SAGOE - Architecture of a 4D Physical Object Simulator

This web site is intended primarily for the use of potential and actual collaborators. If you are reading this material, and find yourself interested in exploring a collaboration with me, then use any of the contact methods found on my Home Page
.

For quick evaluation, I have condensed a complicated software project's design, produced over 3 decades of laborious iterative trial-and-error redesign, into this first page summarizing some of the project's most salient features. The project is called Simulator Application Generator Operating Environment (SAGOE - pronounced "say go"), standing for its three implementation layers (S, AG, OE). Additional detailed web pages are linked to below, and so on.

Please understand this is all proprietary copyrighted information owned by Science Business Software, Inc. This web page, and all www.scibizsw.com web pages it links to, constitute the equivalent of a journal publication or book, Copyright 2021. I obviously do not intend that public access be entirely eliminated, or I would be unwise to put this information on this public web site. I only ask that you give proper credit where credit is due (to me). So, if you end up copying any of this material, I cannot stop you, but please give reference credit to Dr Greg Colello (aka, my handle: "DrG").

Note, the reader should be aware the following somewhat theoretical discussion is intended in a step-by-step fashion to lead logically to the design of a generalized Object Data Model for SAGOE, that lays the foundation for a Universe/Earth Simulator. This discussion is accompanied by a series of associated figures, hopefully assisting the overall comprehension of a general (lay) readership, for which this discussion is also intended. In the beginning this discussion will seem very theoretical and somewhat simplistic, but it lays a foundation for the most complicated material, much of it Physics, which will come at many of you all too quickly I suspect. I have tried to balance the discussion between simplicity for a general audience, and too simple for a professional audience.

INTRODUCTION:

The primary goal of the SAGOE architecture has been to articulate a computer implementable systematology, relating to all physical phenomena. As such, the following discourse constitutes a Philosophy. A sort of psuedo-mathematical proof, sufficient in the end to devolve into a seamless set of software modules. The "problem space" I am addressing is the Universe as we know it. The tersest statement of the overall systematology argues that the Universe as we know it is composed of:

"Reactive Objects Moving In SpaceTime"

"Objects" is a general concept, which is presumably obvious to all humans. Objects possess "Properties"; where the most obvious property is "Size". Physical Objects also possess "Physical Contents", which can be seen as a descending (diminishing) series of internal size-scales (more on size-scale later).

"Movement" actually implies Time and Space, so it is not necessary to specify them in the most terse Universe statement, which is "Reactive Objects In Motion"; but to be clear, and in deference to Dr. Einstein, it is better to say "...Moving In SpaceTime". The most general observation of an object's motion is that it occurs in a "straight-line" at a constant velocity, following the "shortest distance" curvatures created by gravity in an otherwise "perfect" vacuum of SpaceTime, implicitly meaning being unaffected in any other way.

Theoretically, whenever moving Objects retain a constant mass-energy composition, while in an unimpeded motion state; they also retain a constant "Inertia" or "Momentum", which are the combined mathematical consequences of relativity mass-energy composition and velocity. However, this fixed state concept can be (and presumably is) altered at least slightly by an object's own internal reactions, for example energy loss due to temperature-mediated infrared photon radiance, which affects total relativity mass-energy balance (more on reactions later).

Ok. Nothing much special above. The concepts of Objects, Motion, SpaceTime, and Relativity are familiar to all of us in the 21st Century.

However, note the almost hidden innocent word "Reactive". This concept covers a lot of important territory not so commonly thought about.

Objects can react with other objects, when any of their properties come into close enough contact with the properties of another object. Objects can also have internal reactions with their own properties.

For example. Molecules are Objects. Any two molecular objects must have Movement to come into mutual contact with sufficient proximity to effect their inherent individual "reaction sets". That is, both objects under consideration have individual "property-states" that are changed by their contact. If their proximity is insufficient to invoke any of their potential individual reactions, then no reaction can be said to occur in one or both. This is a more general way for example to think about molecular Receptors and their molecular Ligands.

Movement and Reaction also relates to the underlying meaning of "Perception". Objects must react in order to perceive each other. In order to react they must move. If there were no motion in the Universe, then no existence could be perceived. Even in a moving Universe, if no reaction occurs between two objects, then one or the other or both appear as "non-existent" to their opposite. Hence perception is a relative concept in the sense that perception is relative to the composition of a given entity. An object can exist for one observing entity, while appearing non-existent to another. So, does it exist? Who judges? It is relative.

As to Universal Perception, there is the case of "General Perception", which can be applied to all Objects in the Universe. Then there is the special case of "Human Perception", which includes the special property of "Human Memory", a biological means of retaining the pattern of a previous perception, that can be "Recalled" and experienced, or compared to a subsequent perception. Nonetheless, in a totally general sense memory applies to everything that reacts, because an impression is left behind, that could be termed a "memory". However, the corresponding corollary metaphor to the human memory concept of recall is less compelling.

In all of this the idea of "Granularity" must be included. That is, the granularity of the Universe itself, which determines whether any two perceived Objects are sufficiently close to React; or the granularity of our own perceptual apparatus or any device enhancements, which determine whether we perceive something, for example the existence of an Object or one of its properties, for example a star or its temperature. Hence granularity is also a relative concept, in the sense that it is relative to whatever perceptual mechanisms are involved. It is the source of what we perceive as size-scale in the Universe. It is also the source of our conclusion that reactions of smaller scales give rise to the "emergent (consequent) behaviors" of larger scales immediately above them.

Within this, "Stochastic/Statistical" mathematical concepts like "Uncertainty" and "Probability" and "Tolerance" and "Error" and other related ideas, should be included. Nothing can be perceived without some uncertainty being present. At the limit of uncertainty, perception dissolves into invisibility or non-existence.

Note that an important aspect of size-scale is that the mathematical prediction of a given smaller scale's local behaviors is typically never good enough to predict the emergent behaviors of more than two powers of ten scales above it (for example where scale-size is measured in meters). This has to do with prediction-uncertainty accumulation. This can also be thought of as a rule of thumb arising from one interpretation of "Hierarchy Theory" (credit to Chris Fields). For example an accurate mathematical model of the atomic scale could predict the emergent mathematical behavior of the molecular scale immediately above it, which in turn might be capable of predicting the emergent macro-molecular scale immediately above it; however due to accumulated uncertainties, likely no further.

Stochastic concepts apply directly to the concept of "Measurement", where one of a given Object’s properties measured as a "Property-Value", always involves the following items:

(1) A "Ruler" (Scale) specified in a given "Unit", which is the same as a category (see below).

(2) The Unit's "Count-Quantity" measured along the ruler, which is specified in a given count encoding, like decimal.

(3) "Percent-Uncertainty" of the measured quantity.

(4) "When" the measurement was performed, in some sort of relative time coordinate specification, that includes both object and observer.

(5) "Where" the measurement was performed, in some sort of relative spatial coordinate specification, that includes both object and observer.

(6) Other miscellaneous related measurement conditions, information that can be loosely termed meta-data, like "How" and "By Whom" the measurement was performed.

Further, the concept of "Categories" can be invoked to enhance generality. That is, each human can perceive the structure of the Universe in different ways by defining it being composed as a different set of custom categories, where a given category specifies a defined "Pattern" that can be applied to a given perception to conclude that the considered perception conforms as an "Instance" of the considered category. For example whether something is an orange or not. The instances of a category can be counted, hence a category can be treated as a unit. Each instance of a category can be sub-divided, forming sub-units (see below).

Another generality, the concept of patterns, was mentioned above. How patterns are defined is a special topic, too complicated to be considered here, but suffice it to say, at least on a computer, ultimately breaks down into a corresponding binary pattern, that can be compared to another pattern within a specified tolerance.

Note that the concept of categories applies to every term of the basic systematology stated at the beginning, "Reactive Objects Moving In Space". Each term can be broken down into a multitude of categories, where each category has a defined pattern. Not an easy thing to understand at first blush. Some examples may help.

Let's consider the case of "species classification taxonomy". Note in this case that related categories are joined into a sub-dividing hierarchical cascade, a so-called "taxonomic hierarchy" or "ranking", for example, "Domain-Kingdom-Phylum-Class-Order-Family-Genus-Species", where each sub-category is a sub-division of its parent. Now as a corresponding mental exercise consider more generally the entire Earth and all its possible categories and sub-divisions.

Note that each such category has a defined pattern that usually takes the form of a set of measured properties. In the taxonomy case a complete set of properties can be found by taking the union of all the specified properties of all the species being classified. This forms the full pattern of the highest ranking category, in this case, Domain. Each subdivision under Domain specifies a subset of this complete set of properties, and so on, down to the species level. In reverse, if starting at the species level, and moving up one level at a time, it is possible to accumulate the complete set of properties, taxonomic "branch point" by branch point, as a sort of mathematical "roll-up" function.

Further, this relates directly to the Thermodynamic properties of "Extensive" and "Intensive". An intensive quantity is defined as one whose magnitude is independent of the size of the system, like mean or average or color or heat capacity; and an extensive quantity is defined as one whose magnitude is additive for subsystems, as in the above classification example. That is, the "roll-up" function is essentially reflecting the extensive properties of the classification system, like genomic structure (gene possession). On the other hand any intensive properties of this system do not "roll-up" additively, instead they simply "transfer up" or are "shared" across branch categories, like say "skeletal" versus "not skeletal". Hence, they would tend to fall into the "descriptive morphology" properties domain in this example.

Ok. In the interest of computer implementation generality, in the above examples, I was stretching the meaning of intensive and extensive, when considering a taxonomic classification scheme. The reader may find the concepts of intensive and extensive more clear and Thermodynamically meaningful, when considering the properties of something like the "MacroMolecular-Molecular-Atomic" hierarchy. Nonetheless the concepts still apply metaphorically to the taxonomic example, and should be valid, as well as creating potentially useful results.

Note that perceived Categories can be personal. For example there must be 50 different species taxonomies, each personally convenient to a given scientific guild; for example Molecular Biology has several different popular taxonomies, which emphasize various aspects of genomic evolution. And in general that guild developed categories personally convenient to their entire discipline, yielding a unique set of terminology; but alternate categories, and a corresponding set of terminology, could just as easily have been developed by a different set of personalities.

In Toto I hope the above constitutes a completely general set of concepts, whose vocabulary is consistent both with human common sense and scientific observations; and can be thus taught to students as a general way of thinking; and can also be implemented as a corresponding computer application for all to use. There are many details to this that must be elucidated. These details devolve into a computer language modular development. The game to be played and described is how to specify the minimum number of modules to complete the overall application.

SAGOE'S UNIFYING PRINCIPAL - "REACTIVE MOVING OBJECTS":

NOTE: The title of this section, which succinctly states the unifying principal of SAGOE, could alternatively be stated as "REACTIVE OBJECT FLUX IN 3D SPACE" or "REACTIVE OBJECT FLUX IN 4D SPACETIME" or "REACTIVE OBJECTS MOVING IN SPACETIME"; or simply as the title suggests "REACTIVE MOVING OBJECTS", since Motion implies Space and Time. Or even others you can think of. Take your pick. The theoretical implications for software implementation are the same, SAGOE must support four major things:

-----------------------------------------------------------------

- SPACE. (view figure 1)

- TIME. (view figure 2)

- OBJECTS MAPPED TO A SPECIFIC SPACETIME [LOCATION:MOMENT], POSSESSING SPECIFIC PROPERTIES AND REACTIONS. (view figure 3)

- OBJECTS MOVING IN SPACETIME & REACTING. (view figure 4)

-----------------------------------------------------------------

For those unfamiliar with software architecture, the best hope for designing and implementing a complicated application is to first identify modules that can be reused. That is one of my ultimate purposes in the following discussion...to identify those things about Humans and the Universe that can be expressed in the form of programmable subsystems or utilities. The following section is an attempt to delineate obvious aspects of our Universe, so that the Universe "Problem Space" SAGOE is intended to represent is fully covered, has a theoretical foundation, and can be thought about using a defined terminology.

Finally, for the System Programmers (Computer Scientists) in the audience, there is an ancillary project involved herein, that attempts to define a "Universe Programming Language (UPL)", whose purpose is to define all the Objects and Actions in the Universe, including those of the Digital Device Network World, in terms of programming language constructs. This project has long-term application for developing a portable "Operating Enviroment" for the Universe/Earth Simulator, but is also useful as a psuedo-mathematical proof that the Universe's presentation to Humans can be shown to behave "as if" being controlled according to specific "instructions" from the beyond. By implementing such a "UPL instruction set" in some computer language like Java, it should be possible to produce a portable Operating Environment (high level language layer) in which to program all the simulated Objects and Actions of our Universe. Once this is done in one computer language, like Java, then by implementing the same UPL in another computer language, like C++, the entire simulated Universe should execute seamlessly under the new UPL Operating Environment.

My fundamental goal is to implement a four-dimensional (4D) Physical Object (PO) simulator, which can be applied to an integrated Universe Model (a low-detail Astronomical-Universe with a detailed Earth-System embedded within it). The key to this is the creation of a database, which extends in Time from the Big Bang to an equivalent point in the Future, and has a spatial volume equivalent to the current known extent of the Universe. In this way every object that ever was, or will be, has a ready made "Time and Position" slot in the database. Further, it is intended that any PO mapped into this Time/Space Database can possess miscellaneous Property States, Reactions, and Vector Motions; where Movements are tracked as individual or stochastic flux. By flux I mean any size or type or number of PO's moving, as a group, in computer-generated 3D space and 1D time.

Finally, since the end result of such a "Software Application Architecture" would be an analogue of the Human experience of the Universe, the resulting functioning Application should exhibit semi-"Artificial Intelligence (AI)". Note that "semi-AI" is herein defined to be different from a "pure-AI" system, in that a pure-AI system cannot be distinguished from an actual Human Being, as was first proposed by Alan Turing (the so-called "Turing Test"). AI is not the goal of this project. SAGOE is designed to be a practical tool, albeit a very sophisticated tool. The functioning end result of SAGOE should always be clear to its "Users" that it is a Computer Program; but it should be so easy to use, and so closely approximate Reality, that it appears to be semi-Intelligent.

In the following sections a great deal of time is spent delineating the functional aspects of a general process termed "Perception". The reader should keep in mind that the reason for this effort is that it will form a fundamental modular aspect of implemented code. This means that the largest number of Universe processes can be represented with the smallest amount of programming language code.

PERCEPTION THEORY I - INTRODUCTION

The following section is an attempt to delineate some of the aspects of the general topic of Perception. Additional details are in PERCEPTION THEORY II below. This section posits a couple of fundamental thoughts about Perception in subsections (A) and (B) below...

(A) - Three general Sub-Categories of Perception are useful to consider (1-Natural World Perception, 2-Human World Perception, and 3-Network World Perception):

Natural World Perception. (The general case of Universal Perception, which any Natural Object can have with any other.)

A generalized phenomenon, referred to herein as "Perception", can be usefully defined as being applicable to all entites in the Natural Universe.

For the purposes of a generalized Computer Simulator of the entire Universe, which SAGOE is intended to be an example of, it became obvious during early design attempts that processes like "Perception" had to have clear internal definitions; else the entire Architecture of SAGOE would be impossible to use in certain Simulation contexts, particularly those involving Simulated Human "Civilizations".

Normally "Perception" is defined by Psychological practitioners, to whose discipline the term most clearly applies, as a process that only occurs in the "Higher Forms" of "Animate (Life)". Under this definition Perception essentially means the "Detection" of some entity or action in a Higher Life Form's environment, which then typically results in a "Retrievable" (accessible) "Memory" being formed of the Detected entity or action. Subsequently "Recognition" of the exact same or a similar "Pattern" can occur, when encountered again, and compared to the existing Memory. In Humans Memories are further defined as being Retrievable at any time as part of the "Thinking" process. It cannot be proven conclusively whether this exact phenonmenon occurs in other Higher Life Forms; but it is accepted that they can at least form Memories and subsequently compare their Memories to things they encounter.

Using these definitions, Perception is commonly considered either simply the Detection process, or more complexly the Recognition process. Some would go further in Humans and include the Thinking process. In all cases Higher Life Forms will have some "Response" to their Perceptions. Finally the entity or action that is Detected is said to be a "Stimulus". The entire process from beginning to end is termed a "Stimulus-Response Pairing", or "Stimulus-Response Chain" of internal events. Commonly Perception is considered to be more connected with the Stimulus side of the Pairing or Chain.

For the generalized purposes of SAGOE, the above Higher Life Form definition of Perception proved to be too narrow. For one thing it was never going to be clear where to draw the line as to which entities were capable of Perceptions, and which were not. In fact, upon closer examinination, all of the above definitions (Stimulus, Detection, Memory, Recognition, Thinking, Perception, Response) were found to be vague as to what they referred to or what their applicable limits were. It's all semantics, as the saying goes.

First, it is clear that ANYTHING in the Universe can act as a Stimulus. Second, it is clear that EVERYTHING in the Universe exhibits Responses to Stimuli in the form of "Reactions". Third, in order to produce its final net Reaction, an entity must first Detect the initiating Stimulus. Fourth, the Detection step itself can easily be seen to be a Reaction. Fifth, the formation of a Memory, its Retrieval, Pattern Recognition, and Thinking can all be seen as processes involving Reactions; albeit whose mechanisms are only partially determined at present. Hence, the entire panoply of events can be seen to be a collection of "Reaction Chains"; where for each Chain the Response from one step becomes the Stimulus for the next.

In this scenario the sense of what is meant by Perception becomes blurred. Nonetheless, it is clear that the Perception of any entity can only occur if the Perceived entity changes the Perceiving entity by one or more "Reactions" with it, which in short means:

Any Perception Event Requires A Corresponding Reaction Event Within The Perceiving Entity.

Further, Natural Perceptions by a Perceiver is the Natural result of the Natural "Expressions" emanated by a Perceived entity, an Expression of its "Self" so to speak; which is due mechanistically to one or more of its inherently possesed "Properties", impinging upon the Perceiving entity. In short this means:

The Self Expression Of One Entity's Properties Becomes The Stimulii For Its Perception By Another Entity.

Further, it is worth noting that in order for any Reaction to occur some aspect of a Perceived entity must occupy the same Space and Time instant as the Perceiver entity within the "Tolerance Limits" required by the Universe's own inherent Space and Time "Granularity"; where Granularity refers to a limiting aspect, that controls the "Resolution" of a Perception. For example the Human eye cannot Resolve certain Stars in the sky without the aid of a telescope. The limiting aspect in this example is the number of Light Photons that hit the eye's retina. A telescope concentrates the Light from a Star, using lenses or mirrors, so that more than the minimum number of Photons required to Resolve an entity from its background hit the retina.

The concepts of Tolerance Limits, Granularity, and Resolution are critical to the Architecture of SAGOE; since it designed to create Simulations at any individual "Scale" of the Universe, while also allowing different Scales to operate seamlessly together, as an aggregate system.

Typically any Simulation of Reality is built to Represent the Simulation's "Problem Space" on the Computer by creating an appropriately-sized "Grid" or "Mesh" that subsumes its Spatial Scale (for example 1 Cubic Kilometer, km³, of Volume), and then subdivides it into smaller Units (for example into sub-Volumes 1 Cubic Meter, m³, in Size ). In addition an appropriate Time Scale (for example 1 Year, yr) is chosen for the same Problem Space, and it is subdivided into smaller appropiately-sized "Timesteps" (for example 1 Hour, hr), which is the tick of the clock for a running Simulation. These concepts are endemic or implicit to most Computer Simulations regardless of how they are Programmed.

To make all this clearer, I will explore the various Scales of the Universe and its base Granularity, as informed by current Science. In addition I will introduce the "Grid-Scale" Simulation topic.

The best illustration of the various Length Scales of the Universe, that I have encountered to date, has been posted by Pablo Carlos Budassi on this Wikipedia webpage Orders of magnitude (length) (Zoomable Figure Only). Unfortunately the associated Figure was draw counterintuitively with the smallest Scale on top; showing (Quantum Foam) at the top, and the largest Scale (the entire Universe) at the bottom. The Figure is illustrating various choosen Scales, using a typical object at each "order of magnitude", as if it exists in a layer. (I copied the following text from its Figure legend, which I edited a bit to better serve the purposes here, and express the given Length Scales uniformily in meters, m; both as digits and as corresponding exponents of 10. Note, that some Scales are skipped):

0.00000000000000000000000000000000001 (10^-35) m: Planck Length. I added this for completeness. The believed "Pixel" Granularity of the Universe (exactly 1.616229x10^-35 m).

0.00000000000000000000000000000001 (10^-32) m: Here is thought to exist a foam of twisted spacetime (Quantum foam).

0.000000000000000000000001 (10^-24) m: Cross section radius of 1 MeV neutrinos.

0.0000000000000000000001 (10^-22) m: Top Quark, the smallest quark.

0.00000000000000000001 (10^-20) m: Bottom and Charm quarks.

0.000000000000000001 (10^-18) m: Up and Down quarks.

0.0000000000000001 (10^-16) m: Protons and Neutrons.

0.00000000000001 (10^-14) m: Electrons and nuclei.

0.000000000001 (10^-12) m: Longest wavelength of gamma rays.

0.00000000001 (10^-11) m: Radius of hydrogen and helium atom.

0.0000000001 (10^-10) m: Radius of carbon atoms.

0.000000001 (10^-9) m: Diameter of the DNA helix.

0.00000001 (10^-8) m: Smallest virus (Porcine circovirus).

0.0000001 (10^-7) m: Largest virus (Megavirus).

0.000001 (10^-6) m: X Chromosome.

0.00001 (10^-5) m: Typical size of a red blood cell.

0.0001 (10^-4) m: Width of human hair.

0.01 (10^-2) m: Width of an adult human finger.

1 (10⁰) m: Height of an infant human being.

10 (10¹) m: Argentinosaurus is the biggest dinosaur discovered yet (30 to 35 meters).

1000 (10³) m: Diameter of Barringer Crater in the northern Arizona desert (exactly 1,186 m).

100000 (10⁵) m: Jamaica Island (exactly 235,000 m long).

10000000 (10⁷) m: Diameter of planet Earth (exactly12,742,000 m).

100000000 (10⁸) m: Moon's orbit (exactly 770,000,000 m).

1000000000 (10⁹) m: Diameter of the Sun (exactly 1,391,400,000 m).

100000000000 (10¹¹) m: Diameter of the inner Solar System. (exactly 600,000,000,000 m)

10000000000000 (10¹³) m: Outer limit Diameter of the Solar System.

1000000000000000 (10¹⁵) m: Outer limit of the Oort Cloud.

10000000000000000 (10¹⁶) m: Distance to Alpha Centauri.

1000000000000000000 (10¹⁸) m: Messier 13 globular cluster.

100000000000000000000 (10²⁰) m: Diameter of the Milky Way Galaxy.

10000000000000000000000 (10²²) m: Local Group of galaxies including Milky Way, M31(Andromeda), M33, SMC, LMC and smaller galaxies.

100000000000000000000000 (10²³) m: Typical galaxy cluster (2 to 10 Million Parsecs, Mpc).

1000000000000000000000000 (10²⁴) m: Laniakea Supercluster of galaxies. (160 Million Parsecs, Mpc)

10000000000000000000000000 (10²⁵) m: End of Greatness ("Cosmic web" structure).

100000000000000000000000000 (10²⁶) m: Diameter of the observable universe sphere. The entire Universe is larger than 10²⁷ m and possibly infinite.

Note in the above list that, relative to human size, the smallest order of magnitude (-35) is similar in ordinal size as the largest (+26). This suggests that humans occupy a sort of center-point in relative size in the Universe, which is an interesting fact to comtemplate.

It is worth noting, that once a general definition of Perception is in hand, there are many synonyms that can be identified for the elements of the process. Reiterating here one of SAGOE's basic definitions of Perception...a Perceived entity may be thought of as a "Stimulus" on a Perceiving entity...a series of synonyms can be identified. The Reaction change, the immediate Response this Stimulus induces on the Perceiving entity, may be thought of as an "Imprint" made on it by the Perceived entity. This Imprint may also be thought of as "Representation" or "Reproduction" of the Perceived entity within the Perceiver. In a sense this Representation is an "Image" of the Perceived entity, and all Images are "Copies" in the photocopy sense of Copy. In a broader sense still the change in the Perceiver entity induced by the Perceived entity is a "Natural Simulation" of it. This relationship may be summarized diagramatically as follows:

Stimulus --> Response {Reaction = Imprint = Representation = Reproduction = Image = Copy = Simulation = Perception}

;where all the above Responses to a Stimulus, enclosed by the braces, can be considered synonomous with each other.

Since an Image can also be a Computer Digital entity, and SAGOE ultimately must handle all Computer entities in a generalized fashion, it is worth thinking deeper about what an Image is. Everyone is familiar with a Camera Picture. This is a type of Image. Such Images can be produced either on Film, using chemical particles; or in Digital form, using photo-sensitive semi-conductors. Film Images can in turn be converted to a Digitized form by a scanning process that also uses photo-sensitive semi-conductors.

In any case Humans experience such Images as being flat or "Two Dimensional (2D)", although that is not strictly true in a physical sense (see more below). Regardless, a Computer Digitized Image is "abstractly" made to be exactly 2D, having a Height and a Width, expressed as a Plane of Color "Pixels", but having no Depth; unless one considers the electrons used to represent the numbers. In any case the user of Digitized Images is intended to consider such "Virtual Images" to be exactly 2D. This is the underlying abstraction.

In reality, there is no such thing in the Universe as a 2D Natural Existence. Everything is 3D, being composed of Particles, as all current Science tells us. Particles can be simply imagined as Spheres, or more simply even as Cubes. These are the two extremes of Geometric 3D Representation. Every other 3D Shape is somewhere in between these two types.

In general all 3D Shapes can be Represented exactly (or approximatly) as 3D Polygons (a Volume with an arbitrary set of points on its surface, where neighboring surface points are interconnected by lines that do not cross each other, forming a sort of enclosing "Frame"). Both the Spherical and Cubical Geometric entities can be easily imagined possessing center points. It is also possible to visualize a Sphere exactly contained within a Cube (just touching the Cube's surface, sharing a common center point); or a Cube exactly inside of a Sphere (just touching the Sphere's surface, sharing a common center point). It is further possible to imagine this same arrangement as an infinite series of alternating exact enclosing Spheres and Cubes in the exact necessary proportinal increasing sizes. Three Dimensions then can be imagined as three intersecting planes at right angles (90 degrees, Orthogonal) to each other with a common central intersection point that is also common to the center point of any number of enclosing Cubes and Spheres. This 3D generality is derived from the fact that Particles themselves are 3D by definition, meaning they are not flat, possessing the Property of Spatial Volume; possesing Height, Width, and Depth; Geometrically speaking having [x,y,z] Axes; which is the same as the three intersecting planes mentioned above.

[BTW: Theoretical Physicists feel certain that Orthogonal (right-angle) Dimensions higher than 3D operate in our Natural Universe, typically positing 10D or 11D; which are calculated using a sort of Universal Coordinates mathematical trick, but for most simple discussion purposes herein, that fact will be ignored. Although in this context in passing it is worth visualizing the entire Volume of the Universe enclosed within one giant 3D Cube or Sphere. For the sake of simplicity let's say a Cube. Then imagine a Copy of that Cube at every point along the Time-Line of History. Is not Time (t) then a sort of 1D Dimension at "right-angles" to all of these 3D Cubes, hence forming four Orthogonal Dimensions (4D)? This "thought experiment" would seem to validate any mathematical "tricks" used to calculate 4D Coordinates [x,y,z,t] as an extended version of 3D. Especially since this seems to emulate Reality better. Cannot higher Dimensions then exist in a similar manner if they seem to emulate Reality better than just four Dimensions?]

Returning to the film example of an Image, consider whether the film itself can possibly be viewed as NOT having a Depth Dimension? Such a view is not Realistic. Film always has Depth, some "Thickness". So, how do we extract a 2D Image from a 3D substance? The requirement is that whatever Depth we penetrate into the film for a given very small surface area (called a Pixel), the measured Color Value must be "nearly" the same. This then produces a single Value for each Pixel, which in turn produces a flat plane of Values; hence in turn producing a 2D Digitized Image (in Computer Graphics: Height by Width; or more generally for a plane: Length by Width). When we Humans look at a film's Picture Image, presumably a similar process takes place in our brains.

Taking this analysis a step further, I claim the 2D Digitized Image is still a 3D entity; because it has to be Represented in some fashion using some material aspects of our 3D Reality. In the case of the Computer, any Graphic Image is composed of Pixels, which in turn are composed of Values, which in turn are composed of logical "Bits" (a set of 0's or 1's in a specific pattern), which in turn are Represented by electrical signals, which in turn are composed of Electron Particles, which possess 3D form; or the Bits are stored in "Persistent Memory", which in turn is typically composed of magnetic or solid state materials, both of which possess 3D form. Hence, the idea of 2D is really an "abstract" simplification of Reality. It is useful, because it is a simplification, making life more pleasant for us Humans with our limited capacities.

But I want to emphasize here that this simplification is not needed on Computers, with their seemingly limitless capacities, and in the end acts as a sort of corruption of information for the machine. Note, SAGOE could make this simplication or abstraction clear by making it a "settable" Attribute of the Dimension class. Thus for example the Dimension (or set of Dimensions) that do not have this Attribute set, could be taken by the SAGOE Computer program as being Reality in any Simulation that it runs; all else could be taken as a simplified abstraction of Reality. This could potentially clarify liguistic communications between the machine and its Human users.

[BTW: In this sense perhaps 3D can be thought of as an abstract simplification of a Theoretical Physicist's 10D view of Reality.]

The take-away message here is that Perception itself is always a 3D process, but the Reaction involved initially impinges on a "Face" (localized surface area) of the Perceiver's Volume. The Reaction then penetrates into the Perceiver's Depth Dimension through a chain of further Reactions, represented symbolically as follows:

Stimulus --> Response(s) {Reaction1 --> Reaction2 --> Reaction3 --> Reaction(n)}

or

Stimulus --> Response(s) {Perception1 --> Perception2 --> Perception3 --> Perception(n)}

Leveraging the previous discussion about 2D Images, it is possible to conceive this entire "Reaction Depth Volume" as a being horizontally cut into a series of "Volume Slices", where each slice contains Particles that have similar Property Values; and extending the concept of the single Volume Slice of a camera film Image, can be thought of as a series of 2D Image Slices.

One practical means for determining boundaries between these Volume Slices is that their Depth-Averaged Pixel Values are "Significantly Different" than their neighboring Volume Slices, and "Insignificantly Different" from other Values in the same Slice:

Stimulus --> Response(s)
{
Reaction Volume (where Reaction penetrates sequentially into entity's Depth from 1 to 3):
=======================
Reaction1 Image
-----------------------------
Reaction2 Image
-----------------------------
Reaction3 Image
=======================
}

[Technical Note: The procedure of creating separate Volumes like this is sometimes referred to as "Finite Element Analysis", meaning that each Volume is a separate Element in a series of neighboring Elements. Such a series forms a discontinuous "Distribution" of entities, but which can be also represented as a continuous function with Differential Calculus Equations.]

This idea can be extended a bit to say that each Slice can instead be a convenient collection of "Significantly Different Neighboring Values", but whose aggregate "Average Value (Avg)", plus or minus (+-) some Percent Difference (%Diff) or Standard Deviation (SD), is of interest:

Stimulus --> Response(s)
{
Reaction Volume (where Reaction penetrates sequentially into entity's Depth from 1 to 3):
===============================
Reaction Slice 1 Avg Image (+-SD)
-------------------------------------------------
Reaction Slice 2 Avg Image (+-SD)
-------------------------------------------------
Reaction Slice 3 Avg Image (+-SD)
===============================
}

[Note that the overall concept of Significant Difference, which has several facets and many practical applications, is explained in more detail below.]

The above concept can be extended even further. Whether one defines the chain of Reactions as being through a single entity or multiple entities is completely arbitrary. For example Human Perception of an entity is often experienced as having come through an intermediary entity, like the detection of a Star through a telescope. The chain of Reactions of the Light Stimulus from a Star can be traced through Space, through the telescope, through the eye, and then through the brain; and the Reaction Volume Slices concept still applies.

In general Stimulus/Response "Waves" can be viewed as passing from one end of the Universe to another, and interpenetrating each other, while doing so; producing all kinds of possible Reaction Image Slices, that can be viewed as capturing various "States" of the Universe. This produces a complex view of the Universe, as some kind of living entity whose inner workings are chained together; or like Sound Waves passing through a water container, and reflecting off its sides. How one decides when such Waves terminate is completely arbitrary, and dependent on the level of Resolution or Granularity of an "Observer's Detection Methodologies".

The ideas expressed above in defining 2D can by analogy be used to define 1D and 0D also. If the reader can imagine the Plane of Values that produces any 2D Image, then just take any "Strip" of Values going across the Height or Width Dimension of the Plane/Square, and the resulting "Row" or "Column" is a 1D entity, 1D because because it possesses a Dimension of either Height or Width but not both, also called a "Vector" or a "Line". Then take a single Value from any of these Vectors, and that is a 0D entity; 0D because it possesses none of the three Height, Width, or Depth Dimensions; also called a "Point".

Note, however, that any Point must exist somewhere in Universal Space having itself 3D Universe Coordinates [x,y,z] of some kind; plus besides having a Location, it exists at some Time too. I am trying to reiterate my observation that abstract entities are always simplifications of Reality, that also exist somewhere in 4D Reality. This is information we Humans usually choose to ignore for ease of use; but which shortcut practice, if emulated on the Computer, deprives it of vital information that it otherwise has no way of knowing.

Going back to the photocopier analogy of Perception, there is a "Master", and then there is a Copy Image of the Master, which will always have some "Error" associated with it; because it is not the Master itself that is produced, only a Copy, whose Reproduction will always be imperfect in some way. Another term for this Error is "Accuracy", or its opposite sense "Uncertainty". Further, it is worth noting that not all Properties of a Perceived entity will React with the Perceiving entity, which also contributes to the Uncertainty of the Copy; hence, not all aspects of the Perceived entity are Perceived.

If it were possible by some process to "Compare" the Master with the Copy, then any "Significant Differences" could be detected.

This Comparison process would be affected by three things:

The Precision of the Copy.

The Accuracy of the Comparison process itself.

What Tolerance Level is used to judge that a Significant Difference Exists.

In practice the corresponding Statistical Values typically involved would respectively be:

The "Estimated" Percent Uncertainty of a given Master entity's Property for any Copy of it.

The Estimated Percent Uncertainty of the Master/Copy Comparison procedure itself for any given Master Property.

The Calculated Probability "p-value" that a Significant Difference Exists for that Property (for example for a 99% likelihood of a Significant Difference, p is said to be less than or equal to a 1% chance, or p<=0.01). This Calculation can always be inverted to state the Probability that a Significant Difference does NOT Exist for a given Property.

Notice that the term "Significant Difference Exists" contains the word "Exists". Thus, the Existence of a Significant Difference is itself a Perception. Further, by analogy it can be deduced that Perception itself can be expressed as an Uncertainty-Dependent and Probability-Dependent Statistical process.

On a related topic, when discussing the subject of Natural Perceptions, those with a Philosophical inclination may think about that age old question, "Where did it all come from? How did this Reality come into Existence?" The current answers typically come from two camps: Religious and Scientific. The Religious camp will typically ascribe all Existence to a God, but that begs the question as to how God came into Existence. The Scientific camp typically aschews such deistic explanations, and instead simply accepts Existant Reality as a given, essentially saying, "It is what it is", and proceeds with investigation; but which unfortunately also begs the Existence question. So, for the record let's detail how this subject is thought about in SAGOE, producing a terminology for it. To start with it is important to think about possibilities Existing before our Perceived Finite Reality came into Being.

This logically falls into two types:

Nothingness Existence, which is akin to the current idea of the void of Space, specifically containing no Objects of any kind, also being at motionless rest, which implies that no Reactions are possible, precluding the primary Reaction requirement to produce any Perceptions.

Infinite Existence, which can be envisioned as a continuous smeer of materiality, but whose Granularity is Infinite, meaning Indivisible, which implies a Static State in which nothing happens, hence no Reactions and no Perceptions are possible.

Given these two logical possibilities it seems reasonable to think that Nothingness cannot lead to somethingness in any way whatsoever; however, this could be false, since one type of Nothingness logically has exactly the same Granularity as any other type of Nothingness. So, it is imaginable that Nothingness Existence could give rise to a sort of Infinite Existence by in effect parsing itself. This is like saying,

"Infinite Existence Is Nothingness Looking At Itself".

The point of this is a way of positing how Infinite Existence could come into Being from Nothingness. In any case positing the starting Existence of Infinite Being no matter how it arose, it is imaginable that Infinite Existence could give rise to Finite Existence by in effect parsing itself. This is like saying,

"Finite Reality Is Infinity Looking At Itself".

This leads to speculation that many types of Finite Existence could come into Being at any time.

Finally there are two types of Finite Existence:

Perceived.

Unperceived.

This is personal in nature, since for any Perceiving entity it is by definition required that it Reacts with some manifestation of a Perceived entity, and Reactions between any two entities is not a guarenteed phenonmenon, depending on the Properties of each.

This was an introduction to SAGOE architectural concepts of Natural Perception. Much more will be said about all the above topics as the overall discussion of SAGOE proceeds.

Human World Perception. (The special case of Natural World Perception reported by Humans, which can also be Enhanced by Devices.)

When discussing the special case of Natural World Perception that Humans enjoy; the topics of "Memory", "Recall", "Recognition", "Learning", "Thought", "Consciousness", "Cognition", "Documentation", and "Measurement" arise. These are discussed and represented symbolically as follows:

Although it is possible to ascribe many of these qualities to other organisms, Humans are uniquely aware of these gifts, and use them to great advantage (or disaster). In particular it is readily evident to all that Humans have conceived, constructed, utilized, spread, and bequeathed tool-making "Technology" over the Ages to a far greater extent than any other living species on Earth. While these tools have most frequently been used to remediate inconvenient or dangerous living conditions, they have also been used to extend the range of Human Sensory Perception.

In particular, during the last 500 years, Scientific Guilds have used tools in the form of "Instruments" or "Devices", to make Measurements with ever greater Precision, and use them to construct Theories and Laws of Universe Behavior. This process in turn has lead to an acceleration of tool-making at an ever-increasing pace, as one discovery leads to another. The proliferation of this cycle throughout the civilizations of the World has resulted in an exponential "Technological Growth Curve", whose unregulated outcomes are leading to wide-spread reduction in the number of Species, and ultimately even the destruction of most Life on Earth (including Humans).

For example there are currently at least ten well-known possible sources of annihilation, where any one could do the job, but they all appear to be working happily together (Climate Change, Nuclear Holocaust, Perpetual Conventional Warfare/Genocide, Biotechnology, Ecosystem Collapses, Pandemics & Chronic Diseases, Medical System Failures, Economic/Governmental Anarchies, Nanotechnology, and AI/Robotics); not to mention a couple of pending Natural ones (Asteroid Impact and Super Volcano), which could, but might not be addressed, due to Global Human lack of cooperation. The problem may not be Technology itself; but Humans inability to monitor it, reliably predict its negative side-effects, and quickly obtain universal agreement on its control through concensus.

Hence, my belief in the need for a Computer Simulation Architecture that can be in the hands of all persons to monitor, predict, and direct Technology.

Network World Perception. (The very special case of Natural World Perception created by Humans, which includes all the Digital Devices on Earth, and all the Communications Networks connecting them together. Further, within each Digital Device is a "mini-Network Bus" connecting all its components (typically semi-conductor chips) to each other; and within each Digital Device component is a "micro-Network Bus" connecting all of its internal sub-systems together. This special case of Perception can be represented by a Signal Model that has Transmission and Reception as its functional foundations.)

The SAGOE architecture is designed to support all three above types of Perception (Natural, Human, and Computer Network).

If you happen to be a Functional Genetics Aficionado, it may have naturally crossed your mind in the above previous section, that the stated Unifying Principal of SAGOE, "REACTIVE MOVING OBJECTS", which almost any Human can probably relate to, is a direct consequence of Human Perception, which in turn is controlled by our genetic make-up. Our genetic make-up is configured specifically to view our surroundings automatically in useful ways and thus help us survive in the context of "Space-Station Earth".
[BTW: Did you notice that I wrote "Space-Station Earth" instead of Buckminster Fuller's "Space-Ship Earth"? If so, did you wonder why? I note that Earth is technically not a "Space-Ship" as Buckminster Fuller called it, because the Earth is a captive orbiting body going around the Sun, having no impulse thrusters, that can allow it to escape its orbit. In this sense it is more like the International Space Station, although that entity does have some thruster capability that allows it to adjust its orbit a little. This is stated with my deepest apologizes to Buckminster Fuller, a thinker I greatly admire; nonetheless, his consequent principals of suggested behaviors to the inhabitants of Earth apply to a Space-Station just as well as they do to a Space-Ship, "Take very meticulous care of its functional systems upon which survival in the void of Space depends."]

Anyway, as the Artificial Intelligence (AI) community has become so painfully aware, many of our native abilities are "hard-wired" into our bodies, and do not require learning. This is the challenge in creating Androids, reproducing all those hard-wired circuits to avoid doing it all in software. The point of this comment is to make it clear that the above stated Unifying Principal for our Universe is likely a captive of our hard-wired Perceptual being. This means the "true" nature, or other alternate natures of our Universe, may be beyond our Perceptual capabilities.

(B) - "A reasonable conjecture to make, based on our Human Perceptual experiences, is that if Objects did not Move or React, then they would not be Perceived, and hence would effectively not Exist. Perception is the fundamental requirement for the determination of any Existence."

The nature of Existence is a subject that has occupied the minds of Humans perhaps for their entire history. For the purposes of SAGOE, a generalized simulation architecture, I posit the above statement, as a way of both dispensing with the subject and producing a useful design concept.

Given the simple statements in (A) and (B) above, and other common Human Perceptions, it is possible to make some general conclusions about the Universe, which are delineated in the UNIVERSE THEORY section that follows.

UNIVERSE THEORY I - COMMON CONCEPTS

Not all Humans Perceive the same "break-down" of Universe Architecture. So we must start with those basic Universe Concepts that most Humans Perceive naturally, and would likely agree about...

They are listed as follows:

Objects Exist. (An intrinsic aspect of Human Perception is that the Universe is filled with observable entities, that can generically be referred to as Objects. Objects appear to be of different Types on the basis of their various observable Properties that directly affect our senses. The most obvious Properties of Objects are their 3D aspects, which can be verified by the common experiences that Objects of any Type can be brought into immediate proximity of each other and compared side-by-side and rotated; easily revealing their different Shapes, Sizes, Skin Textures, Phase States, and Hardnesses. Representation of Object Shape, Size, and Texture Properties have been perfected on today's Computers, which can deliver Native 3D Polygonal Graphics. However, Object Phase State and Hardness Properties do not have Native Computer Representations, and so have to be Simulated using custom Computer Programming Language Algorithms, as is the same for most Physical Object Properties).

The Judgement Of Existence Or Non-Existence Of A Potentially Observed Object Is Relative To Each Individual Observing Object's Own Perceptual Experience. (An intrinsic aspect of Human Perception is the judgement that Objects in the Universe Exist or do not Exist at a particular time and location. The Perceptual judgement of Existence, or Non-Existence, can never be considered as absolute, only temporary or assumed; since what is now Perceived, or not Perceived, may become un-Perceptible, or Perceptible, in the future. For example take the historical case judging the existence of Atoms, which was not judged true in the Middle Ages, but is judged true now; or the case judging the existence of Witches, which was judged true in the Middle Ages, but is not judged true now.)

Objects Move. (by observation of their relative Location changes).

Space Exists. (An intrinsic aspect of Human Perception is that all observed entities have relative size. based on the observation of Objects Volume and Motion, there must be something for them to exist in).

Time Exists. (by observation of sequential changes in Object Locations within the Universe, termed History).

Objects React. (by observation of their Structural and Motion transformations, when coming in "contact" with each other).

Objects Are Composed Of Sub-Objects. (by observation of their various Reaction consequences).

Sub-Objects Have Their Own Motions and Reactions. (a logical corollary conjecture of how the Universe appears to work in general).

Sub-Objects Net Aggregate Actions Produce Consequent "Emergent" Properties, That We Perceive As Their Parent Object's Presentation. (a logical corollary of the nature of Sub-Objects).

Objects Appear To Come In Two Special "Classes".

Matter Objects (M).

Energy Objects (E).

(by general observation)

Matter Objects Appear To Be Held Together And Impelled By Their Possession Of Energy Objects. (From this viewpoint Energy Objects generally have been held to have no observable form; although this formless appearance is partly a consequence of historical observations and measurements, which used instruments unable to visualize, but instead inferred the presence of Energy.)

Some Energy Objects Can Be Observed Directly In Free Space Apparently Possessing Form. (for example Light).

More Often Than Not In Nature Objects Of A Non-Identical Type Appear In Mixed Groups And Move Together, As A Spatial Distribution, Termed Herein As "Heterogeneous Flux". (for example an Ocean or a Light Beam).

Objects Of An Identical Type Can Also Appear In Groups And Move Together, Usually A Result Of Human Purification Processes, As A Spatial Distribution, Termed Herein As "Homogeneous Flux". (for example a Filtered Water Flow or a Prism's Red Light Beam Fraction).

Objects Of All Types Appear In Special Forms Called "Phase States", That Are A Direct Consequence Of The Environmental Context That The Objects Exist In. (typically Solid, Liquid, or Gas).

PERCEPTION THEORY II - HUMAN METHODS USED TO DESCRIBE THE UNIVERSE

The following section is an attempt to delineate some of the detailed aspects of Human Perception, so that any required SAGOE software related to this subject has a firm functional requirement foundation, and can be thought about using a defined terminology...

Generally speaking, one fundamental statement that can be made about Human Perception is that:

"The Entire Universe Appears To Humans As A Reality That Can Be Described Using Various Basic Written or Spoken Techniques".

There is a sort of logical order to these techniques, possibly even reflecting their historical devlopment:

IMAGES. (Images are probably the earliest form of modeling what Humans Perceived in their world. Whether scratched into the dirt, etched into a rock, painted on a wall, drawn on parchment, or even molded into a figurine; early images reflected scenes of what Humans saw around them, and cared deeply about; often that was game animals being hunted. Early use of this technique was therefore functionally like a modern camera or photocopier. The techniques for making these Images were also handed down from generation to generation, thus preserving and perfecting the technology; and likely making it popular too. Image technology has been perfected on today's Computers into the Science of Editable Graphics. As a functional requirement, SAGOE must use the Java Computer Language to provide Graphics Editing in a generalized manner through a GUI, so that a User can Create and Edit Images for any purpose.)

SYMBOLS. (Once the technique of making Images was perfected, Images started to be used to convey Pictures that Humans created in their own minds from more extradinary sources than game animal scenes. Such special Images are called Symbols. A Symbol is an Image that has a special meaning. A Symbol, like any Image can be Scaled or Distorted, as long as the reference is still clear. The earliest Symbols reflected Shamanistic rituals or other religious connotations. For example the Rock Art that can be seen throughout the Southwestern USA often depicts engaging Images of Shaman with lightening coursing through their bodies, wearing some kind of weird headress, and holding power implements. These Images are Symbols, because they held special meaning to their viewers. The main development that occurred over time was that each Symbolic Image was sacred for a particular meaning, thus preserving it as a special Image. This I believe lead naturally to later generations adopting the concept of a standard Symbol to convey a standard meaning, like an Alphabet Letter. Symbol technology has been perfected on today's Computers into various Data Standards in which each Symbol is represented by a unique Bit string. As a functional requirement, SAGOE must use the Java Computer Language in a generalized manner through a GUI to allow the "conversion" of any User-Created custom Image into a SAGOE-recognized Symbol for use in any context where a Java built-in Symbol would be usable.)

TEXT. (Once the technique of producing standard Symbols was perfected, and spoken language was common place, I suspect it lead naturally to the development of Symbols that represented an entire spoken word. I suspect such Symbols may have been more cross-culturally understandable than the various dialects and languages that were spoken; therefore such Symbols would be a powerful technology to expand, like a universal Sign Language. In any case eventually Alphabets were created. These were composed of individual Letter Symbols, each of which stood for a sound, that could then be combined in groups to form Words, such that when its Letters were pronounced, it sounded like a spoken Word in given language. Text technology has been perfected on today's Computers into various Data Standards in which each Letter Symbol of an Alphabet is represented by a unique Bit string Code, called a Character. These standard Codes are widely incorporated into special Data Entry Devices called Keyboards, that automatically reproduce the Code, and send it to an attached Computer, whenever the corresponding Key is pressed by a User. The same Codes can easily be produced by a Computer Program that effectively acts like a User Proxy. These received Codes then cause their corresponding Letters to appear on standard Display Devices, which are also attached to the Computer. In addition the Letter Symbols can be displayed in a variety of malleable, but still recognizable forms, organized into a standard set of Graphic Glyphs called a Font, whose output is controlled through the specification of standard options by a User. Finally through the use of special User Edit/Display modes, entire Documents can be created by the Entry of any number of Text Symbols along with other special Document formatting Characters and options. As a functional requirement, SAGOE must use the Java Computer Language in a generalized manner through a GUI to allow the "conversion" of any User-Created custom Symbols into SAGOE-recognized Text Symbols for use in any context where a Java built-in Symbol would be usable. [Developer's Note: Originally I believed that UNICODE would fulfill all of SAGOE's Text Symbol requirements, since UNICODE's stated purpose was to include all Text Symbols on the planet into one standard, and as as anyone even glancing at the standard can see, in fact it appears every Asian character ever used is part of the UNICODE set; but then I realized for some inexplicable reason the UNICODE foundation refused to include most of the Scientific Units Symbols, incorporating only a very basic set. This impoverishment would be a devasting blow for a generalized simulation system like SAGOE to depend upon, so SAGOE is forced to provide its own Text Symbol Table. This Table must incorporate both SAGOE custom-created Symbols and Java built-in Symbols, including any UNICODE ones.])

DIGITS. (During the time that standard Alphabet Symbols were being perfected, there was a concomminent need to have standard Symbols to enumerate Count. The full concept of Count is developed below, but the history of Count Symbols will be discussed here. There have been a large number of Counting Systems used throughout history. Each one had its own set of Symbols that represented Digits. For example the Roman Numeral System, which used Digit Symbols like 'I'=1, 'V'=5, 'X'=10, 'L'=50, 'C'=100, and so on. Regardless of the Counting System, its Digits are intercombined to encode Integer Count into some form of shorthand representation, which is always an encoded conversion of simple "Ones Count" (Tally Count, Unary Count, Base1); such that every Integer Count Total from (0-n), where n is the desired maximum Count, is represented without any interruptions. In modern times the only Count System typically used for daily life is the Decimal System (Base10, Digits 0-9). Decimal Digit technology has been perfected on today's Computers; such that along with the standard Alphabet Characters every Font includes special Digit Symbols, typically 0-9. These Digits are intercombined to produce Identifiers and Numeric Count, both of which are discussed below. Finally Numeric Bases of a higher degree than 10, like Hexadecimal (Base16) often used on computers, require extra Digit Symbols, but the extra Symbols required are typically taken from the Alphabet, specifically 'A'=10, 'B'=11, 'C'=12, 'D'=13, 'E'=14, and 'F'=15.)

IDENTIFIERS. ().

Units, Count, Scales, Measurements, and Uncertainties

Units. ().

Count. ().

Statistics. ().

Measurements. ().

The above Description techniques are all familiar elements in our lives. However,

PERCEPTION THEORY III - CATEGORIES

The following section is an attempt to delineate some of the detailed aspects of Human Perception, so that any required SAGOE software related to this subject has a firm foundation, and can be thought about using a defined terminology...

Generally speaking as the best concept for SAGOE modulization, and an elegant fundamental statement that can be made about Human Perception is that:

"The Entire Universe Appears To Humans To Be Infinitely Subdividable Into Arbitrary Categories And Sub-Categories."

(Where a Category is defined as a Named-Pattern, which functions as a Template for individually Named-Instances of that Category. Note, in the above statement the word "Arbitrary" was carefully chosen, implying that not all Humans perceive the same Categories. Note also in the following discussion that Categories are talked about both being directly Perceived as a natural consequence of Human Biology, or Created on the computer as Data-Structures. This is the meaning below, when used, of the phrase "...Perceived or Created...")

In the SAGOE Architecture a Category has some required Attributes, and many optional Attributes:

CATEGORY-IDENTIFIER. A Category's Primary-Name, and its Aliases, are its Identifiers. It is required to have at least an assigned Primary-Name; and optionally any number of assigned Aliases with Alias-Types like Titles, Abbreviations, Shortcuts, Tags, Codes, etc.

INSTANCE-PATTERN. A Category's Pattern is a required Attribute, that functions as a format specification for any Perceived or Created Instances of the Category. A Category's Pattern is like a Template, in which certain Terminal-Values are left open to assignment within a certain range of uncertainty. In its most primitive form this Template specifies a simple computer Data-Type. In its most complex form this Template specifies a Physical Object with any number of Properties.

IMAGE. When a Category's Template has fully assigned Terminal-Values then it is called an Image, where an Image has no further Variability. A Category itself can be an Image, which means all its Instances will be identical to it.

INSTANCE-IDENTIFIERS. A special required part of a every "Parent" Category, is to specifiy the Names of its "Child" Instances, or specify a special Pattern that controls the production of those Names. This is because every Instance of a Category must have their own Identifiers, which are also known as their Primary-Names. A Category-Instance can also have any number of optionally-assigned Aliases. In this way every Category-Instance has an Identification-Attribute that it "inherits" from its Parent Category.

SUB-DIVISIONS. A Category can have an indefinite number of Sub-Categories, and those Sub-Categories can have Sub-Categories, and so on. This "linked-list" forms a "Chain" or "Backbone" of nested Categories, that together prescribe further Pattern complexity, as each Category, and in turn its Sub-Categories, must be fulfilled with Category-Instances. Each "Child" Sub-Category functions like a Sub-Division of its "Parent" Category. This is how Humans Perceive the Universe; as being composed of arbitrary Divisions, which are composed of arbitrary Sub-Divisions, and so on.

FULFILLMENT. Note that a Category or Sub-Category must be fulfilled in its entirety at the time that an Instance of it is either Perceived or Created. However, the fulfillment of the individual Sub-Divisions in a "Chain" of Sub-Categories can be delayed. For example a Category might be "Corporate Headquarters", which only has one Instance, "Armstrong Inc". Sub-Categories of this might be "Corporate Divisions", where Instances of this could be "Europe", "Africa", or "USA".

UNITS. In this sense of being a Sub-Division, a Category is also a Unit, whose Pattern dictates Instances of the Unit. Note that the Parent Category ??? Units in turn imply Countable Instances of the Unit. Further, a Unit is also a Sub-Division of an Object, where a Property of that Object can be Measured (Counted, Quantified) in that Unit. Finally a Unit is also a Scale, where Instances of that Unit combine linearly into a sequentially aligned set creating a Measurement Ruler.

UNIVERSE THEORY II - MATTER/ENERGY

The following section is an attempt to delineate some of the Measurement aspects of Matter and Energy, so that any required SAGOE software related to this subject has a firm foundation, and can be thought about using a defined terminology.

OBJECT TYPES, CLOSURE LAW - Objects appear to come in two special "classes" based on their motions, but nonetheless appear to be equivalent by dint of the Relativistic equation E = MC²:

MATTER OBJECTS (M) - That which is traveling at a Velocity (V_M) less than the Speed of Light C (V_M < V_C), and possesses the Property of measurable Mass m (m_M > 0).

ENERGY OBJECTS (E) - That which is traveling at a Velocity (V_E) equal to the Speed of Light C (V_E = V_C), and possesses the Property of being Massless (m_E = 0).

OBJECT REACTIONS, LOCAL CONSERVATION LAW - The grand total of Matter and Energy appears to be Conserved in Reactions. Historically speaking, experiments that measured both Matter and Energy were constructed, such that those measurements that were deemed representative of Energy, and those that were deemed representative of Matter, was mostly a case of experimental convenience; but the definitive result of all experiments was that Reacting Objects, and their subsequent Product Objects, always had measured grand totals of Matter and Energy, that were equal. This is interpreted to mean that all Reactions must result in the same totals of Matter and Energy for the Reactants and for their Products, although distributions of Matter and Energy can be different. This was historically called the "Law of the Conservation of Matter and Energy in Reactions". This law has been recently proven to be true, as long as one does Relativistic calculations of Matter and Energy. So, I restate this law for the purposes of computing to be the "Law of the Relativistic Conservation of Matter and Energy Objects in Reactions".

OBJECT REACTIONS, UNIVERSE CONSERVATION CONJECTURE - The grand total of Relativistic Matter and Energy Objects appears to be Conserved, not just in individual Reactions, but in the entire observed Unverse. This is a conjecture that can be inferred from LAW2 and other observations. This means that the Relativistic totals of individual Matter Objects and indivual Energy Objects can be different (partioned differently), but their grand totals must always be a constant. This assumes that there is no addition or loss of Matter or Energy objects to or from the existing Universe, meaning nothing comes from or goes into the void of SpaceTime. At this point in history there is no sure way to measure this everywhere, except locally where it is deemed to be true, so it is a working assumption until proved otherwise.

UNIVERSE THEORY III - SPACETIME

The following section is an attempt to delineate some of the aspects of Space and Time, so that any required SAGOE software related to this subject has a general set of goals and a firmer foundation.

Note that it is easy in today's software to treat Space as 3D, because algorithms exist in software to make that manifold possible in standard units and behaviors. It is easy to treat Time as 1D, because algorithms exist in software to value Time, using standard units. But, in a more general framework, if Space and Time are to be treated as n-Dimensional manifolds, which Theoretical Physicists say must be considered to explain certain particle observations, then extra Dimensions beyond the standard ones must be custom-introduced into the software application.

A quick-thinking Physics Application Architect might conjecture that for this purpose each Dimemsion could be custom-implemented as an independent axis, and inter-combined in some algorithmic way, rather than using the standard built-in 1D-Time and 3D-Space software functionality. Certainly it would be desirable to implement SAGOE, so that this was possible.

On the other hand a high-level Physics Mathematician may conjecture that some form of Riemannian Geometry, Minkoski SpaceTime, or even Generalized String Theory, implemented using arrays, would do the trick. Probably. But then this would violate a primary SAGOE goal to avoid mathematically engineered solutions that result in one isolated software application. Nonetheless, certainly it would be desirable to implement SAGOE, so that this option was not precluded.

Beyond all this, if Space and Time themselves are treated as Objects, then they may be optionally treated as being Reactive, which might be an interesting experiment to perform. Certainly it would be desirable to implement SAGOE, so that this was possible. In addition for the sake of modular centralization of functionality, it also makes sense to treat Space and Time as Objects, so that one Object data structure could represent all required entities.

Since Objects can contain Sub-Objects, and all Objects possess the Property of Volume, and Space has Volume too, and all Objects must be Located in Space; then Space may be treated as an array of "Space Unit Objects" (a manifold), which in turn contains the Physical Objects. In this configuration Space could seamlessly React with its component Physical Objects. Analogously Time may be treated as a vector of "Unit Objects", which each contain a Space array manifold, which in turn contains the Physical Objects.

Thus it is desirable to implement a generalized Object structure that can be a Space Unit or a Time Unit or a Physical Unit; and possesses any kind of Physical Property; but especially Motions, Reactions, and Sub-Structure.

UNIVERSE THEORY IV - FLUX

The following section is an attempt to delineate some of the aspects of Flux, so that any required SAGOE software related to this subject has a general set of goals and a firmer foundation.

Now returning to my orginal discussion of Flux, started before my above digressions; note that the concept of "stochastic flux", which for example is commonly utilized in Statistical Thermodynamics to explain the "emergent properties" of molecular systems, is not meant herein to preclude the prediction of a simple momentum type of flux by one object, like a baseball. The two circumstances are not mutually exclusive, and must be treated as separate parts of a uniform "flux handler".

However, here are some common examples of "stochastic flux". In climate models, flux refers to mass and energy movements between localized areas of the environmental system (here's a good illustration). In Pharmacokinetics, flux would be defined as the predicted changes in drug concentrations within compartmental spaces, during a treatment course. In a cell model flux would refer to movements of molecules between its sub-cellular spaces.

In all three of these different spatial scale cases, fluxes are currently simulated mostly by "raw-code" (C or Fortran) block-subroutine models that solve systems of differential and algebraic equations, using a mixed bag of numerical methods, and outputting raw data result files (for example like the NASA model I worked on called SiB (explore this web page's links), which was embedded within a General Circulation Model (GCM) called the Colorado State University GCM (CSUGCM) (it's obsolete software now - here's one usage reference).

Such approaches require significant constraint on the software application and computational problem spaces to fit the numerical techniques.

It should be noted that use of the concept of "stochastic flux" of populations of a common object type, is really a convenience of human perception and computational optimization. Within any population that can be treated as a statistical distribution (or swarm), are individuals exhibiting individual motions, which together produces an aggregate emergent behavior of the population as a whole, that can be captured by one or a set of related equations.

Technically in SAGOE, it is desirable that such aggregate equations be generatable, using a simulation sub-system that predicts individual behaviors, and then creates a summary aggregate result "trained" by comparison of simulated values to measured values, for general use in a larger-scale simulation.

Additionally, if SAGOE is to implement Object Populations represented as "Stochastic Distributions", then SAGOE must also have a way for a Distribution to algorithmically interact (React) with any Individuals, or other Distributions, that it comes in contact with. This is of course what happens in Nature, so it makes sense to have the capability in SAGOE; but this is a special challenge, as no such Mathematical discipline exists to my knowledge, that can be leveraged. A similar Mathematical difficulty is evident for the serial propagation of Uncertainties throughout the course of a simulation, which poorly addressed situation is only worsened by the Uncertainty requirements of Stochastic Distributions.

MISCELLANEOUS INCLUDED FUNCTIONALITY:
In SAGOE's design framework, 3D image or 4D movie visualizations, using correct spatial mappings, are planned to mostly replace "data file only output".

Further, in SAGOE's design framework strict differential equation systems are intended to not be required, allowing reactions with miscellaneous objects to be added at will (for example astral body gravity, receptor binding, cell transport, transcriptional activation, nervous system response, or enzymatic biochemistry). Equations are entered into the system in a reaction format that predicts changes to either Object Translocation and/or Object Transformation. Internal and external reactions for individual Objects are triggered by detection of specific object-patterns in the immediate space-unit environment, during each timestep. This emulates the behavior of our Universe

The entire Model/View is available to the user at two seamless levels of presentation complexity:

Simplified - Any combination of quantitative summaries (like values, records, forms, charts, and tables).

Complex - 3D graphical worlds (like a functional anatomy); or 4D time-step sequences of images cast as the frames a movie (like a historical documentary).

A zoom-in feature focuses simulation compute power to local scopes for detailed study such as cellular-level or molecular-level interactions. For optimization purposes a system monitor feature can observe and recast the local reaction phenomena into a simplified summary reaction pattern for computationally efficient use at zoomed-out levels. This is where generalized solution Artificial Intelligence (AI) techniques like Genetic Algorithms, Neural Networks, or Markov Models can be usefully plugged in.

SOME TECHNICAL COMMENTS:
Keep in mind that SAGOE is currently principally still a design. That's not to say it is entirely vaporware. Much of its components are working now in Java 8u171 along with its companion version of JavaFX/3D. A sophisticated Graphical User Interface "GUI front end" has been completely programmed and debugged. Much of its internals have also been implemented. All of its features have been tested one way or another using code fragments. However, these components still have to be stitched together and proven to work as an integrated system. The devil is in the details, as is often the case with the software development of generalized systems.

Here are some of SAGOE's unique technical features, which are targeted to fill the functional niches left untouched by many current simulation technologies...

The SAGOE system is founded on a hierarchical Time-Space-Objects-Database (TSODB). This requires a 3D display sub-system, which fortunately became natively available since Java 8.

SAGOE's design avoids using a core set of "Prognostic" differential equations with an associated equation set solver, as is true of most large data models; where typically each Timestep's Prognostic phase is followed by a miscellaneous set of "Diagnostic" phase equations that depend on the Prognostic outcomes, but were not actually part of its differntial equation set; so Diagnostic phase errors can occur, that are typically resolved in the code based on customized trial-and-error approaches. Meanwhile, creating the core "Prognostic engine" is essentially a custom engineering problem in itself, requiring the help of specifically trained mathematitians.

All of these specialist customizations preclude the simulation domain from all but a rarefied breed in Universities and Corporations. To get around this handicap, and open up the large-scale simulation world to a much wider audience, SAGOE is designed to allow adding of any set of equations to the simulation being constructed, and then SAGOE automatically makes them work together, or helps the user decide which equations are incorrect. SAGOE also provides a large body of standard objects and equations the user can select from.

Among other things each equation's numerical values must be pre-defined during a simulation's configuration stage with an:

Optional conservation requirement.

Assigned value range.

Assigned units.

Assigned uncertainty.

These are then used by SAGOE's automatic numerical solution solver. In a nutshell the course of the solver is controlled at the end of each Timestep by detection of:

Violations of conservation of expected final "conserved-objects" count.

Violations in allowed value ranges of calculated object properties.

These are the two most common mathematical violations that can occur during any kind of simulation, no matter how it is engineered. Such violations presumably occur, because some equations are incorrect or insufficently accurate. When a violation is detected, SAGOE's solution solver "back-tracks", and attempts to apply automatic corrections. Common corrections that are iteratively applied until violations no longer occur (or the system gives up) include:

Automatic redistribution of non-conserved quatities.

Automatic localized subdividing of the Timestep and/or affected Spatial Grid Units. This functionality could be referred to as "sub-grid-scale" allocation.

The solver also calculates the "Percent Uncertainty" of all predicted outcomes, which is an uncommon, but desparately needed feature in simulation technology, to increase the believability of simulation results. For example many non-sayers to Climate Modeling results will point to the lack of accuracy estimates by the models; which depend instead on trial-run spot-check comparisons of simulated values to known measured values, suggesting the overall confidence one can have in the model; as opposed to starting with estimated uncertanties of all input values, and then "carrying along" estimated uncertainties for all calculated vaues.

In general the use of a generic simulation architecture within SAGOE allows detection of independent code sections, which in turn allows the automatic disintegration and submission of independent threads for parallel computation.

An extensive library of physical objects and their reactions are part of the system.

Pattern creation and pattern processing are a special feature available throughout the system, leveraging use of the TSODB.

Configuration of all entities within the system are set up entirely through graphical user interaction.

CONCLUSION:
Historically research scientists have gained powerful insights and productivity improvements whenever they have been able to model the interactions of complex living or non-living components in a more visually realistic form. That is one of the main purposes of SAGOE's design. Another purpose is to bring the power and insights of physical simulations to a much wider audience. Ease of use should also benefit the current body of simulation professionals with productivity improvements.

Currently, I am implementing a prototype, now using Java 14, targeted for release near the end of 2021.

Last Updated by Greg Colello on January 31, 2021.