A Short Course in the GD-world and MA-models as They Relate to Theology

Robert A. Herrmann Ph.D.

1 Jun 2000. Lastest revision 13 JAN JUL 2016.


Abstract The following is a short introductory course to the GD-world, MA, GGU, GID-models as they can be interpreted theologically. (The G-model now only refers to the mathematical structure itself and its application to attributes is now termed the GD-world.) This is a model for God's attributes. The MA-model is part of the GGU-model that refers to the appearance of various entities in mature and functional form. The GID-model is the general intelligent design model.) All the terms in this course have been changed to those now being used.) This short course consists of a series of 13 e-mail postings that I presented to a special creationary science Internet network. They might prove useful in furthering ones comprehension of the material that appears on this website and in the book "Science Declares Our Universe IS Intelligently Designed". This "course" is only relative one portion of the GD-world model and to one interpretation of the GGU-model - the MA-model. It does not contain the GGU-model as it is applied for other purposes. It does contain some of the higher-intelligence aspects of the GID-model. The book "Science Declares . . . ." contains a vast amount of material, discussed in the simplest possible manner, relative to other major portions of the GGU-model. In this course, one pure theological interpretation for the GD-world and MA-models is discussed. There are many other interpretations for the GGU-model including pure secular ones. (Motion picture film, VCR tape, and DVD mimicking illustrations with TV or computer screens were not used to obtain the GGU-model or GID-model interpretation. This model is created by mathematically encoding general languages that describe sequences of physical-events. Processes that yield such event sequences are modeled after human mental processes that occur trillions of times a day. These illustrations were not devised until after 1997.) This revision does not include the recent 2013 refinements.



Subject: 1. How all this started.

Date: March 27, 2000

1. In Aug 1979, after a conversation I had with John Wheeler, I knew that I might solve the General Grand Unification Problem. I was told that any solution would be acceptable as long as it could be shown that all physical-systems (in some of my writings I use the term natural-system) were logically related by one basic theory. I was further told that anyone that did solve this problem would be appropriately rewarded. I didn't know how to get started, however. I had previously constructed a model for statements made by C. S. Lewis and knew that processes used there might be modified and placed into a purely secular environment. All I needed to do was to consult one Scriptural verse Hebrews 1:3 and the general method became clear to me.

The first result was the GGU-model (General Grand Unification Model) that did, indeed, give an almost complete secular solution to this and other problems as well. The GGU-model now gives the complete solution. (However, I've yet to receive the "promised rewards." One might say that Wheeler misinformed me, for it turns out that only certain models are acceptable, not any model.) The constructive methods used to obtain the GGU-model are the foundations for a secular solution; but a parallel theological interpretation soon appeared. The title "MA-model" (metamorphic-anamorphosis model) refers only to specific portion of the GGU-model. The first publication of the theological aspects of the MA-model was the article "The Word" CRSQ 20(1984):226-229. The first actual presentation entitled "The miraculous model" was at the winter meeting of the American Scientific Affiliation at Washington DC 21 JAN. 1983.

2. I'm only the messenger as to what this model predicts. Yes, the "word" is predicts. It answers a significant number of questions that have driven many individuals to accept atheism. I know for a fact that when Lord Whitehead lectured in philosophy and religion he spent a great deal of time creating atheists by bringing up questions he could not answer relative to religious concepts and, therefore, he rejected the concepts as nonsense. His students, of course, also rejected them as nonsense since Whitehead was one of the most famous philosophers of his time. The GD-world, GID, GGU and the MA-models answer these questions. Many of these questions are relative to God's creationary activities. These activities also include the creation of God's invisible supernaturally related world, which we tend not to mention as part of His activities.

3. It's not easy to find answers in these models. But, I'm confident that all the answers, of any interest, to questions that can be answered by means of a human language or that are humanly comprehensible relative to God's almost incomprehensible creationary power and processes can be found within GD-world and GGU-model interpretations. Rather than have individuals search through my many papers to find what the model predicts, I'll prepare an outline for members of this network of some, but not all, of its known predictions as they relate to some of these theological questions. The application I give here is what I accept. There are many other theological applications of the GGU and MA-models. It will take me some time to do this properly. However, let's just see whether the GGU-model predictions yield a true advance in religious comprehension, especially when compared with the works of Paul Davies or Hugh Ross.

Dr. Robert A. Herrmann
Professor of Mathematics
U. S. Naval Academy


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Subject: 2. How to Model Divine Attributes Scientifically.

Date: March 30, 2000

1. Let the subject called "standard" mathematics be used to model processes that occur within the physical world. As far as my experience over the past 42 years is concerned, there is only one form of mathematics that is capably of modeling the supernatural and related worlds. This is a mathematics that properly corresponds the properties of the physical world with those properties that are "above," or "greater than," or "beyond" physical law and will always remain in this state as long as our present universe(s) exists. I'll not present such mathematics in this series of postings since it appears in my Internet books. Abraham Robinson discovered the mathematics in 1961 and it's called Robinson-styled nonstandard analysis. If, however, this is the only structure that exists today that will properly model the supernatural and a related world, as say described somewhat in the Scriptures, then I wonder why the subject isn't a major part of the educational system at every Christian college or university in the world?

2. "And God said, Let us make man in our image, after our likeness; . . . " Throughout the Bible God's attributes are compared with those of His created. We have the "omni" characteristics of God, but, the Scriptures compare such attributes as God's, intelligence, wisdom, goodness, strength, etc. with those of His created since, obviously, such terms are, one hopes, comprehensible by those He has created in His image.

3. Prior to the very, very technical processes used to model a notion, the notion should first be intuitively discerned. How do we quantify such attributes as listed above? Notice that I've just quantified the term "technical." Due to the use of the symbol string "very, very," many would conclude that whatever needs to be done would be much more difficult, much more detailed, that it requires a great deal more knowledge, work etc. than if the processes were merely "technical." Thus it's the string of words, "very, very" that tends to lead to such a quantification. Three "very"s would seem to yield a "stronger" quantification than two "very"s. Further, if one states that "Joe is very, very intelligent," then would Joe not also be "very intelligent"? My answer to this question relative to this quantification notion is, yes. Thus, while sitting at my little desk in Oct 1978, a form of human reasoning was described, a form not previously detailed. I term this as "adjective reasoning" (1, pp. 23, 29) (When I write the term "technically" you can just skip over the little bit that follows for it will refer to a little of the "very, very technical" stuff and is for those who might have the background.) Technically, it was shown that such reasoning is isomorphic (behaves the same as) a subsystem of propositional deduction.

4. Since these attributes are written in a natural language with the information being supplied by the structure of the phrases, a totally new approach to encoding natural languages so that they can be embedded into an appropriate mathematical theory was necessary. This took a great deal of time and had some surprises. The encoding produced some rather unusual mathematical objects in that they aren't the usual ones that appear in the literature (1, pp. 1-23.) What are important, however, aren't the technical aspects but rather what a fixed interpretation for the mathematical predictions shows. These are predictions that are found in the model and not built into the model in any form whatsoever.

5. Consider one final point in this first posting. The significance of nonstandard analysis can be explained somewhat by the following illustration. Consider a set of objects A that are characterized by a set of language statements. When the set A is looked at in the nonstandard model, it changes automatically into another set *A. Many times the original set A can be considered as a subset of *A. The important point about the extension *A is that it behaves in many respects like the original set A. However, there mathematically exists objects in *A that behave in ways very, very different from the objects in A. The challenge is to find the objects that behave differently and to see if we can describe, in an interpretation, this new behavior and how it compares with the behavior of objects in A. You'll see me use throughout these posts such symbols as A and then its extension *A, where I'll interpret the differences that have been thus far discovery between A and *A. For example, if one assumes that A contains only meaning statements each of which corresponds to the notion of specific information, then *A can contain objects that, by comparison, correspond to "very great amounts" of information.

[6. God's intelligent design and creationary aspects are modeled by the appropriate interpretations of the GGU-model.]

(1) The Theory of Ultralogics Part I.
The Theory of Ultralogics Part II.

Dr. Robert A. Herrmann
Professor of Mathematics
U. S. Naval Academy


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Subject: 3. More About Adjective Reasoning.

Date: April 4, 2000

1. What I'm discussing in these first postings are some of the results generated by the basic GD-world, not the MA-model. If one considers all of the comparative attributes of the Godhead as stated within the Scriptures, then a set can be constructed where finitely many "very" symbol strings quantify each such attribute. One obtains a set denoted in (1) by BP. The attributes listed in BP can only be applied as descriptions for entities within our universe. When BP is codified and embedded into a nonstandard structure, BP is extended automatically to the new set *BP. The number of "very"s that appear with one such attribute would be a measure as to the "strength" of this attribute if an additional requirement is met. (The "very" strings can be replaced by other similar terms such as "greater." Further, you can also have non-divine attributes as well such as the term "evil." But extended these beyond the finite is not Biblical.)

2. What is required in order to make a comparison is adjective reasoning. As an example, this is the reasoning that takes an attribute with an attached string of "very"s and when this "reasoning" is applied to a phrase such as "very, very, just" this reasoning implies "very, very, just," "very, just" and "just." An absolute mathematical model is one where all of the significant information is generated by the model itself. This would yield the strongest known theoretical evidence that the interpretation is rationally obtained. Thus, although simply counting the "very" strings might indicate the strength of an attribute, it's more desirable to actually have some operator that resides within the model generate statements that explicitly describe how such infinitely strong attributes compare with the "weaker" attributes. What needs to happen is that a quantified attribute statement that intuitively appears to be the strongest must "formally" imply all of the weaker quantified attribute statements.

3. Theorem 3.3.2 (1, p. 32) and information in its proof tells us how adjective reasoning is the appropriate operator to use. Take an attribute such as "just." Then in the set *BP and not in BP is an "infinitely strong" form of ". . . just " = d. When the extended adjective reasoning (an ultralogic) *C is applied to d, denoted by say *C(d), it yields all of the weaker forms of "just"s that are in BP. But more than that, it also implies forms of the "just" attribute that are not in BP and that are always infinitely stronger than any of the weaker forms. One might interpret this by saying that the d is a very, very infinitely strong "just" attribute. Now the *C denotes an "operator" or function. The *C is applied to the d, and this produces probably different stuff. But, just like a physical laws which are all actually hidden from view, it does this via a "hidden process" that can be described using a special language.

If you consider the proof of this theorem 3.3.2, you'll see that the same thing will hold for every comparative attribute used to obtain the statements in BP such as "intelligent." Thus, we also have a rationally produced statement that describes the basic aspects of the infinitely strong (powerful) intelligence. This is termed a "higher-intelligence." So, rationally one can assume the existence of an entity that can be partially characterized as having these infinitely strong attributes. Now these are what one might call "supernatural" attributes since they are always stronger and not equal to the quantified attributes that are used to describe entities within a physical world. But, this doesn't mean that there are not numerously many such entities in a "supernatural" world that can be so described. Is there an actual Scriptural concept that can be used along with an ultralogic (a special operator that means what it says, extremely powerful thinking process, when interpreted within general intelligent design) that will verify that there is one such set of infinitely strong Godhead descriptions that cannot be associated with any other type of supernatural entity?

4. These postings only yield some aspects of the entire modeling procedures as an illustration of the methods used. I'll answer the last question in the next posting when I discuss a logical form I term, "reasoning from the perfect."

(1) The Theory of Ultralogics Part I.
The Theory of Ultralogics Part II.

Dr. Robert A. Herrmann
Professor of Mathematics
U. S. Naval Academy


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Subject: 4. Final GD-world Remarks.

Date: April 5, 2000

1. This will be my last GD-world illustration. I know that this attribute stuff is considerable more vague than the much more specific creationary science predictions and verifications presented by aspects of the MA-model. Since it doesn't lend itself to analogue models, an attributive model is more difficult to illustrate. New electronic hardware allows the MA-model predictions to be more easily presented by means of analogue models. This last GD-world illustration is but one example as to how one can establish that a deity is a scientifically rational concept. [The reason I use the term "scientifically" is that the logic used to obtain these results is first-order predicate logic, the logic one applies in order for it to be considered as scientific, a specific form of classical logic, the common logic used for human discourse. This differs from other logics such as various dialectic arguements as used by philosophers and some theologians.]

2. Obviously, there are terms that describe the character of God that are specific to a supernatural being. In some cases, God can be negatively compared with His created. This is especially so with the "omni" characteristics. The GGU-model will display the infinitely powerful creator aspects. What is done in this GD-world illustration is to concentrate upon some of the aspects of God's character as they are described by attributes that are very comprehensible. Indeed, God's creative power is a most significant aspect of His character. When this aspect is deeply analyzed within the GGU-model, the ultranatural laws are predicted. (The ultranatural world is the world all "ultra" objects.) The exact nature of such laws is hard to determine, but they can express, using the higher-language, processes created by God to sustain both His physical, a background universe and a related supernatural world. However, with certain important exceptions, they are mostly laws that cannot be described in a language used by any intelligent creature within His universe. The reason for this is that the model is actually constructed developmentally. The model uses as a basis all languages that have ever existed until the moment I term NOW. It uses the concept of a "general language" that includes images, diagrams and, indeed, all human sensory aspects that can be reproduced via virtual reality. (Note that, for technical reasons, the set of all ultranatural laws also contains the described physical laws as well.)

3. No addition of any new symbols and terms to our language while we remain confined to the present material universe will suffice to state these different ultranatural laws. This is actually a coding process that cannot be eliminated. The mathematics allows one to return to the standard language symbols, the same way that the symbols you see on this screen are decoded. The model actual shows a barrier to knowledge since you cannot decode the symbols that represent certain ultranatural laws and a lot of other stuff. This is based upon certain characteristics of "sets" that deal with the existence or non-existence of certain types of functions. Thus relative to attributes and other descriptions for God's character, the model predicts that many of the descriptions for God's character are, at present, incomprehensible to His created. (This brings added meaning to 1 Cor 13:12.) However, relative to the creationary aspects certain descriptions can be decoded by the addition of one or two "new" symbols and the results are comprehensible.

4. Consider the very special supernatural and Scriptural notion of God being "prefect." One need not spend a week discussing what this concept means when it refers to a God attribute. For the GD-world processes, all one needs is to simply adjoin to the set BP a definition for the most simplistic aspect of "completeness, finished, etc." This is done by adding a well-defined set of statements to BP that simply say, that, at the very least, "complete" in the physical world would be a notion that would imply logically each member of BP. Of course, this immediately implies that none of God's created are, as yet, "completed." As pointed out last time, there is, as yet, no absolute requirement that members of *BP be attributive descriptions for a special supernatural entity. This will now change.

5. Theorem 4.3.5 (1, p. 43) is a rational argument that yields that no supernatural entity, even one with all of the *BP attributes, can achieve this special type of supernatural "perfectness" unless "perfectness" is one the basic attributes of the entity in the first place. Hence, it's rational to consider that there is a supernatural entity characterized as "perfect" in this special way and that this is a basic defining attribute that implies all other quantified attributes. This may not be of particular significance to us, but it's certainly significant to any entity that thinks it can gain through its own endeavors all of the attributes of God. One of the major results obtained by applying the reasoning from the perfect "ultralogic" is that it shows that various Trinity notions are scientifically rational. However, the operator does not determine which Trinity notion is correct.

In the next few postings, I'll attempt to illustrate by modern devices such as the DVD some of the somewhat startling verifications and predictions made automatically by the MA-model and how they not only relate to a very Biblically literal interpretation of Genesis 1, but imply that, where words have multiply denotations, which Biblical meaning is most likely with respect to linguistic principles.

(1) The Theory of Ultralogics Part I.
The Theory of Ultralogics Part II.

Dr. Robert A. Herrmann
Professor of Mathematics
U. S. Naval Academy


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Subject: 5. Metaphoric-Anamorphosis Model

Date: April 6, 2000

1. During the period from 1985-1986, I discussed in a series of papers in the CRSQ a theological interpretation of a mathematical structure. Due to this one application, the structure became known as the "Metaphoric-Anamorphosis model" - MA-model - since the application was about sudden change and distortion of information. It is a restricted portion of the GGU-model. Usually, the name applies to physical applications where physical-systems either suddenly appear in mature and functional form, or behavior is suddenly altered. The MA-model comes about due to how "developmental paradigms" (event sequences) are constructed. Theologically, it usually refers to certain literal Genesis 1 interpretations for the General Grand Unification Model. Of course, the MA-model can also be used to model other notions. (As of JAN 2016, for general applications, the rapid-formation model is a more formal form of the MA-model.) I'll not discuss here the actual history of how I came to the ideas except to mention that, although the model is actually secular, I was led to the ideas after my consideration of Heb. 1:3. You can find the actual history and parts of a low level (and highly incomplete) 9 - 10th grade school talk I gave using this model at http://www.serve.com/herrmann/grand1.htm

Since it models Heb. 1:3, certain recent questions relative to God's active presence as a necessity for the existence of our universe and other discussions on CRSnet are related to the results predicted or verified by this model. The GGU-model shows how miracles and other inputs from the supernatural world are possible without violating such Scripture as Genesis 2:3; how God has knowledge of the past, present and future; how all of history is slowly converging to a specific final conclusion as outlined in Scripture, why the Bible gives no details about the present functioning of the supernatural world, and a lot more puzzling aspects of Scripture are "explained" by this model.

2. My daughter Laura constructed for me a new computer. It is an incredible machine. She demonstrated what its high level features could do with a computer game. In this game, as long as you are given apparent motion, the screen image is a 3-D reproduction on a flat screen. The program actually computes and draws the altered perspective you would have as you move and look about. It also produces the proper distortion for reflections, shadows and all that stuff. This of course fools the brain into supplying the perception of depth. The fact that this is a computer "game" means that it's widely available and I can add this to my general discussion that yields a mathematical model for the creation of universes. Indeed, infinitely many different universes.

3. The most basic aspect of the model is that it models human perception via the basic senses, the human perception used in order to have any knowledge as to how any physical-system behaves. How such perception is representable by strings of symbols will be discussed in my book "Science Declares Our Universe is Intelligently Designed." The more we construct imagery, such as the 3-D display that computer game, the more evidence one has relative to a correspondence between strings of symbols and any knowledge we can have as to the behavior of a physical-system.

4. The model is concerned with alterations in physical-system behavior. A physical-system is, of course, a rather ad hoc collection of physical entities that are named and assumed to have behavior that can be studied as a whole. A virus, a star, a solar system, a universe are defined as physical-systems. Of course, one of the great questions the GGU-model solves is the question that asks "Is there some type of relation that binds together all of the physical-systems that comprise a universe?" (The answer is yes, even from a secular view point.) Also note that to be of any real significance the model most not depend particularly upon so-called physical law. The basic model gives operators that create universes and these universes might differ due to the different so-called physical laws, laws that don't need to be an explicitly expressed part of the model.

5. The terminology I chose in the early 1980s had to be changed in to the late 1980s since another scientist had done some research in quantum logic and had coined the term "superlogics." So, I altered all secular terms to the form "ultra" things. In the next posting, I'll begin a very simple discussion of the "developmental paradigm," standard physical events, ultranatural events, how these cannot be eliminated from science and how they relate to the "supernatural" as it's implied by Scripture.

Dr. Robert A. Herrmann
Professor of Mathematics
U. S. Naval Academy


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Subject: 6. The Miraculous Model.

Date: April 8, 2000

1. I first present some of the general features of the MA-model. (Note: this is one of the longest e-mails.) Note that unless I'm forced by circumstances, say for example models that I and others perceive are dangerous to ones salvation, I don't critique other creationary models unless specifically asked to do so. I always attempt to present all facts, nothing hidden, about the model I accept and any models I might critique - information that is relative to the model itself. It's the individual's responsibility to make a choice based upon the actual facts and not through coercion. My first concern is rationality relative to scientific logic. (Technically, nth-order predict logic with constants, where often only n = 1 or 2.) Usually, before a model can be considered as scientific in character it should follow such a logical pattern. This was first strongly and completely recognized by Tarski in 1950. Historically, after the rationally is established, than whether or not the model is only speculative, such as various models for the early universe, or is capable of being differentiated from other models by present day scientific measurement is another matter that usually must await further development.

Although the present Popper viewpoint that prediction is necessary, such a prediction of a differentiating observation can be very, very impractical or not within anything we might call the near future. This is not the actual fact, however, with respect to published work. There are many individuals who produce only theoretical constructs that won't lead to any form of laboratory verification. Indeed, I have papers from all of the major scientific journals, Physical Reviews, etc. and they all print papers in theoretical areas where the conclusions cannot be verified experimentally and, in some cases, they predict nothing that can ever be measured. Of course, one major example of this is all of the published work and research efforts put forth relative to the Everett-Wheeler-Graham multi-world approach to quantum formalism. The facts are that what is considered as scientific is not dependent upon my philosophic viewpoint. It is the policies of the various journals and funding organizations (NSF for example) that determine whether an article or research falls within "their" scope and definitions of scientific. This is why one should research journals themselves to determine the type of articles the journal publishes prior to submission. I have a model for certain theologically related concepts that has been peer reviewed and that explains a large number of present day observations. Secular journals would not consider this as scientific since Divine intervention is required at one point.

This model first required that I construct a logically consistent mathematical theory prior to applying this theory to physical objects and thereby obtaining predictions that can be observed today, and even be measured. With that said, I don't intend to discuss the often violent dichotomy that exists between the two camps termed by me as theoretical and laboratory science. To continue, I mention all of this for this is the present state of a theological interpretation for MA-model and GGU-model - the building of a rational Biblically based model for the supernaturally related processes and how the supernatural world might impinge upon the physical world. Although I've personally experienced certain physical effects predicted by this model, since these effects are neither specifically controllable nor universal, in their present form, the MA-model should be considered as scientific speculation. At the moment, I have no idea whether universal types of predictions will be forth coming since, as these postings will indicate, unless one is very clever, little can actually be known about the detailed workings of the MA-model.

2. I'll always point out aspects of Biblical speculation within the MA-model. Such speculation is almost always relative to areas where the Bible is silent or some nuance is applied that was not previously considered. I firmly believe that all such speculation should be highly restrained and should never contradict directly or, by implication, any specific Biblical statement with its ancient meanings. Also note that the MA-model uses the General Grand Unification Model which has many different interpretations that are completely secular, completely theological and many combinations of the two. What it does do, if one accepts its ability to describe certain vague aspects related to the a supernaturally related ultranatural world - God's unseen, "invisible" world - is to show how very, very distinct certain supernaturally related aspects are from the physical. This verifies the large amount of Scripture that implies how exceptionally different, in many ways, are God's attributes from those of His created.

3. After only a few years of analyzing the MA-model, I became convinced that some individuals make errors in describing pure supernaturally related events. I wrote the following in a 1983 article "Comprehending Supernatural Concepts." "The first step in an intellectual comprehension of the supernatural is to study and reflect upon the Scriptures. Except for negative statements relative to material objects (i.e. statements that say that pure supernatural behavior is not the same as some observed physical or materialistic behavior) or Scriptural pronouncements relative to human behavior, it appears that we cannot comprehend to any significant degree the behavior of the supernatural by using any previous behavior for physical objects or materialistic concepts as has been attempted by prior philosophic methods." The MA-model predicts specifically that with respect to the Biblical supernatural that the languages and philosophic methods used during the historical periods when the Bible was first transcribed were inadequate in their descriptive power. Once again verifying such statements as Paul's 1 Cor 13:12, among others.

4. Just two attributive aspects of the model imply that all of creation actually displays the extreme power of Divine processes and the unmeasurable strength of the God's mind. A better descriptive language for these attributes has only been developed recently. This may be one reason why the Scriptures forbid imaging God in any physical form. The concepts and notions needed to even have a slight comprehension of the model's predictions as to the supernaturally related aspects of God's creation had to wait. It appears that it has taken thousands of years for language and ideas to develop to the point where additional human comprehension is possible. Possibly, this is one reason the Bible actually states very little about the properties of God's invisible supernatural world; a world that is far more complex and startling than even the Scriptural description of the new Jerusalem. This is one reason I've been forced to reject such models as those presented by Hugh Ross, Paul Davies and many, many others. For me, these models do not, even slightly, convey the almost incomprehensible creationary power displayed by the model I support.

5. Consider the VCR (or DVD) feature called the "freeze frame," "frozen-frame" or a "still." For a short period of time, the same effect can be achieved with a motion picture film projection and, of course, with a single frame of the film itself. Except that it is only visual in character (unless you also consider the sound carried by a sound "track" encoding), no matter how detailed such a "still" may be, it can be faithfully described in the form of a string of language symbols. Technically, as will be discussed in my previously mentioned book, all other sensory aspects of scientific interest relative to the "freeze frame" as a description for a physical-system at one moment in its time development can also be represented by an actual string of symbols. This assumes that certain of the symbols are properly encoded. An important term here is represented. In what follows, the concept of "time" as we experience it need not be considered. All that is necessary is that such "stills" be given sequential names. Independent from how you might identify them, a string of symbols that correspond to the "still" is technically called a "frozen segment." This term was chosen so that it corresponds intuitively to the "frozen-frame" concept and the notion of a finite segment of symbols, strung together, from left-to-right. This last idea of a finite string of symbols as so constructed is taken from the theory of Markov algorithms with respect to a language, and it is not my idea and is well-know in the area of mathematical logic.

6. For a general language, a frozen segment gives a description for the all aspects of the comprehensible "appearance" of physical entities at a moment within their sequential development. (I could have written this as "within their time evolution." I wonder why I didn't do so?) We call the actual objective physical phenomenon being described "an event." The process is as follows and should be assumed throughout the remainder of these postings. It starts with "general descriptions." (As mentioned, this can include images and even encoded human sensory information). Then the specific information being conveyed by a description is employed to obtain "properton combinations" by application of the "instructions" concept. The last step is a special process that operates upon these combinations and the description becomes the "real" event. Finally, I'm able to present the very first startling conclusion that may be used for Biblical speculation; a conclusion that re-enforces the distinction between such actual events and the related supernatural world. The oldest of the concepts used in what follows is 110 years.

7. [This is a simplified approach. As of 2016, the approach has been refined. However, intuitively, the concepts have not changed.] For any sequential moment, consider a scientific alphabet A that includes digital coding for sensory representations and the set of all finitely long words W constructed from these symbols with a spacing symbol included. Let T_i, a totality, be the set of all of the possible finitely long descriptions composed of members from W joined together - descriptions for any possible event. (We actually select special representations from W but intuitively just consider W itself. I discuss this stuff intuitively not technically.) Each member of T_i has been previously encoded by a natural number in such a way that the encoded descriptions in (T_i) can be decoded uniquely to give the meaningful descriptions in T_i. (Note: There is no problem here if you wish to use natural, real, etc. number symbols as part of your symbol strings, since different collections of symbols are used than those used for the encoding.) Embed the encoded descriptions (T_i) into our mathematical structure. The structure "automatically" generates a new set *(T_i) such that (T_i) < *(T_i) (i.e. < means a subset of). Further, (T_i) is not = to *(T_i). Members of *(T_i) have all of the characterizing features that would classified them as being "descriptions, in our general sense, for some type of event." But what are the descriptions in *(T_i), the *-frozen-frames, that are not in (T_i) saying? Indeed, can we comprehend them?

8. It is not easy to extract information from the MA-model. You must ask the right question and describe properties about the physical world in a very special formal manner. But, here is a result that uses very recent ideas. Suppose you considered my notion of "specific information." Then it can be shown that there can be descriptions w in *(T_i) for *events that contain more meaningful information than all of the combined meaningful information contained in every event that ever or will ever occur within our own universe. This is most certainly a very powerful *event. Using the very intuitive language concept that for a fixed language the number of words used indicates the complexity of a given event, it also follows that w is more complex than the complexity of our entire universe. Such an *event w could not take place within our universe for we would have a contradiction. This *event is one of many different *events that are termed as "ultranatural" events. (Note: The "ultranatural world" is a type of interface between the pure "supernatural" and the physical (i.e. natural) world. The "ultra" means just what it states. The information contained in w may be vast, great, beyond any physically fixed limit.) I point out that as an interface such a w could be describing an event in a related background universe that is not part of a physical universe or it could describe a pure supernatural event. In most cases, we cannot, as yet, know which.

But, in this model, how would the *events be perceived by the Divine mind? The model says that *behavior in the w that corresponds to a *event is no more complex for the Divine mind than an event in the physical world with but a small finite amount of complexity or meaningful information.

9. As a final aspect of these general MA-model rational conclusions, can we describe these particular *events in any form of human symbolism, except for such a representation as w? The answer is no. For in general, we don't know anything about the internal structure for almost all of these ultranatural events and, moreover, the model will not allow us to decode the w. However, in a few cases, although we cannot completely decode a few pure ultranatural events, we can have significant information as to their behavior. The possible rational existence of such a w cannot be eliminated from any scientific theory that uses mathematical methods. It can be ignored or assumed to be extraneous, however. In the next much shorter posting, I'll discuss additional information relative to some of these w where we can decode almost all of their content and gain some insight into the behavior of some ultranatural events. The ability to make such a partial decoding is directly related to Genesis 1, and the first, "Let there be. . . " statement.

Dr. Robert A. Herrmann
Professor of Mathematics
U. S. Naval Academy


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Subject: 7. The Model Speaks.

Date: April 14, 2000

1. Prior to continuing, let me emphasize that these models use very few axioms beyond that of the mathematical axioms themselves. They only use a few axioms modeled after observed human behavior human. These include human deduction, finite human choice of words used to communicate and, as in what follows, descriptions for a most basic and well known behavior for created physical systems. These absolute facts often confuse those who wish to criticize the findings. Some individuals claim that certain "supernatural" or other such theological notions must be part of the axiom-system. I can only conclude from such remarks that such individuals have not read the available material for no such notions appear as fundamental concepts.

The GGU-model processes can be used to model, a Northrup, Hartnett, Humphreys, Hugh Ross types of theological cosmologies, among others, and all secular cosmologies such as the inflationary Big Bang, quasi-steady state, cyclic, eternal, etc. and has application to quantum physics and a lot more. I don't first decide upon my favorite theological interpretation, then try and fit my interpretation to the model. I use the modeling concept of simplicity, or minimizing in a well-defined sense. (Yes, the minimal part is the Occam's Razor concept.) Then I see if there is a reasonable Scriptural interpretation that fits the model's predictions. Of course, this doesn't mean that the notions are not complex in character when compared to other concepts. It's hoped that the interpretations are the simplest or most "straightforward" that can be found within a class of complex notions. The GD-world and GGU-models, when theologically interpreted, PREDICT behavior that has (A) strong Scriptural support and corresponds to (B) the almost incomprehensible power and intelligence of the Creator of both the supernatural and physical worlds.

As I continue presenting some elementary aspects of the MA-model portion of the GGU-model, one might keep in mind 1 Cor 2:9. "No eye has seen, no ear heard, no mind conceived, what God has prepared for those who love him, but God has revealed it to us by His Spirit."

2. "And God said, Let there be light. . . " There is one aspect of the MA-model that's very difficult for some scientists to understand. Generally, when one models the behavior of a physical-system, one is in control of the modeling procedures. A specific language is transferred to or interpreted within a mathematical structure. Then the modeler determines which direction to take, which paths to ignore or declare as extraneous, etc. Actual arguments and theory predictions are often, but not always, a back-and-forth process of using the mathematical structure to predict, but then returning to the specific language descriptions and using logical deduction only with respect to these descriptions.

3. I don't follow this procedure with the GGU-model. Whatever I use is always part of the mathematical structure. There is even an aspect over which I have no control at all. The model can actual "speak" in a scientific language itself and, when it does so, it adds new descriptions, new entities, by insisting upon new characteristics distinct from those entities that we believe exist in objective reality. As far as I can determine, this is the very first time in human history that it has been demonstrated that a mathematical structure is capable of speaking for itself.

4. Light has a very unusual property, a continuous spectrum. Suppose you simply write down a set of descriptions D that state that "light" can have all of the "light" wavelengths between 0.5 microns and 0.6 microns. Let L denote the set of all of these almost identical descriptions. Now encode these descriptions and embed them into the nonstandard structure. What are the descriptions in *D as a subset of the "language *L?

5. The model is constructed in such a manner that, in this case, you can actually follow what happens to each and every symbol used in the objects in D. We can decode all of the members of *D as descriptions that are not members of D (notationally in *D - D), but you cannot decode a single symbol that appears in each member of *D - D that is not a member of L. The descriptions obtained have exactly the same meaning as the original descriptions except that the symbol that represents the wavelength number is missing. (The method is called the General Paradigm method.) You can, however, determine that this new wavelength lies between various physical world wavelength measures. No previous wavelength symbol used for each of the physical world wavelength numbers between 0.5 and 0.6 microns can be used since they all appear in other sentences. A new symbol is invented, but one must always keep in mind that whatever these automatically generated statements signify, they are not describing wavelengths for any light-type entity within the physical world. They are in the Nonstandard Physical(-like) world (a term used in my J. Math. Physics paper), a substratum or background universe, or, the possibly related supernatural for a theological discussion. Such entities are called "ultranatural objects" and this leads to the theory of propertons. I don't mentally image a properton as being any thing similar to an actual "particle." These results are not obtained using of GGU-model processes. Nevertheless, they are still interpreted as describing entities within the substratum world.

Please note that the MA-model is just that - a "model." The MA-model considers objects that mathematically exist in the sense that the model yields certain specific statements that describe properties and the model states that there exist objects with these properties. This only means that there is a scientifically rational argument for such an existence. It doesn't mean that such objects exist in objective reality. Mathematical operators control these "objects." The results of these operators also have properties that can be characterized. The model mimics behavior. I often view such models as a type of black-box. What actual forces the GGU-model processes being used to produce the final results in objective reality, I consider as unknown, at present. In general, it seems to represent behavior that changes "thoughts" into physical reality. But, the model is a weak attempt to comprehend, what may be incomprehensible in detail.

The discovered objects and processes yield the same results as the black-box results from the same inputs. It's the same idea used in physical science. The physical processes actually represent a black-box where physical stuff is inserted and possibly new or altered physical stuff immerge. But, I don't consider the model's objects and processes as necessarily an actual reality. I put stuff in one end of the box, I turn the handle (i.e. use the model), and out comes a universe. I doubt that there are any word-forms that can describe in detail how God "actually" does His work. On the other hand, the model does mimic certain behavior that is somewhat comprehensible, but behavior relative to linguistics and how humans apply a few processes to construct physical-systems. God commands and it is done. God said, let . . . . etc. I assume that the strictest from of Biblical interpretation is maintained. Under this assumption, I have confidence that the general physical-like methods for universe creation described in "Science Declares Our Universe IS Intelligently Designed" and the refinements that appear on this website and in my archived articles are close to the actual facts as can, at this time, be comprehended by the human mind.

6. There are basic mathematical operators used. Let's discuss one of them. This is a very significant operator that can be applied to a properton description. It's called the "standard part" operator, and is one of the most important in nonstandard analysis. If you apply this operator to one of these special strings of symbols, the new symbol used to measure this ultranatural world wavelength disappears and in its place is an ordinary symbol for a physical world wavelength such as the 0.5. Now what can this mean? It seems to say that these propertons are very closely associated with an actual physical world object or event.

7. There is a special mathematical set of numbers, discovered in 1961 by Abraham Robinson, that behave like the "infinitesimal" numbers postulated, but never discovered, by Leibnitz and Newton. Robinson discovered all of the properties of these numbers. They don't behave entirely like the real numbers, rational numbers or any popularly known number concept that existed prior to 1961. Now we don't need to use the real numbers, we can use the rational numbers in what follows, but in the new set of numbers called the hyperreal numbers, *R, that contain the real numbers, there exists all of the numbers which are composed of a real number, say 0.5, plus each of these infinitesimals. For example, if non-zero E is an infinitesimal, then 0.5 + E is one of these new numbers. The wavelength mentioned above and spoken about and characterized by the model corresponds to one of these 0.5 + E wavelengths. The standard part operator simply removes the "E" from the measure (but in a special and highly significant manner).

8. What is an electron, a photon, a drop of water? These physical entities are identified by a set of properties and a set of measures. They are different one from another only because of the lists of properties that identify them are different. But we can even "see" some of these things. Well, I suppose that being able to "see" a drop of water can be reduced to its properties, those properties that will allow it to be "seen." Why do I mention the obvious? It's this very simple observation that is used to generate the basic notion of the ultrapropertons, objects that can be combined together in a very simple manner to yield everything within our physical universe. Indeed, everything in many different universe as well. An ultra-properton is simply composed of +E and -E measures, for a fixed E, in coordinate positions, where coordinate positions correspond to real measures(rational, real, complex, (real) vectors) for physical properties. These yield property numerical representations and, hence, necessary differentiating characteristics for basic physical atomic or field entities within our universe.

I have recently shown how to actually encode, by the same encoding used throughout this work, all possible quantum states within an ultra-properton coordinate. Indeed, any descriptive piece of identifying information can also be related to a specific coordinate that contains either -E or +E. (See http://www.arxiv.org/abs/quant-ph/9909078) A simple mathematical process combines these ultra-propertons together so that when the standard part operator is applied, there will suddenly appear within our universe physical world objects. Prior to the application of the standard part operator, unrealized objects (objects that is not altered by any "physical law") can be rationally assumed to exist in some form within the ultranatural world. This form can be a developing form or be in suspended animation. We may be at the boundary here between the possible ultranatural world (the related supernatural stuff) and the physical worlds, but let's not forget that this is only a model - a model that mimics behavior. (It's a matter of choice whether one considers the supernatural world as anything that is not physical or not physical and distinct from the substratum entities. I have used the term "preternatural" for this substratum non-physical world and all else not physical as "supernatural.")

To indicate the power of the Divine mind , each combined collection of ultra-propertons can actually have a different identifying "name" within the ultranatural world. This "name" doesn't show itself when the standard part operator is applied. So, although in the physical world we are supposed to assume that any two electrons are identical in physical world characteristics, they can have different "names" in the ultranatural world, names known by the Creator. This certainly indicates a power that is even greater than that mentioned in Luke 12:7.

9. Oh! yes. For those that know what virtual particles and processes are, these "things," these properton combination processes can replace all of this virtual stuff. (But not the theory.) How to do this was published in my 1983 paper, "Mathematical philosophy and developmental processes" Nature and System 5(1/2):17-36. But what is the relation of all of this "simple" stuff to Genesis? I'll show this next time, where I'll start at about, say, Genesis 0.5. Note that the properton combination processes can be found in Chapter 11 in my book "The Theory of Ultralogics Part 2" found on my Web site or at http://www.arxiv.org/abs/math.GM/9903082. They also appear in a recent advanced physics book, published by Nova Publishers, but that costs to much. I do think, however, that when these ideas are applied to actual Scripture that some small controversy may develop since the actual number of words used within a ancient language such as Hebrew to describe behavior is somewhat limited. Consequently, one group of symbols may have multiply meanings that can be applied, meanings that will lead to different scenarios. But then we also have 1 Cor 2:9 and 1 John 2:27 to consider in such cases.

Dr. Robert A. Herrmann
Professor of Mathematics
U. S. Naval Academy


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Subject: 8. The GGU-model. MA-model and Day 0 - 1.

Date: April 16, 2000

(What appears next is still useful. However, via GGU-model refinements, I now accept There are hints within the Bible that the God created a "foundational world" (foundations of the earth anyway) prior, in a sequential sense, to His physical world creation. It is mentioned, at last three times in the Bible. (This creation process takes place in Genesis 1 and the substratum and entities are members of His second heaven.) Two of these processes will be described later, but they are capable of being applied by God in the creation of this preternatural world, a world about which little can be known in any detail. However, when compared to the physical world, this world is highly complex and wondrous. To indicate slightly, at this point, how wondrous this "invisible" preternatural relates to the general ultranatural world and how powerful are the Divine creation processes, suppose that there is a single physical world clock that would time how long it took for God to create this exceptional "place" that contains everything He would need in order to create and sustain His physical world creation and a lot more. It would take God exactly 0 physical time to produce such an invisible and wondrous world. I wish there were more expressive words that could describe other aspects of this wondrous world, but this is one of the difficulties with this research, trying to find or even create new words that give a description for concepts that I understand but only intuitively. This is creation day-0

2. As I mentioned, I don't select a special Scriptural meaning for a term, and then try to fit it to a model. I look only to the model's predictions and then see if there is a meaning for a Bible term or a Scriptural statement that fits the predictions. This approach is what yields the rational (scientific logic) interpretation. Recall that the preternatural world can contain objects that do not carry the "ultra" prefix. I point out that the mathematically generated processes "perfectly join together" these two general entities, God's "invisible" and "visible" worlds, the "ultranatural," "preternatural" and "natural (physical)" worlds. These processes model accurately, I believe, such Scripture as Hebrews 11:3.

3. For any entity to materialize and become a real entity within our universe, the model states that the standard part operator must be applied. But, if this operator were the only one used, the object would appear to be in the "suspended animation" or "frozen in time" form. For any entity to display any development within the physical world, the model states that an "ultralogic" must be applied to an "ultraword" (or a object eqiovalent to a ultraword). The basic sequence of events consistently associated with the "And God said, . . . " is the application of an ultralogic to an ultraword, along with a few more processes modeled after mental processes, and these lead to properton combination to which the standard part operator is applied. When this Bible phrase is not used, the model states that the ordering of this sequence may be altered.

4. We are told first in Genesis 1:2, that the earth ('erets - that is mostly considered as "land" throughout Scripture) is formless (tohuw) and void (empty). Since the "And God said. . . " does not appear here, the "earth" would not follow the patterns associated with any physical laws if it was a realized earth. Later there is such a "And God said" statement pertaining to the "land." There are only two model possibilities. Either the earth (land) was not yet realized as a physical world object, or if it was so realized, then it appeared as if "frozen in time" - in the suspended animation form. In this frozen in time form, there would be comprehensible and fundamental "physical laws" but the laws have not as yet been activated. Thus there would be absolutely no change taking place within any of "land" physical-systems. The second possibility is that the standard part operator has not as yet been applied. This means that the object, in all of its details, is unrealized; it's not yet part of the physical universe. Further, this unrealized form need not be in suspended animation with respect to ultranatural events. Which of these GGU--model possibilities might be the case?

5. The next characterization is that the "earth" is "empty." Indeed, the Hebrew word here translated as "void" is actually developed from "to be empty." The only simple GGU-model interpretation is that the "earth" was in unrealized form. It's interesting that this is an exact meaning reinforced by the Hebrew tohaw. One of the significant meanings for tohaw is that it signifies the formless confusing character that matter was formally supposed to have before the development of physical law. The word "confused" implies to me "incomprehensible." Thus the entire description for the "earth" or "land" follows this simple GGU-model interpretation of being unrealized within the physical world. This doesn't seem to indicate at this moment a particular "powerful" Divine creation sequence. But . . . .

6. There is an indication that the standard part operator is applied to unrealized frozen-frames, and this comes from the first portions of any of the event sequences used to yield any of the know cosmologies. As further indicated by Scripture, this would yield an additional and strong "spirit" control over all aspects of the sustaining and creation of our physical universe. This occurs where we are told that "the spirit of God moves (hovers, vibrates, shakes) over the face of the waters." The Hebrew rachaph for moves, hovers, vibrates, shakes is used only three times in the Scriptures and is developed from "to brood." The only possible GGU-model process with which this could be identified is the standard part operator. In this case, the notion of "over the face of" would need to be more closely associated with the idea of being "in the presence of." Hence, this is how I interpret the GGU-model at this point. The significance is that the "water" was, indeed, the only realized material within our universe at this point in Genesis 1, but it was in a form that was without any further physical-system development. The water was, at this point in this creation scenario, in suspended animation. Of course, this shows the almost incomprehensible power that God has over His creation and this is not the only example within Scripture were He demonstrates this particular aspect.

7. I can't continue with this GGU-model interpretation until a few aspects of the "ultraword" "ultralogic" processes are discussed. This can be a very technical area with many surprising and, shall we say, deep areas of some interest. I'll not go into these very technical areas, but simply direct you to where you can find further information, if you find these result interesting.

Dr. Robert A. Herrmann
Professor of Mathematics
U. S. Naval Academy


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Subject: 9. Higher-Intelligent Design, Genesis 1:2.5

Date: April 16, 2000

1.Twenty-one years ago (actually with this revision it's been 36 years ago), the GGU-model and its MA-model portion were in their first developmental stage and I knew, intuitively, what they were starting to display. Although a new language would need to be developed, my goal was then, is now and will be continue to be, to show by rational means the extreme differences between the Creator and His created, to increase our knowledge of His greatest, to maximize His powerful deeds by means of this model while minimizing to the greatest possible degree the modeler.

Hawking told Clinton that shortly scientists would know all the laws of nature. In my view, this is the exact philosophic driving force behind much atheistic science, the desire to be as intelligent as God, if not to actually be a god. Thus, many atheistic scientist should agree that the universe is intelligently designed, even if by chance, and the intelligence being displayed is the same as that of a Hawking. In certain areas where one might question that there is a humanly comprehensible design, we have statements such as from Feynman who states about his theory of partial reflection that ". . . you won't understand why Nature works" in a certain describable way. "But you see, nobody understands that." He also states that "I am not going to show you how photons actually 'decide' whether to bounce back or go through; that is not known. (Probably the question has no meaning.)" [As you should know by now Feynman and Hawking are both incorrect.] There are also creationary models that, indeed, show an intelligent design, but again only the intelligence of the modeler. Indeed, I personally reject any claimed creationary model that gives the appearance of godliness but denies the power there of.

2. My recent CRSQ paper ("Information theory, consequence operators and the origin of life," CRS Quarterly, 36(3)(1999):123-132) is probably not a great conversation piece in creationary circles. This may not be due to its technical nature. What has been shown there, among other things, is that the concept understood as randomness within atheistic theory building is not random when viewed by the Divine mind. We have spent a great deal of effort in denying that information is increased when "random mutation" occurs. The atheistic community disagrees with such arguments. I would let them have their way since the CRSQ paper shows that if a "random" mutation does increase information, then this is a more significant example of intelligent design then a mere non-random alteration, since a very significant consequence operator must be involved, indeed, one that the Quantum Logic people have been looking for but have failed to find. It's actually a mental-like process that doesn't correspond to human thought.

A recent technical paper on chance ("The non-random character and intelligent design of 'chance' events," TJ, 15(2)(2001), 103-109) goes considerably beyond this. It shows that any and all humanly comprehensible theories that are not classical in that they use the "individual event" random concept and predict behavior probabilistically using notions that are humanly comprehensible, actually show that behavior is being totally controlled by a "super" intelligent mind. Sending such a paper to any atheistic or secular journal is a waste of my time also. This was done in the past just to illustrate a point that I now discuss. Such material contradicts the mind-set of the editors, reviewers and journal readers and would never be accepted, unless by mistake by the editor since, although it answers a basic question in Quantum Logic, it points to the logical existence of a "super" intelligence. Now the logical pattern being displayed, in this last mentioned paper, I'll attempt to describe a little later. It's called a "pure ultralogic." How do these two recent results correspond, if at all? Well, the "pure ultralogic" in the second paper appearing in TJ happens to be a member of the same defined set as the one in the CRSQ paper.

3. But, first we need a small introduction to the "ultrawords," then the "ultralogic" that does its work on an ultraword. These things have, partially, the same philosophic meaning as a metric in spacetime. Well, what is spacetime? If we can leave the science fiction junk behind, spacetime in General Relativity (GR) is not an objective real "thing." As Lawden states it "Physical space is, then, nothing more than the aggregate of all possible coordinate frames." But, I personally, unless I draw an image of one, have never actually "seen" a coordinate frame within the physical world itself. What GR tells us is about measurements within the universe; something else Nature doesn't seem to actually do without our help, measurements that are somehow altered by a gravitational field and nothing more. That is, GR and Riemannian geometry is, but, a model for behavior within a still unknown thing called a gravitational field. Indeed, John Wheeler himself states the same thing. He states that Riemannian geometry is but a model for behavior and that the language of geometry itself gives absolutely no indication as to the "stuff" that comprises the universe. Then Fock states that predicted GR behavior of entities within such a "field" itself only has meaning when we can compare such behavior with the intuition obtained by "observing" the behavior of similar entities within our local Euclidean environment. Thus GR, without any additional stuff attached, is but a model for how test objects will behave. It gives no indication at all as to what entities, if any, are being used to "force" objects to behave in the predicted way. (Although somewhat technical in character, you might be interested in my paper on what terms such as Space-Time really mean.)

4. Then consider the much better "understood" Heaviside equations for the electromagnetic field. "Heaviside? Gee, Herrmann made a big error this time. Don't you know that they are Maxwell's equations." Well, this is not really so. I have right here on my desk Maxwell's paper that lists Maxwell's 20 equations. They are not stated in any vector analysis form. Although there may be some confusion on this point, it appears that Heaviside translated them into something like what you see in your basic textbooks and not without a lot of controversy from Gibb's and others. But as hard as I observe those iron filings and the circular patterns they make on a piece of cardboard, patterns that are suppose to represent an "electromagnetic field," I've never observed attached to a space location those "little line segment vector representations" for this field. In fact, what I observe, when I take the cardboard away, is exactly "nothing" attached to space locations. In most such applications, such "vectors" just model behavior and, for me, they don't exist in objective reality. As you'll see, ultrawords and ultralogics do the same thing, they predict behavior but give no atheistic answer as to what it is that "forces" Nature to behave in the predicted manner. But they also model Scriptural statements that imply literally that God is the ultimate object that "forces" the physical and ultranatural to behave in all of its ways.

5. Unfortunately, when the modeling process becomes technical in character, the modeler (me) often appears to become the most prominent. For this I apologize, for this is never my intention. But I've no control over how one might view the following slightly technical discussion. We are trying to describe, haltingly to be sure, some very elementary aspects of the true intelligence that has designed and controls every aspect of everything. So, let's return to the VCR or DVD. I was playing with my "still frame" bottom (pause on DVD machine controller) and tape speed control. (For the DVD, think of th "next button" as taking you through one frame at a time and slowly press this button.) Slowly, the images changed on my monitor as the frames changed. I believe that these frames normally change at a rate of 30/sec, maybe. But now suppose that the frames changed at a rate greater than 10^(10,000,000) per sec. Yes, the VCR tape or DVD that produces such a set of images would be very large. But anyway just suppose. (This is only an illustration.) Remember that these images are actually translations of strings of symbols and these strings are obtained from a set of "words" taken from a totality.

6. Well, consider the entire collection of all of these images that in a sequential order represents how a physical-system develops, that is we let the VCR or DVD go at its "normal speed," which might be very high for this illustration. In linguistics, the term "paradigm" means a word with an ordered list of its inflections or changes. It also means a "pattern" or "model." Thus I call this entire collection,  d, of representations for the behavior of a single physical system a "developmental paradigm." Each image in d is suppose to represent the specific information that yields an actual real event. Please note that such a developmental paradigm, d, yields an event sequence and may only represent the behavior of one single electron as it "moves from place to place" as Feynman would say. Further, a developmental paradigm for physical behavior need have no beginning or no ending. But it can also have a beginning as well as an ending and other possibilities. (I have not illustrated all of these possibilities in my book "Science Declares Our Universe Is Intelligently Designed.") But, in all cases, the VCR tape or DVD does have a beginning and ending. This is not easy to explain in simply terms, so you need to trust me here. Also today I tend to call a development paradigm an "event sequence" where the context indicates that only representative descriptions or images are being considered or the actual real events they represent.

One of the more remarkable facts is that there are development paradigms, d', that contain no images for any physical event at all, but contain only images at such a "level" that we cannot detect them at all. That is images that depict ultranatural events that are being described by stuff in *T_i - T_i (i.e. members of *T_i that are not members of T_i). If we encode d and embed it into our mathematical structure, we obtain a new developmental paradigm, *d. Well, is there anything new in *d?

7. If we would characterize in a simple scientific language the behavior of the electron say by another collection of statements, then everything in *d, at the least, has the same characteristics for a similar language. But as I pointed out with "light" they can have additional properties being, at least, partially described by things in *d - d. There can be additional pure ultranatural events within any physical developmental paradigm. What can these be? Under certain circumstances, the model predicts that they act like additional "glue," from the preternatural, that is required or the development paradigm cannot exist. They sustain and hold together the physical world and some can be considered as forming a "connection" with a higher level world, God's supernatural world. Well, is this what Heb 1:3 means? Well, not exactly. Heb. 1:3 says God sustains the universe by means of a single powerful declaration (word) and this isn't such an object. The object d is, however, a sequence of words or images. But does such a powerful "word" exist hidden somewhere within the mathematical structure?

Dr. Robert A. Herrmann
Professor of Mathematics
U. S. Naval Academy


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Subject: 10. Higher-Intelligent Design, Genesis 1:2.75

Date: April 19, 2000

1. Genesis 1:2.75? What does this mean? It means that we are getting closer to the first "And God said. . . ," the phrase that changes suspended animation into animation, the phrase that yields a universe that "develops and changes" but probably developments "perfectly" in the sense that nothing within the universe was yet created that had the power to change, within limits, the required behavior of a physical-system. However, there may be "something" in the model that describes a Divine command and "increases" our understanding of the great "power" being displayed by actual material creation, especially when we compare such power to that of a human being. Obviously, there is nothing yet in the VCR or DVD images, except for the number of images we might need that characterizes such a "powerful command." Well, things might start to get just a little more "complex" if I were to detail all of the technical aspects of what comes next, which I won't.

2. I've an illustration at http://raherrmann/chance.zip that shows how assumed physical law and human deduction yields a developmental paradigm. Consider the description of the electromagnetic radiation emitted by a collect of excited hydrogen atoms as they travel further and further into an ever increasing gravitational potential. Approximately 12 physical laws or processes are combined together by 9 human deductive processes and the result that one would "see" and be able to describe on the monitor screen is a developmental paradigm, d, that reveals that emitted "photons" decrease in frequency and this is indicated by a sequence of changing colors on the monitor screen and only this. We have for this particular scenario a developmental paradigm that yields one aspect of the combined physical-systems of a collection of hydrogen atoms and a changing gravitational potential. But, there are no actual physical laws or processes being formally displayed. They are actually hidden. It seems that if this all can be verified by experiment, then "Nature" is simply "forcing" some hydrogen atoms to behave this way. Further, the human mental processes that would produce such a collection of images are also not displayed. Of course, one can now describe a physical law relative to such a scenario and "light" frequency. But, such a description would also require human mental activity. The actual development paradigm, d, need only be composed of the images and nothing else.

3. Thus, step-by-step, the human mind creates a developmental paradigm associated with an event sequence from descriptions for physical laws or processes. This is only one illustration, however. Clearly, I've used the general method of idealization as a first step. That is that, with respect to a particular circumstance, in the beginning one starts with but one ideal developmental paradigm for the emission of electromagnetic radiation and it's not assumed that there is any type of perturbation in the process. Indeed, in this "perfect" case one might even simply start with the images themselves, that might be somehow pre-selected, and claim that the true physical law is that "Nature" simply requires the emitted radiation to conform to these images. Or "Nature" might also simply require these images to be the results of the combining together of other images that display developmental paradigms for the physical laws used in the human derivation. The images give a type of plan, that replaces physical law in a certain sense. A long time after these interesting ideas were formulated, I learned of the following quotation from one of the original five members of the Institute for Advanced Study, Hermann Weyl, who asked the question, "Is it conceivable that immaterial factures such as images, ideas, or 'building plans,' also intervene in the evolution of the world [universe] as a whole."

4. One of the definitions for a "word" is that it's a collection of symbols that replaces the spoken sounds and that it gives "information." Now the VCR tape, a CD, or DVD, has such information encoded upon it. A great deal of information can be so encoded. When Maxwell modeled an electromagnetic field, he assumed that there were infinitely many magnetic "lines of force." However, to work with regions within such a field, he invented a powerful mental microscopic so that there were now only finitely many magnetic field lines in his "field of view" which he "counted." Clearly, if we were to describe an ideal behavior for the electromagnetic radiation produced during the entire "existence" of these hydrogen atoms as they move through various gravitational potentials, it might take a continually finite but ever increasingly large description. There is no single "word" in any of my dictionaries that could convey all of the information needed for this complete description since its length is indeterminate. We do have a sequence each member of which is an increasingly large collection of symbols, however, but no single word, no single fixed finite collection. This is certainly a problem, but, there is another one. What has been described is a humanly comprehensible "theory generated" developmental paradigm. A truly powerful Deity should be able to produce a developmental paradigm even if is part of a universe different from ours. That is the basic developmental paradigm should be very human-theory independent. Hummm.

5. Well, what to do? First, I won't do as Maxwell did and assume that something is an "infinite" collection and then use my imagination and turn it into a finite view. I always suppose that all of the necessary mechanisms and objects within the ultranatural world for the creation and sustaining of the physical world were created in the very, very beginning. Further, maybe everything I need is already there somewhere within the mathematical structure and I don't need to play with my "imagination" and force an object or mechanism into existence. I "simply" need to find a "word" that will fit the bill in all ways, not just for the ideal behavior of electromagnetic radiation, but for everything that the human mind scientifically describes, whether theory generated or not. But, wait don't you need physical laws? No, all I need is to observe and describe. As illustrated, the actual images I see on my monitor aren't the physical laws. Physical laws are used to produce the images for a theory generated developmental paradigm, but are not actually part of them. (Although they can be made part of it but as a separate parallel part.) We can answer Weyl's question with a, "Yes! it is conceivable." Not only that but one might actually conclude that, from an ideal viewpoint, what Nature does is to "simply" force material entities to conform not only to an image, but even to a pre-selected plan composed of images.

6. Many interesting pre-selected images can be produced that actually would contradict physical laws for our universe. I've a VCR tape that when I play back the images, it shows me a humanoid robot that "morphs" into a piece of floor covering. Then "morphs" from that covering into the humanoid robot once again. Each image has an encoded description and, I guess, only human imagination was necessary. For a developmental paradigm that starts at a particular image, adjoin the first image to the very next image and you have a sequence of two images. Zip (i.e. encode and compress) these images, and dump it onto a zip.file named M.zip and you will get a single word that contains the two-image information. Now adjoin the very next image in the sequence to these two, where these three images are connected together symbolically and compress this three-image word into a single zip.file. Now repeat the process for the entire sequence of all images. What you get is a set of encoded "words" contained in M.zip. (Yes, I know each word is getting longer and longer, but, at the least, each word is a finite string of symbols anyway, not an infinite list of symbols.)

Let's "see" what we get if we download one of these words, decode it, and view the "play-back" on the monitor. Well, the physical-system may just set there and do nothing. Yes, you can include the "do nothing" behavior as well. Or the system may slowly alter its appearance. But, there will come a moment when the information contained in one of these words ends and my monitor screen goes blank. Note that the objects in M.zip, since they are "words" from an encoded language, also have various describable characteristics that will make them "words" and not say, "pigs." But the blank screen is clearly not very satisfactory. So, I'll encode the whole M.zip file and embed it into the mathematical structure and "see" what happens.

7. Well, as usual, I get a new *M.zip and there is something in *M.zip that is not in M.zip. Any objects in *M.zip not in M.zip are called "ultrawords." But what makes them "ultra"? The internal structure can be analyzed as is done in (1). What is discovered is that there is a w in *M.zip that if I could play it back on my monitor, it would display the entire developmental paradigm, d, for the developing physical-system no matter how long it would run. If you had a physical-system that had no beginning, or no ending, then the w' that corresponds to this physical system has a few slightly unusual properties when compared to human concepts. For example, w' has a beginning or even an ending image, but what the beginning or ending images are we can have no detailed knowledge since these images cannot be decoded. Further, in the language used for pure ultranatural world where w' could be completely decoded, w' behaves just like a finitely long string of symbols, although from the physical world viewpoint it's not this simply described. It's "something" that behaves like a "word" in a language restricted to descriptions of the stuff in the *M.zip. (Actual behavioral descriptions for members of *M.zip and how their behaviors compare requires a different yet meaningful language, which I'm not introducing.)

Again I emphasize if w or w' can be decoded, then all the necessary information becomes available to produce the complete developmental paradigm, d, even in the correct sequential order. There are portions of w, indeed most of w, that cannot be decoded at all. If I could play these back on my monitor, they wouldn't appear, but they are still necessary. I wouldn't "see" them, but they cannot be eliminated, they must be there. These hidden images are called the ultranatural events and can be described as the ultranatural "stuff" that is necessary to uphold and sustain the physical-system behavior being described by d. But, there is a problem. I cannot as yet decode any of these ultrawords properly and produce the physical-system images since there is one general process missing. I've not included any process to extract the information from the ultrawords. I don't as yet have a computer chip or program, so-to-speak, that will do this. At the moment, ultrawords are "words" that behave just like a "superball" filled with a great deal of "power" or information but this power can't as yet be displayed. However, I know that such a *M.zip extraction process does exist somewhere within the mathematical structure.

If I can find an appropriate extraction process, then maybe w might model the "word" of Heb 1:3. For the Greek term used there means a "spoken" world and this extraction process might model the "spoken" part of this meaning. Oh! There is a something else that would be needed and I think it also exists in some *M.zip. There needs to be an ultraword w that contains enough information so that when God applies the extraction process an entire ideal universe is forth coming. This would also mean by implication that God "knows" what is in such an ultraword. It's part of His dictionary, so-to-speak. He would, for such a universe generating ultraword, know the "past, present, and future" for the universe that would be displayed.

Dr. Robert A. Herrmann
Professor of Mathematics
U. S. Naval Academy


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Subject: 11. Higher-Intelligent Design, Genesis 1:2.9

Date: April 24, 2000

1. From the reductionist point of view, there most be basic physical-systems from which everything else is composed and which contains many famous "undefined" technical terms. From a properton viewpoint, there are but a few of these "basic" physical-systems. But the universe is a physical-system. So how can we get a slight idea as to how a universe with all of its physical-systems is constructed? Since a solution to the General Grand Unification problem has only been solved by the methods of ultrawords, etc., it should be self-evident that the complete solution would tend to become somewhat complex. Further, as you'll notice, I hope, certain cosmologies are definitely not necessarily complex from an ultraword viewpoint. The basic idea behind a Big Bang cosmology is almost trivial in that it's the least complex, and would show the least creationary power. Other applications of the ultraword concept lead to more highly complex mechanisms, mechanisms that require an exceptionally powerful intelligent agent. This doesn't contradict the simplicity notion relative to the basic processes. It refers to how these processes might be combined together such that creation demonstrates powerful processes that are, indeed, rationally obtained.

2. (The following is in the original course e-mails and refers to how I approached the generation of a universe in the above mentioned book. I no longer use this method, but rather consider only one ultraword (actually an entity equivalent to such) for any entire universe since what constitutes a physical-system is arbitrary. This one ultraword approach also produces any emergent properties. This eliminates one of the ultimate ultrawords here discussed. However, ultimate ultrawords can still used for other purposes discussed in the book. For example, collections of libraries. The physical-system method satisfies the reductionism philosophy.)

There are various ways to generate hyper-developmental paradigms, the *d, and corresponding hyper-event sequences. There are *developmental paradigms (the * is interpreted by the term "hyper") composed completely or partially of images that are not "decodable" and that correspond to ultranatural events. But, even for those composed of decodable information, different modes of generation for *developmental paradigms can have some very significant consequences. In this lesson, I won't discuss the additional complexities that result when participator actions "appear" to alter physical-system behavior. Unfortunately, we now arrive at necessary notational complications. Suppose you have a physical-system called NS with its basic image developmental paradigm; the sequence d_j = {d_i}. NS is still composed of many subphysical-systems that are combined together to form the images that represent the step-by-step development of NS. I point out that what a science-community defines as physical-systems need not be the actual ones needed for this construction. We cannot really know what subphysical-systems are needed, but there are probably many. Our notion of physical-systems and subphysical-systems etc, is intended only as a model for behavior.

[(1/13/2012) This is a view of the step-by-step development of the physical-systems that comprise a universe-wide frozen-frame as a universe develops as primitive sequence. Recently a type of developmental paradigm is used in designing each universe-wide frozen-frame that occurs for each sequentially presented universe-wide frozen-frame. This described ultimate ultraword approach should probably be skipped and you might skip to 4.] The second level subphysical-systems developmental paradigms are {d_(1,i)}, {d_(2,i)}, etc. where the number of coordinates in a subscript denotes the subphysical-system level. (This can be made more mathematically precise.) Then we have the subsubphysical-systems i-th image {d_(1,1,i)}, {d_(2,1,i)}, . . . {d_(1,2,i)}, {d_(2,2,i)}. . . and their subsubsubphysical-systems etc. are each represented by a developmental paradigm. Because of the use of propertons, there need be only finitely many sub . . . subnatural systems. (Note: even in the case of a universe with no beginning or no ending such objects mathematically exist.) Now each of these developmental paradigms, which correspond to the event sequences, has its own generating ultraword w_(., ., .,j). Then for each such collection of {developmental, subdevelopmental, subsubdevelopmental etc. paradigms} = D, it's shown in (1), that there is a single ultraword w_j', an "ultimate" ultraword, that contains all of these images, all of this information, that will generate in a step-by-step manner all of the images contained in each member of D, all of the sub...subphysical-systems combined, when we apply an, as yet not discussed, extraction process. If we have started with a universe as the first level physical-system, then w_j' generates a universe. In the nonstandard model, each of these developmental paradigms d in D, becomes a hyper-developmental paradigm *d. The extraction process applied to w_j' gives you the w_j and then applied to each w_(., ., .,j) along with "hyperfinite" ordered choice gives you the step-by-step ordering of the event sequences. But, you also have other stuff in each *d. Each w_(., ., .,j) and w_j' can be considered as super-compressed collections of information. From the viewpoint of zip compression, although it may not be necessary, one can think of w_j' as a further compression of the combination of all of the originally compressed zip files w_(., ., .,j). (In certain cases, there may be things in w_j' that are not any of the w_(., ., .,j).)

3. Now you store all this information as zip-type files on your hard drive. You first apply the "super"-computer extraction process to w_j. It decodes the entire NS as described by the {d_i} information only. Suddenly one window on your screen begins to display images of the actual moment-by-moment development of NS. There are bottoms you can "click" that will open other windows. You can open one of the level 2 windows and it will display the moment-to-moment development of a specific level 2 subphysical-system. This is easily done since each w_(., ., .,j) is identified. Then one button says "complete image." You click this and if you have just a few subphysical-systems, you'll see the moment-to-moment combined behavior of all the subphysical-systems. It's like looking at an x-ray image with decreasing intensity the "deeper" you probe the subphysical-systems. Moreover, there is a little note at the bottom of the screen, one of those error messages, it says that the software you are using will not allow for the display of many other "images" contained in these levels. These are the "ultranatural events" that must always be part of this process. Can we illustrate how they might fit into this process?

4. Well, there is a lot of stuff going on "behind" the scenes so to speak while the NS is being displayed. We have the electrons used to "make" the images, the electronics, microprocessors etc. all of which we are not suppose to notice. Hence, one might think of these ultranatural events in the same context. They are necessary to produce the NS, to sustain the development, to uphold the images, and they might also be described in this context as a type of "ultranatural glue" that must always be part of this NS development or this NS will simply not exist as a real object. This NS world w_j' exists, however, as an entity stored in a file on the "super"-server that contains the information. Things are starting to get a little complex even for one physical-system such as NS. But, having complex processes within Nature are is not a new concept.

5. The notion of complexity using this approach is easily understood. However, it does depend upon a somewhat arbitrary definition as to what constitutes a subphysical-system. Call the "dimension" (i.e. the level) of a subphysical-system the number of coordinates in the subscript ultraword representation. The complexity of the NS physical-system is simply the highest "dimension" number. [1/7/04 How the subphysical-systems are use to form w_j' and the notion of complexity are not illustrated in my forthcoming book "Science Declares . . . ."]

Actually the descriptions we call the physical laws or processes that state that the pieces of this specific physical-system and all of its constituents must be combined together in a specific manner in order to produce a developing NS can be replaced by the "images." The physical laws are how we perceive regularities as the images progress. In this model, the actual entities that control the development of these images are various operators that can be considered as physical in character or they can be considered as intelligent actions. What is displayed on the screen is the result of such a composition, a composition that can be produced by an information extraction process that follows procedures that are similar to those of an infinitely powerful mind.

The Creator of these processes knows what information He has placed into each of the ultrawords. Hence, if this information is realized, within a physical world, this Creator continues to have knowledge of the "past, present, and future" for the physical-system NS. Indeed, in the case of realization (i.e. the production of the physical stuff), the extraction process, under ideal conditions, would "force" propertons to combine together, and the standard part operator to activate so that the physical world objects will conform to the immaterial "images" or "building plans" (ultranatural theories and ultranatural laws) that exist. (In our "super"-computer, ultranatural theories and ultranatural laws correspond to part of the "programming.") Indeed, this is why, except for one requirement for propertons, that this approach is (humanly constructed) theory independent. These "building plans" need not correspond to anything that can ever be humanly comprehended. One can, of course, characterize aspects of the GGU-model in different terms. Theologically, one might say cautiously that the GGU-model characterizes the Creator aspects of the "mind of God." This is the only reasonable theological description I can give, at the moment, as to "where" these "images" are located since I'm welling to accept, due to the required constraints, that I'm not intelligent enough to comprehend these notions otherwise.

6. Well, after all of this, one might think that the extraction process must be very complex and difficult to comprehend. But, this is not really the case. So, in part 12 of this little course relative to how the GD-world and GGU-model relate to theology, not only can the extraction process be discussed but we can progress rapidly from the "And God said Let . . ." of Genesis 1:3 all the way to Day 6. (And, yes, as I pointed out what I detail as possible Genesis events comprises only one collection taken from infinitely many possibilities.) Notice that after the extraction process is discussed, the General Grand Unification problem will also be solved for it's this extraction process that "binds together" all of the physical-systems that comprise a universe.

(1) "The Theory of Ultralogics"

Dr. Robert A. Herrmann
Professor of Mathematics
U. S. Naval Academy


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Subject: 12. I do not know the answer! Genesis 1:3 - ?

Date: April 28, 2000

1. (Only two more to go.) I've certain personal beliefs that I've developed from my understanding of the Bible. I do not, and I repeat, I do not have the slightest idea of how God created the supernatural world or of what this invisible world is composed unless Biblically stated. I'm not intelligent enough nor do I have a large enough vocabulary to describe in any detail the true methodology He uses. I've absolutely no idea as to how God created the processes that control all of His created entities. I cannot even conceive how it's possible for God to "force" stuff to behave in specific ways. The GGU-model, when theologically interpreted, is just that - a model. It mimics behavior that I cannot comprehend except in this form. I take Gods "work" or "business" as not merely the creation of our universe, but the creation of the supernaturally related ultranatural world and, more importantly, the creation all of the processes He uses to sustain and alter His creations. Such a statement as in Genesis 2:2, for me, simply signifies that God completed all aspects of creation and this includes all of the processes and activities He can use to alter His creation.

In my personal view, there is absolutely nothing termed as physical law that gives even the slightest indication of the extreme power and intelligence of our Creator since such physical law is deduced by His created, a very inferior mental element in comparison to the Creator. Did God actually "speak" as we comprehend such an exercise in the physical world and stuff was created? No, from my viewpoint. God did something, however. The Scriptures give collections of words that do describe creation in terms of humanly comprehensible concepts. Even Colin Brown once stated, that the Bible is a model that uses basic concepts to model Divine behavior. This, of course, I tried to explain in the very beginning of this series.

2. What I've been describing is a linguistic model that is rationally deduced from a mathematical structure. You can substitute for the term "ultraword" something like "information" (often an undefined technical term) such as hyper-information or whatever. I've no idea what the term "images" or "building plans" mean to God. I've no idea if God specifically requires a hierarchy of ever more complex levels as I've described previously. I do know that such a hierarchy reveals an exceptional creationary ability and control when compared with my abilities. I can only describe behavior using a language that is comprehensible to me. Under no circumstances do I contend that such a language depicts accurately the actual "stuff" or processes that God uses. What the model does is to replicate a "progression" of events that leads to the same results as that produced by God's "Black Box." The MA-model puts "stuff" into its mechanism. The mechanism rationally produces material stuff. Using the idea that the ultranatural world was created in sequential order prior to the physical world as a foundation at the moment I discussed previously, these modeling ideas, as theologically interpreted, only show that there is a scientifically rational description that corresponds to or parallels some of God's creation activities. I make absolutely no claim that "this is how God actually produces these physical world results" although the processes do give an exquisite correspondence between the model and literal Biblical meanings. But there is a general description. It does appear, but in a very unknown way, that God changes His "thoughts" into various realities.

3. As to "properton theory," there is no present quantum styled theory, even all of the very imaginative string theories, that cannot be replaced by properton theory, especially any theory that deals with "indirect evidence" or even "no evidence." Such humanly constructed theories with all of their mathematical artifacts, recall my "vector" example, that one might claim do correspond to something in an "invisible" reality, where nothing can be directly detected, can but be considered as "book-keeping" theories and nothing more than that. Properton theory simply "jumps over" these book keeping theories and reproduces all of the required characteristics of any physical entity that does appear to exist in the objective "natural world." What the term "book-keeping" also means, to me, is that God has allowed the human mind to have just enough ability so that we can create models using humanly comprehensible "images" that help us to predict behavior, behavior that may aid us in actual constructions of material stuff or to avoid dangerous situations, and the like.

4. Mathematical "operators" can be used to alter physical conditions. Returning to my "vector" example, consider the Cartesian vector field <x,y,z>. Well, let this vector field represent a force that is attached to a point (a position) (a,b,c). Hence, if we evaluate <x,y,z> at (1,2,3), we get the "vector" <1,2,3>, then the "force" attached to the point (1,2,3) yields the displacement vector with initial point (1,2,3) and terminal point (2,4,6). This vector has the magnitude or the force has the strength of (14)^(1/2) in the Euclidean sense. Now there is a well-known operator that destroys this force field in that the terminal and initial points coincide and the magnitude of the force is zero. The operator is the curl. The curl of <x,y,z> = <0,0,0> and can represent the entire destruction of these forces. Of course, it can also represent other things as well. In another interpretation, it would only mean that there is no local rotational effect produced by this field if the objects could be affected by such a rotation. Well, what this demonstrates is that there are mathematical objects that represent but are not equal to physical stuff. And there are operators that change mathematical statements into other statements. And then the results are interpreted to mean either the actual changing of physical stuff into other physical stuff or, in this case, into "nothing" that yields a physical effect; or by changing the interpretation, they can just be measuring the presence of a physical effect if the objects are affected by that effect. This same modeling procedure holds within the MA-model.

5. But what would the operator be? Because we are dealing with things that behave like "words" and language concepts, then "logical operators" model the "spoken" notion. The curl operator follows specific rules that will always yield the same "vector" expression when applied to a specific fixed vector field. A logical operator, say in the form of a "finite consequence" operator, takes strings of symbols, words, and also uses a fixed set of rules and processes written as sets of symbols. One specific difference is that when the operator is applied to say one word, it can produce a set of results, containing many different words usually, rather than one result as in the curl case. Logical operators are called "set maps" for this reason. Now what are the rules that are used? These rules are logical in character in the following sense.

6. I don't know how the human brain comes to deductive conclusions. For "logic," the human brain is considered as a "black box." A word or words are put into this "machine" and then words, phrases, even books or libraries filled with stuff are produced from this one word or words. If the words put into our "black box" produce certain symbolic results and don't produce others and almost all individuals produce the same equivalent symbolic results and not the others, then we say that we are thinking "rationally." This is specially so if some of our deductions also lead to observed physical-system behavior predicted from observed physical-system behavior.

The formal rules used to produce the same results mathematically by means of a mathematical operator cannot be traced to anything we actually do mentally. These rules are logical in that they allow for the same results to be produced from the word or words put into the operator as that produced by the majority of human brains. Indeed, the rules will always lead to the exact same symbol string results for a fixed impute when a properly defined logical operator is used. Thus, the notion of rules and processes for generating the same results as human thought is exactly the same notion as the physical processes we call physical laws or processes. These so-called physical laws don't appear in any of the actual "images" that comprise the behavior of a physical-system as I've observed the systems. Of course, we may use devices such a diagrams and arrows, numbers, words, symbols etc. to represent these laws in a humanly comprehensible form, we hope, and obtain describable predictions. But I personally have never observed a physical law itself, something that would exist even if no intelligent life is present, and that states in some form, apart from the images, that a physical-system must behave in a certain manner.

7. So, since we are using changing images in place of these stated physical laws, then we might be able to supply a logical operator that will satisfy the requirements for this modeling process - for the changing of these images. Using the concept of simplicity, one can define a specific finite consequence operator, where the rules for this operator are the simplest possible subset of the ordinary formal rules used to model the ordinary everyday human mental process called "propositional" deduction. It's interesting to note that these very simple rules also satisfy the requirements of "quantum logic" as well. Call this operator S. This operator is embedded into the nonstandard mathematical structure, as before, and automatically becomes *S. Now the "fun" begins.

What are some of the properties of *S? It turns out that from theorems such as 7.3.4 and 10.1.1 in (1), that *S has the exact properties needed for our "extraction" process. *S is one of those "ultralogics" and, depending upon the hierarchy, when it's applied to an ultimate ultraword, w', it generates the other ultrawords, and will immediately generate all of the subdevelopmental (hierarchy) paradigm images. There is a second operator that immediately comes into play, the hyperfinite ordered choice operator, that puts everything into correct order. This process is based upon the important mental process of choosing and ordering a finite collection of objects. There is a mathematical operator that mimics this process.

Next, another mathematical operator is used that mimics a process that forces ultra-propertons to combine together in a rather simple way and to form the characteristics for every constituent so that the results duplicate each sequential image as it changes. But these images are not realized until the standard part operator is applied. All of these process are intelligently designed, and the first applied - the most important one - yields actual characteristics for such intelligent agency. The ordering of these processes need not be maintained except under the one specific command "And God said, let . . . ." This is what I mean when I state in my U-cosmology paper that events occur due to application of the ultrawords, ultralogics, properton combining processes and the standard part operator. The end result of these processes is exactly what one observes in the physical world where the "invisible," so to speak, physical laws also yield changes in the observed events.

8. I don't intend to repeat here, in any great detail, what now appears in the latest version of my "U-cosmology" paper. But I'll show, with three specific examples, how these processes correspond to what I accept as the strict (common) meaning of Genesis 1. All of the applications of the ultralogics throughout all of my theological interpretations should be taken as statements that reveal that God, not physical law, controls all aspects of all physical-system behavior, even those physical-systems that He allows to have some degree of free-will. There is certainly no language that can adequately described such a "powerful" being. I give in sections 7 and 8 of the U-cosmology paper listed below, a detailed, full and complete justification for the following very brief description.

9. [I have altered the material this section in my most recent articles on the Eden Model, which I now accept.] The following is only of historical interest.) "And God said, Let there be light . . . that it was good." By the above process, the operative properties of the entire electromagnetic field suddenly appear (an MA-model application). This indicates that "light" is the most important aspect of God's creative entities. I've contended for years that this is physical fact, a fact that alters the "chaos." We must have creation of real physical entities when this sequence of processes is applied. For further use, God has separated portions of the actual spectrum. The next "And God said. . . ." is the creation, by the above processes, of the "firmament." I consider the above processes as activating the "frozen in time" water image separating it into a movable outer portion, or outer boundary and an "inner" portion. I contend that the waters mention in the first part of Genesis 1 comprise these two parts and the "inner" portion is as Scripture states the water used on and in the original created Earth.

The separation is produced by a simple but "rapid" "stretching" or "unfolding" of an object composed of a "dense" collection of the predicted propertons. As pointed out in the main article, this cannot alter the "firmness" to an extreme degree of the (sub-quantum) substratum. I would have liked to have done this work say 40 years ago so that the following would not be after the Big Bang predictions rather than present them now, but it appears that when one rapidly stretches out this collection that it will actually show its presence by radiation changes that will be exactly the same as what is now measured for the microwave background radiation. This radiation necessarily correspond to the "heat" notion associated with the "stretching" (natan) of malleable metal when it's being hammered-out (raqa), which are some of the most basic meanings for these scriptural terms. Such radiation need have no relation to the so-called Big Bang cosmology. (The end of the day-two).

10. "And God said, Let . . ." There are certain ways that ultrawords can add to or change the previous physical-system behavior as I'll discuss them in the next and last posting in this series. But for this last example, just assume that within the event sequence being used here that, within the remaining inner portion of the water, "dry" land appears (i.e. is realized) from the substratum in the usual manner. I consider the use of the word "dry" as a clear indication that the process was by sudden appearance in material form and new material appeared within the universe and the land didn't appear due to any other physical process. The same activation of ultrawords produces all the other entities mentioned in Genesis 1:11-13. God commanded and it was so. (End of the day-three.) Remember, that for me, this is but a model for what is in reality incomprehensible in detail.

http://www.serve.com/herrmann/pp3.htm

(1) "Ultralogics and more. . . ."

Dr. Robert A. Herrmann
Professor of Mathematics
U. S. Naval Academy


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Subject: 13. Quantum Theory, Perturbations and Beyond.

Date: May 3, 2000

1. In articles on this website, I discuss three different day-four models and won't repeat that discussion here. It has often been said that those who construct creationary models refuse to change their model even if under the strongest attack. For me, this is not so. But I will change my stuff only if new research indicates that such a change is necessary. Until the most recent discovery relative to the remarkably designed "ultralogic generated" results that correspond to probabilistic predictions, I accepted the conclusion that all quantum theory styled probabilistic descriptions are but the method God uses to establish the "decaying" aspect of physical-system behavior immediately after the "Fall" and at the "Flood." However, it now seems that we can have a little knowledge of some of the ultralogic details that govern the behavior of the created physical-systems. A remarkable ultralogic P, when applied, will reproduce the actual probabilistic sequences predicted by these theories. This demonstrates an additional and remarkable Divine control over such behavior that previously was characterized by me and others as perturbations that contradict such a Divine control.

This also answers a question posed a long time ago. Why, as an example, when one calculates the decay rate of a material does the actual rate become more accurate when more material is used? This is the exact conclusion one obtains from this ultralogic sequence when the "number" of entities that can decay is correlated to the "trial number" associated with a decay event. Also, I no longer give any consideratioin as to whether quantum physical "virtual" objects or processes exist in objective reality. Since I consider such theories as but "book-keeping" theories that predict characteristics that are used to "mold" propertons into intermediate propertons etc. The reality of the objects involved is of little importance to me. These virtual things all have identifying characteristics and can be included within properton theory if one wishes.

2. Due to this newly discovered ultralogic P, I no longer consider theories that are not classical in the sense that they only predict probabilistic statements as an indication that the universe is "decaying." This has produced an additional complexity, however. This complexity relates to a correspondence between this probability generating ultralogic and the "images" generated by ultimate ultrawords and the like. Although it's possible to use a created mechanism such as the one used for other types of perturbations, I feel that we may not be able to comprehend such a correspondence for it's probably hidden within the ultranatural theories and ultranatural events. Further, I point out that all such processes that would control the development of our universe would be processes created over a "zero" interval of observer time in the "beginning" and physical-systems only appear after realization.

3. For the remaining perturbations, there is a reasonable approach that is related to a mechanism the would be needed in order to have "created," but not realized, developmental paradigms available when God created, during day-three and five, entities that can perturb His created physical-systems due to a certain amount of "free-will." This is a created semi-automatic process that, due to the application of an ultralogic, will always model Heb. 1:3 relative to sustaining the universe, but it's somewhat automatic. It might be correlated to something like "breathing" and it might indirectly relate to say Job 34:14 -15.

4. What I give next is only the DVD model for the perturbation notion. (That is the information is encoded onto such a device as a model.) [1/7/04 As discussed in my book "Science Declares . . ." there are two forms of perturbation. One form is simply caused by the existence of the ultranatural laws of which we can have no knowledge. These laws eliminate this notion of perturbed behavior. The second type is that produced by the behavior of animate objects. This second type is what is discussed next.] What we would have are "covirtual" earths and "covirtual" universes. Each collection of these would represent all of the allowable perturbations. They are all "known" since from the Divine viewpoint the quantity of possible perturbations behaves as if it's finite in character. This has been described by some as "exhaustive" knowledge. As an example, after day-four, each possible perturbation produced by an animate object and that isn't controlled by an a priori probability would actually yield an altered universe as say represented by a different DVD model that originally contained within its DVD sequence a non-perturbed "ideal" pattern. Hence, one would have a collection of DVDs one for each possible perturbation. (A lot of them.) Although it may be difficult to comprehend, there is actually one ultimate ultraword w', that when the single *S ultralogic is applied to w' this entire collection of DVDs (universes) is formed. Talk about a powerful "mind." As described in my recent paper on the entangled pairs notion, the GGU-model predicts the possible existence of "ultrafast" "state changing" propertons and there are a lot of these. It would be just such ultrafast propertons that would mediate this quasi-automatic selection.

Well, now comes the rather fantastic part, a part that requires a further analysis of such statements as Heb 11:3. The model predicts that the material universe is created by means of "immaterial" notions or stuff, as suggested by Weyl. From analyzing Heb 11:3, among other Scripture, I'm convinced that the Scriptures do allow such "creation" process. In my personal view, the "material" universe is created from "images" or "building plans" in the mind of God and created immaterial processes that are modeled by linguistic operators. "What is seen was not made out of what was visible." This is a model, as previously discussed, that states that the actual Divine processes apparently "cannot be perceived" in a more concrete way.

5. What these processes imply is that the material universe as we know it is being re-generated, not of course re-created under the definitions I have given, from moment-to-moment, when any perturbation from the ideal occurs. This re-generation replaces the appropriate portion that has been affected by the perturbations. From the DVD illustration, this would mean that "ultrafast" propertons determine by "reading" the perturbation that a specific DVD corresponds to that perturbation, and that DVD is for a moment activated. Of course, God must uphold this process by application of an ultralogic. Once again, an incomprehensible Divine power is being displayed. "You mean that instantaneously this occurs throughout the entire universe? I've never heard of such a possibility?" Well, here is one of my favorite totally secular theories that "instantly" yields "many" different universes and that is still being seriously considered by some. As physicist Bruce DeWitt writes: ". . . every quantum transition taking place on every star, in every galaxy, in every remote corner of the universe is splitting our local world on earth into myriads of copies of itself [a very large potentially infinite number]. . . the splitting of the universe is unobserved . . . [this theory] can never receive operational support in the laboratory . . . ." DeWitt considers that ". . . the view from where Everett, Wheeler and Graham sit is truly impressive." (DeWitt, Bruce, Quantum mechanics and reality, Physics Today (Sept. 23 1970):30-35.) This Everett-Wheeler-Graham multi-worlds theory isn't scientifically verifiable. The actual formalism states that there can be no evidence, in our universe, that such events are actually taking place in objective reality. But the Divine processes I've presented here, the "results" of the above re-generation, can be verified, in a sense, since the predicted results exist everywhere around us.

6. Technically a single DVD corresponds to a sequence of ultimate ultrawords that leads to "images." Then we have a sequence of DVDs; hence, a sequence of sequences, etc. One last requirement is what happens when sin enters into the picture and physical-systems begin to "decay"? This is accomplished in two cases, in Genesis 3 and 7, by "simply" considering two other created sequences of DVDs. As usual, all of these DVDs lead to created images that are activated and become what we perceive about us. [1/7/04 This is expanded upon in my book "Science Declares . . . ] God also knows all of this information relative to what we would term as the past, the present and future. It's also interesting that these DVD sequences can be created so that they will converge to a specific ending. The only indeterminate is the "time frame." That is, the rate of convergence "may" depend upon the perturbations that occur as they are produced by the animate objects. Please remember, as I continue emphasize, that this is a "model" for behavior and I do not assume that I can describe in a comprehensible language the exact way God does all of this. It is, at the least, rational to postulate that some sort of process does achieve the same results.

7. Now that I have completed this course material, please remember what I wrote at the start. "When I have completed this course, you do not need to accept the final model presented. You can constructed one of your own." I sincerely hope that this series of postings will aid in a better understanding of some of the GGU-model theological interpretations and predictions and, especially, the material that appears in my "seemingly never ending" papers that appear on my website.

Dr. Robert A. Herrmann
Professor of Mathematics
U. S. Naval Academy


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