Ultrawords, the Hyper-language and the GID-model

Last revision 9 MAR 2017.

If you don't know what a mathematical model is nor the basic notion of how symbols are applied and interpreted, please see the section on mathematical models in this article. Further, certain undefined terms used here are defined in this glossary. You can skip the material between the [ and ] if you have not studied the related ultralogic article. As usual, the "intelligent agent" terminology as employed throughout the GID-model may be but analogue in character in that we may not be able to otherwise comprehend such behavior.

It is important to remember that the GGU-model can also be considered as an "analogue model for behavior" in that it rationally represents behavior and properties, where generalized descriptions F(t) represent actual physical objects. (The "t" is a primitive sequence (time) index.) Indeed, this is all that physical science does. It deals with descriptions as substitutions for physical events E(t). But, directly related to such descriptions is the notion of informational "instructions." These instruction-entities I(F(t)) use propertons (previously called subparticles) and yield an event E(t) that corresponds to the F(t). Thus, it is not the F(t) that generates E(t) but rather the I(F(t)). Each instruction-entity is distinct since, at the least, it carries a different primitive sequence, t, identifier. An instruction can be considered as a member of the set of all generalized descriptions. There are various choices as to the objects to which the ultralogics apply, such as *S or *A. Each can be used for the GID-model interpretation. But, one may be more appropriate for the maximum secular GGU-model. In either case, they are applied to "ultrawords." Ultrawords are "significant" members of the predicted hyper-language (higher-language) *L for the GID-model interpretation.

In some cases, by application of the general paradigm approach, a few members of *L that are not members of the language L can be decoded in such a manner that the addition of one or two symbols renders them meaningful to us. This is how the notion of the ultra-properton is predicted. These cases, however, are rather rare. The GID-model interpretation does state in general that, as based upon the modeled aspects of human behavior, via measures of intelligence, that the rationally predicted behavior of an higher-intelligence implies that such an entity does comprehend the descriptive content of "infinitely" many members of *L that are not members of L. Modern physical science claims that humankind can predict and comprehend the behavior of the physical-systems we describe. Applying this to *L indicates that each member of a *developmental paradigm has meaningful content for a higher-intelligence. Hence, rationally, this applies to each of the ultranatural events.

Recall that for the GGU-model, ultralogics are termed as "intrinsic ultranatural processes," or IUN-processes within a background or substratum region in which physical universes are embedded. They are also sometimes termed as force-like processes. Using this terminology, they are considered as producing physical-systems, and producing, staining, guiding or controlling physical-system behavior. Their relation to intelligent design can be considered as an extraneous interpretation that is ignored as is done in quantum logic. Further, for the GID-model, ultralogics have the same GGU-model "meanings" except their relation to intelligent design is not ignored and these IUN-processes are coupled with the intelligent agent characteristics that are considered a general signature for the intelligent design aspects. The term "signature" is used for certain characteristics displayed by consequence operators or equivalent logic-systems that are directly related to mental processes applied by an intelligent agent.

When I write a linguistic expression, I almost always first compose it mentally in the form of my "mental voice." This "mental voice" model is usually extended to the behavior of a higher-intelligence, where the term "mind" may be the most appropriate term that generally describes such behavior. For simplicity, first consider an ordinary language L constructed from a nonempty finite set of symbols. For our use, also include a spacing symbol |||. Technically, a (Markov) "word" is a finite combination of these symbols written left-to-right. (I note that the actual foundations of much mathematics are human experiences.) Thus aaabcaa is a word distinct from aacbaaa.

There is an intuitive operation defined for "word theory," which is called by various names. Let's call it "juxtaposition." Often, it is not represented by a symbol. (Mathematically, if the empty word is not included this is called a semigroup operator and satisfies a basic algebraic structure. Including the empty word yields a monoid structure.) Thus, aaabcaa is considered as formed by juxtaposition in various but finitely many ways. For example, juxtaposing aaab with caa, and aa with abcaa yields aaabcaa. There are words like - it|||is|||cold. - which are used to replace "itiscold." so that one does not confuse the meaning. I introduced the notion of "meaningful" into word theory and few seem to know this. Certain combinations of such symbols will change their meaning when the spacing symbol is put in different places. Then a method is introduced that allows one to suppress the finitely many different left-to-right juxtaposing operations that yield the same combination. Also, one can replace the alphabet symbols with "images." This yields a generalized language.

The methods introduced allow one to examine each member of a word as well as how the words are constructed by juxtaposition. One can construct certain "words" that correspond to the sequential "appearance" or descriptions for a physical-system as it develops. The general language L being used is coded in a special way. This coded language L is composed of mathematically defined objects. (This language can also be replaced by a corresponding "propositional" language P where distinct symbols correspond to the words. Propositional logic is the foundation for the construction of a computer microprocessor.) Relative to their construction, ultrawords have the same mathematically representable properties as such strings of ordinary linguistic entities.

Words have various algebraic properties and one can "count" the number of positions a word will require for its actual expression. However, a special symbol is needed if the members of L are expressed as meaningful statements. For example, a word w might be "A photon is emitted and then absorbed by the electron." The "and" in this statement should not be confused with the "and" used to logically separate two words. This is no problem if only propositional symbols such a P are used as replacements for such words. However, in certain cases the actual content of a word is investigated. Hence, to avoid confusion for the logical "and" a special symbol for the logical "and" is used, where the symbol appears nowhere in any of the words used. All of this is then embedded into a special mathematical structure. Originally from a very simple informal system that is a sub-system for propositional logic, one obtains a consequence operator S (see ultralogics) defined on the on L that contains these constructed words.

For the original GGU-model, let & denote the logical word "and" that appears nowhere within any other "words" employed. Let F(1), F(2), . . . F(n) represent "n" members of a developmental paradigm. Each F(k) is an abbreviation for a general description. They are necessary distinct via a sequential coding symbol. Now consider the actual word w(n) = F(1)&F(2)&F(3)& . . . &F(n). Using a very simply informal form of human logic, you can take this word and deduce the set of descriptions {F(1),F(2),F(3), . . . ,F(n)}. For this example, let each F(k) be composed of a finite collection of symbols. All such words w(n) as you let n vary over bigger and bigger numerical values are embedded into a mathematical structure. The mathematics predicts the existence of the ultraword w in the extended language *L and not in L. This ultraword can be partially represented by the notation F(1)&F(2)&F(3)& . . ., where the . . . indicates an infinite extension. The ultralogic *S applies to ultraword w. This yields the "hyper" deduced set of descriptions {F(1)&F(2)&F(3)& . . .}. The ultralogic *A applies to a similar ultraword written in a "cause and effect" form. When it is applied the F(1), F(2), F(3), . . . are produced but in the indicated order.

Intuitively, mathematicians do consider various entities as having a "size," even when they are "infinite" entities. They also intuitively use such comparative terms as "more" and "greater" for such entities. Robinson states that there is an "L'-sentence whose length exceeds l" (Robinson, A., On languages which are based upon non-standard arithmetic. Nagoya Math. J. 22(1963, p. 91)). The l entity is an infinite Robinson number and, mathematically, when compared with other "infinite" sets, it is rather "large." The notion of "length" corresponds to a function that intuitively "counts" the symbols in the form even if they are repeated. Using this approach, at this point, all that is needed is to state that w is composed of more language "symbols" than any entity in any decoded member of L. This is one reason that w is call an ultraword. I note that recently it has been technically shown that for the modern approach to nonstandard analysis one can only partially model the "strength" of an ultraword via the notation of "cardinality." The strength is intuitively "greater than" than any of the "sizes" represented by the cardinality concept.

For the GID-model, an higher-intelligence can work with such a w as easily as we work with a word from L. This can be technically established. [Such "easy" work is called hyperfinite work.] Due to the method of construction, the interior construction of any such w can be, at least, partially analyzed. Portions can be decoded, and these portions are images or descriptions in an ordered set d and these are contained in another ordered set d'. For the GGU-model, the d corresponds to a physical event sequence. It is here where one can establish that d' contains symbols that construct words in *L, and these symbols and the words they form are not members of L.

[In more detail, when the ultralogic *S is applied to w and another higher-intelligence process is applied, you get the d' as well as the coded images or descriptions in d. Since it behaves in a general way like an ordinary word, but, in comparison, w is a member of *L, not a member of L and it is longer than any word taken from L, then such a w is a significant ultraword. I often state that such ultrawords as w are composed of "supercompact information" and *S decompresses w so as to obtain the specific information represented by each image.]

As of the date of this article, the general term "ultraword" is extended, now and then, to include other types of thought-elements that can be represented by members of *L and are not members of L.
For the reductionism approach, due to the type of special (i.e. nonstandard) model being used, one can show that if you take the ultrawords that comprise the development of each physical-system within a universe, then there is another single ultraword w' with a very special property. When *S is applied to w', each of the other ultrawords that generate each developing physical-system is produced as well as the individual physical-system developments. Such a w' is called an ultimate ultraword. This is the original GGU-model approach and its GID-interpretation discussed in "Science Declaims our Universe IS Intelligently Designed." Using this approach, if a model requires multi-universes, you have another ultraword w'' that when ultralogic [*S] is applied to w'', each w' or w is produced and then each of the ultrawords contained in each w'. I suppose that one would call w'' an ultimate^2 ultraword or something like that. I discuss in the Book how one interprets such ultimate ultrawords for the GGU-model. (Although this approach is still viable, the new highly-refined approach is used for the complete GGU-model and the ultimate ultraword is not employed for the complete GGU-model. In this refinement, the production of each physical-system within a specific universe-wide frozen-frame is part of a developmental and instruction paradigm.)

Relative to these two approaches, your author has recently shown that the top-down w type ultraword is better to use, when emergent properties, if they exist, are included. One can think of these "ultrawords" as containing all the specific information that leads to instruction-information that will lead to the formation and development of every physical-system within a material universe. However, one does not obtain the physical-systems and their developments unless an ultralogic is applied. Thus, we have that ultrawords are associated with the GID-model notions of intelligent design by a higher-intelligence and, when realized, the patterns produced [by *S] are designed by a higher-intelligence. In the book, I show that the GID-model ultrawords can be considered as pre-designed via, at the least, two processes.

For the GID-model, each such ultraword has associated with it a set of instructions I'. The same approach using the *S can be applied to instruction-entities. However, recently the logic-system approach has been applied using the *A operator. It is the instruction-entities that actually produce the physical entities at each moment in the development of a universe. Thus, ultrawords are considered as objects that contain "supercompressed" specific information or informational instructions, which are released when an ultralogic [*S] is applied. Finally, no physical entity displays, in any way, written or coded characteristics. For the secular GGU-model, only the set of instructions I' needs to be employed. There are, however, other schemes that can be employed. For the GID-model, both the descriptions and their corresponding instructions can be used. Thus, based upon ones choice, the technical GID-model may be slightly different than the GGU-model. Whichever approach one chooses, instructions can be considered as a pure analogue notion in that they are but auxiliary objects that aid in human comprehension.

On the other hand, some symbolically expressed instructions can be considered as representing actual physical-like processes that behave in a rather simple manner. They detail the actual number of entities that are to be combined to produce more complex physical-systems. These details have been mathematically expressed and can be considered as actual physical-like processes that "force" physical objects to conform to a description, where the processes are guided by a set of linguistic-styled instructions. Indirect evidence as used in atomic physics and early history cosmology could be used to declare that such processes exist in the substratum region.