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.
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. Consider the language used in Physics and re-write the second equation in terms of that language.
(1) The force of gravity F between two bodies with masses M and n at a distance R from their centers of gravity equals the gravitational constant G x M x n divided by R x R, where "x" means multiplication.Statement (1) is a "mathematical model" for Newton's Law of Gravity.
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. 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 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.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.
Analogue Models Many physical models can actually be considered as analogue models. Such models can be mathematical models in that they use terms that correspond directly to objects within a mathematical theory. They may be an intermediate step in that, when interpreted in physical terms, they describe observable physical behavior.
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.
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 such device can be considered as an analogue model, which models the behavior of an entity termed as "time."
In subatomic 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 subparticles can produce the same predicted results.
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. 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. 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 theoretical physics, and hypothesized processes or objects to predict each of the cosmologies (A) - (E) and many more. The GGU-model postulates 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 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 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.
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 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, then each GGU-model generated creationary model is not pseudo-science as has been claimed. Due to this fact, the predictions made by these creationary models 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 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 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. Certain mental processes of these types are also 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 axioms 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," which has additional intelligent design characteristics. Most of these operators are "finite consequence operators." For these finite consequence operators, the following example indicates how they are intelligently designed. Mathematical logic is used neither to investigate how human brains function 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. A specific rule of deduction has been accepted for thousands of years. Suppose that you are given a fixed domain D. (1) You know that there exists some member of D and if that member has property P, then it has distinct property Q. Also, your know that (2) some member of D has property P. Then most individuals will simply accept that (3) the member of D that has property P also has property Q. We don't know how we actually arrive mentally at this deduction.
Using methods from symbolic logic, whether taken from Mathematical Logic or the Philosophy of Science, there are other ways that allow one to arrive at (3), ways that require explicit mental steps. In one case, one axiom, one rule of inference and the notion of "constants" are used to establish that (1) and (2) imply (3). (It is not necessary that you know the definition of these terms.) In a second case, the notion of constants is not used (E. Mendelson, "Introduction to Mathematical Logic," 3rd ed. Wadsworth & Cole, Monterey CA (USA), (1987), p. 64.).
The logic-system Mendelson uses is the "first-order predicate" logic-system, a logic-system that yields all of classical-logic. As shown by example 3.5 in this paper, there are infinitely many different logic-systems that yield the same deductive results as this first-order predicate-system. In order to use any of these "logic-systems," mental activity must be applied. It is this explicit mental activity that is an analogue model for the original mental processes that yield (3). Explicit mental activity is substituted for the unobserved mental processes that yield statement (3) from the set of hypotheses {(1),(2)}. It is the mental-steps that "represent" or "analogue model" the unobserved. In scientific discourse, it is important that a science-community have a common logic-system. Accepted scientific theories may need to be analyzed so as to demonstrate, to community members, that no logic-system errors occur.
Individuals employ a basic form of mental activity to all known forms of physical-science deduction and induction. A formally presented general logic-system is composed of a collection of specific objects, the general rules of inference. To obtain a consequence (prediction or conclusion) as illustrated by (3), 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 an analogue model. (See algorithm.htm for the model's explicit description.) The algorithm requires one to make various 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 yield a operator called a "hyper-operator." 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 hypothesized existence of a higher-intelligence. Considering hypothesized behavior that is mimicked by other comprehensible behavior is a basic method used within particle-physics. An example is Quantum Electrodynamics where Feynman diagrams are often employed and physical behavior is mimicked by the diagrams. The higher-intelligence ID-signatures for physical-like behavior are based upon similar but weaker processes that we can comprehend and apply. The fact that similar behavior is used yields a stronger modeling correspondence than occurs in many other accepted physical theories. Indeed, similar mental-processes are used whenever a computer simulation for physical-system behavior is constructed.
In brief form, this is how the GID-model interpretation is specifically obtained. Each of the four 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. The rules of inference, and the algorithm are listed in D. For a set of assumptions, members of B must obtain conclusions only by the algorithm. Without adding any other assumptions not contained in D, the mathematical model generates 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 deductive processes can duplicate the mental processes used by members of B. But, this agent can also apply infinitely many steps to obtain a deduction."In (F), the notion of "infinite" does not merely signify the usual intuitive meaning for this term that a specific object is without bound or unlimited. It is a special form of "infinity" that has special describable properties.
(G) For members of B, it takes a certain interval of physical time to obtain a conclusion using language L. For the higher-intelligence, infinitely many steps using its language *L can lead to deductions. But, only an infinitesimal time interval is needed.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. The language *L has meaning for the higher-intelligence.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, but, almost always, the part contained in *L and not contained in L cannot be used by "anything" within a physical universe.(I) For sets of assumptions taken from L, the higher-intelligence can obtain more logical conclusions than those deduced by any member of B.
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 17 JUN 2009.
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