Dr. Robert A. Herrmann Research Vita
Compiled by the staff of the Institute for Mathematics and Philosophy
Scholarship to Johns Hopkins University. Graduated with general honors from Johns Hopkins University. Elected to Phi Beta Kappa. Special individual three year fellowship from the National Science Foundation to be used for graduate study at any university of his choice. Graduated with honors for M. A. and Ph. D. from American University and elected to Phi Kappa Phi. Elected to Sigma Xi.
(1) August 1987 - present,
Professor, Mathematics, U. S. Naval Academy.
(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.
b. Professional Societies
(1) American Mathematical
(2) Mathematical Association of America.
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 completed his research on the lattice of finitary consequence operators and showed that this class of logical operators is almost atomic. He also has instituted the new area of nonstandard logic relative to the nonstandard modeling of these classes of consequence operators.
b. Applied Mathematics, Theoretic Physics, and other areas.
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.
In 1978, Dr. Herrmann discovered a mathematical method 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 he has discovered a mathematical model for a cosmogony. Using ultralogical operators this cosmogony generates the descriptive content of various cosmologies while preserving their inner-logical processes. This cosmogony - the MA-model 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 MA-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.
Einstein's General and Special theories 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 philosophical 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 this theory makes. 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 Einstein 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 of infinitesimals that captured all of the necessary intuitive notions existed at the time these Einstein 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. Further, due to the existence of this rigorous mathematical theory, certain properties relative to abstract model theory, its relation to scientific logic and the now obtainable rules for rigorous physical modeling can be applied rigorously to these theories. When this is done, it becomes apparent that from a rigorous viewpoint, Einstein and many others have made a basic modeling error. This error is called the model theoretic error of generalization.
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 predicts all of the same results as both of these theories, eliminates all of the known logical difficulties and paradoxes as well as showing 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 the Einstein theories is but a 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 accept since they have put forth considerable effort in the past, and continue do so at this present time, through dedicated research activities using the Einstein approach. For this reason alone, many scientists will continue to defend the Einstein approach. Please note that Dr. Herrrmann's work, in this area, is not intended to denigrate those scientists who have, in the past, contributed to these Einsteinian theories or who continue to do so. However, some may claim that Dr. Herrmann's work in this area is "somehow or other" in conceptual error. Until such an error is actually demonstrated, Dr. Herrmann's theory in this specific area remains a consistent and viable alternative to the Einstein theories.
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 the NSP-world model and nonstandard logic he intends to concentrate his efforts in the area of their application to scientific and philosophic problems while continuing to do a minor amount of research in analysis, standard logic and the modeling of philosophic structures. As of September 1999, Dr. Herrmann has published in scholarly journals more articles than 95% of all of the faculty from all disciplines from all of the colleges and universities within the United States.
Research Articles in Refereed Journals.
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 to specific physical science disciplines.]
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
Mathematical and Theoretical Physics
(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, Article 18.
(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
(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).
(1d) "Mathematical philosophy and developmental processes,'' Nature and System, 5(1/2)(1983), 17-36.
(3g) "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.
(2g) "Ultralogics and More," (1993) http://d74-225.mathsci.usna.edu/bookss.htm or http://xxx.lanl.gov/abs/math.LO/9903081 or (math.HO/9903081) or (math/9903081), and /9903082
(1g) "Some applications of nonstandard analysis to undergraduate mathematics: infinitesimal modeling and elementary physics," (1991) Instructional Development Project, Mathematics Department, U. S. Naval Academy, 572 Holloway Rd, Annapolis MD 21402-5002.
(4h) "Science and Scepticism,'' J. Watkins, Princeton University Press, Princeton (1984), in Creation Research Society Quarterly 23(2)(1986), 74-75.
(3h) "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).
(2h) "Foundations of Infinitesimal Stochastic Analysis,'' North-Holland, New York, (1986) for Zentralblatt für Mathematik (1987).
(1h) "Brownian Motion on Nested Fractals,'' T. Linstrom, Memoirs of the American Mathematical Society No. 420, Providence, RI (1990) for Zentralblatt für Mathematik (1990).
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