Robert L. Rich
Sept 8, 1997
Revision history:
Jun 23, 2000, Jan 14, 2001, Jun 26, 2001
Table of Contents
- Introduction to the Source-Action-Object Model
- Assumption 1: Source
- Assumption 2: Action
- Assumption 3: Object
- Axiom 1: Creation
- Axiom 2: Compound Objects
- Definition: Simple Object
- Axiom 3: Relatable Distinctions
- Definition: Vanishment
- Axiom 4: Time
- Definition: Time Object
- Definition: Moment
- Definition: Properties
- Definition: Quantity
- Definition: Enter
- Axiom 5: Enterability Property of Objects
- Axiom 6: Space
- Axiom 7: Solid
- Definition: Measurement
- Definition: Viewpoint
- Definition: Coincidence / Non-coincidence
- Definition: Dimension & Distance
- Definition: Position
- Axiom 8: Spatial Non-coincidence of Solid Objects
- Definition: Area
- Definition: Volume
- Axiom 9: Measurement of Space
- Axiom 9a: Measurement of Time
- Axiom 10: Change of Position
- Axiom 11: Motion
- Definition: Resistance
- Axiom 12: Resistance to Change
- Axiom 13: Increase of Time
- Definition: Rate of Change
- Axiom 14: Inertia
- Definition: Degree
- Definition: Depth
- Axiom 15: Complexity
- Definition: Density
- Axiom 16: Density of Time Objects
- Axiom 17: Mass
- Definition: Universe
- Definition: Mathematics
- Axiom 18: Detection
- Axiom 18a: Comparison
- Axiom 19: Awareness
- Definition: System
- Definition: Relate
- Definition: Structure
- Definition: Prime Object
- Definition: Prime Source
- Axiom 20: Life
- Axiom 21: Energy
- Axiom 22: Power
- Definition: Influence (n.)
- Definition: Experience (v.)
- Definition: Pervade
- Axiom 23: Pervasion
- Axiom 24: Level of Differentiation
- Axiom 25: Level of Declared Associations
- Axiom 26: Level of Association
- Definition: Identity
- Definition: Identify
- Axiom 27: Identification with Subordinate Sources
- Axiom 28: Multiple Identities
- Axiom 29: Generation of Depth
- Definition: Intention
- Axiom 30: Agreement / Disagreement
- Axiom 31: Multiple Source Objects
- Definition: Attention
- Axiom 31a: Relationship
- Axiom 32: Value and Intention of Distinctions
- Definition: Loss
- Definition: Loss of Properties
- Axiom 33: Dependency
- Definition: Interdependency
- Definition: Intentional Design
- Definition: Implementation
- Definition: Design
- Definition: Optimum
- Axiom 34: Optimum Implementation
- Theorem 1: Assignment of Properties to Copies of Detected Objects
- Theorem 2: Changes to Simple Objects
- Definition: Context
- Axiom 36: General Non-Coincidence of Objects
- Axiom 37: Coincidence and Detection
- Definition: Continuum
- Axiom 38: Reality
- Definition: Drift
- Axiom 39: Necessary Conditions for Detection
- Theorem 3: Changes to Space
- Definition: [X0]
- Axiom 40: Simple Objects Do Not Detect
- Definition: Compound Operations
- Definition: [X*]
- Definition: Relationship Symbols
- Theorem 4: Only Sources Create Relationships
- Definition: Ideal Design
- Axiom 41: Command - The Unit Measure of Source
- Theorem 5: Source-Viewpoint
- Theorem 6: Streaming
- Definition: Interface
- Definition: Interface System
- Definition: Environment
- Theorem 7: The First Intention of Life
- Axiom 42: Perception
- Theorem 8: The Complexity of Life
- Definition: Abstraction
- Axiom 43: Realization
- Theorem 9: (cancelled)
- Axiom 43a: Source is Identified by its Creations
- Theorem 10: (cancelled)
- Theorem 11: Identified Sources in Constant Change
- Axiom 44: The Value of Source
- Theorem 12: Influence of Sources on Sources
- Theorem 13: Power of a Source
- Definition: Compound Source
- Definition: Resource
Introduction
All of the Western physical sciences are modeled upon the assumption of three fundamental elements: mass, length and time. They can be measured in terms of standardized units (e.g.- centimeters, grams, seconds), but in no scientific literature are they otherwise than circularly defined. These items are assumption points: elements which are taken to be "self-evident" and therefore needing no further explanation. Clarence E. Bennett, former chairman of the department of physics at the University of New Hampshire comments;"...it should be noted that it is only by custom that these three particular concepts are taken as basic for the development of the entire subject (of physics). Theoretically any three concepts could have been used, but these three give the most natural, and probably the simplest, development." (Physics without Mathematics: Barnes & Noble, 1949)One could point out that it is only "natural" since it has been the standard for so long. However comfortable custom may be, there is nothing inherently "right" or "natural" about defining all of science in terms of mass, length, and time. While the model does clearly have a certain workability, there are compelling reasons to consider other assumption points as well.One's conclusions, predictions and even observations are directed and constrained by the model one uses. The following is an exercise which develops a new physical model based upon completely different assumption points. The intent is to explore what occurs when the most basic elements of a model are changed. At this time, no claims are made regarding the usefulness of the results.
This material constitutes a logical structure, therefore it must be studied sequentially to be properly understood.
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Assumption 1: Source
Source is that which is capable of causation, declaration, decision, initiation or intention; that which is capable of drawing a distinction; that which is capable of differentiation; that which brings about change; that which brings into existence.Source is a fundamental of the model.
Symbology:
Comment: Primitive* Source has no further definition. By "source" we are referring to any source of causation, whether physical or non-physical, organic or inorganic, complex or simple, cosmological or sub-atomic. One could differentiate Source into any of these or other sub-classifications, but these constraints have no place in the primitive definition.
- Upper case letters standing alone are identifiers for sources with fixed, non-variable identities.
Example: A is a declaration which means "A exists as a Source".
- Lower case letters standing alone are identifiers for variable sources; that is, sources as yet undefined or having no fixed identity .
Example: x is a declaration that some Source (x) exists but it is not yet uniquely specified.Comment on Symbology: The concept of what identity may be assigned to a source and what that all means shall be covered later.
*Primitive: Original; primary; not derived. A primitive definition contains only what most essentially defines the concept.
Discussion: Source can be anything which causes anything; it is that from which anything comes. Living creatures cause changes in their environments. Lightning causes chemical bonds to break and form. Erosion causes rocks to crumple. Planets were brought about by a complex process involving gravity and interstellar gases.
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Assumption 2: Action
Action is
Action is a fundamental of the model.
- The fact of differentiating, declaring, causing or deciding; the bringing into existence a state or condition.
Symbol:
OR
OR ~ (the tilde symbol)
- The reversing of a distinction such as to bring about a reversion to the original state or condition.
Symbol:
OR
OR /
Comment: Change is defined as either of these primitive operations. (1) Any change of state or condition is an action -- for example, changing red to blue. (2) Any reversal of change is an action -- for example, having changed from red to blue, then reverting back to red is reversion to original condition.
The current physics model recognizes only (1) as an action. The Source-Action-Object (SAO) model proposes (2) as a new fundamental class of operation (action). The reversion operation can be thought of as similar to the "undo" command in a word processing program. The rationale and applications of this operation will be introduced later.
Discussion: Differentiation (in English) includes the following meanings which may help to illustrate the meaning of this Assumption further: "(1) to distinguish or mark by a specific difference; (2) to effect a difference in, as regards classification; (3) to develop differential characteristics in; to specialize." (Webster's Dictionary, 1913)
A child playing in a sandbox is an example of a Source in action.
Other examples of drawing distinctions are: grade point averages, national boundaries, family group lines, social class boundaries, cell walls, the surfaces of fluids or solids, and physical thresholds such as radioactive critcal masses and atmospheric moisture versus temperature (saturation levels).
- He draws distinctions ("This is my side, across that line is your side")
- He assigns it meaning ("This is a pie ... this other lump over here is a hill ...")
- He declares values for his creations ("All the sand in that pile is bad")
The drawing of a distinction is a very fundamental idea and can be found in every field of human experience. Each distinction is drawn by some source. This source may be living or non-living, physical or non-physical, but whatever else characterizes the source, above all each is characterized by its ability to in some manner draw a distinction.
Reversal of distinction (anti-differentiation) is simply the exact opposite of drawing a distinction. There is no longer a political distinction between the Northern and Southern US states (as there as in 1863). The child in the sandbox no longer considers that pile of sand to be "bad"; the box is no longer divided into "yours and mine"; the sandpie is now just sand.
In general, more attention is paid to the drawing of distinctions. In commerce, we advertise to establish differences ("my product is better than yours"). In academics, we distinquish between bodies of data ("Science is not art"). In politics, we often conduct wars to keep others' lands different from our own. But reversals of distinction can have vast consequences as well.
What would happen:
Reversal of distinction is not the idea of forcing a distinction to no longer be valid. Breaking a water bottle causes the contained water to no longer be distinct from the general environment, but this not what we mean. Reversing a distinction is making the distinction as if it never were. When we break the bottle, the shattered pieces are conserved. There is no loss of mass. On the other hand, reversing a distinction means vanishment without residue.
- if gold were no longer distinct from any other metal?
- if the human eye perceived as well in infrared and radio bands as it does in the visible bands?
- if cell walls no longer held protoplasm distinct from the general environment?
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Assumption 3: Object
An Object is a state or condition resulting from source drawing a distinction.Object is a fundamental of the model.
Symbology:
OR
Comment: Primitive Object has no further definition. By "object" we are referring to any state or condition resulting from any source drawing a distinction. As with Source, an object may be physical or non-physical, organic or inorganic, complex or simple, of cosmological or sub-atomic size, etc. One could declare an object to be of any of these or other sub-classifications, but these constraints have no place in the primitive definition. Later axioms and definitions will define special classes of objects (objects with properties).
- An object symbol [ ] with an upper case letter immediately inside is an identifier for an object with fixed, non-variable properties.
Example: [A] is a declaration which means "A exists as an Object" or "Object A exists".Comment: The concept of what properties are and how they may be assigned to an object shall be covered later.
- An object symbol [ ] with a lower case letter immediately inside of it is an identifier for an object with variable, not specifically identified properties.
Example: [x] is a declaration which means "x exists as an Object" or "Object x exists".
- An object symbol [ ] with no identifying letter symbolizes an unidentified distinction, that is, a distinction with no properties. The symbol [ ] represents the idea or concept of the model element called "the distinction" rather than any particular distinction or even a distinction of variable properties.
Discussion: "Object" is simply any distinction drawn by any source. There is no requirement that it be solid or have any particular size or dimension. Since the distinction may be wholly non-physical, the object(s) resulting might be non-physical as well. For example poetry as distinct from prose. The objects "poetry" and "prose" result from drawing a distinction between styles of speaking or writing. One can draw a distinction between types of love: romantic and platonic, and so forth. Of course an object can be physical -- halves of a room, the countries created by drawing national boundaries, the inside and outside of a box.
A saucer is not a cup though both are curved china. Until someone devised a distinction between the two, they both may have been just concave pottery with no one caring whether they were 1/2 inch or 4 inches deep.
An object is the result of drawing a distinction, and therefore objects vanish when that distinction is reversed or removed. The object known as a balloon ceases to have any meaning or definition once its skin ceases to exist.
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Axiom 1: Creation
Source drawing a distinction brings about an object. This is creation.Symbolic expression: dS ---> S[ ] (where ---> means "results in")
Discussion: This axiom states that all "things" are created by the fundamental action of some source drawing a distinction. See the discussions in Assumptions 1 and 2 for some examples. Notice again that the source of the distinction, the "drawer" of the distinction, can be animate or inanimate. The constant heating and cooling of boulders cleaves them into fragments -- where there was one rock there are now many. Each fragment is distinct from the original boulder. Before the distinction was drawn, the boulder had no distinct components.
So called "natural forces" can draw distinctions (create) as well as any living thing. The manner in which the distinction is drawn is not our concern at this point; just the fact of it being drawn (and thereby bring about a creation) is the issue.
The claim is thus made that Axiom 1 is the general formula for the creation of all objects.
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Axiom 2: Compound Objects
Source may draw one or more distinctions upon (within) an existing object, making it a compound object.Symbolic expression: [Y [A] ] where [Y] is a compound object resulting from distinction A being drawn upon (within) distinction Y.
Comment: An object with more than one distinction drawn upon (within) it could be represented in this way: [Y [A] [B] ] .
Discussion: First of all, remember that in the language of this model the terms and concepts "distinction" and "object" are fully interchangeable.
Axiom 2 says, for example, it is possible to declare a distinction called "science". Within this distinction, we may declare to exist subdivisions called "biology" and "geology". The formula for this would be: [science [biology] [geology] ]
Synonyms: Complex object, complex distinction
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Definition: Simple Object
A simple object contains no further distinctions.Symbology:
Comment: Simple object is synonymous with "simple distinction".
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Axiom 3: Relatable Distinctions
Two or more distinctions may be related (associated) if and only if they are declared within (upon) a common distinction.Symbolic expression:
A and B are unrelatable.
[A] and [B] are relatable.
Comment: The fact that two objects are relatable does not imply that they are necessarily related.
Discussion: Let's say you have written a story we shall call [s1]. It contains a list of characters [c1] and a series of plots [p1]. These last are all relatable by reason of being elements of story [s1]. We can represent this situation as: [s1 [c1][p1] ]
Let us now consider there exists another, unrelated story called [s2]. The fact that [s2] is unrelated to [s1] we represent in this way: [s1] [s2]. Since [s1] is unrelated to [s2], then the contents of [s1] are unrelated to [s2]. That is, one cannot related the characters or plots of story 1 to the characters or plot of story 2 unless the stories are somehow related.
You might object to this idea, claiming the characters of a story could very well be the same in one story as in another, unrelated story. True, this could happen, but then the logical connections are quite different. In this case, the logical structure could be:
[c [s1[p1]] [s2[p2]] ]
or restated in a more easily read format:
- [Character Set]
- [Story 1]
- [Plot Set 1]
- [Story 2]
- [Plot Set 2]
What this says is: Character Set [c] contains within it stories [s1] and [s2], which contain plot set [p1] and [p2] respectively. In other words, the whole matter is being looked at from the viewpoint of the characters involved instead of the stories.
To say all this another way: Two objects [p] and [q] have no possibility of contact with one another in any way (no communication, no influence, no recognition, no e-mail) unless they are in the same universe.
Thus
[p] [q] are unrelatable because they have no universe in common. [t [p] [q] ] are relatable because they both occupy Universe t Keep in mind, a universe is simply a distinction; it is an object.
Examples: "Romeo & Juliet" is an object identified as a play. It is quite impossible to relate it to the "Binomial Theorem". The Binomial Theorem is an object in the universe known as Mathematics. It has nothing whatever to do with the universe known as Literature, therefore it is unrelatable to any theatrical object.
(Note: Strictly speaking, you could make a case for their relatability by declaring them as examples of the object universe "Abstract Thought". The reason I don't want you to bring up this objection at this point is because you could make a case for the relatability of anything you can think of by declaring it as an object in the universe "Anything I Can Think Of". But if I let you get away with this I couldn't give you any example, could I?)
On the other hand, the object Seaweed can be related the object Toenails. Even though the relationship is slight, both occupy several common universes (objects). They both are Biological objects. They are both Physical objects (can be observed with physical sensing devices such as eyes, microscopes, and mass spectrometers).
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Definition: Vanishment
Vanishment is to pass out of existence.Comment 1: No need to get overly philosophical here. Vanishment means an object no longer exists insofar as the observer is concerned. Anything which has vanished can no longer be experienced in any way. It can no longer exert an influence in any way within the frame of reference under consideration.
Comment 2: Vanishment implies the reversal of distinction. See Assumption 2.
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Axiom 4: Time
Time is any series of changes to an object.Comment: Let's observe a series of changes to an object [A [B]]:
Change Resulting State Notes 1 ---- [A [B]] Beginning state. This is what you are given. 2 [A /[B]] [A] This says we are taking object A and declaring a reversal of contained object B. Thus object B vanishes as a distinction (object). Assumption 2 allows this. We end up with object A as a simple object. 3 [dA] [A [B]] Now we are taking simple object A and declaring within it a new instance of object B. Assumption 2 permits this. We end up with object A containing newly created object B. 4 [A [dB] ] [A [B [C]]] This time we'll take compound object A and cause a distinction to be drawn within object B. We'll arbitrarily name this object C. Since we are drawing this distinction within (upon) object B, object C is contained within object B. Assumption 2 allows this. We end up with a compound object with [A] containing [B] which in turn contains [C]. 5 [A [B /[C]]] [A [B]] Now we'll take the object we just created above and "anti-differentiate" object C. This causes object C to vanish. Assumption 2 permits this. What remains is what we started with: Object A containing object B. The series an observer would notice is listed in column 3 (resulting state). This series is time. If there were no changes to objects, there would be no time.
Example: [A [B]] , [A [B]] , [A [B]] , [A [B]] ... This is a series of states but there is no change, so there is no time being demonstrated here.
We experience time by changes occurring. Time isn't a force that "brings" changes. It doesn't "make" things grow old. Time is the experience of constant change. In the above examples, Object A is undergoing constant alteration -- sometimes having internal structure added, sometimes having pieces vanish. But it is only this fact of change that IS time.
If there were an object that did not change, we would call it "timeless". We find this in the field of architecture. Certain ways of laying out a family dwelling are found in every age and culture. These patterns are so successful and so ancient that it seems like they have always existed. They always seem "modern". These patterns are so satisfactory that no changes have been made to them for as long as men have been building houses. This quality of "timelessness" in architecture is a crude example of what happens when objects don't change.
Businesses usually thrive on change. The fashion industry is exemplary of constant change. The high rate of change of styles relative to the lifetime of the human being causes the perception of "new" becoming "old" quite rapidly.
At the extreme, some sub-atomic particles have life spans measured in millionths of a second. That is to say, they go through changes at an extremely rapid rate relative to human scales.
How we experience time -- whether we think something takes a "long time" or a "short time" is a result of comparison of an event against the yardstick being used to measure it. Consider a man, already late for an important meeting and waiting for his train to arrive at his destination. His anxiety sets his internal clock running at a mad rate. Thus he will experience the painful "slowness" of an otherwise speeding train.
Another man, parting with a loved one, savors the moments (making them "timeless") and thus sees clock hands speed around the clock. Again, the culprit is the expectation of change, that is, the rate of change relative to some yardstick.
There is much more to say about the perception of time at a later point. I am bringing up a few examples here only to illustrate the basic definition rather than to open season on speculation about its corollaries and applications.
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Definition: Time Object
A time object is an object that is undergoing a continuing series of changes. (Refer to Axiom 4: Time).Symbolic expression: [x]T where [x] is some object.
Comment: For an object to be a time object, it must be continuing to undergo changes. To restate the matter: If there are no changes, there is no time and therefore no time object.
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Definition: Moment
A moment is a single instance of creation or reversal of creation in a time series (timestream).Synonym: Instant (noun)
Comment: A moment has no duration! Time itself is continuous creation and reversal of creation. A moment, being an element of time, has no time.
Example: The object-moment
has no time. This is because time necessarily requires an ongoing series of d and /d operations. A moment, however, is one single instance of result of these operations.
We are now into something that is apparently contradictory. That is, time is this "thing" made of a number of individual moments that themselves have no duration. However, taken collectively, all these timeless moments add up mysteriously to this thing called "time".
Well, this is not so odd, really. If time isn't anything but a series of changes then it is only the passing from one state to another that IS time. We get a bit twisted around on this subject because we have time so closely associated with watches and clocks, which are only attempts to set a standard against which other rates of change can be compared. However, the measurement of time is not the same thing as time itself.
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Definition: Properties
Properties are distinctions drawn upon an existing object. These distinctions are considered qualities or distinguishable characteristics possessed by an object.Objects with properties are compound objects.
Clarification: In
, [A] and [B] are properties of [Y].
Comment 1: This is a familiar logical concept. For example, let [Y] be a polygon. Let [A] represent the property "angles greater than 90 degrees" and [B] represent the property "more than 7 sides". The statement [Y[A][B]] therefore declares the object Y to be a polygon with angles greater than 90 degrees and more than 7 sides.
Simple objects have no properties. However one could make a case that they are their own (and only) properties.
Comment 2: Looking again at the Discussion in Assumption 3 (Object), you will see that the objects being given as examples (types of writing, love, cups & saucers, countries) are obviously Compound Objects -- objects with many properties.
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Definition: Quantity
Quantity means multiple instances (existences) of an object which are identified collectively as belonging to the same object type by reason of possessing the same properties but at least one.Comment: That is, they are similar or identical in all but at least one property.
Example: Here is a quantity of 3 objects (A1, A2, A3) which could be considered as being of the same object type since they have nearly identical (similar) properties:
Discussion: When we speak of a quantity of wheat, we are limiting our topic to objects which have very specific biological properties. All kernels of wheat are, for our purposes at that moment, identical to one another. We don't care that no two kernels are in fact absolutely identical in terms of their coloration or molecular structure. Insofar as the properties we are concerned about at the moment of discussion, these 42,000,000,000 kernels of wheat are just a quantity of "the same thing".
If any 2 kernels truly had 100% of their properties in common (including occupying the exact same position in space), they would not be distinct objects. They would be the same, exact kernel. Hence they would not be 2 kernels but 1. So for this reason we have to include the line about being similar or identical in all properties but at least one.
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Definition: Enter
To enter is to cross the boundary which marks the limits of an object, the crossing of which boundary places the crossing object within the definition of the crossed object.
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Axiom 5: Enterability Property of Objects
An object may be declared to possess the property of enterability. The values of this property are: Enterable and unenterable.Symbolic expression:
[A] is an enterable object.
[B] is an unenterable object.
Comment: Enterability is the first property of a compound object; it is that declaration which makes it possible to create nested objects. Before enterability has been declared, an object is neither enterable nor unenterable.
Discussion: Without the distinction of enterability being drawn upon an original object, it would not be possible to draw other distinctions upon (assign other properties to) an original object.
For example, a geometric point is defined as an object without any properties but having position. Geometric points have no content but they are distinct from their surroundings. In human speech, another example could be an "empty" word. The invented word-object "Lghraftemiftzei" has no meaning in any known language, but it is a word distinct from all others. It is a distinction without content.
Before we can declare this new word to have any meaning, we have to consider it possible for it to have a meaning. This idea is usually overlooked because it is so obvious, but the fact is that no meaning can be assigned to any symbol until one considers that assignment of meaning is possible.
In above examples we see the operation of the enterability property on a non-compound object. But what of the opposite value of this property?
Unenterability is the declaration that it is not possible to assign additional properties to the object in question. In geometry, it is considered that points are unenterable, that is, they may not be assigned any content. The ideas of a "blue point" versus a "red point" or a point with some internal dimensions are contradictory to the mathematical definition of "point". So, according to this model, a geometric point is defined as an object having position
*but with only one property: unenterability.Compound objects can also be unenterable. An example in human experience would be a series of decisions on a subject, the last of which is that these decisions are now inviolate. In essence, declaring a set of decisions on a topic unchangeable makes that topic "unenterable" to some degree. In this way, the topic could become a hidden influence on the individuals who accept it. They "know" nothing can be done to change these decisions, so they cease to inspect them. In the physical sciences, until someone considered the atom possibly divisible (separatable into consituents, hence, enterable) it remained something of a mystery.
*"Position" is not a property of an object, according to the SAO model. This concept of position is developed elsewhere in this material.Table of Contents
Axiom 6: Space
Space is an enterable object.Symbolic expression:
Comment: Physical space (or any other space, for that matter) is a distinction. One of the properties of the object "Space" is its enterability. It may have other properties as well.
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Axiom 7: Solid
A solid is an unenterable object.Symbolic expression:
Comment: The most primitive solid object would be an object which has been declared or agreed upon to be unenterable. It has no other defined property.
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Definition: Measurement
Measurement is the quantification (counting) of instances of objects.Comment: This definition implies that Source and Action are not directly measureable; however, these elements can be quantified insofar as they produce changes in objects.
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Definition: Viewpoint
Viewpoint is the distinction from which another distinction originates or from which it is observed.
In the above figure, the viewpoint of [B] is [A] because (in this case) [B] originated from [A].
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Definition: Coincidence / Non-coincidence
Two objects are coincident if they contain 1 or more identical properties AND if these properties exist in the same timestream. They would be coincident with respect to their identical properties.Two objects are non-coincidence if they contain no identical instances of properties in the same timestream.
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Definition: Dimension & Distance
Dimension is a property or combination of properties which can be measuredComment: A simple subordinate object can be considered a basic unit of dimension for its context. For example, given
where [A] is the property "length", [A1] [A2] [A3] are three discrete units of length. Objects nested within distinction A are special cases of the property called length. Since [A1], [A2], and [A3] are simple objects declared within a universe with the property of length and since they are distinct from each other, [A1], [A2], and [A3] are therefore non-coincident units of length. This, incidently is the definition of distance.
[A [A1] [A2] [A3] ]
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Definition: Position
Position is the concept of an object existing in a non-coincident spatial relationship with another object.Synonym: Location
Comment: Position is not a property possessed by the object being positioned. An object within a spatial system has a spatial context. The objects which form its context are doing the positioning.
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Axiom 8: Spatial Non-coincidence of Solid Objects
Two related solid objects may not coincide spatially.Comment: Spatial coincidence of solid objects would imply a contradiction of their unenterability properties.
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Definition: Area
Area is a measurement of physical universe space in two dimensions.
Let Z symbolize the physical universe. 1d is the distinction of length. Nested upon this property of Length is declared an additional distinction (2d) which is Area; a special case of length.
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Definition: Volume
Volume is a measurement of physical universe space in three dimensions.
Let Z symbolize the physical universe. Distinction 3d (Volume) is a special case of Area.
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Axiom 9: Measurement of Space
Physical universe space is measured by a judgment of the number of units of (time) it takes some object to change position with respect to one or more of its dimensions.Table of Contents
Axiom 9a: Measurement of Time
Time is measured as a detected quantity of changes to an object relative to a standard time object.Table of Contents
Axiom 10: Change of Position
The position of an object may be caused to change relative to another related object. Change of position is:(1) the vanishment of the object from one position and its appearance at another, or
(2) the reduction or increase of one or more of the dimensions of space between related objects.
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Axiom 11: Motion
Simple motion is change of position.Complex motion is consecutive or continuing changes of position.
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Definition: Resistance
To counteract; to act in opposition to; literally - to stand against.By definition, the two primitive actions oppose and therefore resist each other.
Comment: In common experience, resistance can be viewed as a force saying to an object; "You're going somewhere else!" However, the object objects to this and tries to remain where it is. In other words, a force is being opposed by inertia. But on a more fundamental level, resistance is the concept of you deciding something shall be a certain way and another person preventing you from doing that. Anything that prevents you from drawing a distinction or prevents you from reversing a distinction (making it cease to exist) is resistance.
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Axiom 12: Resistance to Change
Resistance to change is caused by the failure to bring about vanishment and/or the failure to draw a distinction.Table of Contents
Axiom 13: Increase of Time
The failed attempt to produce a change in a time object increases the time of that object.Comment: The failed attempt itself creates a non-identical instance of the object. Also, the object itself had to change to cause an attempt, that would have otherwise been successful, to fail.
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Definition: Rate of Change
Rate of Change is the number of instances of change (differentiation and/or reversal of differentiation) of any object measured against some standard.Table of Contents
Axiom 14: Inertia
Inertia is resistance to change of rate of change of position.Table of Contents
Definition: Degree
The number of same level distinctions within a compound distinction.
"G" is a third degree distinction.
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Definition: Depth
The number of levels of contained distinctions within a compound distinction.
[Z] is a distinction of depth 4.
Comment: The word "level" can be used be used to indicate the depth at which some object or source exists within a nested series of objects.
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Axiom 15: Complexity
Complexity is the degree and depth of a compound distinction.
Object R has a measurable complexity.
Comment: The term density is synonymous with complexity. Usually density is applied to cases where physical universe space is involved.
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Definition: Density
The density of an object is its complexity (Axiom 15).Table of Contents
Axiom 16: Density of Time Objects
A time object has, at any moment, an identifiable density.Example: The constant change of a time object.
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Axiom 17: Mass
Mass is
Comment:
- A time object unenterable by another impacting object by reason of too much density.
- The detected rate of internal change (of density) of a time object.
All nested time objects of a compound time object change. The more nested time objects there are, the more change there is within the compound time object. Therefore mass is a function of the number of contained time objects and the rates of change of those objects.
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Definition: Universe
A universe is any distinction and all it contains.Table of Contents
Definition: Mathematics
The quantification (calculation) of relationships using the dimensions of a given universe.Table of Contents
Definition: Locate (verb)
To measure the position of an object in terms of the dimensions of the viewpoint universe.Table of Contents
Definition: Detect
To detect is to register (indicate, record) the presence of or change in an object (state, distinction).Table of Contents
Axiom 18: Detection
Detection is the creation within an object of a property which itself exists as a relatable object.Logic:
Object B can detect Object C if and only if:
1 [C] [B] Assumption 3. [C] and [B] are distinct objects -- that is, they are not the same object. 2 [A [C] [B] ] Axiom 3. [C] and [B] are relatable. 3 [A [C] [B [C]] ] Axiom 2. [B] gains [C] as a property. Comment: By definition, only Objects can be detected, not Sources or Actions.
Discussion: If [A] is a project and [C] is the concern about cost, and [B] is some task of project A, then [B [C] ] is the fact of cost being a concern of task B.
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Axiom 18a: Comparison
Comparison is the distinquishing (declaration) of the difference between two non-identical distinctions.Logic:
1 [A [C] [B [C]] ] Axiom 18. [B] detects [C]. 2 [A [C [e] ] [B [C]] ] Axiom 2. [C] changes (obtains property e) 3 [A [C [e] ] [B [C] [C [e]] ] ] Axiom 18. [B] detects the new state of [C] and keeps a copy of [C]'s original state. 4 [B *[C] [C [e] ]* ] Axiom 3. [C] and [C [e]] are relatable. 5 [B *[C] [C [e] ]* [e] ] Source B distinguishes the difference between [C] and [C [e]]. This is Comparison.
Symbology:
A{*}[r] states Source A has done some unspecified comparison (between the curly brackets), producing comparison result [r].
For example, the expression B{[C] [C[e]]}[e] states that Source B compares detected objects [C] and [C[e]], drawing [e] as the difference.
Comment: Comparison, in practice, consists of some series of graduated differences from identical to completely different. Distinguishing that 2 objects or properties are identical can be defined as a special case of distinguishing differences wherein the differences are zero (i.e. - no difference). Distinguishing a similarity between two objects involves discerning one or more differences plus one or more identities. Thus, a similarity is a compounding of differences and identities.
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Axiom 19: Awareness
- Awareness is the capability of a source to perform comparison.
That source which is capable of comparison is aware.
- The word awareness is also used to indicate the use of that capacity to compare.
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Definition: System
A system is an organization of nested, relatable elements (sources and objects) which together perform one or more identifiable actions (operations).Comment: A system is a compound object, but not all compound objects may engage in actions identifiable to an observer.
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Definition: Relate
Elements are related if one element can detect another.Comment: Now review the declaration in Axiom 3: Relatable Distinctions.
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Definition: Structure
Structure is the organization of objects in a compound object.
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Definition: Prime Object
Prime Object is the highest level of a compound object which is itself not known to be nested in another object.Example: In the compound object [A [B[C]] ], [A] is the highest level object.
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Definition: Prime Source
Prime Source is the highest level of source for the operations of some system.Example: In the compound object [A [B[C]] ], Source A is Prime Source.
Comment: It can be said Prime Source operates (performs actions using) a system.
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Axiom 20: Life
Life is an aware Prime Source operating a system.Comment: The crucial point which distinguishes living from non-living is the ability of a Prime Source to perform actions by means of (using) a system in response to comparison of objects, states, or conditions.
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Axiom 21: Energy
Energy is the action of change by which a distinction is drawn or reversed. (see Assumption 2 - Action - #1).Energy may be expressed as a capability (potential energy) or as the act itself (kinetic energy).
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Axiom 22: Power
Power is the relative number of objects throughout which (in which) a change (an action - d or /d) can be detected.Comment: Power is the extent over which a change is effective.
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Definition: Influence (n.)
Any change (action) which can be detected.Table of Contents
Definition: Experience (v.)
Experience is the detection (perception, recognition) of a distinction.Table of Contents
Definition: Pervade
Pervade is:
- To be present throughout (standard English)
- To detect all subordinate objects within some object to a specified degree and depth (SAO Model definition)
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Axiom 23: Pervasion
Source is capable of pervading objects.Comment: Pervasion is only possible with respect to compound objects. Simple distinctions (objects with no subordinate objects) have no degree or depth (and therefore no content) to be pervaded.
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Axiom 24: Level of Differentiation
Differentiation originates from one level of depth above the object created.Example: With respect to the object [p [q [r]] ], object [r] is at level 2 of the nesting object [p], but it originates from source q which is at level 1.
Source, performing differentiation within a simple object, produces a new level of depth below that level from which it is currently operating.
[dA] ---> [A [A1] ]Comment:Table of Contents
Axiom 25: Level of Declared Associations
Objects are declared associated from one level above the highest level object involved.Example 1:
[V] and [R] are associated at level 0.
Example 2:
[S] and [T] are associated at level 1.
Comment: This axiom is derived directly from Axiom 3. In example 1 above, [V] and [R] are declared within a common distinction [N] and are therefore relatable (able to be associated). If [V] and [R] were associating, they would be declared associated at the level of object [N], that is, level 0 of [N].
In example 2, [S] and [T] exist within 2 common distinctions: [R] and [N]. However, if they associate they would be declared associated at the level immediately above their common level of existence, that is, level 1 of object [N] -- which would be level 0 of object [R].
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Axiom 26: Level of Association
Objects detect (experience) one another at their level of declared association.Comment:
In the figure above, object V experiences object R, but not object S directly. Object V experiences object S only as a property of object R.
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Definition: Identity
Identity is a distinction by which an element is known.Comment: A source is not a distinction, however, it is convenient to label a source or associate it with one or more distinctions (objects or properties) so that it can be spoken of by some name. Bear in mind, however, that according to this definition, a source has no real identity. A source, when it is being a source , is not a distinction. Even if a source is a complex or compound source (such as in the case of Life (Axiom 20), when it is considered as the source of some action, it is a source, not a distinction. This is not a nit-picking point of language; it is vital fact to be understood about the nature of Sources.
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Definition: Identify
Identify means to consider as or to act as being the same or having all the same characteristics, properties, purposes, effects, etc, as something else.Table of Contents
Axiom 27: Identification with Subordinate Sources
A source can identify itself with a subordinate source.Explanation: Given [P [Q]], P can identify with Q.
Symbolic expression: P=>Q
Corollary 1
Source may cease to identify itself with a subordinate source.Symbolic expression: P /=> Q
Corollary 2
If P => Q, then [P [Q]].Comment: This says, if source P can identify with source Q, then Q must be subordinate to P. This is how objects (such as Q, in this example) become sources. Q as [Q] becomes identified with source P. This is an object becoming a source. Thus ...
Corollary 3
If P => Q, then P => [Q].Comment: Source-Objects: A Model Element is What it is Doing
Assumptions 1 and 3 define model fundamentals Source and Object. The only means of perceiving these as distinct elements is by identifying how they perform. Element A is a source if it is performing an operation (e.g. - dA). Element A is an Object if it is being acted upon by a source (e.g.- dB[A] ---> B[A [C]] ). But since B must identify with A in order to complete the operation (B => A), the fact is that the interplay between A as object and A as source is continuous. Until A as source "switches" to A as object, it cannot detect the change it declared while it was being A as source. But once it does detect it, A is now an object which contains a distinction. Table of Contents
Axiom 28: Multiple Identities
A source may identify itself with multiple subordinate sources.Explanation: Given [P [Q] [R] [S]], the following identities are possible:
Comment: This process of identification with subordinate sources is, in essence, "endowing" the new identity with the power to act as source. To say it another way, the authority to act as source is obtained (derived) from the superior source.
- P=>Q and/or
- P=>R and/or
- P=>S
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Axiom 29: Generation of Depth
Depth of objects is brought about by successive instances of drawing distinctions (Assumption 2) and identifications of sources with subordinate sources (Axiom 27: Identification).
Discussion: This axiom involves a bit of a fine point about the behavior of sources and how they are symbolized. Source P differentiates and creates object [Q] in step 2. We know from Assumption 1 that a non-variable source (a source with some defined set of characteristics) is symbolized by an upper case letter. What happens next (step 3) is source P identifies with Q. Until this happens, just what is "Q"?
Declaration / Action Resulting Object / Comments 1 P Assume source P exists 2 ~P results in P[Q]; Assumption 2 3 P => Q Axiom 27: Identification 4 ~Q results in P[Q [R]]; Assumption 2 5 Q => R Axiom 27: Identification 6 ~R results in P[Q [R [S]]]; Assumption 2 We know that [Q] is the symbol for the object Q (Assumption 3). And we know from Assumption 1 that "Q" is the symbol for some source Q. So the question arises, why is P=>Q necessary? Isn't the fact that Q has been declared to exist by source P adequate to create an identification of P with Q? The answer is; yes, it is. Source P continues to exist as itself (P=>P). Source P also equates itself to new source Q. (Remember that multiple identities are allowed per Axiom 28.)
New source Q is a source and can therefore perform diffentiation, producing [R]. Q then identifies itself with R (Q=>R, step 5), endowing R with the properties of a source.
By the "time" step 2 is complete, strictly speaking, Q is potentially a source but without the "endowment" necessary to act (perform Assumption 2 actions). In fact there is no time interval between steps 2 and 3; they are essentially simultaneous, non-time events.
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Definition: Intention
Intention is determination, resolution or decision directed at some goal, result or effect (the drawing or reversal of a distinction).The act of intending is the drawing or reversing of a distinction.
The intent is the object thus created or made to vanish.
Comment: Also see Axiom 32: Value and Intention of Distinctions.
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Axiom 30: Agreement / Disagreement
Agreement is fundamentally detection.Instantaneous agreement includes no concept of time. Continuing agreement is continuing detection.
Explanation: Object A is in instantaneous agreement with object B if
In the above case, object A may or may not be a time object.
- object B is a non-time object (Axiom 4)
- object A perfectly detects (detects with no alteration of properties) object B (Axiom 18)
Object A is in continuing agreement with object B if
Example: This is an example of one-way agreement
- Object B is a time object
- Object A continues to detect changes in object B as they occur
The degree of agreement is the ratio of unagreed with objects to agreed with objects as measured at the same depth.
Declaration / Action Comments 1 [ [A] [B] [S] ] [A], [B], [S] and [T] are relatable objects (Axiom 3) 2 [ [A] [B [S]] [S] ] [B] detects [S] (becomes in agreement with [S] ) 3 [ [A [S]] [B [S]] [S] ] [A] detects [S]; [A] and [B] now mutually agree on [S], but neither recognize at this point the fact that they both agree on [S] 4 [ [A [S]] [B [S] [A[S] ] [S] ] ] [B] now detects [A]'s agreement with [S]. [A] is still unaware of [B]'s agreement with [A].
Example:
Corollary: Disagreement
Disagreement is imperfect detection.Logic:
1 [A [C] [B[C]] ] Axiom 18. [B] detects [C] 2 dC ---> [C [G]] Axiom 1. C as source creates property G. 3 [A [C[G]] [B[C]] ] Disagreement. [B] now imperfectly detects [C]. Comment: Disagreement is not non-agreement. Non-agreement is no agreement in the first place. Disagreement requires as a pre-condition the fact of agreement. Disagreement is a disruption of agreement.
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Axiom 31: Multiple Source Objects
Objects may have multiple sources. Multiple source objects consist of those objects upon which two or more sources agree.Example:
But it is possible that [A] and [B] have many more elements never agreed upon and therefore do not exist in the shared universe-object [AB].
Multiple Source Objects exist as a first-order subordinate of the deepest common object.
The new MSO 1.1.3 exists as a child of the deepest common object 1.1
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Definition: Attention
The application of awareness upon a specific object or set of objects.Comment: Attention, in effect, creates a time stream for the source-object using it.
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Axiom 31a: Relationship
A relationship is an instance of continuing detection (agreement) between two or more objects.Comment 1: In [A [C] [B [C]] ], there is detection of [C] by [B]. But this is continuing detection, so if [dC] ---> [C [K]], then [B [C]] ---> [B [C[K]] ]. That is, [B] updates its copy of [C] in response to the change in [C].
In the example above, [A] could be an air transport system (which includes airplanes, airports, passengers, airlines, etc.) [B] could represent aircraft and [C] could represent the concern of cost. [B] "detects" (is sensitive to) the property known as cost. Cost could change and thereby influence the cost of the aircraft.
Comment 2: There are several possible types of relationships:
Comment 3: The above examples are only "snapshots" of relationships. In an actual illustration of a two-way total relationship, [B] would contain a copy of [C]'s copy of [B], etc. This could be called "reflection", a copy of in [B] of [C] looking at [B]. This matter and its consequences will be examined at some later point.
Example Nomenclature Notes [A [C] [B[C]] ] One-way, total
(1, T)[B] detects [C] and all its properties (in this case it doesn't have any showing), but [C] does not detect [B]. Cost doesn't care about the existence of an airplane. The object "cost" simply says how much money can be spent. [A [C[x][y]] [B [C[x]]] ] One-way, Partial
(1, P)[B] detects [C] and some of its properties. [C] does not detect [B]. [A [C[y][B[x]]] [B [x][C[y]]] ] Two-way, Total
(2, T)Both objects detect one another completely (all properties). [A [C[y][z][B[x]]] [B[x][C[y]]] ] Two-way, Partial
(2, P)[C] detects [B] totally but [B] only partially detects [C]. (Another possibility is that they could only partially detect each other.) Table of Contents
Axiom 32: Value and Intention of Distinctions
The value of a distinction is the intention of that distinction.The intention of a distinction is the distinction itself.
Comment: This serves to point out that the distinction is the intention. The distinction is not any of the symbols that may be used to represent that intention. Any symbols used merely refer to that intention.
The intention of a compound distinction is the intention of the prime object as modified by any subordinate elements and the relationships amongst those elements.
Comment: For the object [A], the intention or value of this object is [A].
For the object [A [A1]...[An]], the intention or value of this object is [A] modified by the intentions of objects [A1] through [An] plus the effects of any relationships amongst objects [A1] through [An].Table of Contents
Definition: Loss
- The undesired creation or uncreation (reversal of creation) of a distinction.
- The desired uncreation of a distinction.
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Definition: Loss of Properties
- An undesired change (increase or decrease) in the quantity, degree, depth, and/or relationships of objects.
- The desired reduction (reversal) of quantity, degree, depth, and/or relationships of objects.
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Axiom 33: Dependency
Dependency is the condition of an object influencing another's required properties.Comment: The fact that object [A] can detect object [B] implies that object [B] influences object [A] (definition of influence). If the detection by [A] of what emanated from [B] influences a required property of [A] then object [A] can be said to be dependent upon object [B].
Dependencies exist between related objects at their level of declared association (Axiom 26).
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Definition: Interdependency
Interdependency is mutual dependency, that is, influence of one another's required properties.Comment: See Axiom 33: Dependency before studying this definition. Also keep in mind that interdependencies exist between related objects at their level of declared association (Axiom 26).
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Definition: Intentional Design
An intentional design is a non-time structure which includes all intended characteristics (properties) and relationships.Comment: The intentional design is what you intend the object to do and/or how you expect it to perform. It is not a time object, that is, it is not yet a "real world" object. It is the idea, the intention of what is expected.
Related Concepts: Intentional object, intentional structure, intentional system
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Definition: Implementation
An implementation is a time structure which is intended to reflect the characteristics (properties) of an intentional design.Comments: This means that the content of the implementation is constantly changing per Axiom 4: Time.
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Definition: Design (noun)
A design is a plan for implementation.Table of Contents
Definition: Optimum
"Optimum" describes the implementation of a structure of intentions which achieves declared goals with the least loss of intended characteristics (properties).Comment 1: Trades may be required where intended characteristics are implemented in such a manner as to create dependencies between implemented characteristics. "Least loss of characteristics" refers to definition #1 of Loss of Properties.
Comment 2: It is possible that an implementation results in one or more characteristics favorably exceeding the intended characteristic(s). This favorable excess would be the opposite of a loss of properties, that is, a desired change (increase or decrease) in the quantity, degree, depth, and/or relationship of objects.
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Axiom 34: Optimum Implementation
An optimum implementation is a time structure whose detected state approximates some intentional structure with the least loss of intended characteristics (properties) of all implementations considered.Comment 1: "Detected state" refers to the fact that a time object is in a continuous state of change but is detected by an observer in the time stream as being in a relatively constant or predictable state.
Comment 2: Favorable excess of one or more properties in an implementation can be either
- disregarded
or
- considered as new values (intentions) for those properties, thus redefining the structure of intentions (see the definition of optimum).
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Theorem 1: Assignment of Properties to Copies of Detected Objects
In a relationship, the detecting entity may assign properties of arbitrary complexity to its copy of the object detected.Proof:
1 [A [C] [B [C]] ] Axiom 18. Detection of [C] by [B] 2 B=C Axiom 27. Identification 3 [A [C] [B [dC]] ] ---> [A [C] [B [C[C1]]] ] Axiom 1. Creation. QED Discussion: In the example above, Step 1 may show engine [A] with the property Cost [C] and Component [B]. The cost of component [B] may be some subset of the overall cost [C], thus this distinction is declared by Source C as [C1].
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Theorem 2: Changes to Simple Objects
The only changes possible to a simple object are to come into existence and to cease to exist.Proof:
Comment: There are no other possibilities if [B] is a simple object since only 2 types of operations (changes, actions) exist per Assumption 2. Simple object can only be themselves or nothing at all.
1 [A [B]] Given 2 [A /[B]] ---> [A] Assumption 2; Distinction B is reversed (ceases to exist). 3 [dA] ---> [A [B]] Table of Contents
Definition: Context
Context is the distinction in which one or more subordinate objects exist.Example: In [A [B]], the context of [B] is [A]. Contexts are "external properties"; properties which do not originate within a subordinate object but rather are imposed upon that object by definition.
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Axiom 35: Context of Objects
A subordinate object exists within the context of its superior object.Comment: A subordinate object may exist only when its context (its nesting object) exists.
Corollary
For multiple source objects, at least one context must exist for a subordinate object to exist.
Comment 1: If [AB [C]] and /[A] then [C] if and only if [B].
Comment 2: Any subordinate object is a distinction drawn within (upon) the context that contains it. That is to say, in [A [B]], [B] is a special case of [A].
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Axiom 36: General Non-Coincidence of Objects
An object x may exist coincidently with the momentary non-existence of some object y if and only if [y] is not the sole context of [x].Comment:
Case 1Given some simple objects [y] and [x], then the following is possible:
Object y | | | Object x | | | where the character " | " represents a moment of existence of an object and " " (a blank space) indicates the momentary non-existence of that same object.
This is a case of total non-coincidence. These objects are unrelatable.
Case 2
Given [y [x]], then this is possible:
Object y | | | | | | Object x | | | | While a non-multiple source subordinate object can only exist when its context (superior object) exists, the subordinate object does not necessarily exist in every moment that its context exists. This is a case of partial non-coincidence.
Case 3
Given [z [x][y]], then the following is also possible:
Object y | | | | | | Object x | | | | Objects x and y exist within the same context and are at the same level. They are partially relatable.
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Axiom 37: Coincidence and Detection
An object detects another object only if they exist coincidently.Corollary
An object x detect the properties of another object y only if those properties exist coincidently with object x.
Example:
Given [y [a][b]], relatable object [x] and the following table of coincidences ...
[y] | | | | | | | | [a] | | | | | [b] | | | | | [x] | | | Object x detects only [y [a]] since [b] is non-coincident.
Comment: A object cannot detect that which does not exist during its moments of existence.
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Definition: Continuum
A continuous extent, succession or whole, no part of which can be distinguished from neighboring parts except by arbitrary division. (American Heritage Dictionary, 1996)Table of Contents
Axiom 38: Reality
(Refer to the figure in Axiom 37)Reality is a continuum of coincidences of a context (superior object y) and some subset of its properties (subordinate object a) with the moments of existence of some detecting object x.
Comment: In everyday terms, reality is a collection of moments in which some object y can be identified as being the same object from moment to moment by some detecting entity x. While other instances of object y and its subdistinctions may exist, they exist at moments not coincident with entity x. Since these other instances do not exist in the continuum in which entity x exists, they are beyond detection by entity x.
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Definition: Drift
Drift is the gradual, cumulative change to the properties of a time structure.Comment: Common examples of this are the life cycles of biologic and geologic structures: The creation, growth, decay, and death of entities as diverse as animals and volcanic islands. Time itself (Axiom 4) demands that objects and all their components change.
(Note for further inquiry: Does this mean that the instances within a continuum must change from moment to moment as well? Is drift a necessary condition for all time objects? Would a time object which does not change at all from moment to moment within any given continuum violate conditions of existence? Is "everything always becoming something else"?)
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Axiom 39: Necessary Conditions for Detection
Necessary conditions for detection to occur include:Comment: This may not be a complete list.
- Similarity of implementation structure
- Coincidence of continuums (Axiom 37)
Note for further inquiry: Similarity of intentional structure may or may not be a necessary condition. Probably not.
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Theorem 3: Changes to Space
In a space system (a universe for which space has been defined), time necessarily involves changes in space.Proof:
1 All time objects are subject to continuous change. Def: Time Object 2 Space is an object. Axiom 6 3 Time space is subject to continous change. (modus ponens) Table of Contents
Definition: [X0]
[X0] means [X] is a simple object.Table of Contents
Axiom 40: Simple Objects Do Not Detect
Simple objects do not detect other objects.Comment 1: Simple objects [x0] detect neither continuing nor instantaneous (non-continuing) objects. Other objects may detect them, but simple objects are non-dependent and unrelated to other objects.
Comment 2: As a matter of curiosity, extremely dense objects seem to mock the behavior of simple objects in this regard. Dense objects are apparently uninfluenced by objects several orders of magnitude less dense. This is, however, only apparently true; they are actually influenced.
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Definition: Compound Operations
A compound operation is 2 or more operations (instances of d or /d) performed on 1 or more objects and identified collectively as a single operation.Comment: A compound operation specification contains the details of the operation's logic, i.e. - which fundamental operations performed on which object(s) or types of objects.
Example: Let f be assigned the following operational specification:
"IF there exists some [x [y]]
THEN [dy] ---> [y [u]] (where [u] designates an unenterable object)
AND IF there exists some [y [x [u]] ]
THEN [x [u]] ---> [x]Thus for any domain (object) to which this operation f is applied,
all instances of [x [y] ] will become [x [y [u]] ]
AND
all instances of [y [x [u]] ] will become [y [x] ].Table of Contents
Definition: [X*]
* indicates unexpressed content.[B*] indicates [B] has unexpressed content. For example, [B*] might be [B [c] [g] ].
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Definition: Relationship Symbols
The following symbology is used to describe relationships:
Symbols Meaning Example S > T One-way detection; S detects T [S [T]] and [T] S <> T Two-way detection [S [T]] and [T [S]] S -> T One-way, S partially detects T [S [T[A]]] and [T [A][B]] S +> T One-way, S totally detect T [S [Q][T[A][B]]] and [T [A][B]] S <-+> T Two-way, S partially detects, T totally detects [S [Q][R][T[A][B]]] and [T [A][B][S[Q]]] S <++> T Two-way, total/total detection [S [Q][R][T[A][B]]] and [T [A][B]][S[Q][R]]
Symbols Meaning Example S >> T One-way relationship (continuing) [S [T]] and [T] S <<>> T Two-way relationship [S [T]] and [T [S]] S ->> T One-way, partial relationship [S [T[A]]] and [T [A][B]] S +>> T One-way, total relationship [S [Q][T[A][B]]] and [T [A][B]] S <<-+>> T Two-way, partial/total relationship [S [Q][R][T[A][B]]] and [T [A][B][S[Q]]] S <<++>> T Two-way, total/total relationship [S [Q][R][T[A][B]]] and [T [A][B]][S[Q][R]]
Symbols Meaning [C ->[T*] +>[J*]] C partially detects [T*] and C completely (totally) detects [J*] Table of Contents
Theorem 4: Only Sources Create Relationships
- A relationship is a continuing creation of a related object.
- Only sources are capable of creation.
- Therefore, a relationship is a continuing creation by a source of a related object.
Demonstration:
S, T Assumption 1 (twice) [S], [T] Axiom 27, Corollary 3 [[S] [T] ] Axiom 3 [dS] ---> [S [T]] Axiom 18 [S >>[T]] Axiom 31a Table of Contents
Definition: Ideal Design
Implementation structures cannot, in all moments, be identical with their intended structures. However, it possible to optimize an implementation so that the moments when its time structure meets or exceeds the requirements of its ideal structure are also coincident with dependent structures. Such a design would inhibit drift below the acceptable level.Table of Contents
Axiom 41: Command
The unit measure of Source is the Command. Command is defined by itsScope (Degree x Depth) of effectiveness Continuance (time) of its effects Fineness (granularity): To what depth the distinction is defined Significance (abstraction, meaning) - which can vary depending upon the viewpoint of the observer Table of Contents
Theorem 5: Source-Viewpoint
- Viewpoints are, by definition, the origins or observers of other distinctions.
- If a viewpoint can be looked from, then causation is possible from that viewpoint.
- Thus, source is possible from any point where a viewpoint can be assumed.
Comment: The viewpoint for the conventional object model (OOP) is somewhere outside the current object of interest. This is in itself OK; however, what is missing is the ability to "look up" and "look down" the hierarchy.
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Theorem 6: Streaming
Streaming is a special case of detection, whereby detection is coupled with reversal of distinction in the detected object.
- Objects [A [C]] and [B] are related objects
- [B] detects [C] producing [B [C]]
- [C] vanishes (/d) from object [A]
Thus, [A [C]] [B] ==> [A] [B [C]]
Comment: The source object [A] in a streaming event is the "originator" of the detected object [C]. The detecting object [B] is the "target" of the streaming event. The example given above is called "simple streaming".
The key difference between detection and streaming insofar as the observer is concerned is that detection does not reduce the content of the originating object [A]. Streaming necessarily does result in the reduction of content [C] of what is observed, even if it is replentished by subsequent detection on the part of the originating object.
Compound or complex streaming is repeated instances of streaming of the same original object:
[A [C]] [B] [D] ==> [A] [B [C]] [D] ==> [A] [B ] [D [C]]
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Definition: Interface
- The fact of detection of one object by another.
Comment: If one or the other of these objects is a system, and if detection has any impact on the intended performance of the system (i.e. - if it influences another system's required properties) then the interface expresses a dependency (Axiom 33).
- An object which performs a relay function between an originator object and a target object during detection (Axiom 18) or streaming (Theorem 6).
Comment 1: In the streaming example
[A [C]] [B] [D] ==> [A] [B [C]] [D] ==> [A] [B ] [D [C]] object [B] can be considered an interface. Note: Insofar as final target object [D] is concerned, object [B] is an interface.
Comment 2: An interfacing object can alter what is being relayed (Theorem 1 - Assignment of Properties to Copies of Detected Objects).
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Definiton: Interface System
An interface system is any interface which contains more distinctions than just the object being relayed.Table of Contents
Definition: Environment
The environment of a source-object is the collection of all possible source-objects with which it may relate.Symbology: [A](*) indicates object A has an environment (symbolized by the parenthesis) of unspecified content (symbolized by the asterisk).
For example, [B]( [m][n] ) states object B has an environment consisting of objects m and n.
Comment: That is to say, the environment of a source-object consists of all source-objects which it may possibly detect. A source-object may have multiple, distinct environments.
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Theorem 7: The First Intention of Life
- The first action of source is differentiation. (Assumption 2)
- Life is a complex source. (Axiom 20)
- Intention is the decision to draw or reverse a distinction. (Definition: Intention)
- The first intention of Life is differentiation. (Substitution)
Comment: Reversal of distinction is thus anathema to the first instincts of Life. Yet it is the only "permanent" way to rid itself of unwanted objects.
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Axiom 42: Perception
Perception is awareness1 of distinctions already drawn or agreed to.1 Axiom 19 - In the sense of active use of the capacity to compare distinctions.
Comment: Axiom 19 says awareness is the capability of a source to perform comparison. Axiom 18a says comparison is the distinguishing (declaration) of the differences between two non-identical distinctions. Thus, perception is essentially the capability of a source to declare differences. There is no perception where differences cannot be determined.
Theoretically, perception could be improved by increasing the capacity of a source to draw distinctions.
The conventional English use of the word perception suggests a passive event - receiving energy messages originated by some emitting source. However, in this case we are talking about detecting characteristics/objects in a universe that was agreed to and not in any great measure (insofar as the viewer is aware) self-constructed.
We shall take the word perception to mean awareness of what distinctions a source has agreed to -- perhaps on an uninspected, wholesale basis. The word decision2 shall signify a drawn distinction or set of distinctions.
2 "Decide" comes from the Latin de meaning from and caedere meaning to cut. In essence, to cut or separate from, thus to draw a distinction.
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Theorem 8: The Complexity of Life
Life diversifies (differentiates, becomes more complex) relative to the degree of complexity of its perceived environment.If it does not so diversify, the effort to not do so results in either unintended internal complexity or reduced perception, or both.
Logic
- Life is an aware Prime Source operating a system. (Axiom 20)
- Where Life exists in an environment of which it has some awareness (active use of capacity), then
- It is the creation of comparisons within the life-object that is the additional internal complexity.
- In order for these comparison structures to "disappear", the life-object must either:
- Close them to perception by making the comparison objects unenterable (Axiom 5). The result is an object internal to the life-object which it itself cannot pervade. The comparison objects still exist, they have complexity, they may even interact with other related objects, but the source may not internally alter them.
- Reverse the distinction(s) created and make itself no longer aware of that portion of its environment.
Demonstration
Step Symbolic Expression Assertion Justification 1 [X*] There exists some environment x* As 3, Def [X*] 2 A Source A exists As 1 3 [A] Source A can be viewed as Object A Axiom 27, Corollary 3, Comments (bullets 3, 4) 4 [m], [n] Non-specific objects m and n exist As 3 5 [X* [A] [n][m] ] Objects A, n, and m exist within the context X* Def: Context 6 [A]( [n][m] ) Objects n and m exist within the environment of [A]. Def: Environment 7 [n]T Object n is a time-object Def: Time Object 8 [X* [A [n]T] [n]T [m] ] [A] detects object n. Axiom 18: Detection 9 A{[n]T} ==> [A [n]T [r] ] Source A performs comparison on 2 moments of object n's existence and determines the difference to be the distinction r. A is aware of object n. Axiom 18a, Axiom 19 10 The complexity of [A [n]T [r] ] is greater than that of [A] Def: Complexity At this point we have demonstrated how a life system (lifeform) becomes more complex due to awareness of a single property/object of its environment. By repeating this process for each property/object detected in its environment, one can see how additional complexity would result.
Efforts by the lifeform to prevent adding internal complexity can take two forms:
11a A d[r] ==> [A [n]T] [r]U Source A prevents perception (detection) of the resulting distinction by declaring it to be unenterable or ... Axiom 5, Axiom 42 11b [A /d[r]] and [A /d[n]T] ==> [A] Source A reverses the detection of environmental object n as well as the result of the comparison (object r). As 2 In 11a, the lifeform is essentially perceiving the presence of the environmental object r but is occluding it from use in later efforts. In 11b, the action of detection of the environmental object is cancelled, so no detection henceforth occurs. Theoretically, a lifeform could do 11a on one environmental object and 11b on another.
Comment: In cases where a life-object has multiple and complex agreements with that portion of the environment, there may be multiple sources of resistance to vanishment of some particular component of an agreement.
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Definition: Abstraction
- (from the Webster Dictionary, 1913) .. (Metaph.) The act process of leaving out of consideration one or more properties of a complex object so as to attend to others; analysis. Thus, when the mind considers the form of a tree by itself, or the color of the leaves as separate from their size or figure, the act is called abstraction. So, also, when it considers whiteness, softness, virtue, existence, as separate from any particular objects.
Abstraction is necessary to classification, by which things are arranged in genera and species. We separate in idea the qualities of certain objects, which are of the same kind, from others which are different, in each, and arrange the objects having the same properties in a class, or collected body.
Abstraction is no positive act: it is simply the negative of attention. Sir W. Hamilton.
- (SAO definition) A subset of the distinctions that define an object.
Original object A: [A [B] [C] [D]]
Abstraction of object A: [A [D]]Table of Contents
Axiom 43: Realization
Realization is:(1) the detection of a heretofore undetected object, and (2) the perception of distinctions in a heretofore unenterable object.
Comment: When the unenterability property of an object is reversed and as pervasion occurs, the immediate result is perception of heretofore imperceptible contained distinctions.
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Axiom 43a: Source is Identified By Its Creations
A source is identified by the creations it sources.Proof:
Comment: Thus source A altering source B's creation is to a greater or lesser degree altering source B's identity.
Corollary 1
The apparent continued existence of a source is the identification of that source with an object. When that object ceases to exist, so does that source's identity.
Comment: There is no limitation as to the number of identities a source may have unless arbitrarily designated. If a source is identified by a combination of objects, then the loss of an identifying object will be detected as the source losing the properties of that object.
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Theorem 11: Identified Sources in Constant Change
Where a source is identified with one or more time objects, that source cannot be seen otherwise than to be in a state of constant (continuing) change.
Demonstration
Step Symbolic Expression Assertion Justification 1 S Source S exists As1 2 [P]T Object P exist as time-object Def: Time-Object 3 S => [P]T Source S identifies itself with time-object P Axiom 43a 4 Time-Object P is in constant (continuing) change Def: Time Object 5 Source S appears to be in constant change. (modus ponens)
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Axiom 44: The Value of Source
The value of a source is value of its detected influences.Comment: Sources are judged by the value of the changes it makes to objects or properties
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Theorem 12: Influence of Sources on Sources
One source is judged to have influence upon another source if the first can influence the creations of the second.(Need to finish proof)
Proof:
1 S, T Source-Objects S and T exist Assumption 1 2 [ [S] [T] ] S and T are relatable. Axiom 3 3 [S] -> [T] S partially detects T Axiom 31a 4 Comment: Influencing a source means adding, deleting or changing a property of the influenced source's creation.
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Theorem 13: Power of a Source
The potential power of a source in a time continuum is inversely proportional to the complexity of its objects.(Proof needed)
Comment 1: Sources may vary in their potential. Each of two sources which are sourcing objects of the same total complexity will have less potential power relative to themselves than when they were sourcing objects of lesser complexity. However, the diminishing of their potential power is proportional to what the potential each started with, not necessarily to each other. That is, one source may be involved with objects of much greater complexity than another and yet have more remaining potential than another source involved with objects of lesser complexity. Sources do not necessarily start out with the same potential power.
Comment 2: Where this inverse relationship seems to fail, it will turn out that the source and/or the time continuum has changed, not the above rule.
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Definition: Compound Source
A compound object performing as a source (i.e. - drawing distinctions, reversing distinctions or any of the actions derived from the fundamental actions such as detection or comparison.)Symbology: A*
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Definition: Resource
A resource is a Source-Object that provide desired influences.
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