direct reference to the transformation involved.

13.3. Forming a compresence unit is constructing conditions for something to come about. Bringing together and arranging makes it possible for something to happen.

13.3.1. The compresence mode of togetherness permits expectation. When all that can be said of a set of elements is that they are compatible there can be hopefulness but not expectation. For the latter theie must be some degree of arrangement, configuration, or patterning. The more well defined the pattern is, the greater is the degree of confidence which can be placed in an expectation.

13.3.2. There may be patterns which are not wholly within the present moment of a single scientific Will; but which may be embraced by the compresence of the present moments of several such Wills. Expectation may then be described as the confidence that some transformation more or less conforms to a pattern which embraces events outside present experience for the particular self in question.

13.3.3. Consider the compresence formed by numerous automobiles driving on a highway. Then, for any particular driver there is a pattern or configuration, which if it holds together, permits anticipation and expectation. The driver can anticipate what gap "will occur" in the traffic ahead as if it is happening now, i.e. within his present moment, and drive accordingly. This is only possible inasmuch as there is a compresence mode of togetherness with which the driver is cognitively in contact.

13.3.4. In a scientific present moment Q expectation can take the form of prediction based upon calculations which act as guides to successful outcome. Calculations of this directly practical type only become possible when there is a compresence unit.

13.3.5. The arrangement which characterises a compresence unit also introduces the possibility of reproducibility.

14. A compresence unit [P, P, ... , P] can be transformed by operation into a coalescence unit {P, P, ... , P}.
      This is a further transformation within the total coalescence.

14.0.1. This operation may be represented

{{E, P} {[P, P, ... , P] {P, P, ... , P}}} S ...................................(50)

From prop. 13.2.2 it follows that (50) can be expressed more concisely by

{{E,P} {P, P, ... , P}} S .........................................................................(50a)

14.0.2. The elements of a coalescence unit are called "members" (c.f. prop. 12.4.3.).

14.1. Upon transformation, what was a grouping, a constructed configuration of relatively distinct components, coalesces into a working whole. There is a vanishing of boundaries, a merging of distinctions. The components of the compresence unit unite further to result in a relatively autonomous structure.

14.1.1. The members of a coalescence unit do not have the same freedom of separability and distinctness that pertains to the components of a compresence unit. They are subordinated to the whole.

14.1.2. To be what it is within the coalescence unit, each member requires all the others within the unit. The relation of mutual relevance which the members bear to one another has become intrinsic. In the case of a compresence unit it is extrinsic (prop. 13.1.6).

14.2. The coalescence as a working whole is at the disposal of the scientist and can be regarded as an extension of his agent. Thus when the stage of coalescence is reached (in the performance of an experiment, for example) the scientist's agent can be regarded as the sum of his bodily skills coalesced with the apparatus which is itself coalescent. If we take this point of view the agent must be considered as the sum of bodily skills and instrumentation, {P, P, P, ... , P} where P represents the bodily skills.

14.3. The transformation from compresence to coalescence constitutes a further step towards realisation.

14.4. The purpose of the symbols [P, P, ... , P] and {P, P, ... , P} is to distinguish descriptively two modes of togetherness which are clearly recognisable within experience. No essential relationship is implied between the two modes, so that there may be two structures which are different in all respects other than that they are coalescent. For example, a working mechanical contrivance is very different from a person and yet they both have the coalescence mode of togethemess. A mechanical contrivance can also be reduced to a compresence unit whereas a person cannot. Thus any value which this istinction may have resides in its use.

14.4.1. The numeration of the entries in {P, P, ... , P} is purely formal. If such a unit arises, as we have introduced it, through the transformation of a compresence unit, then we adopt the convention of enumerating the members of the coalescence unit and the components of the compresence unit in the same way, i.e. writing P, P, ... , P in both cases. This is
adequate since we are only concerned with indicating a difference in the mode of togethemess. But it must be remembered that the members of the coalescence unit cannot be separated in the same way as can the components of the compresence unit. The separation implied by the formalism, i.e. by writing the entries as P, P, ... , P is again purely formal.

15. When we come to construct formal descriptions for operations performed in scientific procedure, making a set of measurements for example, we shall find that the descriptive simplexes will be composite. If we adhere to the rules strictly this will result in a cumbersome number of coalescence brackets as well as frequent repetition of " {E, O, P} ". To
avoid unnecessary ungainliness we relax the rules and allow "improper" descriptive simplexes. We construct the following rule for improper expressions: Whenever there are several consecutive simplexes beginning with " {E, O, P} " take this symbol out, write it once only, and run the simplexes together into a transformation (or change, depending on which is appropriate) chain which is ultimately contained within a coalescence bracket. Formally such an improper expression will appear as

{{E, O, P} {X X ... X}} S ................................................(51)

where X stands for any entry, simple or compound. If we treat the improper simplex {X X ... X} as though it were a simplex then (50) as a whole does have the form of a descriptive simplex. But it must be remembered that such an improper expression, which is introduced purely for representational convenience, does not show the topology of the present moment correctly.

16. The elements of the model are summarised in the following table:

	Element	Name	Element	Name
Fundamental Element ..	Q	The present moment	S {E, O, P}	The scientist
	E	Executive element	{E, O}	Creative element
Basic Recuring Elements	O	Cognitive element	{E, P}	Operative element
	P	Passive element	{O, P}	Instrumental element
		Act, decision		Insight
Flux Linkages		Transformation		Operation
		Change		Scientific action
	(    )	Compatibility
Modes of Togetherness	[    ]	Compresence
	{    }	Coalescence
Additional Symbols		Is included within
	N	Is equivalent to Not, negation

III COMBINATIONS OF PASSIVES

Experimental procedure consists in producing, modifying, observing and recording combinations of passives. We shall find it convenient, at this stage, to distinguish, with the help of our descriptive model, different types of combination. Any such combination is a whole that is both complex and organised. Organised complexity can be "internal", in which case we describe it as a coalescence; and it can be "external", when it is a compresence. There can be meaningful transformations between the two kinds of togetherness. We obtain six types by taking the three elements of (1) compresence, (2) meaningful transformation and (3) coalescence in the six possible combinations. We shall refer to these as:

(1) Assemblages or simple compresences.
(2) Irreversible Artefacts
(3) Reversible Artefacts
(4) Reversible Wholes
(5) Irreversible Wholes and
(6) Identities or simple coalescences.

Each of these is distinguished from the rest by the kinds of operations that are permissible. Since all of them have a place in scientific description we shall examine them briefly before going on to give an account of experimentation and measurement.

(1) An assemblage is a complex with the togetherness of compresence but lacking the conditions for transformation into a coalescence. We can write

N{[P, ... , P] {P, ... , P}} Q.....................................................................(52)

where Q stands for a present moment of indeterminate character. An example of an assemblage is a stock of scientific apparatus and material in store in charge of a storeman who does not know its significance and therefore cannot construct a coalescence.

In scientific work, the system of interest [a common term in measurement theory, see: eg. D. Bohm, Quantum Theory, Chapter 22] may have a characteristic disorder. In statistical mechanics, random assemblages play an important part just because they have to be studied without transforming into ordered systems. Thus (52) can be regarded as a descriptive type for statistical work.

(2) An irreversible artefact is a complex with the togetherness of compresence whose nature is to transform into a coalescence and remain so. It is formally defined by

{{[P, ... , P] {P, ... , P}} N{{P, ... , P} [P, ... , P]}} S........(53)

In setting up an experiment, it is often necessary to produce irreversible artefacts; for example in glass-blowing or cutting and welding metal sheets or wires.

A type of experiment involving an irreversible artefact is thermal decomposition, exemplified in the conversion of coal into coke.

(3) A reversible artefact can transform from compresence to coalescence and back again without loss of identity. Thus we have

{{[P, ... , P] {P, ... , P}} {{P, ... , P} [P, ... , P]}} S............(54)

We introduce the notational device IIn to signify "repeat n times and connect with n—1 transformation links". We can then write (54)

{[P, ... , P] {P, ... , P}} S ..................................................................(55)

which means that the reversible transformation from compresence to coalescence and back again can be repeated indefinitely.

Comparing (53) with (54) it can be seen that an irreversible artefact corresponds to the case n = 1/2. This means that the cycle can be realised only half way. Using this notation, we can now write (53) in the form.

{[P, ... , P] {P, ... , P}} S ..................................................................(56)

The reversible artefact is exemplified in the apparatus required for a scientific experiment whenever the component parts can be disassembled and returned to store.

It is also of special importance as a characteristic system of interest. Where a test piece is made to undergo reversible changes such as thermal expansion, elastic deformation, fluorescence or electric charge; it behaves substantially as a reversible artefact.

No organised complexity can be perfectly reversible when changes of energy distribution take place upon transformation, for this would be inconsistent with the Second Law of Thermodynamics; nevertheless in many cases both the experimental set-up and the system of interest can be treated as undergoing only reversible transformation.

A reversible artefact is an important type of organised complexity since, by its very nature, there is considerable freedom in what can be done to it before a limit is reached and it is destroyed. When we come to the description of experimental procedure (section IV) we shall see how, as a result of the operations it permits, this freedom is of value in experimenta-
tion. Nevertheless, this freedom is in another way a restriction for there are certain types of operation which cannot be performed if a complex can be treated only as a reversible artefact. In particular, there are often measuring operations which must be made while the experiment is "running", i.e. which must be made entirely in the coalescence phase, and cannot be performed at all if the complex is reduced to the compresence phase. From the point of view of making these measurements the complex must be considered as having the kind of organisation which characterises an irreversible whole (c.f. (4)). This demonstrates that, where to the eye there may appear to have been no change in the constitution of the apparatus, from the operational point of view there may have been a significant change in the organisation of the complex. This operational difference is common in physics and is the basic condition for the distinction between "static" and "dynamic" measurement developed below in Section IV.

(4) A reversible whole is a cmplex which has the togetherness of coalescence and which can be reversibly transformed into a compresence. The reversibility means that the original coalescence can be restored and then reduced again, and so on. A single sequence of such transformations is described improperly by

{{P, ... , P} [P, ... , P] {P, ... , P} [P, ... , P]} S......................(57)

which can be written

II2 {{P, ... , P} [P, ... , P] S .........................................................................(58)

It follows from the definition that a completely reversible whole is one for which the cycle described by (58) can be repeated indefinitely. This condition is formally expressed by

{{P, ... , P} [P, ... , P] S........................................................................(59)

A reversible whole is particularly significant inasmuch as it is identical with the content of some present moment of experience. For example, the laboratory which the scientist enters to perform an experiment is already coalesced into an organised complexity. He has to produce disorder in order to create the conditions he requires and so breaks the coalescence down to a compresence. When the job is done the original order is restored.

Reversible wholes appear as systems of interest whenever attention is directed to a partial disorder within a total order. Thus a pathological state in an organism can be studied without destruction of the organism as a whole, which when "cured" reverts to its normal order. Determination of the elastic constants of materials is possible because the specimens behave as reversible wholes, while exhibiting phenomena that can be isolated and measured: elongation, stress-strain ratio, etc.

(5) The irreversible whole is the content of a present moment undergoing transformations that destroy part or all of its order. It starts as a coalescence; but breaks down into a compresence that cannot be restored to the primitive coalescent state. Thus we have
{{P, ... , P} [P, ... , P] N{[P, ... , P] N {P, ... , P}}} S.........(60)

Comparing this expression with (53) and (56) it can be seen that it corresponds to the half-cycle n = 1/2 of (56). We can, therefore, also write