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Information and The Structure of Worlds: A Speculation. Robert M. Hayes.

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Information and the structure of worlds a speculation

Information and The Structure of Worlds:A Speculation

Robert M. Hayes


  • Before proceeding with this presentation, I want to acknowledge a debt to Professor Marcia Bates, my colleague on the faculty at UCLA. The speculation I will here present is a direct result of an E-Mail dialogue between the two of us during a month-long period in early 2004. It was initiated by Marcia as part of her process in developing a paper that was subsequently published by her.

  • Our discussion forced me to deal with the issues she raises in that paper, but in my own way. If there are errors in what I present, they are mine, of course, not hers. But undertaking these speculations was due solely to the stimulus of her creative ideas.


Summary
Summary acknowledge a debt to Professor Marcia Bates, my colleague on the faculty at UCLA. The speculation I will here present is a direct result of an E-Mail dialogue between the two of us during a month-long period in early 2004. It was initiated by Marcia as part of her process in developing a paper that was subsequently published by her.

  • 1. Introduction

  • 2. A Generic World

  • 3. Examples of Worlds

  • 4. The Universe of Worlds


1 introduction
1. Introduction acknowledge a debt to Professor Marcia Bates, my colleague on the faculty at UCLA. The speculation I will here present is a direct result of an E-Mail dialogue between the two of us during a month-long period in early 2004. It was initiated by Marcia as part of her process in developing a paper that was subsequently published by her.

  • What I will present here examines a number of separate but related contexts, called Worlds, by applying a fairly simple framework to each of them. The framework consists of the following elements:

    (1) An Objective or Purpose for a world

    (2) A Space, with substance and structure, within which everything related to that world occurs

    (3) Particles that are the substance of the space

    (4) Dimensions that are the structure of the space

    (5) Entities, as things that exist in the space, formed from the particles of the space and with a continuity of identity and structure

    (6) Processes by which entities are either created from particles or are changed by interactions among entities

    (7) The derived structure of the set of entities that results from those processes

  • The entities and their derived structure may be treated as the substance and organization of a new, more conceptual space, to become the substance and organization of a new world.


Overview of structure
Overview of Structure acknowledge a debt to Professor Marcia Bates, my colleague on the faculty at UCLA. The speculation I will here present is a direct result of an E-Mail dialogue between the two of us during a month-long period in early 2004. It was initiated by Marcia as part of her process in developing a paper that was subsequently published by her.

  • Thus, the simple conceptual framework can be seen as a means by which dynamic changes in the structure of a world can lead to the identification of entities that retain their continuity of identity despite those dynamic changes and fall into a new, derived structure.

  • Throughout that process, structure plays a central role. It appears in the structure of the original space. It appears in the structure of each entity. It appears in the structure among sets of entities. It appears in the structure in identification of the new world.

  • What is structure? It is the organization of something, or the pattern of organization of something. In some terminology, the pattern of organization of something is the Information in that something. In my own terminology, though, information is a measure of the structure rather than being the structure.


An aside on structure and information
An Aside on Structure and Information acknowledge a debt to Professor Marcia Bates, my colleague on the faculty at UCLA. The speculation I will here present is a direct result of an E-Mail dialogue between the two of us during a month-long period in early 2004. It was initiated by Marcia as part of her process in developing a paper that was subsequently published by her.

  • My use of the term “information” is based on a generalization of the traditional Shannon measure of information as applied in systems for communication. It is based on probabilities.

  • If my usage is to be meaningful, for information to measure a structure, it must be related to the probability of that structure. But what does that mean?

  • Beyond that, presumably the more complex the structure, the less likely it is and therefore the more information it contains. So how does one define complexity?

  • I will try to deal with both of those questions.


Summary of presentation
Summary of Presentation acknowledge a debt to Professor Marcia Bates, my colleague on the faculty at UCLA. The speculation I will here present is a direct result of an E-Mail dialogue between the two of us during a month-long period in early 2004. It was initiated by Marcia as part of her process in developing a paper that was subsequently published by her.

  • In the following presentation, this simple framework will be illustrated by applying it to a succession of worlds. First among them will be a “generic world”, number (1) in the list that follows, in which the overall framework is illustrated independent of specifics but with special attention to the definition of symbolism that provides means for talking about elements of the framework in a precise way. That is then followed by examination of each of the specific examples, from (A) to (L) in the list that follows. Each will be discussed, not in detail but as means for exploring and illustrating the several elements.



Objectives
Objectives contexts that will be discussed:

  • The objectives of the thirteen spaces certainly are quite different. That of the physical world either is simply existence (its objective being just to be, as perhaps the existentialist would view it) or it is the will of God (as perhaps the religionist would view it) though it is impossible to tell what that is.

  • For the observer world and the perception world within the observer, the objective presumably is to provide means for the observer to deal with the external world and, from an evolutionary perspective, to be able to cope with it and to survive.

  • For the worlds of processing, concept, and communication, the objectives are more difficult to characterize, deriving from the contexts in which they occur. All three represent the means by which persons, as human beings, can relate to each other and to the worlds in which they live and interact.

  • The objectives of the academic and disciplinary worlds relate to larger frames of reference. They each step outside whatever other worlds there may be with the intention of learning about those other worlds.


Objectives1
Objectives contexts that will be discussed:

  • The objectives of the documents world are evident. They are to support the worlds of communication, society, culture, academe, and discipline by preserving and making available for future use the messages by which interactions take place in each of those worlds.

  • The objectives of the economic world presumably are efficient and effective use of resources for the well-being of mankind, either in general or in self-oriented specifics.

  • The objectives of the religious worlds are more difficult to characterize, since they may be seen either from the perspective of the driving force behind them – some concept of God – or from the perspective of the religionists themselves. In a sense, the dichotomy is reflected in a basic question, “Did God create mankind in God’s own image or do people create God in their own images?”


An aside on implicit vs explicit objectives 1
An aside on Implicit vs. Explicit Objectives - 1 contexts that will be discussed:

  • It is worthwhile to explore the difference between objectives that are explicit in the sense that they are defined by an external being versus those that are implicit in the sense that they simply derive from the fact of being.

  • The distinction is most clearly exemplified by the battle between, on the one hand, the “creationists” or those committed to the view of “intelligent design” as the basis for life as well as for the physical world as a whole and, on the other hand, the “evolutionists” who are to one extent or another committed to the view that the basis for life is simply the processes of the physical world itself.

  • The creationists believe that God created the world and life within it and that, in doing so, God set the objectives of the world and of life within it. The objectives are therefore explicit as God’s objectives.

  • The evolutionists believe that the world simply exists and that life within it is a result of the natural processes that occur within the world. The objectives are therefore implicit, deriving from what happens.


An aside on implicit vs explicit objectives 2
An aside on Implicit vs. Explicit Objectives - 2 contexts that will be discussed:

  • Later, we will return to this distinction when we consider the differences between entities that are externally defined, explicit, versus those that are internally defined, implicit. The effects of those differences are exhibited especially in conflicts between the two if there are explicit entities.

  • The issue of implicit vs. explicit objectives, though, arises from the very reason for looking at a world. One may do so simply because it is there and one is trying to understand it.

  • But it is possible that, in a very real sense, one can create a world for the purpose of examining it, exploring it. A world of fiction is in that sense as valuable as a world of fact and in some respects may be even more valuable.

  • In such a context, it is important to note that the person, in creating such a world and then examining it, plays a double role. And there may be difficulties in separating the two roles.

  • In a very real sense, the religionists, especially when they base their world upon the Bible, are creating their world. Of course, they view the world as God’s creation and that may well be. But this illustrates the difficulties in confusing the two roles of creator and examiner.


Particles
Particles contexts that will be discussed:

  • In each of the worlds, the substance of the space consists of what will be called particles, that is as fundamental units of substance that are individually not divisible.

  • Of course, particles may change over time in their locations and attributes, but not in their individual identity.

  • The nature of the particles in each of the spaces will be quite different and, indeed, that is probably the most basic defining characteristic of each space.


Dimensions of time location
Dimensions of Time & Location contexts that will be discussed:

The several spaces involved in the twelve contexts also can be quite different.

  • Dimension of Time. Time has a very different character in each of the worlds. Of course, in the physical world and, to some extent the observer world, time is simply time as we generally think of it. But in much of the observer world and in each of the other worlds, time is really quite different from simple physical time. The two are likely to be related, of course, but not necessarily so. As we look at each of the thirteen worlds (not in detail, but as examples), it will be necessary to explore the different meanings of time and the relationships between those meanings and simple physical time in each of them.

  • Dimensions of Location. The dimensions of location for the physical world, the observer world (in part, at least), and the societal world (again at least in part) are clearly Euclidean space. Physical things and persons are located in the physical world; they interact with each other in the physical world. So the dimensions of the physical world are central to determining their physical locations as they interact.

  • However, having said that, it must also be said that, in other than the purely physical world, things may be located by other than merely physical locations. Indeed, in some worlds, physical location may be irrelevant to some of the processes in the world.


Dimensions of attributes
Dimensions of Attributes contexts that will be discussed:

  • To deal with dimensions other than location, we need to consider the dimensions of substance (what are called attributes) because they become not only means for characterizing the substance but for locating particles of the substance in space. Simply to illustrate, within the societal world, persons interact not simply because they are physically located nearby to each other, but because of their relative positions in their attribute dimensions – their age, sex, social position, cultural background, personal wealth, etc. In fact, for some interactions among persons, being physically located nearby may be irrelevant to the interaction (though, of course, it may be relevant).

  • The key point is that the dimensions of attribution may serve two roles. One is to characterize the nature of particles as the substance of the world. The other may be to locate the pieces of substance within the world of attributes so that the interactions among pieces can occur within the context of those attributes.


Sub spaces
Sub-Spaces contexts that will be discussed:

  • In some worlds, it may be desirable or even necessary to identify sub-spaces whose structures are sub-sets of the total set of dimensions. This arises if the particles fall into categories to which only some of the dimensions apply.

  • To illustrate, when we examine a Perception World, the particles will be sensations, such as those occurring in the senses of vision, hearing, smell, tactility, balance, pressure and temperature. Each of those senses has attributes that are quite distinct from the others.

  • Of course, the entire set of attributes applies to the entire space, but it is useful to be able to sub-divide the total space into sub-spaces, one associated with each of the senses.


Selections of particles
Selections of Particles contexts that will be discussed:

  • Throughout the subsequent discussion, “selections of particles” will play a central role. A selection of particles is simply that; it could consist of all of the particles (the universal selection); it could consist of a single particle (an atomic selection); it could consist of no particles (the null selection).

  • And also throughout the subsequent discussion, “similarity of selections” will also play a central role. The measure of similarity is a function of the attributes of the particles in the selections involved. The nature of the measure can vary widely, including consideration of the physical locations of particles, the attribute locations, the nature of the individual particles as defined by their attributes, the numbers of particles, the physical or conceptual arrangements of particles, the stability or change of any of those aspects.


Structure and similarity of selections
Structure and Similarity of Selections contexts that will be discussed:

  • There are two considerations and related measures that will play significant role with respect to selections. The first is Structure and the second is Similarity.

  • Structure, at least initially, will relate to individual selections.

  • Similarity, at least initially, will relate to pairs of selections.


Measures of coherence continuity
Measures of Coherence & Continuity contexts that will be discussed:

  • A specific and rather crucial example of structure and similarity is that representing physical cohesiveness or coherence. It embodies the fact, first, that a selection “holds together” and, second, that it continues to do so over time.

  • This applies to the things we tend to identify in the physical world – the chair or table in a room, the person we are talking to, the sun or moon in the sky.

  • How can we define entities that we so readily identify in the real world, like those just listed? And the answer to that question is by no means simple or trivial; it is a very complex question, the answer to which will be presented when the generic and physical worlds will be discussed.

  • In a sense, the answer, as I will present it, is perhaps the simplest example of structure and similarity. The structure might be characterized by what will be called contiguity or adjacency of particles. The similarity might be characterized by the percentage of particles that two selections have in common.


Entities
Entities contexts that will be discussed:

  • So, among the possible selections of particles are those that will be called “entities”. The definition of an entity in each world is determined by the nature of structure and similarity as they are applied to sets of selections of particles of substance.

  • The relationship between structure and similarity and the entities that they define is, of course, very close. Indeed, it is sometimes difficult to tell which comes first. In the definition of an entity, it is assumed that structure and similarity are defined first, so that the entity then arises from those definitions. But the fact is that one may want to talk about a kind of entity and must then determine what structure and similarity would lead to such an entity. That having been done, of course, the definition then becomes the basis for defining the entity as it was wished to be.

  • There are many possible criteria for structure and similarity. The most obvious ones, perhaps, are those related to the dimensions of location in the physical world. But those related to the dimensions of attributes are also important. In particular, they may be especially applicable in those worlds that involve people – those that lead to identifying communities because of structure and similarity in the attributes of people.


Processes
Processes contexts that will be discussed:

  • A crucial point about each world is that it is dynamic. It changes over time. And those changes result in interactions among selections of particles within the world and, indeed, may be caused by those interactions. Those interactions are caused or created by processes, and those processes differ from world to world.

  • In the physical world, of course, the primary processes are the physical and chemical interactions in the substance of physical space. They operate at both a gross level and an atomic or sub-atomic level. The study of them is the domain of the natural sciences, physics and chemistry especially.

  • In the world of the observer, as in perception and in processing, those processes are neural (in animals and perhaps even in plants) or electronic (in computers and similar man-made devices). They are embodied in the built-in structures of logic that serve as the building blocks for the more complex programs that either grow out of experience or are inserted de novo.


Processes1
Processes contexts that will be discussed:

  • In the worlds based on people – communication, society, and culture – they are the bases of inter-personal interaction, both physical (as in mating and warring) and conceptual (as in arguing, joining together, convincing, encouraging, inciting).

  • In the academic and disciplinary worlds, they are the very processes of research and teaching – the tools by which objects of investigation are brought together into new configurations that identify issues of importance in understanding the relationships among entities. They are the paradigms of research.

  • In the world of documents, they are the means by which documents are created, acquired, organized, and, most importantly, used. Two interesting examples of those processes are “citation”, as the reference from one document in another, and “co-citation”, as the joint reference of two documents by another document. But that is simply one pair of examples.


An aside on limits on my objectives
An aside on Limits on my Objectives contexts that will be discussed:

  • It is important to note that there are significant limits on my objectives in developing this model and they arise specifically with respect to the Process component of the model.

  • It is not my objective to deal with the specifics of the processes. This arises, in particular, when I examine the real physical universe. The physicist is concerned with the specifics of the dynamic process, as represented by the equations that govern them and measure their effects.

  • Obviously, this limitation for my objective makes the model, as such, valueless for the physicist.

  • In the same vein, I do not try to deal with the specifics of biological processes or political processes, as they reflect the dynamics of biological, political, or economic systems.

  • Obviously, this limitation for my objective makes the model, as such, valueless for the biologist, politician, or economist.

  • Given that, one might ask what value the model has. And the answer simply is that I am trying to provide means for examining the similarities among the several worlds rather than the differences among them.


The derived structure of space
The Derived Structure of Space contexts that will be discussed:

  • I turn now to the final element in the framework, the derived structure for the space. Specifically, I will define it as follows: “The derived structure of the space is the decomposition of the lattice of similar selections of particles under the relationship of containment into the direct product of sub-lattices”. Let’s briefly examine what that means.

  • Containment

    Selections of particles in the space are characterized by several levels of “containment”. Selections may be components of other selections, and selections may be grouped into categories based on some criterion of similarity.


The derived structure of space1
The Derived Structure of Space contexts that will be discussed:

  • Meet and Join of Selections

    We can then consider the sub-selections that two selections may share in common, called the meet, and the selection that results from combining two selections, called the join. Of course, for some pairs of selections, the meet may be the zero selection because they have no sub-selections in common.

  • Lattices

    As a result of the containment and the meet and join of selections, the most important result of the dynamics of processes operating on selections is that the selections relate to each other within the structure of a standard mathematical concept of a lattice.


The derived structure of space2
The Derived Structure of Space contexts that will be discussed:

  • Decomposition of a Lattice

    The resulting lattice can be represented as the “direct product” of sub-lattices within it. That direct product constitutes a “derived structure” which provides a new way of looking at the substance of the world and thus a new world at a higher level of abstraction. The component sub-lattices constitute the dimensions of the space in that new world.

  • The Dynamics of the Derived Structure

    Note that the selections of particles in the world, the relationships among the selections, the lattice of those relationships, and the resulting dimensions for the selections all arise from the dynamics of what happens in the world. They are not pre-defined; they are not inherent in the original space or its dimensions; they are the result only of the interactions that actually occur among the selections, as they are created and as they interact.


2 a generic world
2. A Generic World contexts that will be discussed:

  • A generic world will be used as the means for describing the general pattern and for defining symbolism that will be universally applied in each of the more specific worlds.

  • Each of the illustrative worlds, as previously listed, provides an example to which the generic world can be applied.


Overview of what follows
Overview of what follows contexts that will be discussed:

  • Generic Objective

  • Resulting Space and its Structure

  • Particles

    • The Matrices of the Space

    • Selections of Particles

      • Structure of a Selection

      • Selections in Time

      • Sets of Selections

      • Similarity of Selections

    • Dynamics of Particles

    • Continuity of identity of Selections in Time

  • Entities

    • Structure of an Entity

    • Information and Complexity

    • Induction from Continuity of an Entity over Time

    • Identification of Equivalence Classes

    • Structure of the set of Equivalence Classes

  • Derived Structure of Space

  • Measurement of Space


Generic objective
Generic Objective contexts that will be discussed:

  • There is an Objective or reason for existence of a world. The crucial point about the objective is that it determines what the space for the world will be, what the structure of it is especially as represented by its dimensions, what things (substance) will be included in the world and what their form will be, what criteria identify entities within it, what the processes are by which entities are created and interact, how the output from the world will relate the world to whatever is outside of it.

  • The objective for a world may change over time both as a result of a change in the reasons for identifying it and as a result of its own operation, the latter especially for an objective that is self-defining.

  • The objective for a world may be simple or it may be complex, including sub-objectives, in which case the objective will have a structure relating those sub-objectives.


Particles1
Particles contexts that will be discussed:

  • A given space will contain Substance, located within the space and made up of particles. It is assumed that there is a finite number of particles, even though that number is likely to be exceptionally large. Each particle, when present in the space, has a specific location in space at a given point in time. However, particles may appear and disappear at different points in time.

  • A given particle will be permanently identified by a number determined, in sequence, from the time of its initial appearance in the space and the location of it in space at that specific point in time. It is assumed that only one particle can make its initial appearance at a given location at a given point in time. Therefore, that initial time and initial location can serve as the unique identifier for it at any subsequent point in time.

  • It is assumed that, at the origin of time, only one particle can be at a given location so that the initial location at the origin of time is a unique basis for identifying each starting portion. However, at future points in time, varying numbers of particles, from zero to the totality of particles, may be at a specific location.


Structure of the space
Structure of the Space contexts that will be discussed:

  • The space will have dimensions that represent its basic, underlying structure and provide means for identifying the location and form of substance (i.e., particles) within the space. The distinction between location and form is meant to be evocative of counterparts in the real physical world, but it is not an essential distinction, since the concept of dimension includes both without essential difference between them.

  • The world is to be seen as dynamic, changing over time. Therefore, there must be a means for measuring time in the space so that, as change occurs in the space, it can be related to the point in time at which that change occurs. There is a specific point in time, called the origin of time, at which the world is taken as beginning to exist for all subsequent times. That will be the dimension of time.

  • Among the dimensions of space are those that provide the means for locating particles within the space. The dimensions may be physical, in the usual Euclidean sense of dimensions, but they can be other than physical. These will be the dimensions of attributes.


An aside on einstein and time
An aside on Einstein and Time contexts that will be discussed:

  • Albert Einstein is reputed to have said, “The only reason for time is so that everything doesn’t happen at once.”


Structure of space
Structure of Space contexts that will be discussed:

  • The dimensions of time, location, and attribution provide the basis for the structure of the space.

  • However, although a given world can be treated as a uniform space, there is frequently value in subdividing it into components, each of which may have different properties, and indeed different dimensional structures, within the overall context of the space.

  • This kind of subdivision creates a structure for the space in which the several components can each be treated separately or the entire set of them treated as one space, with proper means for reconciliation of different dimensional structures.


Dimension of time
Dimension of Time contexts that will be discussed:

  • While, in principle, time could be measured on a continuum, it will be assumed that time is measured in finite units of time, the size of a unit of time defining the resolution of the measurement of time. Let that unit of time be 1. The origin of time will be taken as 0, so that all times are positive integers.

  • A set of times, A = {t1,t2, … ,tk}, is in time-sequenced-order if, for 1 < i < k – 1, ti≤ ti+1. If the set of points, A = {t1,t2, … ,tk}, is in time-sequenced-order and ti+1 = ti + 1, for 1 < i < k – 1, it is called a time interval and symbolized by (t1,tk). Note that, for a time interval, A, if any point in time, t, is such that t1≤ t ≤ tk, then t is included in A. A set with a single point in time, t, would be the time interval (t,t).

  • A set of points in time-sequenced-order, A = {t1,t2, … ,tk}, ti≤ tj for i < j, can be divided into m discrete time intervals (t1i,t2i), t11 = t1, t2i + 1 < t1(i+1) and t1(i+1) = t2i+1, 1 ≤ i ≤ m - 1, t2m = tk.


Dimensions of location
Dimensions of Location contexts that will be discussed:

  • Among the dimensions of space are those that provide the means for locating particles within the space. The dimensions may be physical, in the usual Euclidean sense of dimensions, but they can be other than physical. The dimensions for a given space must be identified and the resolution for measurement of location, as measured by the size of the smallest unit for measurement, must be identified. The smallest unit of measure for each dimension of location will be taken as 1.

  • To some extent, the minimum resolution depends upon the maximum size of a particle, since the initial location of particles is determined by the location, so the minimum size of a location must be greater than or equal to the maximum size of a particle.

  • There is a point in space, called the origin, from which all locations are measured. The origin will be identified by the value of 0 for each dimension of location, so all points in space are identified by x-tuples of integers (positive or negative), where x is the number of dimensions of location.


Dimensions of attribution
Dimensions of Attribution contexts that will be discussed:

  • Beyond the dimensions of location are those of form, which will be called attributes. These are the means for characterizing the nature of a specific particle of substance. To illustrate, substance in the real world consists of mixes of matter and energy. Recognizing that the one may be converted into the other, at a given point in time the form of any portion of the substance of the real world is determined by its position on the two dimensions of matter and energy. The values of the dimensions of form, the attributes, will be taken as positive integers.

  • Some attributes are categorical, in which case the integer values identify the categories involved in the attribute. Other attributes may be sequential in which case the integer values identify the position in the sequence. Some attributes may be regarded as variables measured at a resolution; for such attributes the measure will be taken from an origin with the value 0 and the resolution as 1 so that all values are integers.

  • Each particle has a form or nature, as identified by its positions on the dimensions of attribution, that is specific at a given point in time.


An aside on variables and scales
An aside on Variables and Scales contexts that will be discussed:

  • It is traditional in dealing with variables, which attributes are, to identify the various possible sizes of the set of values and the various possible scales for measurement.

  • Specifically, the set of values for a variable can be finite, countably infinite, or uncountably infinite. A finite variable might be as limited as a dichotomy, with simply two values. A countable infinite variable might be represented by the integers. An uncountably infinite variable, by the continuum of real values.

  • I am taking the set of values for all attribute variables as finite, though potentially very, very large.

  • The set of scales for measurement can be nominal (i.e., simply names, with no other relationships among values), ordinal (i.e., in a sequence), interval (i.e., differences between values are measurable), and ratio (i.e., an interval scale with a zero value).

  • I am taking the scales for measurement of an attribute as any of the traditionally defined ones, as enumerated above.


Adjacent or contiguous locations or attributes
Adjacent or Contiguous Locations or Attributes contexts that will be discussed:

  • Within the dimensions of location and attributes, there are what will be called adjacent or contiguous locations or attributes. Two locations or attributes are adjacent or contiguous if they differ by one unit in just one dimension and are equal in all other dimensions.

  • Note that the concept of adjacency or contiguity applies to the dimensions of both location and attributes (with the exception of nominal attributes for which adjacency cannot be defined). For ordinal scales, adjacency of two locations would require that there by no value between the two values.


The matrices of the space
The Matrices of the Space contexts that will be discussed:

  • The entire structure of the space can be represented by a set of matrices, one matrix for each point in time, the rows of which are the particles, the columns of which are the dimensions of location and form, and the values of which are the values for the particles at the given point in time. The values in the matrices are all integers.

  • The matrix for the origin of time will include, at its end, a set of rows that have zero values and that represent particles that will appear at subsequent points in time. The prior rows are sequenced in inverse lexical order by the values in the succession of dimensions. The number that identifies each particle is that for the sequence in which it appears in the rows.

  • The following display illustrates the set of matrices, with m being the number of dimensions of locations, n being the number of dimensions of attributes, and t being the number of points in time.


Selections of particles1
Selections of Particles contexts that will be discussed:

  • A selection is a subset, S, of the N particles taken at points in time: S = {Pi1ti1, … ,Pijtij}, where if p < q, tip≤ tiq and ip < iq if tip = tiq. Thus, the order is by time and then by particle number within time.

  • Taking a selection of particles is clearly simply taking a set of rows from the set of matrices, and that can be done in any way desired. For example, they could be selected quite at random – in time, in location in space, in attributes – or they could be selected for specific times, locations, and/or attributes.

  • One might focus on a specific location and consider all particles that appear in that location over time; one might focus on a particular particle and consider it at various points in time; one might focus on an attribute and consider particles that have a specific value for it; one might focus on a specific time (i.e., one of the matrices) and select particles within that time.

  • A selection with no particles is the null selection. A selection of all N particles is the universal selection.


Structure of a selection
Structure of a Selection contexts that will be discussed:

  • The structure of a selection is defined as the array of k*(m + n) values for the (m+n) dimensions of the k particles in the selection. This structure may be called the organization or perhaps the pattern of organization exhibited in the selection, as determined by the positions in the dimensions of location and form of the particles in it.

  • The structure may be represented in ways other than the array, though always dependent upon it and derived from it. For example, one might have a selection of three particles and represent the structure by the triangle of their locations.


Structure of a selection1
Structure of a Selection contexts that will be discussed:

  • Of course, although the structure is indeed based on the array of attributes, that is much too simplistic. One has the feeling that there needs to be means for recognition of various types of structure (such as the example of the triangle exhibited by a set of three particles).

  • The problem, though, is that recognizing a type of structure implies that that type has been, in some way, pre-identified. It thus pre-supposes much of what I am trying to have arise from the dynamics of the space itself.

  • The task I have set for myself, therefore, is to develop means by which the structure based on and embodied in the attributes can arise from the dynamics of the space rather than being pre-defined.


Structure of a selection2
Structure of a Selection contexts that will be discussed:

  • I want the set of structural elements to reflect simple things that come directly from the set of particles themselves, without imposing any externally identified patterns (such as “triangle”).

  • The following structural elements seem to satisfy that desire:

    • Number of particles. This seems self-evident

    • Distance between pairs of particles. This is measured by a metric for the space; the metric could be either the usual Euclidean metric, the “city block metric”, or another metric.

    • Variance of the set of particles. This is measured by the sum of the squared deviations of each particle from the mean of the set of particles (as determined by the metric) divided by the number of particles.

    • Adjacency. For each pair of particles in the set, this identifies whether they are adjacent in space or not adjacent.

    • Connectivity. This is more complex and not yet well defined. One possible measure is the number of paths of adjacencies that are embodied in the adjacencies.

    • Compactness. This too is more complex and not yet well defined. Basically it measures the extent to which the particles are concentrated in a region of the space. It thus relates to density as reflected in variance, adjacency, and connectivity.


Structure of a selection3
Structure of a Selection contexts that will be discussed:

  • Of course, the number of particles and the distance between pairs is the basis for all of the others, so we should start by examining the nature of those two.

  • The number of particles involved is unequivocal, but the measure of distance is not. It can be based upon any selection of dimensions and any of the means for measuring distance within them. For simplicity in description and because it is in a sense the most natural, I will use the dimensions of location as the dimensions involved and the “city block” measure as the measure within them. But that is simply for the purposes of illustration and example.

  • I reiterate that the measure of distance need not be limited to the one being used for purposes of illustration. In many worlds, in fact, the dimensions of physical location may be totally irrelevant and the dimensions of attribution may be critical.


Structure of a selection4
Structure of a Selection contexts that will be discussed:

  • It turns out that “cluster analysis” provides a set of methods, with associated structural elements as identified above, that are needed for the objectives here.

  • In particular, the “one-dimensional hierarchy linkage” method examines pairs and groups those that are closest, iterating the process until done.

  • Hence, given n particles, there are n*(n-1)/2 pairs. Let {p1, …, pn} be the set of particles and let dij = d(pi,pj) be the distance between the pair pi and pj.

  • If two particles, pi and pj, are contiguous (i.e., in adjacent locations) then dij = 1.

  • In the same vein, if there are two selections, S1 and S2, let g1 and g2 be their respective centers of gravity. Then d12 = d(S1,S2) =d(g1,g2) is the defined as the distance between the two selections.


Structure examples
Structure Examples contexts that will be discussed:

  • I am going to use selections of 16 particles as examples to illustrate the elements of structure as I will try to develop them. The space, for purposes of illustration, will be limited to simply two dimensions of location. Further, particles will be located at most one to a location value (x,y).

  • It is important to note that, though I use as my example only two dimensions and those just of location, the principles apply to any number of dimensions and to those of attribution as well as to those of location.


Structure examples density
Structure Examples: Density contexts that will be discussed:

  • The first and probably the most evident element of structure is the density of a selection of particles in the space. For example, consider the two selections of 16 particles shown to the right. As the top one shows, they could be sparsely distributed in the space.

  • Alternatively, as the second example shows, they could be concentrated, with an average density of 1.

  • Subsets of the selection could vary in their density.

  • The following displays will show, first, the values of locations for the first example and then the resulting pair distances.


Structure example 1 density
Structure Example 1: Density contexts that will be discussed:

  • For the top figure, let’s suppose that the 16 particles are located as follows

    • (4,10)

    • (2,9), (5,9), (9,9)

    • (3,8), (6,8), (8,8),

    • (6,6), (10,8)

    • (1,5), (7,5)

    • (4,4)

    • (2,3), (8,3)

    • (6,2)

    • (9,1)


Structure example 1 pair distances
Structure Example 1: Pair Distances contexts that will be discussed:


Structure examples adjacency
Structure Examples: Adjacency contexts that will be discussed:

  • The second element of structure is the adjacencies of a selection, as represented by the extent to which particles occupy adjacent locations in the space.

  • A set of particles may be partitioned into subsets of particles that occupy adjacent locations in the space.

  • The first example to the right shows a partition into six subsets (3, 5, 1, 4, 1, and 2 particles, respectively). The second shows the partition into one set (of 16 particles).


Structure example 1 pair distances1
Structure Example 1: Pair Distances contexts that will be discussed:


Structure example 2 pair distances
Structure Example 2: Pair Distances contexts that will be discussed:


Structure examples subsets
Structure Examples: Subsets contexts that will be discussed:

  • As the next step in identifying structure that is derived from the particles themselves in a selection, I consider means for identifying structural subsets.

  • The most evident means is differences within the selection with respect to the several elements I have identified. The most direct is if there are subsets that have adjacencies.

  • To illustrate, consider the first selection of 16 particles and contrast it with the second one, also of 16 particles.


Algorithm for determining structure
Algorithm for Determining Structure contexts that will be discussed:

  • The following screen displays an algorithm for generating structure from a given selection of particles. It has been configured to generate a structure for a selection of 16 particles, but obviously that number could be set to any value.

  • The basic criterion for the structure is to combine groups that are at a minimum distance from each other, starting with the particles themselves as groups of one particle. The distance between two groups is measured by the distance between their two centers of gravity (i.e., the average of their positions on each dimension).

  • The algorithm generates a nested hierarchy, with the particles at the lowest level and the entire selection at the top. Each level of the hierarchy is a partition of the selection.


Illustrative applications of the algorithm
Illustrative Applications of the Algorithm contexts that will be discussed:

  • I present this algorithm not for the purpose of specifying it as the means for determining structure but simply to demonstrate that there can be means for doing so and to provide a basis on which to illustrate the nature of the structures that can result from such algorithms.

  • Specifically, the following screens show the results of applying the algorithm to representative selections of 16 particles, such as those shown in the prior illustrations.


Above is a set of sixteen particles and to the right is contexts that will be discussed:

the succession of groups resulting from the algorithm.

The first column shows the group number; the second,

the number of particles in the group; the next two

columns, X and Y coordinates (for the generated groups

that being for the center of gravity); the final column,

the assignment to the group at the next level of the

hierarchy. For example, particles 1, 2, 3, and 4 are

assigned to group 17, which in turn is assigned to group

21, which in turn is assigned to group 23, the total

selection.


Again, the diagram above shows the locations of contexts that will be discussed:

the particles and the listing on the right shows the

succession of groups. Group 17 is interesting as the

group that extends from the top down the middle

and includes three particles to the right at the top.


This example shows a coherent cluster of contexts that will be discussed:

particles and the listing of groups to the

right shows that the algorithm immediately

identifies the cluster.


This example shows a group of coherent clusters contexts that will be discussed:

and the listing of groups to the right shows the

groups that the algorithm identifies in the

hierarchy.


The display to the right shows the contexts that will be discussed:

nesting of groups represented in

the succession of groups shown in

the just prior screen.


A selection in time
A Selection in Time contexts that will be discussed:

  • A selection made at a specific time is called a selection in time of particles. It is an ordered subset, St, of the N particles all taken at a specific point in time t:

    St = {Pt(1)t, … ,Pt(k)t}, with 1 ≤ t(1) and t(i) < t(i+1) ≤ N for i = 1 to k-1

  • Note that a general selection may contain a number of selections in time.

  • A selection in time may contain no particles in which case it is called the null selection. It could contain a single particle, in which case it is called an atomic selection at that time. It could contain all N particles, in which case it is called the universe at that time. Ut = {P1t, … ,PNt}.


Maximal coherent selection in time
Maximal Coherent Selection in Time contexts that will be discussed:

  • A coherent selection in time that is a subset only of itself will be called a Maximal Coherent Selection in Time.

  • At a given point in time, the set of maximal coherent selections in time constitute a partition of the set of particles, since, if two maximal coherent selections contain a particle in common, they must be identical in their particles.

  • The algorithm just presented, if applied to the universal selection, determines the set of maximal coherent selections in time as the first set of clusters.


An aside on partitions of integers
An aside on Partitions of Integers contexts that will be discussed:

  • A partition of an integer is a representation of that integer as the sum of integers. For example, the integer 5 has 7 partitions:

    5 = 1 + 1 + 1 + 1 + 1 = 2 + 1 + 1 + 1 = 2 + 2 + 1 = 3 + 1 + 1 = 3 + 2 = 4 + 1

  • The following table shows the number of partitions, p(n), of integer n.

  • The following screen provides an algorithm for generating partitions.




Subsets of a selection
Subsets of a Selection representative:

  • Consider two ordered selections in time, S1t and S2t at the same point in time, t. If every particle in S1t is a particle in S2t, S1t is a subset of S2t as a selection in time.


A set of selections
A Set of Selections representative:

  • A set of k selections in time, S = (S1, … ,Sk), is simply that. Each of the selections in the set may be independently identified, but usually one has a reason for creating a set of selections.

  • In particular, a S, of k selections may be a time-sequenced set:

  • S = {S1t1, … ,Sktk}, with t1 ≤ t2 ≤ … ≤ tk

  • Note that a general selection can now be seen as such a time-sequenced set of selections.

  • A time-sequenced set of selections may have no selections in which case it is called the null set. The set that consists of an atomic selection in sequence at every point in time is the atomic time-sequenced set for that particle. The set that consists of the universe in sequence at every point in time is the universal set.


Measure of similarity of selections
Measure of Similarity of Selections representative:

  • Given two selections in time, S1t1 and S2t2, there is a measure, M(S1t1,S2t2), of similarity between them that is a function of their respective particles and structures. The values of M are in the unit interval, so that 0 ≤M≤1, with a value of 1 being interpreted as a maximum match and that of 0, as a minimum match. The measure M has the following properties:

    M(St,St) = 1, for all St (reflexivity)

    M(S1t1,S2t2) = M(S2t1,S1t2), for all S1t1 and S2t2 (symmetry)

  • The definition of the measure M in any particular situation is determined by the objectives in definition of entities (which is based on the measure of similarity, as will be seen).

  • In the examples given to this point, the distance between two particles has represented a measure of similarity both of two particles and, based on the centers of gravity, of groups. And, in general, it is to be expected that a measure of similarity between selections will be effectively equivalent to such a distance measure.


Continuity of identity of a set of selections
Continuity of Identity of a Set of Selections representative:

  • Perhaps the simplest measure of similarity is the number of particles or, perhaps better, the percentage of particles, that two selections have in common.

  • If a set of selections in time consists of the same or nearly the same set of particles, it is said to have Continuity of Identity. The degree to which they are the same set of particles is measured by the percentage of them from one time to the next that are the same and constitutes the degree of identity.


Continuity of identity of a selection
Continuity of Identity of a Selection representative:

  • Consider a set of selections in time S1t1,S2t2,…,Sktk for which the times {t1,t2, … ,tk} constitute a time interval. If the selections Siti and Si+1t(i+1) consist of the same particles, or largely so, the set of selections is said to have “continuity of identity” for that time interval.

  • The phrase “or largely so” in this definition permits some changes in the set of particles from one time in the interval to the next. For example, continuity of identity might require that a percentage (e.g., 99.9%) of the particles be identical from one time to the next. That percentage, of course needs to be specified.

  • Note that the set of particles at the end of the time interval could, in principle, be quite different from that at the beginning and yet there could still be continuity of identity for the set of selections.


Dynamics of particles
Dynamics of Particles representative:

  • The space is dynamic in the sense that the location of a particle and the form (i.e., attributes) of it can change over time. Things from the outside of space can affect the particles in the space. For all spaces except the real physical world, particles can enter the space from outside or can disappear from the space to the outside. For the real physical world, though, it is assumed that the laws of thermodynamics apply, so that the total amount of substance (in the form of matter and energy combined) is constant.

  • The process of change may itself be characterized by attributes of the particle – a dimension of momentum that might represent the rate and direction of change in position, for example – and, if so, they are included among the attribute dimensions.


Continuity of structure
Continuity of Structure representative:

  • The issue at hand is what happens to particles and the sets of selections containing them as a result of the dynamic processes operating in and on the space?

  • Recall that we identified “continuity of identity”, as a relatively simple criterion of similarity, based on the percentage of particles that two selections in time have in common. But the particles may well jump wildly in their locations and metamorphose equally wildly in their attributes.

  • If the properties – locations and attributes as well as particles – of a set of selections in time are similar, they are said to have “continuity of structure” (at that level of similarity).


Continuity of structure1
Continuity of Structure representative:

  • Consider a selection of particles at two points in time, t1 and t2. Let {d(pit1,pjt1)} and {d(pit2,pjt2)} be the respective distances between pairs of particles in the selection at those two points in time. (This continues to uses the distance measure as the surrogate for the structure.)

  • Consider the set of differences {ABS(d(pit1,pjt1) - d(pit2,pjt2))}. We can now apply to this matrix means for identifying structures that reflect the components of the selection that remain constant within the dynamics of change in the selection.

  • The result will be a structure for the particles in the pair of selections, in which the particles again fall into successions of groups but this time representing the continuity of structure between the two points in time.

  • The most obvious times to be considered in this process are those that represent successive points in time, so that t2 = t1 + 1.


Continuity of structure2
Continuity of Structure representative:

  • Let’s consider some examples to illustrate what can happen. Again, I will use selections of 16 particles.

  • The charts to the right show three configurations of 16 particles at three points in time.


Continuity of structure3
Continuity of Structure representative:

  • The associated three matrices of distances between pairs of particles at each point in time are shown to the right.


Continuity of structure4
Continuity of Structure representative:

  • And the displays to the right now show the differences between the pairs of distances at the three points in time.

  • The top one shows the differences between the first and second points in time. The middle one, the differences between the second and third. And the bottom one, the differences between the first and third.

  • The components clearly shown in the top display: (1,2,3,4,5,6,7), (8,9,10,11,12),(13,14,15,16)

  • In the middle display: (1),(2,3), (5,6,7,8,9), (10,11,12,13,14,15,16)

  • In the bottom display: (1),(2,3), (4,5,6,7),(4,5,6,7,),(8),(9,10,11,12), (13,14,15,16)


Equivalence class
Equivalence Class representative:

  • Consider the measure of similarity between all pairs within a time-sequenced set of selections, S = {S1t1, … ,Sktk}:

    Mij = M(Siti,Sjtj), for all i and j = 1 to k.

  • If Mij > C for all i and j, the set S is called an Equivalence Class at the level of similarity C.


Maximal equivalence class
Maximal Equivalence Class representative:

  • Let S = {S1t1, … ,Sktk} be an equivalence class at the level of similarity C, and let Si = {Si1ti1, … ,Siktik} be any subset of the selections contained within it. Any subset of an equivalence class at the level C is also an equivalence class at the level C.

  • An equivalence class that is not a subset of any other equivalence class except itself will be called a maximal equivalence class. The time from the first and last selections in a maximal equivalence class will be called the life span of the equivalence class.


Entities1
Entities representative:

  • Consider an equivalence class in which the set of selections involved are all coherent selections with continuity of substance and continuity of structure

  • Such an equivalence class and the set of all of its component selections taken together will be called an Entity (at the level of similarity C). Each component selection will be called a manifestation of that Entity. Consider the sequence of times represented in the Entity. That sequence of times can be divided into discrete time intervals. Each time interval will be called an appearance of the Entity. The total set of time intervals will be called its life span.

  • Note that an entity represents three things: (1) it is an equivalence class, so it consists of nearly the same set of particles during its life span, (2) during each of its manifestations it is a coherent selection, so during its life span it holds together in the space, either by location or by attribute, (3) it maintains a substantially uniform structure, as determined by the similarity measure, during its life span.


Appearance over time of an entity
Appearance over time of an Entity representative:

  • A given entity may leave the space and then return at a later time. And that may be repeated many, many times. Each time, though, the entity is identified because of its particles with immediate continuity of identity. The set of those appearances will be an equivalence class unless the entity changes while outside the space to an extent that the level of similarity C no longer holds.

  • Any maximal category that consists of a single selection is an entity but will be called an ephemeral entity to emphasize the shortness of its life span.


Structure of an entity
Structure of an Entity representative:

  • Recall the derived characterization of the structure of a selection as the set of distances between pairs of particles that make up the selection: dij = d(pi,pj).

  • Let the selection {p1t,…,pkt} be the manifestation of an entity at the time t and let {dijt} be the set of distances between the pairs of particles in that selection at that time t.

  • Let Ct = {C1t,…,Ckt} be the hierarchical set of clusters for that manifestation of the entity and measure of distance.

  • For simplicity in discussion, let’s assume that the set of particles for that entity is the same at the next time t+1. (Recall that the particles for an entity will be nearly the same from one time to the next.)

  • Compare the two sets of clusters Ct and Ct+1 and consider the subset of clusters that contain the same particles (or nearly so, within the identified basis for continuity of identity; i.e., at the identified level of similarity, C) from one time to the next.

  • That subset will be the basis for identifying a continuity of structure, which will be defined as the structure of the entity.

  • We can think of the groups or clusters that comprise that structure as sub-entities within the entity.


Information and entities 1
Information and Entities - 1 representative:

  • Let there be T particles. The Entities, as defined above, represent a grouping of those T particles. Let that grouping be

    {Ti, i = 1 to Y}, T = i Ti

    where Y is the number of Entities and Ti is the number of particles in Entity i.

  • The set {Ti, i = 1 to Y}, T = i Ti, will be interpreted as the structure of the set of Entities, since it represents the distribution of particles among them.

  • The number of ways to select T1 items from T is T!/(T1!(T – T1)!)

  • To select T2 items from (T – T1), the number of ways is

    (T – T1)!/(T2!(T – T1 – T2)!)

  • And so on for each successive Ti.


Information and entities 2
Information and Entities - 2 representative:

  • As a result, the total number of possible groups of that kind is

    W({Ti}) = T!/iTi!

  • Stirling’s approximation for the factorial is

    ln X! = X ln X – X

  • Substituting that in the formula for W:

    ln W = ln T! – i ln Ti! = (T ln T – T) – i (Ti ln Ti – Ti)

  • Let Pi = Ti/T. Then

    ln W = (T ln T – T) – i (TPi ln TPi – Ti) + T

    = – T i Pi ln Pi

    The following screen shows an example for T = 8 particles. The first row is Ti. The second row is –(Ti/T)*log2(Ti/T). The other rows contain the number of Entities with Ti particles. Each row therefore represents a potential structure for a set of Y Entities.


Illustration 8 particles
Illustration: 8 Particles representative:


Complexity 1
Complexity - 1 representative:

  • Now I turn to the issue of “complexity”, with the intent of identifying means for characterizing the complexity of the pattern of structure.

  • Let’s start with the two extreme cases, for each of which there is only one possible structure. Specifically, for pattern 1, there are 8 Entities each with just 1 particle; that can occur in only one way. In the same vein, for pattern 22, there is 1 Entity with 8 particles; that too can occur in only one way. On the surface, each of those extremes would appear to be relatively simple in structure.

  • Looking at the dynamic process by which these entities were created, pattern 1 appears to represent a situation in which the particles moved in a random fashion, forming no lasting relationships. And pattern 22 represents a situation in which the particles were rigidly cohering.

  • Pattern 2 is not much different, with just 2 particles managing to combine but the remaining 6 being quite independent.

  • The remaining patterns become increasingly more interesting as the diversity of potential combination grows.


Complexity 2
Complexity - 2 representative:

  • I am going to use the number of potential structural patterns for Y Entities as a measure of complexity. The rationale for doing so is that it shows the richness of options for the structure of the space.

  • To illustrate, in the example of a space of 8 particles, note that the number of different structure patterns that potentially could be represented by a given number of Entities Y varies greatly. For example, for Y = 3 there are five different possible structural patterns; similarly for Y = 4. But for Y = 1, there is only a single pattern; similarly for Y = 8.

  • For a space of 16 particles, the number of structural patterns (equal to the number of partitions of 16) is 231. The following graph shows the number of structural patterns associated with each number of Entities.

  • Again, the extremes (of 16 Entities and 1 Entity, respectively) would seem to be rather simple in structure, as is the pattern with just 14 Entities. But the number of options for a given number of Entities is substantially great for other numbers of Entities.


Complexity 3
Complexity - 3 representative:

  • Note that the maximum complexity, with this definition, occurs with 5 Entities. Using that to illustrate the import of this definition, there would be 37 potential structural patterns for 5 Entities, so the computational task for identifying the particular pattern is entailed by the choice among those 37 potential ones.

  • In contrast, if there is just 1 Entity, there is only one potential pattern, and similarly, if there are 15 or 16 Entities. The computational task in those cases is trivial.

  • It is of some interest to see the array of 37 potential structural patterns for 5 Entities, as shown in the following screen.



Complexity 4
Complexity - 4 representative:

  • I want now to turn to the next level of complexity, in which each of the Entities can now be treated as a collection of its component sub-entities.

  • That is, consider Entity i, consisting to Ti particles. There are, as a result of the dynamic process of the space, sub-entities contained within it. Let there be Yi such sub-entities, with the particles of Entity i distributed among them. The resulting set

    {Tij, j = 1 to Yi}, Ti = j Tij

    can now be analyzed in the same way as has been done for the original set of Entities.

  • And the process can be repeated at each of the ensuing levels.


Processes as they affect entities
Processes as they affect Entities representative:

  • Impact between sets of entities

  • Merging of two sets of entities

  • Growth of an entity

  • Decay of an entity

  • Subdivision of an entity

  • Birth of an entity

  • Separation of an entity into two or more Entities

  • Creation of Entities


Induction from an entity
Induction from an Entity representative:

  • The similarities of an entity over time provides a basis for induction of the related similarity function. That similarity function, once identified, may then be applied to other entities. It may be called a “property”.

  • Entities with the same property then constitute and equivalence class.


Derived structure of space
Derived Structure of Space representative:

  • Given the set of Entities that results from the dynamics of the space, we can now begin to consider the resulting derived structure.

  • As a starting point, recognize that the particles of the space have now been distributed among the separate Entities. The derived structure is therefore represented by the pattern of that distribution.

  • Recall the algorithm by which the structure of a selection could be determined as a hierarchy of successive clusters. Apply that algorithm to the entire set of particles as a point in time.

  • The first set of clusters will be coherent selections (indeed, they will be maximal coherent selections) and thus include manifestations of every entity present at that point in time. The hierarchy of clusters will thus provide a structure for the entire space and of the entities within it.

  • Applying that structure over time and deriving the structure for the entities from it, we have the structure for the entire space.


The derived structure of space3
The Derived Structure of Space representative:

  • Lattice of Entities

    • Relation of “Containment”

    • Meet and Join of two Entities

    • Interactions among Entities

  • The Decomposition of the Lattice of Entities

    • Sub-Lattices of a Lattice

    • The Direct Product of Two Sub-Lattices

  • Output to Space

    • The Substance of Output

    • The Structure of Output

  • Cascading Measures of Similarity and Entities


Measurement of space

Location of material and energy in Space representative:

Number of dimensions for Space

Magnitude of material in Space

Number of pieces of material

Number of possible Selections

Number of pieces of material in a Selection

Time in Space

Degree of stability of a Selection

Information conveyed by a Selection

Degree of stability needed to identify an entity

Time period of stability needed to identify an entity

Information conveyed by an Entity

Number of Entities with a specified stability

Number of Components within an entity

Pace of movement and/or change of materials within the Space

Pace of movement of an Entity within the Space

Effect of an Entity on Space and on Entities

Complexity of the Structure of an entity

Complexity of the Structure of Living Entities

Measurement of Space


3 examples of worlds

A. representative:Physical World

B. Observer World

C. Perception World

D. Processing World

E. Communication World

F. Conceptual World

G. Societal World

H. Culture World

I. Academic World

J. Disciplinary World

K. Document World

L. Economic World

M. Religious World

3. Examples of Worlds


A physical world
A. representative:Physical World

  • A real physical world is the first example of a world and for most other worlds represents the contexts within which they occur.

  • As will be seen when examples of the physical world are discussed, a physical world can be considered at different levels of resolution or detail, for each of which the particles, entities, and processes are dramatically different.

  • The physical world can also be taken as all encompassing – the total physical universe – or as quite delimited – a single room in a house, for example.


Objective of the physical world
Objective of the Physical World representative:

  • For the real physical world, as a total universe, the objective is either existential (the purpose is simply to be) or the will of God.

  • For other, more limited physical worlds, though, more concrete and specific objectives may be identified. For example, the physical world might be simply a room in a house, and the objective is to create an appropriate décor or style for that room.


Examples of physical worlds
Examples of Physical Worlds representative:

  • 1. Subdimensional interface array

  • 2. Subnuclear (wave/particle) position/velocity pairs

  • 3. Atomic position/velocity/type

  • 4. Simple molecular position/velocity/type

  • 5. Complex molecular position/velocity/type

  • 6. Inanimate microscopic object definition

  • 7. Animate (live/powered) microscopic object definition

  • 8. Small (<10m) inanimate object definition

  • 9. Medium (10-50000m) inanimate object definition

  • 10. Large (50000+ m) inanimate object definition

  • 11. Small (<10m) animate object definition

  • 12. Large (10+ m) animate object definition


Examples of physical worlds1
Examples of Physical Worlds representative:

  • From Richard P. Feynman, The Character of Physical Law, quoted in God and the New Physics, p224:

  • We have a way of discussing the world . . . at various hierarchies, or levels. Now I do not mean to be very precise, dividing the world into definite levels, but I will indicate, by describing a set of ideas, what I mean by hierarchies of ideas.

  • For example, at one end we have the fundamental laws of physics. Then we invent other terms for concepts which are approximate, which have, we believe, their ultimate explanation in terms of the fundamental laws. For instance, "heat". Heat is supposed to be jiggling, and the word for a hot thing is just the word for a mass of atoms which are jiggling. But for a while, if we are talking about heat, we sometimes forget about the atoms jiggling -- just as when we talk about the glacier we do not always think of the hexagonal ice and the snowflakes which originally fell. Another example of the same thing is a salt crystal. Looked at fundamentally it is a lot of protons, neutrons, and electrons; but we have this concept "salt crystal", which carries a whole pattern already of fundamental interactions. An idea like pressure is the same.


Examples of physical worlds2
Examples of Physical Worlds representative:

  • Now if we go higher up from this, in another level we have properties of substances -- like "refractive index", how light is bent when it goes through something; or "surface tension", the fact that water tends to pull itself together, both of which are described by numbers. I remind you that we have got to go through several laws down to find out that it is the pull of the atoms, and so on. But we still say "surface tension", and do not always worry, when discussing surface tension, about the inner workings.

  • On, up in the hierarchy. With the water we have waves, and we have a thing like a storm, the word "storm" which represents an enormous mass of phenomena, or a "sun spot", or "star", which is an accumulation of things. And it is not worth while always to think of it way back. In fact we cannot, because the higher up we go the more steps we have in between, each one of which is a little weak. We have not thought them all through yet.


Examples of physical space
Examples of Physical Space representative:

  • As we go up in this hierarchy of complexity, we get to things like muscle twitch, or nerve impulse, which is an enormously complicated thing in the physical world, involving an organization of matter in a very elaborate complexity. Then come things like "frog".


Relationships among examples
Relationships among Examples representative:

  • These several levels of physical worlds exemplify the relationships that result from the analysis being presented here.

  • Specifically, the entities at each level can be treated as the particles at the next level, and the structure of those entities becomes the dimensional structure of the space at the next level.

  • As a result, the succession of levels become the succession of worlds, from those that deal with virtually sub-dimensional phenomena to those that deal with astronomical phenomena.


Physical particles
Physical Particles representative:

  • It is when we turn to the particles that form the substance of space that the level of resolution becomes most significant. At the more esoteric levels, those of sub-atomic particles for example, the particles and their attributes become very conceptual. The nature of strings, for example, seems to be dramatically different from what one normally thinks of as physical particles. Indeed, the history of these concepts involved contrasting views of whether the phenomena of the world represent particles or waves. And strings simply carry that debate to a great level.


Dimensions of physical space
Dimensions of Physical Space representative:

  • The obvious dimensions for time and location in real physical space are the normal ones for time and Euclidean space. It must be said, though, that at the more esoteric levels of resolution for physical space – those involved in string theory, for example – other measures of both time and space may turn out to be more appropriate.

  • For more limited physical worlds, such as a room in a house, the most likely physical dimensions are again the normal ones for time and space. But, again, for some objectives other dimensions may be required.


Sub spaces of a physical world
Sub-spaces of a Physical World representative:

  • Of course, physical space can be treated as a totality, with the several dimensions applying uniformly throughout the space.

  • However, there is frequently value in subdividing the space into component sub-spaces, like rooms in a house, each of which may have its own physical properties. Just as the rooms in a house may have different temperatures and dimensions, so the sub-space may do so.


Physical entities
Physical Entities representative:

  • As I have pointed out, the succession of steps I have identified, leading from particles to entities which then in turn become the particles at the next level of space, are well exemplified by the ladder of examples previously shown.


Dynamics of physical particles
Dynamics of Physical Particles representative:

  • Of course, the sciences of physics, engineering, astronomy, and cosmology are concerned with the dynamics of physical particles. Indeed, their primary objective is to understand the processes by which physical particles behave.

  • It is not my objective, as I pointed out earlier, to deal with the specifics of those sciences.


Derived structure of physical space
Derived Structure of Physical Space representative:

  • The transition from each level to the next constitutes the derived structure for the next level.


Measurement of physical space

Location of material and energy in Space representative:

Number of dimensions for Space

Magnitude of material in Space

Number of pieces of material

Number of possible Selections

Number of pieces of material in a Selection

Time in Space

Degree of stability of a Selection

Information conveyed by a Selection

Degree of stability needed to identify a Physical Entity

Time period of stability needed to identify a Physical Entity

Information conveyed by an Entity

Number of Physical Entities with a specified stability

Number of Components within a Physical Entity

Pace of movement and/or change of materials within the Space

Pace of movement of an Entity within the Space

Effect of an Entity on Space and on Entities

Complexity of the Structure of a Physical Entity

Complexity of the Structure of Living Entities

Measurement of Physical Space


B observer world
B. representative:Observer World

  • The important thing about an observer world, aside from what goes on within it, is its relationship to the world outside it. Thus, an observer includes means for “observing” what happens externally and determining, through its own internal processing, what is happening in the external world.

  • In the worlds that are herein presented, the observer world is itself divided into two sub-worlds: (1) a perception world that is the means for the actual observation, and (2) a processing world that is the means for assessing what the perceptions mean in terms of the observer’s own interests.


Objective of an observer world
Objective of an Observer World representative:

  • On the surface of it, the objective of an observer world is to provide the observer, as an entity in the physical world, with means for dealing with other entities in the physical world.

  • Thus, with this as its objective, an observer world should be seen as an entity in the broader physical world and thus as interacting with other entities in that physical world. By observing what is happening, the observer can better deal with what happens. It may be able to avoid collisions with other entities, or it may be able to absorb them, or eat them. It may be able to mate with them.

  • For the example of a computer as an observer world, the data it receives from the outside world becomes the basic raw material for its internal processing. And, of course, the same thing applies to a sentient being.


Examples of an observer world
Examples of an Observer World representative:

  • There are two examples that will be used to represent an observer world:

    • A sentient being (e.g., a person)

    • A computer

  • Of course, for each there are a number of more specific possible examples. A sentient being might be, as indicated above, a person, a human being. But it might be an animal or a bird, though some might question whether they are sentient. It might even be an insect, an amoeba, perhaps even a plant. Obviously, the level of sentience differs as one moves from a human being to a dog, to an amoeba, to a tree, and at some point it surely is an issue as to whether the word “sentient” is appropriate.

  • A computer might be a general purpose computer. It might be a specialized computer, such as functions in modern day cars.


Components of an observer world
Components of an Observer World representative:

  • In both of the examples (sentient beings and computers), the observer space can best be analyzed in terms of four components:

    • (1) Perception Component

    • (2) Storage Component

    • (3) Process Component

    • (4) Effector Component

    • (5) All other parts

  • Each of those components will have its own dimensions, reflecting the role it plays in operations of the observer world.

  • Instead of discussing the several elements as they relate to an observer world, I will now discuss them for two of those components, the perception and processing components, treating them each as a world.


C perception world
C. representative:Perception World

  • A perception world is that component of an observer in which the actual observation of the external world takes place.

  • For a human being it is represented by the several sense organs and the related receptors of input from the external world (or, incidentally, from the observer itself).

  • It is relevant to note here that each of the several sense organs potentially leads to a separate sub-space.


Objective of a perception world
Objective of a Perception World representative:

  • The objective of a perception world is to serve as the interface between the world external to the observer and the world internal to it. It is the means by which sensory input from the outside world are received and put into the form necessary for subsequent processing.

  • Here, I want to return to an earlier comment concerning the difference between explicit and implicit objectives and comment concerning their relevance in the context of a perception world.

  • It is possible that the objective of a perception world is externally defined, typically by imposing a priori structures on the processes of perception. In a very real sense, this results in information being use not to make decisions but to justify decisions that have already been made.


Examples of a perception world
Examples of a Perception World representative:

  • The examples of perception worlds that will be used are the same as for an observer world

    • (1) Sentient beings

    • (2) Computers

  • The means for perception in the two examples are, to some extent, parallel. Thus, for each there are means for seeing (the eye or an optical scanner, respectively), for hearing (the ear and a microphone, respectively), for sensing heat or temperature (the skin and a heat sensor, respectively), for sensing pressure (again the skin and a pressure sensor, respectively), etc.

  • On the other hand, for each there may be means for perception that are not so obviously parallel. In particular, computers accept input from keyboards or from mouse-clicks, and there are no obvious counterparts for a person (though one might artificially create them).


Particles in perception space sensations
Particles in Perception Space: Sensations representative:

  • The particles for an observer are what will be called sensations as the means by which the observer represents input from the outside world. The sensations are the particles of which the substance of the perception world consists.


Time in perception space
Time in Perception Space representative:

  • It would seem that a perception space must deal with two dimensions of time, not simply one. There is the external dimension of time, the clock of the real world if you will. But there is also the internal dimension of time, the internal clock. And while those two clocks may be synchronous, they may not be.

  • For example, in a computer, there is an internal clock that governs the sequence of internal events. While that internal clock may be closely tied to the external clock of regular time, it could be quite different; it could vary in its pulse rate, for example.

  • Clearly, the relationship between the two dimensions of time must be dealt with as part of the processing of the observer, but some of it may be handled within the perception component.


Dimensions in perception space
Dimensions in Perception Space representative:

  • Similarly, it would seem that an observer space and therefore its perception space must deal with two sets of dimensions for location. One is the set of internal dimensions, the ones that locate sensations within the observer. The other is the set of external dimensions, the ones that locate the sources for the stimuli leading to the sensations.

  • Clearly, as with time, the relationship between those two sets of dimensions of location must be an integral part of the processing done by the observer.

  • Finally, particles in perception space have internal attributes, but at least some of them presumably are derived from the input from the external world.


Structure of a perception world
Structure of a Perception World representative:

  • It makes sense to impose a structure upon a perception world in which each type of sensation (e.g., sight, hearing, tactility, heat, pressure, balance, etc.) functions within an independent sub-space of a perception space.

  • For a person, as a sentient being, this seems to be physiologically the case, with the several sense organs located in different physical locations, involving different type of sense organs and receptors, and sending their signals to different locations within the brain.

  • For a computer, the distinction seems less clear cut. Though the sensory organs for the type of sensations are also different, they are received through essentially interchangeable ports and send their signals to what are essentially equivalent locations in the memory.


Perception entities called sense images
Perception Entities, called Sense Images representative:

  • Definition of Sense Image

    • Selections of Sensations

    • Structure of a Selection

    • Categories of Sensations

    • A Category of Coherent Selections

    • The Nature of Stability or Coherence

  • Categories of Sense Images

  • Symbol


Processes on sense images
Processes on Sense Images representative:

  • Definition of Processes

    • Input Processes

    • Internal Processes

      • Interactions of an Sense Image with Sensation Space

      • Impact between Sense Images

      • Merging of two Sense Images

      • Growth of an Sense Image

      • Decay of an Sense Image

      • Subdivision of an Sense Image

      • Birth of an Sense Image

      • Separation of an Sense Image into two or more Sense Images

      • Creation of Sense Images

      • Creation of Living Sense Images

    • Output Processes


D processing world
D. representative:Processing World

  • A processing world is that component of an observer in which sentient behavior, in contrast to merely sensory behavior, occurs. It involves memory, as the means for the retention of the past, as well as the ability to process.


Examples of processing space
Examples of Processing Space representative:

  • As before, there are two primary examples of processing space:

    • Sentient beings

    • Computers

  • For computers, though, there are applications that will provide some more specific examples:

    • Management information systems

    • Command and control systems


Data the particles of a processing world
Data: The Particles of a Processing World representative:

  • Data are the particles for a processing world.

  • Selections of data constitute the basis for processes within a processing world.


Structure of a processing world
Structure of a Processing World representative:

  • It is useful to impose a structure on a processing world, distinguishing between the memory component and the processing component in particular.


Dynamics of observer space
Dynamics of Observer Space representative:

  • It would seem that the most evident cause for dynamics of an observer space would be the dynamics in what is being observed.

  • However, there may be internal dynamics as well, as sensations interact, and the relationships between internal and external dynamics clearly needs to be resolved in the processing.


Processing entities called ideas
Processing Entities, called Ideas representative:

  • Definition of an Idea

    • Selections of Data

    • Structure of Selections of Data

    • Categories of Data

    • A Category of Coherent Selections

    • The Nature of Stability or Coherence

  • Categories of Idea

  • Symbol


Derived structure of observer space
Derived Structure of Observer Space representative:

  • The discussion of the derived structure for an observer world will be deferred until it will be covered in consideration of a processing world, since a processing world is a component of an observer world.


E communication world
E. representative:Communication World

  • A communication world depends upon the physical world to provide the means by which the processes of communication take place.


Objective of a communication world
Objective of a Communication World representative:

  • The objective of a communication world is to provide the basis for transfer of data and ideas derived from them between physical entities. It therefore combines physical worlds and processing worlds.


Examples of a communication world
Examples of a Communication World representative:

  • The examples that will be used of a communication world are:

    • Interpersonal communication (especially one-on-one)

    • Mass media communication


Symbols communication particles
Symbols: Communication Particles representative:

  • I will use the word “symbols” to represent the particles in communication space. In general, I interpret symbols as data that are intended to represent something other than themselves.


Structure of a communication world
Structure of a Communication World representative:

It is useful to impose a structure upon a communication space, distinguishing among the following components:

Transmitter

Channel

Receiver

Memory

Coder and Decoder


Communication entities called messages
Communication Entities, called Messages representative:

  • Definition of a Message

    • The Nature of Stability or Coherence

  • Categories of Messages

  • Symbol


Processes on messages
Processes on Messages representative:

  • Definition of Processes

    • Input Processes

    • Internal Processes

      • Interactions of a Message with Communication Space

      • Impact between Messages

      • Merging of two Messages

      • Growth of an Message

      • Decay of an Message

      • Subdivision of an Message

      • Birth of an Message

      • Separation of an Message into two or more Messages

      • Creation of Messages

      • Creation of Living Messages

    • Output Processes

  • Structure of Processes


F conceptual world
F. representative:Conceptual World

  • A conceptual world is, in a fundamental way, quite different from a physical world, an observer world, or a communication world. The difference lies in the fact that it does not depend upon any physical manifestation. Indeed, a conceptual world can be totally disparate from any real physical world, even antithetical to it.


Conceptual world objective
Conceptual World Objective representative:

  • The objective of a conceptual world is to explore the implications of departures from reality.


Examples of a conceptual world
Examples of a Conceptual World representative:

  • The examples of a conceptual world that come immediately to mind are:

    • Fiction

    • Philosophy

    • Mathematics

    • Theoretical physics


Ideas particles in conceptual space
Ideas: Particles in Conceptual Space representative:

  • Here we enter a never-never land, since the particles in a conceptual space can be anything the creator of it wishes to make them.

  • However, let’s take the word “idea” to represent a particle.


Conceptual entities called concepts
Conceptual Entities, called Concepts representative:

  • Definition of a Concept

    • The Nature of Stability or Coherence

  • Categories of Concepts

  • Symbol


Structure of a conceptual world
Structure of a Conceptual World representative:

  • Within each of the examples of a conceptual world, it is useful to identify a structure that sub-divides into genres and specialties. In each case, the sub-components are characterized by different dimensions but within the general framework of the world of which they are parts.


G societal world
G. representative:Societal World

  • With a societal world, we probably return to the physical world, within which many societal processes take place. Having said that, however, there are also many societal processes that are essentially conceptual and independent of physical manifestation. A societal world must therefore be treated as a mixture of both physical and conceptual components.


Objective of a societal world
Objective of a Societal World representative:

  • Again, I want to return to the distinction between explicit and implicit objectives. The issue here is whether the objective of a societal world is external imposed or internally driven.

  • It arises specifically when social entities, such as a country, are externally identified versus arising from the dynamics of the people themselves. It is exemplified by the colonial conquests that created artificial countries in Africa.


Examples of societal worlds
Examples of Societal Worlds representative:

  • The examples that will be used for a societal world include:

    • Inter-Personal Interaction

    • Physical Communities (such as cities)

    • Families

    • Religions (and similar conceptual communities)

    • Shared Ideas


Persons the particles of societal space
Persons: The Particles of Societal Space representative:

  • Individual persons are the particles of societal space.

  • While the physical location of a person clearly is important, for most of the processes in societal space, the attributes of persons are far more critical.


Structure of a societal world
Structure of a Societal World representative:

  • For each of the examples of a societal world, it is useful to identify components that represent a structure for the world, with differences in the nature of the space each represents but with the common features that characterize the total world.


Societal entities called communities
Societal Entities, called Communities representative:

  • Each of the kinds of societal worlds gives rise to different kinds of social entities, which as a group I will call communities: friendships and marriages, families and clans, cities and towns, churches and sects, academic disciplines and departments.


Processes on communities
Processes on Communities representative:

  • Definition of Processes

    • Input Processes

    • Output Processes

      • Interactions of an Community with Societal Space

      • Impact between Communities

      • Merging of two Communities

      • Growth of an Community

      • Decay of an Community

      • Subdivision of an Community

      • Birth of an Community

      • Separation of an Community into two or more Communities

      • Creation of Communities

      • Creation of Living Communities

      • Interactions of a Community with Societal Space

    • Output Processes

  • Structure of Processes


H cultural world
H. representative:Cultural World

  • In some respects, each societal world may include a cultural world, but there are sufficient differences between the overall processes in a societal world and those that are cultural to make it worthwhile to consider the cultural aspects separately.


Objective of a culture world
Objective of a Culture World representative:

  • The objective of a cultural world is to represent those aspects of a societal world that are essentially conceptual, in the sense that the term has been used in discussion of conceptual worlds.


Examples of a cultural world
Examples of a Cultural World representative:

  • This is an interesting dilemma! What am I going to use as examples of cultural space?

    • Religion?

    • Primitive cultures?

    • The arts and humanities – “Kultur”?


Ideas particles in cultural space
Ideas: Particles in Cultural Space representative:

  • In using ideas as the particles in cultural space, I am, in a sense, treating cultural space as a derived space from a processing space.


Cultural space
Cultural Space representative:

  • Time in Cultural Space

  • Cultural Space and Knowledge within it

    • Knowledge

      • Form of Knowledge

      • Location of specific Knowledge

      • Selections of Knowledge

      • Categories of Knowledge

  • Dimensions

    • Dimensions of location in Cultural Space

    • Dimensions of form of Knowledge


Knowledge the entities of cultural space
Knowledge: The Entities of Cultural Space representative:

  • I will use the word “knowledge”, which I interpret as the shared ideas in a societal world, as the entities in cultural space.


I academic world
I. representative:Academic World

  • The academic world seems almost self-evident as a focus.


Objectives of an academic world
Objectives of an Academic World representative:

  • There are two primary objectives for an academic world: research and teaching. The first is intended to add to our knowledge about the issues involved in each specific academic world. The second is intended to convey that knowledge from one generation to the next.


Examples of academic worlds
Examples of Academic Worlds representative:

  • Clearly, the set of departments in an academic institution is the obvious example of an academic world.


Faculty the particles in academic space
Faculty: The Particles in Academic Space representative:

  • Persons, as members of faculties, are the particles of academic space.


Structure of an academic world
Structure of an Academic World representative:

  • The dimension of time in an academic world is a combination of physical time, as we normally think of it, and an artificial time, governed by the calendar of academic life, with only a tenuous connection to real physical time.

  • The attributes of members of a faculty are both individual and institutional.


Dynamics of faculty members
Dynamics of Faculty Members representative:

  • Faculty get appointed and promoted. They move from one institution to another. They carry out research and they interact with students. They collaborate with each other in shared research and teaching responsibilities. They publish and become recognized by others.

  • Thus, some of the dynamics relate to changes for the individual person. Others relate to interactions among persons.


Academic entities called disciplines
Academic Entities, called Disciplines representative:

  • Given the individual persons who are faculty members, the dynamics of them as a whole lead to the identification of entities that represent their similarities in activities. These I will call disciplines.


Processes on disciplines
Processes on Disciplines representative:

  • Definition of Processes

    • Input Processes

    • Internal Processes

      • Interactions of an Discipline with Academic Space

      • Impact between Disciplines

      • Merging of two Disciplines

      • Growth of an Discipline

      • Decay of an Discipline

      • Subdivision of an Discipline

      • Birth of an Discipline

      • Separation of an Discipline into two or more Disciplines

      • Creation of Disciplines

      • Creation of Living Disciplines

    • Output Processes


J disciplinary world
J. representative:Disciplinary World

  • A disciplinary world is one in which the focus is on objects of research.


Objectives of a disciplinary world
Objectives of a Disciplinary World representative:

  • The objective of a disciplinary world is to bring to bear identified means for investigation – what are called paradigms of research – to the investigation of a specific and more or less well delineated set of issues of investigation.


Examples of disciplinary worlds
Examples of Disciplinary Worlds representative:

  • The examples of disciplines are evident in the derived structure of the academic world:

    • The physical sciences

    • The social sciences

    • The humanities

    • The arts (as an academic focus, not as performance)

    • The professions (as an academic focus, not as performance)

    • Mathematics

    • Philosophy


Objects of investigation
Objects of Investigation representative:

  • In a very real sense, the objects of investigation for a discipline are represented by the particles, structure, processes, and entities that are embodied in a world, such as those we are presenting here.

  • Given that, a discipline arises whenever there is a world to be investigated.


Structure of disciplinary space
Structure of Disciplinary Space representative:

  • Disciplinary Space

    • Time in Discipline Space

    • Discipline Space and Issues within it

      • Objects of Investigation

        • Form of Objects of Investigation

        • Locations of Specific Objects of Investigation

        • Selections of Objects of Investigation

        • Categories of Objects of Investigation

    • Dimensions of a Discipline

      • Dimensions of Location of a Discipline

      • Dimensions of Form of a Discipline


Dynamics of objects of investigation
Dynamics of Objects of Investigation representative:

  • The dynamics of Discipline Space


Disciplinary entities called issues
Disciplinary Entities, called Issues representative:

  • Definition of an Issue

    • The Nature of Stability or Coherence

  • Categories of Issue

  • Symbol


Processes on issues
Processes on Issues representative:

  • Definition of Processes

    • Input Processes

    • Internal Processes

      • Interactions of an Issue with Discipline Space

      • Impact between Issues

      • Merging of two Issues

      • Growth of an Issue

      • Decay of an Issue

      • Subdivision of an Issue

      • Birth of an Issue

      • Separation of an Issue into two or more Issues

      • Creation of Issues

      • Creation of Living Issues

    • Output Processes


The output from discipline space
The Output from Discipline Space representative:

  • Substance of Output from Disciplinary Space

  • Structure of Output from Disciplinary Space


K document world
K. representative:Document World

  • A document world is one of “recorded information”, of the records by which mankind communicates. Of course, a document world is an example of a communication world so most of what can be said may already have been said in that context. But it is a communication world of special significance because it serves as the means for communication not only at a given time but across many times, even centuries of time.


Objective of a document world
Objective of a Document World representative:

  • The objective of a document world is to preserve and provide access to the media that represent the tangible embodiment of the message by which people communicate in each of the worlds in which such communication is part of the process.


Examples of document worlds
Examples of Document Worlds representative:

  • Examples of document worlds:

    • Libraries

    • The Internet

    • Archives

    • Corporate records

    • Legal records


Particles in a document space
Particles in a Document Space representative:

  • The obvious choice for particles in a document space is indeed “documents” as the forms of embodiment of communications.

  • However, one might want to start with narrower choices, perhaps even down to individual symbols.

  • Thus, as in physical space, there may be value in identifying levels of documentary structure, from symbols (such as bytes) to successively larger units of structure.


Document space
Document Space representative:

  • The role of time in a document space is a fascinating issue! Clearly normal time as we think of it is relevant, but it hardly seems to be the dominant role of time. Perhaps we need to think in terms of time in the rate of decay in use of materials.

  • The role of location clearly is important, but not in the simple terms of regular Euclidean space. Perhaps we need to think in terms of the decay in use as a function of accessibility.

  • The role of attributes is perhaps the most critical, so we would need to examine carefully the attributes of documents: the language, the currency in time, the medium, etc.


Dynamics of recorded symbols
Dynamics of Recorded Symbols representative:

  • What then are the processes involved in documentary space?

  • They would appear to be creation (authorship, for example), acquisition, citation or reference, combination or anthology, abstracting, describing.


Document entities
Document Entities representative:

  • If we adopt the view that the particles are in a succession of spaces, then the entities are, in each case, the next level of that succession.


Processes on documents
Processes on Documents representative:

  • Definition of Processes

    • Input Processes

    • Internal Processes

      • Interactions of an Document with Documents Space

      • Impact between Documents

      • Merging of two Documents

      • Growth of an Document

      • Decay of an Document

      • Subdivision of an Document

      • Birth of an Document

      • Separation of an Document into two or more Documents

      • Creation of Documents

      • Creation of Living Documents

    • Output Processes


Derived structure of document space
Derived Structure of Document Space representative:

  • Structure, Function, and Change of Documents Space


L economic world
L. representative:Economic World

  • This is going to be interesting. It is my first attempt to apply this model to something that was not part of its origin.

  • The identification of economic particles, dimensions, measures of coherence and similarity, and, especially, of entities, will be a most interesting challenge!


Objective of an economic world
Objective of an Economic World representative:

  • The objective of an economic world is to use available resources in the most effective and efficient manner so as to meet needs of the population of the world and/or the individual person.


Examples of an economic world
Examples of an Economic World representative:

  • Individual economic decision maker

  • Corporation

  • National economy


Economic particles
Economic Particles representative:

  • I think the particles are persons as economic decision-makers, ala game theory.

  • The dimensions of attributes are, I think the basic dimensions of criteria for decision-making:

    • Level of available wealth

    • The balance between individual greed and common interest

    • Level of need

    • Willingness to take risks

    • Level of knowledge


Economic space
Economic Space representative:

  • What is the dimension of time in economic space? I think it is not standard spatial time, but something else, although standard spatial time must certainly underlie it.

  • How about the dimensions of location? Normal Euclidean space seems almost irrelevant, so probably the dimensions of attributes become dominant in identifying location.


Dynamics of economic particles
Dynamics of Economic Particles representative:

  • The individual decision maker makes decisions about the use of resources in the context of all of the other decisions that are made.

  • Beyond that, however, the decisions are made in the context of changing attributes of each decision maker.


Economic entities
Economic representative:Entities

  • What then are the entities in an economic world?

  • They may well be coalitions, in the context of cooperative game theory.


Economic processes
Economic representative:Processes

  • Definition of Processes

    • Input Processes

    • Internal Processes

      • Impact between Entities

      • Merging of two Entities

      • Growth of an entity

      • Decay of an entity

      • Subdivision of an Entity

      • Birth of an entity

      • Separation of an entity into two or more Entities

      • Creation of Entities

    • Output Processes

  • Structure of Processes

    • Structure of an Individual Process

    • Structure of a Sequence of Processes


Structure of economic entities
Structure of Economic Entities representative:

  • The Nature of Stability or Coherence

  • Categories of Entities

  • Types of Similarity Measures and Resulting Entities

    • Static, Inert Entities

    • Distinct Entities

    • Stable Entities

    • Growing or Decaying Entities

  • Sub-Entities


Derived structure of economic space
Derived Structure of Economic Space representative:

  • Lattice of Entities

    • Relation of “Containment”

    • Meet and Join of two Entities

    • Interactions among Entities

  • The Decomposition of the Lattice of Entities

    • Sub-Lattices of a Lattice

    • The Direct Product of Two Sub-Lattices

  • Output to Space

    • The Substance of Output

    • The Structure of Output

  • Cascading Measures of Similarity and Entities


M religious world
M. representative:Religious World

  • To some extent, I have already dealt with religious worlds as one example of a societal world. In that example, the persons who are the particles become parts of entities that we call churches. These are communities in much the same way that families and clans, cities and towns are.

  • But surely a religious world is something more than a societal one. And it is this that I want to explore.

  • Here I face the problem, even barrier, that I am not a religious person myself, even though my grandfather was a Presbyterian minister. In fact, I have little experience or sympathy with the usual trappings of churches as the societal constructs of religions.

  • Oh, I admire the architecture, the painting and sculptures, the music, the literature that are the physical manifestations of the religions. But those are that the substance of a religious world.


Objective of a religious world
Objective of a Religious World representative:

  • The objective of a religious world, though, seems self-evident. It is to understand and deal with aspects of the world that it is thought cannot be dealt with by the mere rationality and the means of science.

  • In the large sense, that is interpreted as requiring understanding of God, so much of a religious world is likely to be focused on that objective. Indeed, most recognized churches focus their tenets on this objective

  • But more narrowly, it might be interpreted as understanding the nature of good and evil, of right and wrong, of purpose and will, of self and community. And there are religions that focus their tenets on these objectives, in some cases without needing reference to the objective of understanding God.


Particles of a religious world
Particles of a Religious World representative:

  • But when I try to identify the particles, indeed the substance in whatever way one may wish to characterize it, I face the barrier that I have identified.

  • My somewhat feeble attempt is to identify particles in a religious world as the aspects of the real world that, to be understood, require invoking religious methods rather than rational ones.

  • Thus, a particle is something we currently cannot rationally explain. So the particles in religious space are the set of things that we currently cannot explain.


Structure of a religious world
Structure of a Religious World representative:

  • The dimensions of religious space now become highly conceptual and in some respects even fictional. Because, if the particles cannot be rationally explained, how then can one rationally even describe them? And that is what the dimensions of space are expected to do.

  • The barrier seems clear. The very nature of religious phenomena almost precludes very methods I am trying to apply.

  • But there are some aspects that perhaps can be recognized. In particular, the issues of moral judgment seem to be amenable to rational investigation. And of course that is the concern of moral philosophy during the entire history of philosophy.


4 the universe of worlds
4. representative:The Universe of Worlds

  • Consider the entire set of worlds, those that we have considered in the discussion to this point as well as others that we might define in similar ways.

  • In some respects, that set of worlds constitutes a new world, which we might call the universal world, in which the worlds are the particles. The dimensions for the worlds are the several aspects by which we have characterized each of them – the particles within them, the dimensions that each has, the processes by which entities are created, the entities that result.

  • And, as in each of the worlds, there are similarities by which that universe itself has a structure.


The overall structure
The Overall Structure representative:

  • As an approach to visualizing the structure of that universe of world, I am going to identify a set of dichotomies and to try to characterize each of them:

    • Worlds of Physical Things vs. Worlds of Non-Physical Things

    • Worlds of Sentient Things vs. Worlds of Non-Sentient Things

    • Worlds of Living Things vs. Worlds of Non-Living Things

    • World of Human Beings vs. Worlds of Non-Human Beings

  • Each dichotomy in turn will be regarded as a sub-division of the first element in the prior dichotomy.


Physical things vs non physical things
Physical Things vs. Non-Physical Things representative:

  • The first element in this dichotomy is almost self-evident. It is the physical world as we know it, taken at the several levels at which physical things can be examined, as detailed in the listing of levels described by Richard Feynman.

  • The second element, though, is by no means self-evident. One can identify at least three kinds of non-physical things:

    • Parallel spaces, as represented in some theories

    • Spiritual spaces, as represented in some religious thinking

    • Conceptual spaces, as represented in sentient things

  • In what follows, I will concentrate on the third of those kinds of non-physical things frankly because I do not know how to deal with the first two.


Sentient things vs non sentient things
Sentient Things vs. Non-Sentient Things representative:

  • This is not so much a dichotomy as a spectrum determined by the extent to which changes in a particle are due to the particle or the entity itself or to what happens outside the particle.

  • At one extreme, the particle itself causes no changes, and all changes in it are the result of what happens outside the particle. In this case there would be zero sentience in the particle.

  • At the other extreme, all changes to a particle are caused by the particle itself. This extreme is unlikely because, if nothing else the force of gravity would be operative. However, the principle is there.




The nature of particles
The Nature of Particles representative:

  • The most evident of the similarities are those of the particles. Note that the physical world, the observer world, the perceptual world, the societal world, the academic world, the documentary world, each involves particles that are essentially real.

  • In contrast, the processing world, the communication world, the conceptual world, the cultural world, the disciplinary world, the economic world, the religious world, each involves particles that are essentially symbolic.

  • However, although the particles are essentially symbolic in the latter worlds, in the case of the processing world and the communication world, the particles are also physical and therefore to that extent also real.


The nature of entities
The Nature of Entities representative:

  • Similarities of the entities in the several worlds are much more mixed. For physical worlds, as we have pointed out, the entities arise as essentially real but successive stages in visualizing the structure of physical space. For the societal world, the entities – communities – are a mixture of real things and symbolic things; families and cities are real but they are also conceptual. Similarly for the document world, where collections are real things but also conceptual ones.

  • For all of the other worlds, the entities are essentially symbolic.


The nature of processes
The Nature of Processes representative:

  • Similarities of the processes in each world is much more complex. However, in the physical world, the processes are completely real.

  • In the observer world and the perception world within it, the processes are a complex mixture of real and symbolic. Similarly in the communication world and the societal world.

  • In all other worlds that we looked at, the processes are essentially symbolic.

  • Again, though, as with the particles, the processes in the processing world and the communication world are also physical and therefore very real. For example, the processes in the brain are very real, physical in the activities of the neurons by which the processes occur.


The end
The End representative:


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