There cannot be new physical theories without new mathematics, and there cannot be new mathematics without new numbers. - Dr. R.M. Santilli
Palm Harbor, Florida (PRWEB) January 20, 2014
Richard Anderson, Trustee, of the R. M. Santilli Foundation, announces that the novel Iso-, Geno-, and Hyper-Mathematics proposed by the Italian-American scientist R. M. Santilli when he was at the Department of Mathematics of Harvard University will be developed and applied at the forthcoming 2014 ICNAAM Conference in Greece (see Session 108 of the conference http://www.icnaam.org/sessions_minisymposia.htm).
"With the ever increasing advancement of our knowledge of nature, 20th century mathematics has shown more and more limitations, because it can generally approximate reality via linear, local and Hamiltonian treatments that are reversible over time." Dr. Santilli stated. "Therefore, it became necessary to put the foundation of broader mathematics for non-linear, non-local and non-Hamiltonian treatments of physical reality that are generally irreversible over time. Numerous scholars have contributed to the development of the new mathematics, among which I indicate H. C. Myung, M. L. Tomber, Gr. T. Tsagas, D. S. Sourlas, K. M. MacCrimmon, J. V. Kadeisvili, A. K. Aringazin, A. Kirhukin, R. H. Ohemke, G. F. Wene, G. J. Lohmus, E. L. Sorgsepp, D. B. Lin, J. V. Voujouklis, P. Broadbridge, P. R. Chernoff, J. Sniatycki, S. Guiasu, E. Prugovecki, C.-X. Jiang, R. M. Falcon Ganfornina, J. Nunez Valdes, A. Davvaz, N. Lygeros, B. Davvaz, P. Nikolaidou, A. S. Muktibodh, N. Schmidt, R. Katebi, and others. Among the physicists who have contributed to the development and application of the new mathematics, I recall S. Okubo, S. Adler, J. Fronteau, A Tellez-Arenas, A. O. E. Animalu, J. A. Kobussen, Y. Ylamed, N. Salingaros, T. Giill, A. J. Kalnay, H. Rauch, G. Eder, P. Caldirola, R. Trostel, A. Schober, R. J. Slobodrian, J. Sun, A. de Wet, A. D. Jannussis, G. Brodimas, D. S. Sourlas, N. Salingaros, N. Tsagas, D. P. K. Ghikas, E. Kapushik, F. Rohrlich, J. Snyaticki, G. Cassinelli, G. Lochak, D. Y. Kim, J. Salmon, M. Grmela, E. Tonti, J. G. Gilson, V. K. Agrawala, W. H. Steeb, M. Mijatovich, R. Broucke, J. Ellis, E. Mavromatos, D. V. Nanopoulos, J. Dunning Davies, A. Bhalekar , C. Corda,and others. It has been rewarding for me to see that the broader mathematics have already provided significant scientific and industrial advances." (http://www.santilli-foundation.org/Iso-Geno-Hyper-Math-2014.php).
Santilli IsoMathematics is characterized by the lifting of the trivial unit +1 of 20th century mathematics into a positive-definite, thus invertible, most general possible function, matrix, or operator with unrestricted functional dependence on time, coordinates, velocities, wave functions, etc, +1 → U(t, r, p, ...). Isomathematics is then given by the lifting of numeric fields, functional analysis, differential calculus, metric spaces, Lie's theory, topology, etc. into a form admitting U, rather than +1, as left and right unit. The prefix "iso" indicates the preservation of conventional 20th century axioms under broader realizations. An illustrative application of IsoMatheatics is the exact representation of all characteristics of the neutron in its synthesis from a proton and an electron inside a star (Fig. 1) for which 20th century mathematics is inapplicable for various technical reasons (http://www.santilli-foundation.org/docs/Corda-iso-mathematics.pdf).
Santilli GenoMathematics is characterized by the lifting of the trivial unit 1 into two non-singular generalized units, a genounit R(t, r, p, ...) for all ordered products to the right and a second genounit L(t, r, p, ...) for all ordered products to the left. These ordered products are then physically interpreted as representing motion forward and backward in time, respectively. Forward GenoMathematics is characterized by the lifting of IsoMathematics in such a way to admit F(t, r, p, ...) as the left and right unit at all levels. The prefix "geno" is used in the greek sense of inducing new axioms. GenoMathematics was conceived, and remains best suited for quantitative treatment of all energy releasing processes due to their irreversibility 0Fig. 2) (http://www.santilli-foundation.org/docs/RhodesGreece-AAB.pdf).
Santilli's HyperMathematics is the most general mathematics that can be conceived nowadays by the human mind. It is characterized by the hyperstructural lifting of GenoMatjematics whose basic units to the right and to the left are now given by ordered sets of values. HyperMathematics was proposed by Dr. Santilli at the Rendiconti Circolo Matematico Palermo, Suppl. Vol. 42, page 7-82 (1996) for the representation of biological structures (Fig. 3). This original formulation was in terms of ordinary operations. The extension to hyperoperations has been done by Dr. Santilli and Dr./ T. V. Vougiouklis of the Democritus University, greece. Hypermathematics was conceived, and remains ideally applicable for biological structures due to their complexities (Fig. 3) (http://www.santilli-foundation.org/Lie-adm-hyperstr.pdf).
The R. M. Santilli Foundation has been organized and funded for the support of fundamental advances in mathematics, physics and chemistry and for the promotion of scientific ethics and accountability. Dr. R. M. Santilli is the author of about three hundred scientific papers in mathematics, physics and chemistry published in refereed journals around the world, the author of twenty post Ph. D. monographs, and the recipient of several honors (http://www.world-lecture-series.org/santilli-cv).
The R. M. Santilli Foundation