Compiled by the staff of the Institute for Mathematics and Philosophy
General Research Accomplishments
Some Awards and Biographical Listings
The following is a link to Dr. Herrmann's list of publications.
- 1. Education (Partial Listing):
- Ph. D., Mathematics, 1973, American University.
M. A., 1968, Mathematics, American University.
B. A., 1963, Mathematics, Johns Hopkins University.
Dr. Herrmann graduated, with honors (first in the June class), from the Baltimore Polytechnic Institute (Advanced College Preparatory Course). ("Poly" course content.) He received a scholarship to Johns Hopkins University. He graduated with general honors from Johns Hopkins University and was elected to Phi Beta Kappa. Dr. Herrmann then continued in the M.Ed. program at the Johns Hopkins McCoy College. He continued his education towards the M.A. in Mathematics. He received a special individual three-year fellowship from the National Science Foundation to be used for graduate study at any university of his choice. Dr. Herrmann was elected to Phi Kappa Phi as partial recognition for his graduate school achievements (4.0 average), which include "distinctions" on comprehension examinations. This is Dr. Herrmann's transcript for his (AU) graduate school education in mathematics. He was elected to Sigma Xi for his research activities. Having a 4.0 average for university level physics courses, Dr. Herrmann is also a certified physics instructor.
- 2. Professional Experience:
- a. Teaching
(1) August 1987 - June 2004, Professor, Mathematics, U. S. Naval Academy. (Retired June 30, 2004.)
(2) January 1981 - August 1987, Associate Professor, Mathematics, U. S. Naval Academy.
(3) August 1968 - January 1981, Assistant Professor, Mathematics, U. S. Naval Academy.
(4) August 1962 - August 1968, Instructor Advanced Placement Mathematics, Board of Education of Baltimore County.
Note: After graduating from Johns Hopkins, many graduate schools offered Dr. Herrmann fellowships and assistantships. Due to family responsibilities, he rejected all of them and continued as a public high school instructor in advanced placement mathematics while continuing his graduate studies on a part-time basis. Various grants, including the NFS Fellowship, were used for his graduate studies. At age 21, his IQ was officially recorded as 160. He has an eidetic memory. Of additional historical interest is that Dr. Herrmann served in the Armed Forces of the United States and was honorably discharged.
b. Professional Societies
(1) American Mathematical Society
(2) Mathematical Association of America
- 3. General Research Accomplishments:
Dr. Robert A. Herrmann has published (without coauthors) 75 articles in 31 different journals from 14 countries. He has written over 250 published reviews as well as 7 books, 5 of which where funded by the Federal government and, hence, are available free of change from his Internet site or the Mathematics and Physics arXiv.org archives. He has personally presented 31 papers at scientific conferences and over 1,300 scientific disclosures. Of the 300,000 individuals who produced approximately 1.6 million published papers or books in the mathematical sciences and for whom there was sufficient information in the MR archives at the time analyzed, Dr. Herrmann ranked in the top 2% in the production of such material.
[It should be noted that Dr. Herrmann's brother, Ernest C. Herrmann (Jr.) Ph.D. (Microbiology) discovered the first commercially viable antiviral agent and was a pioneer in antiviral drug research.] While in graduate school, besides the course material, Dr. Herrmann passed seven written four-hour comprehensive examinations, and an additional oral defense, and wrote two original research dissertations. For the M.A. degree, his 65-page dissertation is titled "Some Characteristics of Topologies on Subfamilies of a Power Set" (University Microfilms, M-1469); for the Ph.D., his 150-page dissertation is titled, "Non-Standard Characteristics for Topological Structures" (University Microfilms 73-28,762). In 73-28,762, portions of Theorem 8.38 are not established correctly. A correct proof appears in the Bulletin of the Australian Math. Soc. 13(1975) No. 2, p. 277.]
- a.Pure Mathematics
Dr. Herrmann's original research activity was in nonstandard topology. Portions of his dissertation were published in 1975. He continued his efforts in this general area and established most of the presently known nonstandard properties associated with extensions of maps, monad theory on rings of sets, the relations between nonstandard structures and convergence spaces, perfect maps, closed maps, and showed that almost all of the known standard generalizations for continuous, open, closed and perfect maps are simple corollaries to his nonstandard theories. He also showed that there exists a nonstandard and, hence, standard hull for semi-uniform spaces in general and applied these results to standard topological groups. In standard topology, Dr. Herrmann constructed the widely used near-compactifications, essentially completed the theory of one-point near-compactifications, and showed that the theory of S-closed spaces is purely topological in character while giving a method to translate standard topological results into results relative to S-closed spaces.
He continued his research into general topology and discovered the pre-convergence spaces. Once again he established much of the presently known mapping theory for pre-convergence spaces and showed that many of the convergence structures of interest to the mathematical community are but trivial examples of his pre-convergence spaces.
Not content with applying nonstandard methods to topological questions, Dr. Herrmann turned his attention to algebraic structures. He established many of the known properties for nonstandard implication algebras, lattices, and Boolean algebras and the like.
In standard mathematical logic, Dr. Herrmann's research activities are on the lattice of finitary (finite) consequence operators. For example, he showed that this class of logical operators is almost atomic and that the set of all finitary consequence operators define on a fixed language is a join-complete lattice. Recently, he has shown that general logic-systems and finitary consequence operators are equivalent notions. He also instituted the new area of nonstandard logic relative to the nonstandard modeling of these classes of consequence operators.
b. Applied Mathematics and Some Theoretical Physics
In 1981, Dr. Herrmann turned his attention to applied modeling. He rigorously described the methods of infinitesimal reasoning and modeling and then solved the d'Alembert-Euler problem in differential equation derivation. Previously, in about 1979, he had discovered new methods in physical modeling and began in 1982 to apply these methods to various unsolved problems in the philosophy of science, quantum theory, and cosmology as well as other areas. He found a solution to the discreteness problem in quantum theory in 1983.
c. The Theory of Everything and General Information Theory
In 1978, Dr. Herrmann discovered mathematical methods to model discipline language theories that are not necessarily describable by means of numerical quantities. He has applied these methods to various scientific disciplines. In particular, in 1979, he began constructing a mathematical model that generates a cosmogony, the GGU-model. Using ultralogical operators this cosmogony generates the descriptive content for various cosmologies while preserving their inner-logical processes. This is the first mathematically generated cosmogony. The hypotheses are that the formation and behavior of each real physical-system is controlled or sustained by a specific set of significant general ultralogical processes. Mathematically, general ultralogical processes are (1) objects that satisfy the standard and nonstandard consequence operator axioms and (2) the finite, hyperfinite, and general standard and nonstandard choice operators. The theory is testable and (Popper) falsifiable. The GGU-model is verified by a vast amount of direct and indirect evidence.
This cosmogony and associated portions of the NSP-world model are consistent with such theory logic as deductive quantum logic, finitary logic, classical logic and the like. The GGU-model satisfies the Wheeler requirements for a pre-geometry and the very restricted conditions required by many groups of scientists who specialize in cosmogony studies. Moreover, the modeling procedures automatically generate the theory of propertons (subparticles) and properton (subparticle) mechanisms that satisfy the Wheeler requirements for the ``substance'' of which space itself is composed. It also satisfies the participator requirements in that active life-forms alter physical-system behavior.
The GGU-model solves the General Grand Unification Problem. This yields the first true Theory of Everything associated with our universe. Dr. Herrmann has shown how to use various processes to unify all physical-system behavior. Of considerable significance is Dr. Herrmann's explicit method that will yield the best possible unification for any collection of physical theories. This result is an application of Dr. Herrmann's pure algebraic characteristics for the lattice of finitary consequence operators.
In information theory, Dr. Herrmann has shown that the empirical theory of Gitt information can be obtained from first principles by application of the theory of general consequence operators. He has shown, using Gitt information, that the complexity of a physical-system can be altered only if the necessary consequence operators satisfy a unique and unusual symmetric property. General information theory has other applications.
d. General Intelligent Design (This is not the Discovery Institute's restricted ID theory.)
Relative to specific information, in 1979, Dr. Herrmann showed how to interpret scientifically a specific theory in a dual manner and, with this approach, originated the scientific analysis of physical-system intelligent design. That is, that all of the physical processes that have formed our universe and control all aspects of physical-system behavior, as well as the results of such processes, can be interpreted as designed by intelligent agency. In particular, Dr. Herrmann has shown how to interpret the GGU-model in the language of intelligent design using the notion of specific information and operator signatures. This interpretation yields the General Intelligent Design Theory (GID) or simply General Design Theory. This interpretation shows that it is rational to assume that all physical-system behavior as investigated by science-communities is designed or controlled by intelligent agency. Since all physical-system formation and behavior is either direct or indirect evidence for the existence of specific intelligent agents, this is the first general solution to the problem of intelligent design. Since GID is but an interpretation for the signatures presented by the GGU-model operators, it is a matter of choice whether one considers these signatures as significant. Indeed, as with various cosmologies, the additional intelligent agency characteristics can be considered as extraneous in character. Note that the most basic GGU-model operator S satisfies the requirements for a Quantum Logic operator.
e. The Special and General Theories of Relativity
The Einstein-Hilbert General Theory of relativity and the Einstein Special Theory of relativity have been controversial from the moment that they appeared in published form. In the past, the basic reasons for these controversies have been philosophic in character rather than scientific. However, scientists such as V. Fock pointed out that the General Theory contains an error relative to how physical postulates are associated with the particular mathematical structure employed. This particular error does not detract from most of the results obtained or the verified predictions these theories make. Moreover, many scientists have shown that both of these theories seem to contain various logical inconsistencies and, due to these difficulties, have created alternate theories based upon different foundations - theories that also predict many, but usually not all, of the same results as predicted by the General and Special theories.
Both of these classical theories are based upon the properties of the mathematical object known as the infinitesimal. But no such consistent mathematical theory for infinitesimals that captures all of the necessary intuitive notions existed at the time these theories were created. Such a mathematically consistent theory was discovered in 1961 by Abraham Robinson. One of the basic reasons that mathematics is used within such theories is to maintain rigorous logical argument. This Robinson discovery now allows for a reconsideration of these theories using a rigorous mathematical theory. Due to the existence of this rigorous mathematical theory, its relation to scientific logic, certain properties relative to abstract model theory, and the now obtainable formal rules for physical modeling, this mathematical theory can be applied rigorously to these physical theories. When this is done, it becomes apparent that from a rigorous viewpoint, Einstein, Hilbert and many others have made a basic physical modeling error. This error is called the model theoretic error of generalization. This error was pointed out for another purpose in the philosophy of science of Mill, and can be explicitly demonstrated.
In 1990, Dr. Herrmann pointed out this error to the scientific community and began to re-construct both of these theories using Robinson's theory of the infinitesimal and infinite numbers in the hopes of avoiding this modeling error. Dr. Herrmann has, indeed, created a theory that stays within the required language for the foundations for these two theories and this new approach predicts all of the same results as the General and Special theories, eliminates all of the known logical difficulties and paradoxes. This new infinitesimal approach shows that, from the viewpoint of indirect evidence, a special type of "ether' or "substratum" may exist. Further, each of the relativistic alterations in physical behavior associated with these theories is but an interaction with this substratum. Of course, Dr. Herrmann is aware that his logically rigorous theory might be difficult for members of the physics community to understand since they have put forth considerable effort in the past, and continue do so at this present time, through dedicated research activities using the original classical approach. For this reason alone, many scientists will continue to defend this classical approach. Please note that Dr. Herrmann's work, in this area, is not intended to denigrate those scientists who have, in the past, contributed to these theories or who continue to do so. Dr. Herrmann's results are only relative to the foundations for the General and Special theories.
f. Future Efforts
Dr. Herrmann believes that his most important contributions to physical science are the methods and results that he discovered for generating mathematical models for philosophical concepts and cosmologies since these discoveries have helped explain and solve certain perplexing and long standing problems. When these methods become more widely known, they may revolutionize modeling techniques for the physical sciences. Due to the apparent significance of such models as the GGU-model and nonstandard logic he intends to concentrate his efforts in the area of their application to scientific and philosophic problems. In particular, he intends to popularize the GGU-model, its various interpretations and their mathematical foundations.
- 4. Awards and Biographical Listings:
- (1) AMWS Achievement Award in Physical Science.
(2) "American Men & Women of Science,'' (Bowker publication.)
(3) "Who's Who in Theology and Science,'' (Center for Theological Inquiry, A Templeton Foundation publication,) and many other such biographical listings.
(4) Templeton Prize Nominee. (Dr. Herrmann rejects the philosophic stances taken by the Templeton Foundation.)
(5) DoN Meritorious Service Award
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