A GID-model Illustration -
Constructing a World Globe

Robert A. Herrmann,
26 DEC 2013. Revised 6 APR 2018

Although not originally constructed in this manner, each Complete GGU-model process can now be directly related to real human mental and physical processes. This is an example of such a related construction process. Of considerable importance is that the General Intelligent Design interpretation (GID-model) predicts the existence an higher-intelligence, where such an intelligence is compared to human intelligence relative to deductive thought. Such an higher-intelligence is not postulated, it is predicted from how humans behave. Its relation to various defined creationary operators is inductive in character.

All of the basic GGU-model processes are modeled in specific and significant ways. The mathematics directly predicts other fundamental objects. Each GGU-model process can now be directly related to real human mental and physical processes.

The following scheme (0) relates directly to many human forms of behavior. These are described via the "H" statements following this scheme. [[Usually, but not always, mathematicians write the members of this (0) scheme, as it relates to operator application, from left-to-right (i.e. C(X) "C" applies to or "operators" on X). All schemes of this type that appear in this article are written in an application mode from right-to-left, in that the "operators" apply to the entities on the left. The symbol Λ is a capital lambda.]]

A GGU-model Scheme

                 H1      H2    H3        H4           
     ↓        
(0) ((Λ(n), I(a,b))A') → (GSt)

Bob works for "The World Construction Company," a company that constructs detailed globes that depict our "world." The instructions Bob will use are contained in a book. This book contains instruction-entities for building, in a step-by-step manner, via laminations, a large wooden globe. The laminates are to be made from very thin wooden disc-like sections. The measurements for the laminates must be very accurate so as to have the usual slight "flatness" at the poles and "bulging" in the middle. The laminates are to be ordered from the south-pole to the north-pole. Relative to the poles and equator, there are ten different globe designs from which to choose. The number of laminates used to construct the globe is the complexity used for this particular construction.

H1 The complexity number n = 96. Since each laminate is to be constructed from two pieces, then there are actually 48 laminates. This is indicated in (0) by writing n = 96, in Λ(n).

H2 Bob employs a book B, Λ(96) of H1, that starts with page 1, I(1,1), and contains 96 pages of instructions. It contains on each page instructions for the half-sections, the half-discs, of the laminates, but there is an additional instruction at the bottom of each page. This instruction is often assumed, when such a book is printed, but the author adds it to remind Bob not to stop work. On page 1 it states After the page 1 instructions have been fulfilled, then go to page 2. (These are, of course, "page-turning" instructions. A notion not usually stated, but assumed.) With the appropriate page numbers, the same instruction appears at the bottom of each page. The first instruction-entity is printed on page 1 and is for the half-disc with code name I(1,1). The second instruction-entity is printed on page 2 and is for the half-disc with code name I(1,2). The code names are written on the laminate piece when it's completed. On page 3 are the instructions for glueing the two pieces together to make an entire first laminate L(1).

H3 Bob begins his laminate constructions. Relative to the instruction at the bottom of each page, Bob uses a mental form of logical deduction, A', that allows him to follow this instruction in order to continue the step-by-step ordered construction of all the laminates. In displayed form, what Bob does might look like this.

(a) Starts with page 1. From page 1, he goes to page 2. From page 2, he goes to page 3., . . . , From page 95, he goes to page 96.

(b) Page 1. Page 1 to page 2. Page 2 to page 3., . . . , Page 95 to page 96.

(c) 1,1 → 2, 2 → 3, . . . , 95 → 96.

(d) {1,(1,2),(2,3), . . . ,(95,96)}

The (d) above is the actual mathematical model to which the A' is applied. The end result is a rule for rational deduction that yields the laminates via a specific "ordered" construction based upon the ordered pages numbers. Today, the rule as applied to a symbol form such as above is called, the "Rule of Detachment." You "deduce" from the 1 on the left, the 2 on the right, etc. by "detaching" the 1. For physical science it is as "If A occurs, then B occurs." A occurs. Then B occurs is deduced. (There is another name for this you might know "modus ponens.")

For the Book, this "deduction" is as follows:

‡ A(1)= Page 1 instructions are fulfilled. If A(1) = page 1 instructions are fulfilled, then B(1)= go to page 2. . . . If A(95) = page 95 instructions are fulfilled, then B(95) = go to page 96.

In Mathematical Logic, this is symbolized in the same manner as (c) above.

A(1), A(1) → B(1), . . . , A(95) → B(96).

Relative to deduction, any hypothesis, any "premise," used is considered as a trivial deduction. Hence, the result of this repeated deduction is the "ordered" deduction of the instructions from page 1 through and including the instructions on page 96.

A(1), B(1), B(2), . . . , B(96).

H4 Bob considers the elemental material and the instructions on page 2. Using his brain and without considering how his brain is translating the instructions into his physical actions, he constructs the piece of the laminate. He gathers his tools together, including a jigsaw, strong glue and selects a rectangular piece of wood. This corresponds to the G as an operator. He first marks the portions to be cut out from a rectangular piece of the material for a semicircular-disc, a half-disc. He uses the jigsaw to give the outer edge of a half-disc little peaks and indentations as required by the instructions. This is done so that, when the globe is finished, it has high and low places for land features, rivers, lakes, bays, and oceans, where artists will complete the final appearance. Thus Bob produces the piece I(1,1). He marks the piece as I(1,1).

Bob repeats all that he has done for the second I(1,2) piece. He now glues the two pieces together. [This gives him a complete laminate with two codes I(1,1) and I(1,2).]

As indicated, what occurs in order to construct the set of laminates is that step H4 is repeated as he deductively continues to select the correct ordered pages of the instructions. Thus, Bob next selects page 4 for I(2,1). Then he selects page 5 and the half-disc assembly page 6. ETC. In this notation, the first number written left-to-right is the laminate number and the second is the number for the half-disc. Bob actually gets use to this sort of deductive thinking since its actually the most common form of everyday "cause and effect" deduction.

But Bob stops after each constructed half-disc and makes a final check. (I note that the instruction-entities that appear on the ordered numbered pages yield an "instruction paradigm.")

What is the final check? There is another scheme, the GID-model scheme, that looks this:

        H'1      H'2    H'3
         ↓        
(0') ((Λ(n), f(a,b))A')

Bob goes through the same procedures as before and here marked as the H'i as i varies from 1 to 3 except that the pages on the similar marked book B' do not contain instruction-entities for each constructed object. They contain a description in words or a drawing or an image of how each half of the constructed laminates should appear. And they are viewed using the same mode of mental deduction. In this case, before continuing to the next step in his constructions, Bob compares his finished result with the corresponding drawing. These drawings are made by the designer of the globe and the instructions are written by a technical writer. These are the exact procedures used throughout our world. If the constructed half-disc does closely match such a general description, then Bob constructs the next one.

In this case, what appears on the description pages is the (standard) GID-model developmental paradigm d, for the globe. And, an exact same deductive process as displayed below corresponds to the (standard) modeled GID-intelligence. This deductive process is the only rule of inference used for "propositional" deduction. HOWEVER, other rules are established using this rule and what are called "axiom schemata."

‡‡ Page 1 description matches laminate. If page 1 description matches laminate, then go to page 2 description. If page 2 description matches laminate, then go to page 3 description., . . . , If page 95 description matches laminate, then go to page 96 description.

(d') {1,(1,2),(2,3), . . . ,(95,96)}

The World Construction Company does not consider these laminates as existing in "physical reality" until they are inspected. An inspector views each complete laminate via an electronically transmitted image as it quickly passes under a camera lens. Perceiving this image is modeled by the standard part operator, St. But, it's at this point where this illustration does not exactly depict the final step. There is, however, an aspect of human physical behavior that does. This is our "persistence of vision." That is, we do not visually perceive a continuous display of visual images. The image is maintained in one area of our iconic memory for a very brief period of time.

For the older motion pictures that use film-stock, as an object moves rapidly, the disjointed motion picture images and brain functions give us an illusion of movement although we actually are being presented with this movement in small steps. That is, some of the movement is actually missing from the film. The same is true when we are presented with TV images.

What is important is that each visual image is momentary held as a fast decaying store of visual information. For this aspect of our iconic memory, each step is "erased" and replaced with the next step in the progression. Other aspects of our iconic memory retain this information for longer periods of time. When I recall previous visual images, they have a different character. They do not carry the same texture that they would have if I were actually viewing them via my eyes. I "know" that I am not actually "seeing" them.

So, the inspector okays a Bob constructed laminate, and then views the next laminate, if any. Although the previous one still exists, it is no longer physically real as far as the inspector's vision is concerned. Visionally, they are only physically real momentarily. The same idea is employed for the GGU-model.

After the entire set of 48 coded wooden laminates pass the inspections, they are sent to another department for final assembly. This illustration describes standard physical procedures that are similar to those that model most GGU-model processes for universe creation. For example, the very significant (standard) forms (a') and (d'), where the descriptions (the general designs) are those for finitely many "n > 1" 3-D slices of a universe, where each slice is called a "universe-wide frozen-frame" (UWFF). (Note: Since this is application of "universal logic," the exact "If and then" form is not necessary since form d'' is the one actually used.)



The Refined GID-model.

The refined GID-model approach, which includes the designs for the physical-systems that comprise each UWFF, is

(a'') UWFF physical-system design 1 = f(1,1). After UWFF physical-system design 1, then the "next" is UFWW physical-system design 2 = f(1,2). After UWFF physical-system design 2 = f(1,2), then the "next" is UFWW physical-system design 3 = f(2,1). . . . . . After UWFF physical-system design f(k,1), then "next" is UFWW physical-system design f(k,2).

Expressed symbolically, we have

(d'') {f(1,1),(f(1,1),f(1,2)),(f(1,2),f(2,1)), . . . ,(f(k,1),(k,2))}

The first entity "f(1,1)" is an hypothesis and is always considered as trivially deduced. Next appling the rule of detachment; that is, remove the first coordinate "a" in each of the forms (a,b) and the second coordinate "b" is deduced, to the corresponding form (d'') yields the UWFF designs in the proper designed order. This "ordered" deduction is expressed below from left-to-right.

f(1,1), f(1,2), f(2,1), f(2,2), f(3,1), f(3,2), . . . , f(k,1), f(k,2).

This can be expressed, as originally done prior to the now refined approach, only in terms the UWFF numbers.

(d''') {f(1),(f(1),f(2)),(f(2),f(3)), . . . ,(f(k-1),f(k))}

Again deduction yields the UWFF as deduced in the proper order.

f(1), f(2), f(3), . . . , f(k).

Of course, these can all be re-expressed using the "design" terms."

The instruction-entity patterns exactly match these patterns. Simply substitute for the word "design" the word "instruction" and for the symbol "f" the symbol "I"




A Nonstandard Technical Addition.

(What follows uses technical GGU-model terminology and is, hence, more complex character. It may not, at present, be useful to you.) So, how do these notions generate a universe, even one of infinite extent or one that has no beginning or no ending in observer-time? This requires that a more technical explanation be given. The following is one of the complete ways this can be accomplished. However, this is not an essential portion of the simple illustration.

[[Note again that, in all cases for the applications, such "standard" schemes as displayed here are not written in the customary mathematics "composition" form.]]

Relative to the language used, the mental processes that Bob employs to obtain each correct page of the book are representable by a technically defined procedure. This procedure is called an algorithm. For universe generation, this algorithm can be mathematically characterized. When this is done, the mathematics predicts the properties of another algorithm *A that selects the correct "page," so to speak, from a much, much larger book. This algorithm *A is applied to (*Λ (λ), *I (λ)) and produces, in order, instruction-entities to which the "properton gathering" operator G is applied. This unites a collection of "ultra-propertons," called an intermediate properton. These are bound into collections that yield the elementary particles and these collections are gathered into other bound collections. This process continues until a universe-wide "info-field" IF(i,j) is obtained. The standard part operator St applied to each info-field, at the least, yields all of a universe-wide frozen-frame. (A 3-D slice of a universe.)

Relative to intelligent design, the ability to follow specific instructions and, using specific building material, produce results that exactly satisfy the instructions is a measure of intelligence. Such intelligence is further enhanced in that the results satisfy intelligently designed and expressed physical laws that satisfy the final realized results. Further, in certain cases, we can describe specific purposes for the designed gatherings. However, our inability to describe such purposes does not affect the basic GID-intelligent design signatures. The gatherings, when realized, continue to satisfy behavioral aspects of such laws via the sequence of info-fields. In comparison, the GID-intelligence being displayed is that of a higher-intelligence.

When the realization operator St is applied it is "coupled with" the gathering operator via the properton formations that produce each info-fields IF(i,j), for the collection of "bound" entities. Physical realization only refers to "certain" bound collections. [There are other collections that can be bound together. But, they represent substratum systems of which we can have little or no knowledge.] The previous coupling is broken as the realization ceases to exist and the previous gatherings need no longer be composed of specific bound collections. Then again, for some schemes, the unrealized info-fields can be retained. Of course, the instruction-entities and descriptive developmental paradigm can still be retained as they would if they were mere positions as coded on DVDs. The information coded on a designed DVD has not been erased, so to speak. It models a type of higher form of memory.

What is discussed in the "Hk" statements is an "interpretation" for the symbols displayed. This interpretation has associated human mental and physical procedures with mathematical symbols from a specific mathematical theory. Although, as mentioned, not first constructed to conform to this type interpretation, one can mathematically model the intuitive concepts displayed by the above schemes.

Nonstandard analysis began its development in 1961. A very general formal approach appeared in 1966. At the suggestion of Abraham Robinson and James Abbott, I began my studies in 1969. In 1979, I applied this method to an area of mathematical logic and languages known today as universal logic. The results predict behavior for objects that are not part of standard mathematics as it existed prior to 1961. These new mathematical entities can be compared with the original standard ones. When this is done, the new entities can be symbolically displayed as modification of schemes such as (0) at the beginning of this article. In order to consistently interpret the new symbols, new terms are necessary. [This is where a language that employs terms such as "internal," "external" and those taken from the more general "meta-langrage."]

A universe can be considered as a physical-system composed of numerously many other physical-systems. Using the new terms and the properties they display, the GGU-model states specifically that, due to the presence of physical-like or "ultranatural" events, the fine-details for universe generation need not be describable via any language we can comprehend. But, there are predictions that descriptions do exist using a higher-language. These special events can indirectly affect physical events. I have speculated that such influences will be observed for large configurations.

Recall that (general) instruction-entities [resp. descriptions] are for moments in the primitive-sequence (previously termed as primitive-time), while pure-instructions [resp. pure-descriptions] are for the *primitive-sequence entities. The term "primitive-sequence" only means that there is a sequence of instructions [resp. descriptions], an instruction paradigm [resp. developmental paradigm] that leads to an "event sequence." For moments in observer (i.e. measurable) time, an event sequence corresponds to actual physical events. When mathematically modeled, scheme (0') is transformed into the scheme (I) as displayed below in an abbreviated notation.

(I) (((*Λ(λ),*f(λ))*A') = d

The scheme (I) is a model for an actual ultraword [1] that is a member of a higher-language *L and d is an extension of the original designed GID-model developmental paradigm d, the step-by-step general design for a developing universe. This ultraword has all of the formal properties of an ordinary word taken from a standard language that we might us. Using such terms as "ultraword," the rational predictions made by the formal mathematical model are translated into statements that yield meaningfully described properties using a higher-language and higher-deduction and similar informal concepts.

Consider the 96 developmental paradigm descriptions employed by Bob. Let's denote these by members of the set of symbols {d(1), d(2), d(3), . . . ,d(96)}. (The symbols {x, y, z} indicate a "set" or "collection" of the "stuff" x, y, z between the { and } symbols. An x is called an element or member of the set. The . . . means that from the members illustrated you should be able to follow the indicated rule and fill in the missing members.) Call these technical drawings.

As above, let's model the pages of "any" book B'. This might be modeled by a left-to-right ordering represented by the pair (d(1), d(2)). (Reading left-to-right, the "first coordinate" is d(1) and the "second coordinate" is d(2).) Thus, what we get if we continue this process and include d(1), is {d(1),(d(1),d(2)),(d(2),d(3)), (d(3),d(4)), . . ., ,(d(95),d(96))}. This is actually the proper notation for a "logic-system," which is also displayed in (d) above. Then you have the corresponding instruction-entities system {I'(1), (I'(1),I'(2)),(I'(2),I'(3)),(I'(3),I'(4)), . . . ,(I'(95),I'(96))}.

For the two schemes (0) and (0'), the I'(1) = I(1,1) and d'(1) = f(1,1), I'(2) = I(1,2), d'(2) = d(1,2). Although GGU-modeled instructions deal with substratum processes, they relate directly to human behavior and mental processes. Prior to embedding into the mathematics structure, the ordered collection of UWFF descriptions and the ordered collection of instructions have the same form as above. The instructions and corresponding d(i) are directly related to a physical event, to a physically realized UWFF.

Λ(n) = {d(1),(d(1),d(2)),(d(2),d(3)), (d(3),d(4)), . . ., ,(d(n-1),d(n))}.

And for the instruction

Λ'(n) = {I'(1),(I'(1),I'(2)),(I'(2),I'(3)),(I'(3),I'(4)), . . . ,(I'(n-1),I'(n))}.

After embedding into the mathematics structure, the first part of (I) changes into

((*Λ(λ),*f(λ), where

*Λ(λ) = {*d(1),*(d(1),*d(2)),(*d(2),*d(3)), (*d(3),*d(4)), . . ., ,(*d(λ-1),*d(λ))}.

And for the instruction

*Λ'(λ) = {*I'(1),(*I'(1),*I'(2)),(*I'(2),*I'(3)),(*I'(3),*I'(4)), . . . ,(*I'(λ-1),*I'(λ))}.

Then the operator *A' that mimics a higher-from of propositional deduction is applied and an extended development paradigm d, where d ⊂ d, is produced in a step-by-step manner. This is symbolized by

(I) (((*Λ(λ),*f(λ))*A') = d, where
.

d = *d(1), *d(2), *d(3), . . . , *d(λ)

For the instruction paradigm, substitute for *f(λ), *I(λ) and, for *Λ(λ), *Λ'(λ). The * entities *d and *I can contain higher-language statements. These sequences are called "hyperfinite" sequences since they are deductively produced by an higher-intelligence using its extended notion of our finite deduction. Further, no entity with a physical universe can duplicate such behavior. This is further discussed in this highly simplified article about the hyperfinite.

I note, that the above is for but one of the four types of universes generated by the Complete GGU-model and I have used an abbreviated notion.


Reference

[1] http://vixra.org/abs/1308.0125 Ultra-logic-systems.