The Wondrous Design and Non-random Character of Chance Events

Robert A. Herrmann

(3 Dec. 1998; Last revision 9 MAY 2004


In this article, it is shown specifically that natural system chance events as represented by theory predicted (a priori) probabilistic statements used in such realms as modern particle physics, among others, are only random relative to the restricted language of the theory that predicts such behavior. It is shown that all such "chance" natural events are related one to another by a remarkably designed, systematic and wondrous collection of equations that model how the natural laws specifically yield such natural events. A second result shows theoretically that all such "chance" behavior is caused by the application of well-defined ultralogics. These results show specifically that the fundamental underlying behavior associated with all natural systems that comprise our universe is controlled internally by processes that cannot be differentiated from those that mirror the behavior of an infinitely powerful mind.


From Nobel Laureate Louis de Broglie, comes the statement:


These two quotations present a rather obvious fact that should come as no surprise. What Feynman and all other materialistic scientists do during their lectures, within their textbooks, and journal papers is to describe in words, diagrams, computer images, and the like, natural laws that they claim will lead to a natural event or a change in a natural system. In this article, the term "natural law" means descriptions for natural-system behavior under specified conditions. For humanly comprehensible "descriptions," as broadly defined, the following is fully discussed in Herrmann (1994) and is denoted as Principle (1). How nature combines together natural laws to produce the moment-to-moment "evolution" (i.e. development or changes in the behavior) of a natural system is modeled (i.e. mirrored, mimicked imitated) by certain aspects of human mental activity. One of the most fundamental deductive procedures that models the development of a natural system is, itself, modeled by the "consequence" operator. Such operators are discussed in more detail later in this article and many interesting properties appear in Herrmann (1987).

In the appendix, Principle (1) is illustrated, where electromagnetic radiation is being emitted by a collection of atomic structures as the collection travels further and further into an ever increasing gravitational potential. There appear to be 12 natural laws being combined together using 9 human deductive processes. It is shown that even to just determine the correct structure to which this natural law applies and to produce the stated outcome requires additionally some type of "natural law" that also mimics human mental procedures. When all of this has been accomplished and this illustrated natural law is applied to a collection of excited hydrogen atoms, then the results that are observed are but "images" that display the changes in the the "color" of the emitted photons. There are displayed no actual descriptions for natural laws anywhere within "nature" itself. The natural laws and regions of application are constructed by means of human mental processes. Indeed, the usual machines used to "verify," by various modes of measurement, various natural laws do not exist in "nature" until they are built by application of human thought processes. If natural laws exist, at all, they must be hidden as actual objects from either direct or indirect human observation. Possibly this is what the following, attributed to Hermann Weyl, is attempting to convey in the form of a question.


Principle (1), although clearly restrictive, completely materialistic and secular in character is verified, relative to deductive science, by the largest amount of empirical evidence that could ever exist since whenever a scientist predicts natural system behavior from a collection of hypotheses deductive human mental activity is applied. This even includes the application of principles used to gather and analyze evidence that would tend to verify a scientific hypothesis. Thus, the secular scientist is using modes of "description" to tell the world "how" nature "works," as well as describing experiments and machines to verify the claimed "how." Since, no one has ever observed such "laws" as some type of objects within nature itself, even those claimed "laws" describing the "how" of the "unobserved" world of particle physics, then a cautious choice for secular science would be to admit that there is "something" going on within nature, called natural laws, that is forcing objects to behave in a predicted manner. And, whatever these "things" are they are but being "modeled" by human modes of "description" and logical deduction. These last two sentences depict the actual character of what science terms as "natural laws." [This notion as to what constitutes "natural laws" is not necessary in the "Solution to the General Grand Unification Problem . . . " (Herrmann 1994) for the natural laws are replaced by the much more general idea - the developmental paradigm. This allows the actual solution method to be apply to infinitely many different "universes" not just the one in which we dwell.]

During his 1998 American tour, Stephen Hawking stated while visiting the President at the White House that in a very few years scientists will be able to "describe" all the natural laws that govern the behavior of every natural system that exists within the universe and use these laws to predict correctly such behavior. Once again, Hawking emphasizes the basic philosophy of science that drives the secular scientist. It is immaterial whether or not the Hawking philosophy is correct for the driving force behind basic research is that the human brain, let's call it the mind instead, is, at the least, capable of describing and comprehending all of the so-called natural laws that govern the workings of our universe. This does not alter the above remarks as to what the phrase "natural law or process" actually signifies. Let's call this Hawking philosophy the Strong Principle (2).




Of course, Max Planck is one of the founders of "Quantum Mechanics." Since strong principle (2) is not as yet established, it is better to consider (2) as but a partial statement. Thus, we modify (2) to include the word "probably," and accept that some of the present day humanly constructed theories are "probably" correct predictors for objective reality. [Philosophically, the theories themselves should be considered as probable in character (Cohen & Nagel, 1934, p. 393).] When theories are considered, they will be tacitly assumed to be among the ones that are "probably" correct predictors.



Principle (3) is the notion that fundamental natural system behavior is probabilistic in character.


First, no one can truly force you to accept this philosophy. You can study chaos theory and other mathematical areas and accept that there are deterministic and highly designed natural world processes being modeled by the mathematics and these natural world processes only give the appearance of random behavior. Of course, I suppose that you would not voice your opinion while a student in such courses at Cal. Tech. But more importantly, does the basic idea of "random" imply lack of design? Is the apparent random character of quantum mechanics the true underlying feature that describes natural system behavior at all levels of human comprehension?





Assuming principle (2) and (4), human beings describe laws and processes of nature as part of human theories and predict correctly from these theories natural system behavior, even if all such predictions are probabilistic in character. Consequently, the following should hold. Let  G  be a set of hypotheses for a scientific theory. The facts are that  G  need not contain all of the natural laws that lead to a prediction. The set  G  need only contain a description for the physical entities to which these natural laws are applied. Then the human brain takes  G  and preforms upon  G  some sort of mental process that yields a prediction  P. This prediction is then verified in the laboratory or, similar to the Big Bang cosmology, is assumed to have occured sometime in the past. These, at present, unknown human mental processes are indicated by the turnstile symbol  |--. If  G  does not contain all of the applicable natural laws, then these laws or processes become part of the human mental process symbolized by  |--. In either case, this simple sequence of events is symbolized by


In all that comes next, the fundamental hypotheses will include the previously mentioned four principles. These principles are re-stated as follows:

(1) How nature combines together natural laws to produce the moment-to-moment "evolution" (i.e. development or changes in the behavior) of a natural system is modeled or mirrored by certain aspects of human mental activity.


(3) Predictions of correct fundamental natural system behavior will always require the behavior to be associated with a statistical statement that implies that natural system behavior originates from behavior that is always probabilistic in character.


It is self-evident that according to principle (2) that [1] displays an absolute fundamental process that occurs within the human brain. Expression [1] corresponds to principle (1) in that it displays a fundamental relationship between human mental processes and natural system behavior. Expression [1] and the next expression [2] can also be related to the informational content of a theory and Preskill claims that information is "physical" (Preskill, 1997, p. 4) in character. Thus Preskill and many others, I included, claim that there exists "something" within the natural world that cannot be observed either directly or indirectly called information. However, information is a notion that corresponds to natural law or processes in the sense that it also is modeled by "language" and "descriptions."


Mathematicians study patterns associated with human mental activity in various ways. There are general properties associated with these mental patterns and these mental properties can be modeled by means of a mathematical object called a consequence operator  C  rather than the turnstile  |--. The turnstile relation defines a consequence operator as follows:

P in C(G). . . . . . . . . . [2]

Expression [2] displays, in the simplest possible manner, the possible existence of a natural process that is being mirrored by the properties of operator  C. Since the consequence operator properties are fundamental to all physical science theory and principle (2) states that some of the probably correct humanly generated theories are known and these theories predict the behavior of natural systems within the universe, then using principle (4) we should accept that it is absolutely true in objective reality that the behavior of operator  C  is mirroring the most fundamental of all natural processes.

One of the major characteristics of a modern scientific community is that it is exceptional myopic when it deals with scientific theory. A scientist learns and then concentrates upon a very complex often mathematically based theory and predicts verified results. But, usually, the scientist cannot step back and observe the actual essence of what has been accomplished through such efforts. What is actually happening in nature itself is almost always hidden among thousands of pages of symbolic representations. This also happens when mathematicians study the patterns presented by consequence operators as models for what, using principle (1), must be natural processes.

A consequence operator is defined upon all of the subsets of a language  L  and  L  can be very broad in character and not only include the ordinary strings of symbols one associates with a language such as those strings displayed in this article but can include audio and visual impressions as well. Indeed, as mentioned, it can include all representations for all modes of human sensory perception via the notion of virtual reality. You need not start with a turnstile operator  |--  as your basic operator. It has been customary to include in the set  G  not only a specific source event (the input) that leads to a specific outcome but all of the assumed natural laws that the human mind would need to predict the probability that the outcome will occur. For example, the natural source event for radioactive decay is the presence of a "decaying" radioactive material. It should be possible to apply certain general natural laws that explain such decay and, of course, application of human mental processes, and predict the probability, with respect to time intervals, of the occurrence of the detector "clicks." Then as another example, using the Feynman described theory for partial reflection, the actual source is a "photon generator" and the detectors are photomultipliers. As Feynman states it on page 17 of the above mentioned book, QED will predict that for a glass surface and a supply of photons of a fixed frequency, say red light, on the average 4% of the photons out of 100 photons will be reflected by the surface at a specific angle and be counted by a specially placed photomultiplier. The input or trials are the 100 photons emitted from the source and the output events are the 4 photons detected by the photomultiplier. This customary approach can be continued. However, as mentioned, since the entire collection of all natural laws could be included  G, then the only differences would be in the source event information. Thus we need only consider  G, for the radioactive case, as a single description for the radioactive material, and, for the photon case, a description for the photon source. All the natural laws can be consider as what actually generates the consequence operator relation, a binary relation that has the set  G  as a first coordinate and the set of all  P  as the second coordinate.



The . . . reason that you might not understand what I am telling you is, while I am describing how Nature works, you won't understand why Nature works that way. But you see, nobody understand that. (1985, p. 10)



The notable exception is a theory of everything (Herrmann, 1994) that solves the General Grand Unification problem. This theory uses processes that satisfy, in general, principles (1) and, since it predicts the behavior of all of the natural systems that exist within our universe, it should, by principle (4), be accepted by all of the scientific community. In general, the model shows, with respect to principle (4), that our universe was created by processes that mirror the processes one would associate with an infinitely powerful mind. The model is called the GGU-model and uses the processes and concepts associated with a mathematical entity called the Nonstandard Physical World that also, according to principle (4), should be accepted as existing in objective reality. The fact that many in the scientific community reject this model is a counterexample to the last sentence in the above Feynman quotation. Since the GGU-model does depend upon the existence of a "background" or "substratum" universe that is the domain for the universe creating operators, then, counter to principle (4) and the Feynman statement, this model is further rejected based upon the philosophical stance that no such undetectable substratum exists. However, postulating away the existence of such a background universe is not sufficient in order to eliminate the conclusion that natural systems within our universe are, indeed, controlled by processes that mirror exceptionally remarkable and wondrous mental processes.

As final re-enforcements to the above four principles, where I have added remarks between the [ and ], Feynman states:


The theory [QED] describes all of the phenomena of the physical world except the gravitational effects . . . and radioactive phenomena [nuclear physics] . . . [ Note: recent research tends to uphold, somewhat, the original Hawking principle in that procedures similar to those used for QED seems to predict some gravitational and most nuclear effects.] Most phenomena we are familiar with involve such tremendous numbers of electrons that it's hard for our poor minds to follow that complexity. [But, in theory, a computer, which follows the specific logical rules of the propositional logic, should be able to make such calculations.] (1985, p. 7-8)

The following discussion and results, although applicable to various physical scenarios, are being restricted to the realm of "particle physics." All probability statements can be re-expressed in terms of the number  n  of describable trials and specific describable natural events A that can occur during these specific trials. Since all of these theories use mathematical procedures to predict a probability  p, the basic requirement for a probability statement is that the trials form a random sequence under a given set of conditions. If during the  n  trials, where  n  is a large number of trials,  m  events A occur, then the event A occurs with a probability  p  approximated by  m/n. The approximation becomes more certain as the number of trials increases "without limit." With the exception that one might claim, as Preskill has done, that certain events seem to follow a mathematical distribution, the "random sequence" statement cannot be established within a laboratory setting with certainty. Also as pointed out in the dictionary by James and James (1968, p. 285 p. 307), such definitions have either logical or empirical difficulties.








There is another minimal mental-like operator that is applied after each  C_i. In human communication, one of the most significant processes is the selection from a vast collection of words and phrases a particular collection that faithfully describes an event. This operator is called the finite human choice operator. This operator mirrors the natural process known as the realism operator and might be considered as a slight generalization of the natural selection operator used throughout secular evolutionary theories. However, this operator is usually considered as but an integral part of each  C_i. This operator, denoted by  R, is restricted to members of   Ç   as they are applied to  {G}  and such operators as  C'. Define  R(C({G}) = C({G}) - {G}. This yields for each (trial)  R(C_i({G})) = {a_i}  and  R(C'({G})  =  B.





Although, there may not be a relation between individual events  a_i  that can be described in terms of the restricted language used for the predictive physical theory, there is the relation [5] between each of the individual operators described above for a probabilistic model and that are needed to predict each  a_i. Using principle (1), the consequence operators  C_i  represent the combined theory dependent natural laws that yield the events as predicted probabilistically. Hence, the natural laws modeled by the  C_i  are individually related by the  n(n - 1)/2  equations that appear in [5]. Expression [5] is what one might describe as being in a symmetric form. But, actually, there are many more such equations since the operator  V  is commutative and, hence, any permutation of the operators between the  (  and  )  will also lead to many more such equations. Consequently, the events  a_i  that are produced by the necessary consequence operators  C_i  are not absolutely random in character when the processes are described by the theory of consequence operators. This also indicates that the actual concept of "randomness" should be considered as only relative to the original theory restricted language that predicts the probabilistic statement.



The GGU-model (Herrmann, 1994) shows that it is rational to assume that an external mental-like consequence operator and an external object that behaves like an actual collection of symbols, a word, are the underlying entities that produce and sustain not only our universe in its evolutionary development but can be used to create and sustain other "universes" as well. The particle physics community tends to accept the original Hawking principle, especially since their contention is that it is the probabilistic rules and processes of quantum physics that will be shown, shortly, to govern completely the four fundamental interactions produced by what are often called the electromagnetic, strong, weak, and gravitational "forces." Due to the often-stated requirement that probabilities be considered as related to potentially infinitely many trials, many would consider the  n  that appears in display [5] to be potentially infinite in character. Notwithstanding this last possible requirement, since the  n  mental-like consequence operators that appear in [4] and [5] must apply to every predictive quantum physical scenario in the vicinity of every spacetime location throughout our universe, as assumed by particle physics, then the fundamental behavior that governs our universe can be described, in general, in the exact same terms as those used to describe the GGU-model conclusions if there exists an ultralogic that is the underlying control. If such is the case, then all natural system behavior for all of the natural systems that comprise our universe is controlled, both internally and externally, by processes that mirror the behavior of an infinitely powerful mind.

The research result Theorem 2, in the appendix, gives a very significant signature for the fundamental control of all natural system behavior. Relative to quantum physical behavior of photons and partial reflection as QED predicates the probability that an event will occur, Feynman writes:

Feynman uses at this point in his lecture the terms "bounce back" and "go through" for what he later terms as new photons (emitted from electrons) and that reach the detector or photons that are "scattered" by electrons. The probability that an observed event will occur depends upon the combined probability that a set of individual events will occur. Since natural systems are also controlled, in general, by ultrawords, it would be the ultranatural events and ultrawords that force the individual probabilities to combine in the appropriate manner that would be described as quantum physical "natural law." Consequently, this combined probability depends upon the probability that a describable individual event E will occur.



Using these event sequence ultralogics, one would conclude that the so-called "unregulated or random" behavior that one often associates with quantum mechanics and the behavior of entities within our universe is actually one of the most powerful signatures that processes descriptively represented by an infinitely powerful mind are controlling all aspects of natural system behavior.


The appendix mathematical theorems have been composed in PDF format and can be obtained from the following: chance.zip. This file can be viewed with the Adobe Reader at 125% and use of the zoom-in tool. The screen view for this particular PDF file is not completely satisfactory. However, printing at 300 - 600 DPI gives excellent results.




Herrmann, R. A. 1987. Nonstandard Consequence Operators. Kobe. J. Math. 4:1-14. http://www.arxiv.org/abs/math.LO/9911204








