Introduction to the GGU and GID-Models

Robert A. Herrmann, Ph.D.

Articles on this website cover various topics. Many of them cover the General Grand Unification Model (GGU-model) or its intelligent agent interpretation - the General Intelligent Design Model (GID-model). These articles vary from the most general through the technical. There are certain basic concepts that are easily understood and are needed for significant comprehension. What follows is presented in stages, where one need not consider a particular stage if the concept is known. This article should help one better understand the GGU-model cosmogony and the GID-model. Of great importance is that the GID-model shows that every physical entity and every physical behavior within any purposed universe is the product of identifiable intelligent actions.

Mathematical Models

Consider symbols F, G, M, m, R, =, /. In mathematics, the symbols F, G, M, m, R have no non-mathematical "meanings." Consider writing these symbols left-to-right in the form FRR = GMn. There are specific rules and a standard everyday mode of logically thinking that allow you to manipulation these symbols and write F = GMn/RR. These symbols can be used, in another discipline, as measures for physical quantities. The symbols are abbreviations for terms, and phrases or sentences stated in a physical or, for the GGU-model, a physical-like language. Consider the language used in Physics and re-write the second equation in terms of that language.

"F" represents "the measure of the force of gravity between two objects that have mass.'' The "M" [resp. "n"] represents "the measure of the mass of the first body [resp. second body]." The "R" is a "measure of the distance between he two bodies centers of gravity." The "G" represents an assumed "universal gravitational constant."

The symbolic form F = GMn/R^2 reads (1) "the measure of the force of gravity between two objects is equal to the product of measures of the two masses times the gravitational constant G, divided by the square of the measure of the distance between the two centers of gravity."

Statement (1) yields a "mathematical model" for Newton's Law of Gravity, where F = GMn/R^2 is an abbreviation for (1). We physically "feel" forces. Initial mass and gravitational mass are equal in measure and this helps with a physical correspondence to the measure of mass. The R can be considered as a reading on a machine or as done prior to Newton as a geometric object. Nature does not provide these measures. These measure do not appear anywhere within Nature. But, this law leads to behavior that can be described in physical terms. It is this behavior that is observed in the physical world. The "mathematical" part preserves the classical rationality of such behavior.

Expressing mathematical symbols in terms of another discipline's language yields a mathematical model. The consistent substitution of such language terms for the mathematical symbols is called an interpretation. For physical models, one often interprets the expressions in terms of measures relative to machine observations. A better interpretation is one that uses only physical terms for mathematical symbols or physical terms for the physical behavior that is being interpreted via the mathematical symbols. Logically obtained mathematical statements, expressed in a physical-science language, yield Physical Theories. These are also called Physical Models. (Models have certain technical features, which are of no significance for this article.)

In physics and elsewhere, symbols can represent "processes." How the symbols are interpreted requires one to learn a different translation procedure than the one that results in (1). In the study of classical logic, the patterns allowed to produce a logical deduction from hypotheses can be written in process language form. We don't consider how the brain actually arrives at a written conclusion. But, these mental processes are "equivalent" to describable procedures, a describable physical process that also yields the same conclusion from the hypotheses.

In this article, to "rationally or logically deduce" requires a specific process. In a step-by-step manner, one writes down expressions using a fixed set of rules. The last expression in the list is "deduced from" or a "consequence of" the previous step(s). (There may be only one or even no previous step.) Usually, some of the steps use expressions taken from a set of hypotheses. The final step can also be classified as a prediction or explanation.

Let X represent any set of hypotheses and Y represent the set of all deductions that can be made using the stated fixed rules. Let the symbol C represent all the mental processes that are used to obtained Y from X. The rules state that if at a particular step in a deduction a statement y is deduced, then this statement and all that came before in the deduction of y can be used to obtain new deductions. (The notion as to what constitutes a deduction were first studied by Aristotle.) Hence, the processes "applied to" (hypotheses) X, yields the (deductions) Y. The symbols C(X) are a shorthand for "all the things deduced from the hypotheses X using the rules of deduction represented by C." This quoted phrase is considered as a basic characterization for the members of the set C(X). Members of C(X) can have many additional characterizations as well. In the notation C(X) = Y, one can consider Y as but a new symbol for C(X). This symbolism itself can be stated as "C applied to X yields Y.''

As an example of a rational deduction, consider the three statements, "If it rains, I'll stay home." "If I stay home, I'll watch television." "It is raining." "Therefore, I'll watch television." The last statement is deduced from the previous three. The word "Therefore" indicates that a deduction has been made. There is one "rule of inference" used to deduce the last statement. Although for this article the rules of inference are those used by the physical-scientist, the mathematician, and almost all humankind, the rules of inference are usually not specifically stated. However, an in-depth analysis can reveal what rules are being applied.

But, where does the mathematics play a role? Suppose that one now uses Y to represent a set of hypotheses. Let z be a statement deduced from Y by the same processes. That is, z is a member of C(Y). Deduction is a finite process. Hence, there are only a finite number of y's taken from Y that yield the z by application of the same logical processes as denoted by C. But, only a finite number of members from X are used to deduce each y since C(X) = Y. One can substitute for these y how they are deduced from X. This yields a finite list of statements contained in X and from which z can be deduced from X by the same logical processes denoted by C. This is what one means by deduction from X. Thus, z is a member of C(X) = Y. This is what happens in high school geometry. A theorem can always be traced back to the original axioms. That is, in this case, if z is a member of C(Y), then it's also a member of Y. How can we write this symbolically?

Let's consider C(Y) = Y. Set "equality" means that if z is in C(Y) ("in" means that z has the same characteristics as members of C(Y)), then it's in Y and if z is in Y, then it's in C(Y). Well, one-half of the requirement was just established. The fact that the members of C(Y) are members of Y. So, we need to consider any y in Y. Well, all of the rational processes being employed allow us to take this y and consider a single step deduction. That is, trivially, we can deduce y from Y. Hence, each member of Y is a member of C(Y). So, we now have the result that C(Y) = Y.

But, by symbolic substitution, this yields the form C(C(X)) = C(X). Now notice that X is any set of statements taken from the language being used. So, this "form" holds for all sets of hypotheses. What form? The form CC = C. This form shows a relation between the processes used to deduce. The term one uses for this form is that C is an idempotent operator. This form leads to various pure mathematical statements that, after the theorems are "proved," lead to new interpreted results about human forms of logical deduction.

I point out that in quantum theory the physical processes that lead to a "simple observation" have the same idempotent pattern.

Analogue Models

Many physical (mathematical) models are analogue models. Such models are mathematical models in that they use terms that correspond directly to objects within a mathematical theory. When interpreted in physical terms, they describe observable physical behavior. The mathematical symbols need not correspond to actual physical entities.

Consider the important mathematical theory called Linear Algebra. Objects in this theory are called "vectors." Specific types of vectors can be interpreted as geometric objects called (free) direct line segments. These can be considered as objects drawn on a piece of paper. So, they are real in that sense. The abstract algebraic processes can be interpreted in that one can "move" these lines segments about the surface of the paper and attach them to certain points. So, we have a type of "geometric" intermediate model. For one physical interpretation, the length of each line segment is the magnitude of a force, and the direction (usually an "arrow" notation or the left-to-right ordering of point names) for this directed line segment is the direction in which the force is applied. These line segments are not attached to the physical object affected by the force. Hence, they form for a type of analogue model for behavior. This "vector" approach is used to such a degree that one often overlooks the fact that such vectors do not appear in Nature as physical objects.

The bar-graphs and pie-charts used by various businesses are analogue models for behavior. Since there is more than one device that measures the length of a time interval, then each physical clock can be considered as an analogue model that models the behavior of an entity termed "observer time."

In particle physics, there are many objects that are claimed to exist but cannot be observed. What is observed is how gross matter is predicted to behave if influenced by these assumed objects. Many of these assumed objects can be considered as mere analogue models for what we cannot otherwise comprehend since other entities such as propertons can produce the same predicted results. Thus far, the particle physics-community has not realized that their mathematical models may be only analogue in character.

In the GGU-model, the physical-like objects that carry the "ultra" prefix can be consider as analogue in character. It is the behavior of these objects that is translated into behavior for physical objects. The behavior for the "ultra" objects is similar to the behavior of the object with the name to which the "ultra" is attached. For analogue models in general, whether the described but unobserved entities exist in some type of reality is a philosophic stance.

Modern Cosmologies

A modern cosmology is a mathematical model, a physical model, logically deduced from a set of hypotheses. Such a physical theory claims to describe how physical laws yield the step-by-step physical development of objects contained within a universe.

There are, at present, many such cosmologies. For example, (A) The Big-Bang, or Standard Model, (B) The Modified Big-Bang, (C) The Quasi-Steady State Model, (D) The Many-Worlds, (E) The Infinitely Many Branes Model.

Certain of these cosmologies claim that they are eternal in that the cosmology has no beginning and no ending in "time." They have "always" existed. These cosmologies all have, at the least, one feature in common. They all claim to predict every observed aspect of our present universe.

A Cosmogony

For this website, a cosmogony is a scientifically rational description for how cosmologies come into being, how they are generated from more fundamental objects or processes. Prior to 1979, a cosmogony was a general philosophic or theological description often using other modes of logical discourse.

The mathematics used to produce such cosmologies as (A) - (E) is called standard mathematics. Beginning in 1979 and using the exact same philosophy of science that produces these cosmologies, the only known mathematical model for a cosmogony was developed. This is the GGU-model. For technical reasons, it is necessary to use a new (as of 1961) mathematical approach termed "Nonstandard Analysis." The term "nonstandard" is a technical term for objects that mathematically exist within modern set-theory. These objects are the "nonstandard models." Hence, these new mathematical methods are all consistent with the standard methods. Indeed, nonstandard analysis includes all of the standard analysis used by the physical-sciences.

The mathematical GGU-model has, at least, three interpretations produced by word and phrase substitutions. The first is the secular interpretation where the symbols correspond to physical terms.

The second interpretation is the General Intelligent Design (GID) interpretation where the symbols correspond to intelligence actions. That is, the GGU-model has mathematical objects that have characteristics that when interpreted describe behavior of an intelligent agent. Nonstandard analysis is the only known mathematical approach that allows a "higher form of mental activity" to be compared with mental activity displayed by any biological entity within a universe.

The third interpretation is a theological identification of the modeled intelligent agent.

The GGU-Model

The term "general" used for the GGU-model signifies that it uses the methods of physical science, in particular, the methods for mathematical modeling and that the results apply to every known and named cosmology as well as others. However, the GGU-model does not assume that there existence entities or processes that are not directly observable. This is a highly significant fact. Further, it predicts each of the cosmologies (A) - (E) and many more. The GGU-model predicts the existence of a background or substratum world not considered as part of any cosmology. Indirect evidence is used to verify its existence. Relative to creationary science, it rationally predicts all known creationary models. Consequently, the GGU-model is a type of scientific "ultimate physical cause."

For many years, it has been claimed that a strict interpretation of Genesis 1 could neither be a rational description for how our universe came into being nor could it explain how it evolves. The generated GGU-model creationary model described in my belief statements counters this claim by predicting that every physical event that can be observed today yields indirect evidence for the acceptance of the Genesis account. "Indirect" evidence is the major concept physical scientists use to state that assumed or predicted entities or processes, which cannot be observed, are the cause for an observed event. Acceptance of a set of unobserved hypotheses is based upon various factors including the accuracy of the observed predictions.

It is difficult for many scientists who deal with theoretical constructs to comprehended how the GGU-model can be considered as empirical science and yet predict a complex world that cannot be directly observed and from which our complete physical world is predicted. The fact is that this is how the mathematics itself behaves and scientists use notions from this substratum world to calculate, via forms of the Calculus, almost every aspect of physical behavior and have simply not completely realized this fact.

Technically, a universe is generated by a fixed set of processes applied to a physical-like entity. For the book "Science Declares that Our Universe IS Intelligently Designed" the basic entity is called an "ultimate ultraword." This uses a "bottom-to-top" reductionist approach. This approach, as used in this book, considers a universe as a vast collection of less complex natural-systems. An ultimate ultraword unifies all of the defined physical (natural)-systems. Many articles on this website and at arxiv.org, use a basic ultraword not based upon the arbitrary definition of what constitutes a physical-system. In this case, such a partitioning may be used for specific investigations. Unless otherwise identified, the term "ultraword" used for an entity that yields a specific universe should be considered as either of these two types of ultrawords.

On this website and elsewhere a new method is described, a top-down-approach, that does not employ a collection of physical systems as the composition of a universe. The predicted ultraword approach is still employed along with other predicted "ultra" objects. When interpreted as the General Intelligent Design Model (GID-model), this new approach gives more details as to the behavior of intelligence agency in forming a physical universe. The new method also includes new ideas such as the notion of instruction-information, a type of substratum physical-like law.

GGU-Model and Choices

Although one can choose the GGU-model as a type of ultimate cause, some other description can be chosen as an ultimate cause. However, one may be convinced from other evidence or from the requirements of a belief-system that there is no ultimate physical-like cause. Such choices are often convictions about matters that cannot be observed.

Pseudo-Science and Creationary Models

Since the construction of the GGU-model and how evidence verifies this model follow all of the same rules as those used for the construction of secular scientific cosmologies and empirical science, then each GGU-model generated creationary model is not pseudo-science as has been claimed. Due to this fact, the predictions made by this creationary model can be compared, in a scientific manner, with secular model predictions. In particular, they can be compared with the predictions made by models that employ an evolutionary mind-set.

A Higher-Intelligence and The GID-Model

The word "General" in the phrase "General Intelligent Design (GID)" signifies that the results include all other known forms of "intelligent design" and others. Many general descriptions on this website, such as index #10, describe a special type of design that relies upon the notion of a "higher-intelligence." The mathematics used allows for comparisons to be made.

Scientists use fixed procedures to construct, via deduction, a physical theory or to correspond data to a physical law and to verify that the data satisfy the law. The logical procedures can be analogue modeled via a mathematical model. Moreover, there are other mental processes used by intelligent beings, such as choosing objects for a specific purpose, placing a list of statements or objects into a specified, making an orderly deduction order and combining basic objects to construct a more complex object. For example, choosing the set of all "clubs" from a deck of ordinary playing-cards and then arranging these 13 cards in their standard order, or taking pieces of wood and other material and building a doghouse. Then there is the process of placing noodles in boxes, these boxes into larger boxes, then the larger boxes into another box, a truck. Certain mental processes of these types are modeled mathematically. Each of these processes can be characterized by a small list of statements.

For different individuals, the mathematical processes used allow their mental processes to be compared. The processes used by the GGU-model to produce a universe have characteristics that imply that the processes are intelligent actions and that they are designed and applied by an intelligent agent. These characteristics are called "ID-signatures." An ID-signature is displayed when each process is applied. Each process satisfies certain statements that characterize the most general aspects associated with intelligent actions. This fact is interpreted to mean that an application of each process is an intelligent application.

Each process is "represented" by an "operator," or simply a "symbol," which displays additional intelligent design characteristics. These operators are either "finite consequence operators" or represent what is called a "logic-system." Mathematical logic is used neither to investigate how a human brain functions physically nor how it actually combines its physical components to produce a deduction nor how it actually combines words and symbols to yield a deduction. (In what follows in this paragraph the symbols are, as usual, abbreviations.) A specific rule for deduction has been accepted for thousands of years. Suppose that you are given a fixed domain D. (1) You have learned the statement "If A occurs, then B probably occurs." (2) So, you see that A occurs. (3) Then you "know," you deduce, that B will probably occur. However, we don't known how we actually arrive mentally at this deduction but without this process we can't perform in our technical world. This process is modeled and forms a basic process within the GGU-model.

Indeed, you can understand how it 's modeled. Write the set of three members {"X occurs," "Y probably occurs"}. Now there can be other such sets of this type put into another set K. Now take the statement "A occurs" and look at the sets in K and when you find one that contains "X occurs" then deduct that "Y probably occurs." But, actually, the X and Y can be specifically described events. So, the set K should be expressed in terms of the actual events. Hence, for an actual event A, you might deduce that many actual events B probably occur. Then you are allowed to use the deduced B to obtain other By the way, this search process is an actual process that one needs to apply if, as mathematicians and logicians do, you want to write a "formal" proof as required within certain portions of Mathematical Logic.

The searching and deduction process is easily characteristics and is mathematically modeled in a general way for the GGU-model since the members of K look like this {A,B}, {B,C}, {C,D} etc. You start with A, which is included in the set of deduced objects, then you can write the an Y is deduced from X if and only if Y is a member of the set {A,B,C,D, . . .}. Then you can model the "order" in which this deduction is made by first numbering the members of each of the sets with but two member, like {A(1),A(2)}, {A(2),A(3)}, {A(3),A(4)}, etc. So, when they are deduced, the order is the same as the order of the set of numbers 1,2,3,4, etc. This also can be characterized by a statement involving relations between the natural numbers 1,2,3,4,etc. I generally don't include these more formal characteristics when discussing the mathematical model since they are rather "trivial."

Individuals employ a basic form of mental activity to all known forms of physical-science deduction and induction. The example above is a formally presented general logic-system and is composed of a collection of specific objects, the general rules of inference. To obtain a consequence (prediction or conclusion) as illustrated by, an informally described general process, the algorithm, is employed. This algorithm requires that specific mental activity be applied. Applications of this same algorithm are required to obtained the formal deductions investigated within mathematical logic and, for physical-science, applications of physical laws and physical-theories. The general rules of inference can vary. For example, each of the general logic-systems that mimic classical-logic differs only in their general rules of inference. The algorithm is fixed and has a characterizing analogue model in that it can be formally characterized. (See algorithm.htm for an informal description.)

The algorithm requires one to make simply intelligent "choices." Mental "choice" is a major indicator of intelligence. Hence, as viewed from the material or substratum-world, the "mental" processes required to apply this algorithm constitute the ID-signature for a general logic-system. Each finite consequence operator is constructed by application of this algorithm. Hence, each such operator is intelligently designed. This type of ID-signature is interpreted to mean that all of the GGU-model operators are intelligently applied. This ID-signature coupled with the fact that the operators are intelligently designed indicates that any physical patterns these operators produce are also intelligently designed.

In all cases, for the GID-model interpretation, the complete way that a higher-intelligence actually yields all physical behavior is not observable. For a higher-intelligence model, the algorithm is informally interpreted in terms of what would occur if the algorithm were formally characterized. It is applied to an extension of the original general rules of inference. These higher-intelligence processes are predicted and symbolized by hyper-operators. When each hyper-operator is applied and the collection of results examined, then this collection contains the original operator's results and many more. The ID-signatures that characterize the higher-intelligence yield an analogue model for what is not observed. The basic method is that indirect evidence verifies the existence of a the predicted higher-intelligence.

Kepler used numerical data to guess at his Laws of Motion. But, one of these laws predicts that as a planet move along its orbit over a fixed time period forms triangle-like region. One line is drawn from the beginning position at the first moment of the time interval to the center of the sun. A second line is drawn from the ending position at the last moment of the time interval to the center of the sun. These lines, along with the path of the orbit, from a plane geometric region in space that his law states is always of the same area. From a pure physical viewpoint, this region is not drawn by Nature. It not directly observed. It might even be classified as imaginary. This law can be used to predict the total "area" of the orbital region, which again Nature does not identify. His law is considered a major example of empirical science.

In brief form, this is how the GID-model interpretation is specifically obtained. Each of the four or five basic GGU-model processes has an ID-signature. These ID-signatures are compared with corresponding ID-signatures that characterize such mental processes as they are displayed by biological entities listed in a set B. The major comparison is related to the algorithm (deduction), how human beings design plans, how human beings gather finite sets of entities and how we can locate a white ball in a spread-out collection of balls where only one is white while the others are black. Using only empirical evidence for these forms of human behavior, the mathematical model predicts ID-signatures that describe the behavior of a higher-intelligence. An interpreted statement that describes this major ID-signature is

(F) "The 'intelligence' being displayed by the higher-intelligence processes can duplicate the mental processes used by members of B. But, this agent also applies these higher-intelligence processes to infinite collections and uses a hyper-algorithm to deduce infinitely many conclusions over a miniscule time period."
In (F) and for comprehension, the notion of "infinite" should signify the usual intuitive meaning for this term that a specific object is without bound or unlimited. In the mathematics, it has been shown that this generic form is better than the mathematical form.

(G) In more detail, for members of B, it takes a certain interval of physical time to obtain a conclusion using language L. A higher-intelligence can "perform" infinitely many steps and, hence, obtain infinitely many deductions using its language *L, which contains L. But, only an infinitesimal time interval needs to be used.
Described linguistically, a language L is based upon a fixed alphabet A. The language *L is similar in construction to L.
(H) The *L portion of the "higher-language" contains infinitely many combinations of the symbols from A and these combinations are not part of the language L. This higher-language has an alphabet AL that contains the A symbols. However, there are symbols in AL that are not in A. Various members of the language *L have meanings for the higher-intelligence but no meaning for entities within any physical universe.

(I) For a set of assumptions taken from the language L, the higher-intelligence can obtain more logical conclusions than those deduced by any member of B.

I acknowledge that these linguistic characteristics may only be a model in the sense that we cannot comprehend these new notions in any other way. On the other hand, such a higher-language can exist in some reality.

Thus, in comparison, these described higher mental-like processes are exceptional more powerful than those of any biological entity. It is such ID-signatures that characterize the higher-intelligence. The GID-model has both direct and indirect evidence for its acceptance. Relative to choice, you might be convinced from other sources that such a described higher-intelligence exists. In this case, these results show that your choice counters statements made for hundreds years that such a choice is "irrational."

A Theological Interpretation

The higher-intelligence interpretation need not be used. But, if it is used, it becomes rather obvious that unless one corresponds such an agent to some specific entity, then employing the higher-intelligence interpretation has no significance. On this website at index #3A is an article that describes the exact mathematical results that compare Biblically described attributes of the higher-intelligence with similar attributes displayed by members of B. Linked to index #15 are my three personal belief statements. These statements use terminology defined in "Science Declares Our Universe is Intelligently Designed," and elsewhere. They described a GGU-model predicted creationary science model that follows an exceptionally strict interpretation for Genesis. This predicted "Rapid-Formation Model" yields every physical entity observed today, by any means, and predicts all alterations in the behavior of any physical combination of physical entities. Since the notion of indirect evidence is described by Paul in Romans 1:20, such rationally obtained indirect evidence for the existence of God and His creationary processes is a powerful faith builder.

As mentioned, the GGU-model predicts every known physical (secular) and creationary science cosmology. Choosing a particular cosmology usually depends upon many sources other than the scientific integrity of a model. If one chooses a creationary science cosmology predicted by the GGU-model, then the results discussed on this website show that the model chosen is a scientifically rational choice. This counters the claim that having confidence in a strict Biblical scenario is scientifically irrational. Using GGU-model methods, other articles on this website show that Biblical descriptions for other defined "supernatural" processes and events are scientifically rational descriptions. This is a major counter to the claims that such supernatural events are irrational in character. Moreover, Biblical statements imply that humankind and God communicate with one another using rational means and that we could not communicate unless our mental methods are restrictions of God's methods. The GID-model re-enforces these Biblical statements. Consequently, it is rational to assume that the Biblical God is the ultimate cause and the He uses processes that are similar to those described by the GGU-model.

In all particulars, the Biblically described God is a scientifically rational concept and all of the processes He initiates and sustains are also scientifically rational in character. Further, God's Biblical principles can be applied rationally by His created. These facts should enhance an individual's personal choice.

15 JAN 2009. Last revision 19 JUN 2012.


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