Dr. Robert A. Herrmann Research Vita
Compiled by the staff of the Institute for Mathematics and Philosophy
- 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 (tied for first in his 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. 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 has a total of 144 university credit hours in mathematics (4.0 average) and was elected to Phi Kappa Phi as partial recognition for his graduate school achievements, 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 graduation 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 higher school instructor in advanced placement mathematics while continuing his graduate studies on a part-time bases. Various grants, including the NFS Fellowship, were used for his graduate studies. 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) 73 articles in 30 different journals from 14 countries. He has written over 250 published reviews as well as 7 books, 5 of which are available, free of change, from his Internet site or the arXiv.org archives. He has personally presented 31 papers at scientific conferences and over 1,000 scientific disclosures. Of the 300,000 individuals who have produced approximately 1.6 million published papers or books in the mathematical sciences and for whom there is sufficient data in the MR archives, Dr. Herrmann ranks in the top 2% in the production of such material.
It should be noted that Dr. Herrmann's brother, Ernest C. Herrmann (Jr.) MD, Ph.D. (Microbiology) discovered the first antiviral agent and is 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 natural-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, intuitionistic 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 subparticles and 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 natural-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 natural-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 natural-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 natural-system intelligent design. That is, that all of the physical processes that have formed our universe and control all aspects of natural-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 natural-system behavior as investigated by science-communities is designed or controlled by intelligent agency. Since all natural-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 electromagnetic 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.
Selected Research Articles in Refereed Journals.
BE ADVISED
The following articles are written for specific audiences. All of these journal papers are "peer" reviewed by individuals who have judged that the material is correct and is appropriate for the interests of the journal's audience.Almost all of the following papers carry a copyright for the journal in which they appear. If you wish a copy for scholarship or research, the first method to secure a copy would be to place an order with Interlibrary Loan or a similar resource. If this is difficult for you to do, then, in some cases, Dr. Herrmann does have reprints available. If this is the case, find the specific number and letter in following list and then simply email your selection and your complete name and mailing address. Dr. Herrmann will determine whether the request is for legitimate scholarship or research, and whether a copy will indeed be sent. When you receive your copy, you will need to comply with all aspects of the appropriate copyright laws.
Selected Published Research Articles
[This is not a complete list of Dr. Herrmann's published articles. These articles are those that pertain to certain purely mathematical and specific physical science disciplines. This list does not include Dr. Herrmann's many articles that present mathematical models for philosophical systems.]
Nonstandard and Infinitesimal Analysis (21a) "A special isomorphism between superstructures,'' Kobe J. Math., 10(2)(1993), 125-129.
(20a) "Consecutive points and nonstandard analysis,'' Math. Japonica 36(1991), 317-322.
(19a) "Nonstandard consequence operators,'' Kobe J. Math., 4(1)(1987), 1-14 (MR89d:03068).
(18a) "Supernear functions,'' Math. Japanica, 30(2) (1985), 169-185.
(17a) "A nonstandard approach to pseudotopological compactifications,'' Z. Math. Logik Grundlagen Math., 26(1980), 361-384. (MR82b:03113).
(16a) "Generalized continuity and generalized closed graphs,''Casopis Pest. Mat., 105(1980), 192-198. (MR81h:54057).
(15a) "Nonstandard implication algebras,'' Matematicki Vesnik, 3(16)(31)(1979), 403-411.
(14a) "Convergence spaces and nonstandard compactifications,'' Math. Rep. Academy of Science of Canada, 1(1979), 187-190. (MR80g:54058).
(13a) "Point monads and P-closed spaces,''Notre Dame J. of Formal Logic, 20(1979), 395-400. (MR83c:54075).
(12a) "Perfect maps and remoteness,''Bull. Cacutta Math. Soc., 70(1978), 413-419. (MR81j:54082).
(11a) "Nonstandard implication algebras,'' Bulletin Mathematique dela Societe des Math., 2(15) (30)(1978), 351-358. (MR81f:03074).
(10a) "A nonstandard approach to S-closed spaces,'' Topology Proceedings, 3(1)(1978), 123-138.
(9a) "Theta-rigidity and the idempotent theta-closure,'' Math. Seminar Notes, 6(1978), 217-220. (MR80a:54004).
(8a) "The nonstandard theory of semi-uniform spaces,'' Z. Math. Logik Grudlagen Math., 24(3)(1978), 237-256. (MR58 #12992).
(7a) "Nonstandard quasi-Hausdorff, Urysohn, regular-closed extensions,'' Bull. Institute of Math., Academia Sinica, 5(1977), 13-25. (MR57 #7571).
(6a) "A nonstandard generalization for perfect maps,'' Z. Math. Logik Grundlagen Math., 23(1977), 223-236. (MR56 #5282).
(5a) "The productivity of generalized perfect maps,'' J. of the Indian Math. Soc., 41(1977), 375-386. (MR80d:54062).
(4a) "The theta and alpha monads in general topology,'' Kyungpook Math. J., 16(1976), 231-241. (MR55 #4125).
(3a) "The Q-topology, Whyburn type filters and the cluster set map,'' Proc. Amer. Math. Soc., 59(1976), 161-166. (MR58 #2785a,b).
(2a) "Nonstandard topological extensions,'' Bull. Australian Math. Soc., 13(1975), 260-290. (MR53 #9192a,b).
(1a) "A note on weakly-theta-continuous extensions,'' Glasnik Mat., 10(1975), 329-339. (MR53 #4037).
Standard General Topology (12b) "Preconvergence compactness and P-closed spaces,'' International J. of Math. and Math. Sciences, 7((2)(1984), 303-310. (MR85i:540001).
(11b) "Closed graphs on convergence spaces,'' Glasnik Mat., 17(37)(1983), 461-465. (MR83j:00027).
(10b) "Extension of maps defined on a convergence space,'' Rocky Mt. J. Math., 12(1)(1982), 23-37. (MR83d:54023).
(9b) "Convergence spaces and closed graphs,'' Math. Rep. Academy of Science of Canada, 2(4)(1980), 203-208. (MR82g:54006).
(8b) "A note on convergence spaces and closed graphs,'' Proceedings of the Conference on Convergence Structures, Cameron University, (1980), 72-77. (MR82b:54006).
(7b) "RC convergence,'' Proc. Amer. Math. Soc., 75(1979), 311-317. (MR80c:54081).
(6b) "Perfect maps on convergence spaces,'' Bull. Australian Math. Soc., 20(1979), 447-466. (MR81c:54016).
(5b) "Convergence spaces and extensions of maps,'' Math. Rep. Academy of Science of Canada, 1(1979), 265-268.
(4b) "Convergence spaces and perfect maps,'' Math. Rep. Academy of Science of Canada, 1(1979), 145-148. (MR80e:54011).
(3b) "Maximum one-point near-compactifications,'' Boll. Un. Mat. Italiana, (5) 16A, (1979), 284-290. (MR80k:54036).
(2b) "One point near-compactifications,'' Boll. Un. Mat. Italiana, (5) 14A, (1977), 25-33. (MR55 #9030).
(1b) "Nearly-compact Hausdorff extensions,'' Glasnik Mat., 12(32)(1977), 125-132. (MR57 #1424).
Nonstandard and Infinitesimal Modeling
Physical Science (15c) "The best possible unification for any collection of physical theories,"Internat. J. Math. and Math. Sci., 17(2004):861-872. (Also see http://www.arXiv.org/abs/physics/0306147 ) and http://www.arXiv.org/abs/physics/0205073
(14c) "The non-random character and intelligent design of 'chance' events," TJ, 15(2)(2001):103-109.
(13c) "Hyperfinite and standard unifications for physical theories," Internat. J. Math. and Math. Sci., 28(2)(2001):93-102. (Also see http://www.arXiv.org/abs/physics/0105012 )
(12c) "Ultralogics and probability models," Internat. J. Math. and Math. Sci., Internat. J. Math. and Math. Sci., Internat. J. Math. and Math. Sci., 27(5)(2001):321-325. (See http://www.arXiv.org/abs/quant-ph/0112037) .
(11c) "Information theory, consequence operators and the origin of life," C. R. S. Quarterly, 36(3)(1999):123-132.
(10c) "The NSP-World and Action-at-a-Distance." Instantaneous Action-at-a-Distance in Modern Physics: "Pro" and "Contra" ed. Chubykalo, A., N. V. Pope and R. Smirnov-Rueda, (In Contemporary Fundamental Physics), Nova Science Books and Journals, New York, (1999):223-235.
(9c) "The Wondrous Design and Non-random Character of Chance Events" (1999) http://xxx.lanl.gov/abs/physics/9903038
(8c) "Newton's second law of motion holds in normed linear spaces," Far East J. Appl, Math. 2(3)(1998):183-190. [Note: A major typographical error appears in display (4), page 187. The lower case subscript "m" in the last line should be a capital "M" subscript.]
(7c) "A hypercontinuous hypersmooth Schwarzschild line element transformation,'' Internat. J. Math. and Math. Sci., 20(1)(1997):201-204
(6c) "An Operator equation, and relativistic alternations in the time for radioactive decay,'' Internat. J. Math. and Math. Sci., 19(2)(1996):397-402
(5c) "Operator equations, separation of variables and relativistic alterations,'' Internat. J. Math. and Math. Sci., 18(1)(1995):59-62 (Note: Name misspelled (Hermann) on title page. It is spelled correctly on interior pages. )
(4c) "Special Relativity and a nonstandard substratum,'' Speculations in Science and Technology, 17(1)(1994):2-10.
(3c) "Fractals and ultrasmooth microeffects,'' J. Math. Physics, 30(4), April 1989, 805-808. (MR#90d:03143)
(2c) "Physics is legislated by a cosmogony,'' Speculations in Science and Technology, 11(1) (1988), 17-24.
(1c) "Rigorous infinitesimal modelling,'' Math. Japonica, 26(4)(1981), 461-465. (MR83j:00027).
Natural Systems (1d) "Mathematical philosophy and developmental processes,'' Nature and System, 5(1/2)(1983), 17-36.
Monographs (5g) "Nonstandard Analysis - A Simplified Approach," (2003) http://www.arxiv.org/abs/math.GM/0310351
(4g) "Solutions to the 'General Grand Unification Problem,' and the Questions 'How Did Our Universe Come Into Being?' and 'Of What is Empty Space Composed?" Presented before the MAA, at Western Maryland College, 12 Nov. 1992
http://www.arxiv.org/abs/astro-ph/9903110(3g) "Ultralogics and More," (1993) http://www.arxiv.org/abs/math.GM/9903081 and 9903082
(2g) "Some applications of nonstandard analysis to undergraduate mathematics: infinitesimal modeling and elementary physics," (1991) Instructional Development Project, Mathematics Department, U. S. Naval Academy, 572C Holloway Rd, Annapolis MD 21402-5002. http://www.arxiv.org/abs/math.GM/0312432
(1g) "Logic for Midshipmen," Mathematics Department, U. S. Naval Academy, 572C Holloway Rd, Annapolis MD 21402-5002. cont1s.htm
Book Reviews (6h) "Nonstandard Analysis," J. Ponstein, Research School Systems, Organisation and Management, (2001) for Zentralblatt für Mathematik (2003).
(5h) "Nonstandard Analysis for Working Mathematicians," P.A. Loeb and M. Wolf (Eds) (2000) for Zentralblatt für Mathematik (2001).
(4h) "Brownian Motion on Nested Fractals," T. Linstrom, Memoirs of the American Mathematical Society No. 420, Providence, RI (1990) for Zentralblatt für Mathematik (2001).
(3h) "Foundations of Infinitesimal Stochastic Analysis," K.D. Stroyan and J.M. Bayod, North-Holland, New York, (1986) for Zentralblatt für Mathematik (1987).
(2h) "Nonstandard Methods in Stochastic Analysis and Mathematical Physics," S. Albeverio, J. E. Fenstad, R. Hoegh-Krohn, T. Lindstrom, Academic Press, Orlando, FL (1987) for Zentralbatt für Mathematik (1987).
(1h) "Science and Scepticism," J. Watkins, Princeton University Press, Princeton (1984), in Creation Research Society Quarterly 23(2)(1986), 74-75.
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