Introduction
This blog aims to be the clearing house of information and queries about the resolution of the centuries-old conjecture post by Fermat in 1637 known as Fermat's last theorem (FLT) and its off-shoot: the development of the new mathematics and physics. Although the threads, articles and posts in various blogs, websites and forums across the internet already provide an overview of the subject, I shall summarize them all right now and provide details later.
1) The failure to resolve FLT for 360 years is attributed to the defects of the underlying fields, namely, foundations, number theory and the real number system.
2) Critique-rectification of these fields was undertaken starting 1992 that yielded:
a) Identification of defects of foundations, particularly, present mathematical reasoning and their remedy.
b) The requirement for contradiction-free mathematical space, since any contradiction or inconsistency reduces a mathematical space to nonsense, and the remedy.
c) Identification of the defects of the real number system and the remedy.
d) The remedy for the major flaw of number theory: lack of valid axiomatization of the integers.
e) The remedy for the present flaw in extension of mathematical space.
f) Characterization of undecidable propositions.
g) The reconstruction of the real number system into the contradiction-free new real number system.
g) The countably infinite counterexamples to FLT.
3) The development of the new non-standard calculus whose base space is the new real number system.
4) Implications of the characterization of the characterization of undecidable propositions
for mathematical physics and the remedy for the flaw of present methodology called mathematical modelling.
5) That remedy is called dynamic modelling. While mathematical modelling EXPLAINS nature in terms of numbers, equations, functions, inequalities and statistical trends, dynamic modelling EXPLAINS nature in terms of its laws. Then the task of the physicists is to discover the laws of nature.
6) The discovery of the basic constituents of matter called superstring.
7) The solution of the 200-year old gravitational n-body problem in 1996.
8) The development of the flux theory of gravitation that now qualifies as grand unified theory or the theory of everything.
For background materials and references visit my website:
http://home.iprimus.com.au/pidro/
Comments, contributions, criticism, contrary opinions and debate are welcome.
E. E. Escultura
1) The failure to resolve FLT for 360 years is attributed to the defects of the underlying fields, namely, foundations, number theory and the real number system.
2) Critique-rectification of these fields was undertaken starting 1992 that yielded:
a) Identification of defects of foundations, particularly, present mathematical reasoning and their remedy.
b) The requirement for contradiction-free mathematical space, since any contradiction or inconsistency reduces a mathematical space to nonsense, and the remedy.
c) Identification of the defects of the real number system and the remedy.
d) The remedy for the major flaw of number theory: lack of valid axiomatization of the integers.
e) The remedy for the present flaw in extension of mathematical space.
f) Characterization of undecidable propositions.
g) The reconstruction of the real number system into the contradiction-free new real number system.
g) The countably infinite counterexamples to FLT.
3) The development of the new non-standard calculus whose base space is the new real number system.
4) Implications of the characterization of the characterization of undecidable propositions
for mathematical physics and the remedy for the flaw of present methodology called mathematical modelling.
5) That remedy is called dynamic modelling. While mathematical modelling EXPLAINS nature in terms of numbers, equations, functions, inequalities and statistical trends, dynamic modelling EXPLAINS nature in terms of its laws. Then the task of the physicists is to discover the laws of nature.
6) The discovery of the basic constituents of matter called superstring.
7) The solution of the 200-year old gravitational n-body problem in 1996.
8) The development of the flux theory of gravitation that now qualifies as grand unified theory or the theory of everything.
For background materials and references visit my website:
http://home.iprimus.com.au/pidro/
Comments, contributions, criticism, contrary opinions and debate are welcome.
E. E. Escultura
posted by E. E. Escultura at 3:43 AM
34 Comments:
Correction: "post" should read "posed"
Posts of dgup
For the benefit of the doubting Thomases, here is an aspirin:
The ScienceDirect TOP25 Hottest Articles is a free quarterly service from ScienceDirect. When you subscribe to the ScienceDirect TOP25, you'll receive an e-mail every three months listing the ScienceDirect users' 25 most frequently downloaded journal articles, from any selected journal among more than 2,000 titles in the ScienceDirect database, or from any of 24 subject areas.
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Nonlinear Analysis
OCT - DEC 2005
1. Initial value problems for higher-order fuzzy differential equations • Article
Nonlinear Analysis, Volume 63, Issue 4, 1 November 2005, Pages 587-600
Georgiou, D.N.; Nieto, J.J.; Rodriguez-Lopez, R.
2. Fixed point solutions of variational inequalities for asymptotically nonexpansive mappings in Banach spaces • Article
Nonlinear Analysis, Volume 64, Issue 3, 1 February 2006, Pages 558-567
Shahzad, N.; Udomene, A.
3. Variational approach to nonlinear problems and a review on mathematical model of electrospinning • Article
Nonlinear Analysis, Volume 63, Issue 5-7, 1 November 2005, Pages e919-e929
He, J.-H.; Liu, H.-M.
4. Approximation of common fixed points for a family of finite nonexpansive mappings in Banach space • Article
Nonlinear Analysis, Volume 63, Issue 5-7, 1 November 2005, Pages 987-999
Wu, D.; Chang, S.-S.; Yuan, G.X.
5. Nonlinear differential equations with nonlocal conditions in Banach spaces • Article
Nonlinear Analysis, Volume 63, Issue 4, 1 November 2005, Pages 575-586
Xue, X.
6. A survey on piecewise-linear models of regulatory dynamical systems • Article
Nonlinear Analysis, Volume 63, Issue 3, 1 November 2005, Pages 336-349
Oktem, H.
7. Fixed point theorems in metric spaces • Article
Nonlinear Analysis, Volume 64, Issue 3, 1 February 2006, Pages 546-557
Proinov, P.D.
8. Dynamic modeling of chaos and turbulence • Article
Nonlinear Analysis, Volume 63, Issue 5-7, 1 November 2005, Pages e519-e532
Escultura, E.E.
9. Existence result for periodic solutions of a class of Hamiltonian systems with super quadratic potential • Article
Nonlinear Analysis, Volume 63, Issue 4, 1 November 2005, Pages 565-574
Karshima Shilgba, L.K.
10. Multiple positive solutions of a boundary value problem for nth-order impulsive integro-differential equations in Banach spaces • Article
Nonlinear Analysis, Volume 63, Issue 4, 1 November 2005, Pages 618-641
Guo, D.
11. Fixed points of uniformly lipschitzian mappings • Article
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Dhompongsa, S.; Kirk, W.A.; Sims, B.
12. High regularity of the solutions of the telegraph system subjected to nonlinear boundary conditions • Article
Nonlinear Analysis, Volume 63, Issue 4, 1 November 2005, Pages 491-512
Apreutesei, N.
13. Viscosity approximation methods for a family of finite nonexpansive mappings in Banach spaces • Article
Nonlinear Analysis
Jung, J.S.
14. New modelling approach concerning integrated disease control and cost-effectivity • Article
Nonlinear Analysis, Volume 63, Issue 3, 1 November 2005, Pages 439-471
Tang, S.; Xiao, Y.; Clancy, D.
15. Existence and approximation of solutions of second-order nonlinear four point boundary value problems • Article
Nonlinear Analysis, Volume 63, Issue 8, 1 December 2005, Pages 1094-1115
Khan, R.A.; Lopez, R.R.
16. Autonomous steering control for electric vehicles using nonlinear state feedback H"~ control • Article
Nonlinear Analysis, Volume 63, Issue 5-7, 1 November 2005, Pages e2257-e2268
Moriwaki, K.
17. A Petri net-based object-oriented approach for the modelling of hybrid productive systems • Article
Nonlinear Analysis, Volume 62, Issue 8, 1 September 2005, Pages 1394-1418
Villani, E.; Pascal, J.C.; Miyagi, P.E.; Valette, R.
18. Existence and uniqueness of a wavefront in a delayed hyperbolic-parabolic model • Article
Nonlinear Analysis, Volume 63, Issue 3, 1 November 2005, Pages 364-387
Ou, C.; Wu, J.
19. Positive solutions of second-order two-delay differential systems with twin-parameter • Article
Nonlinear Analysis, Volume 63, Issue 4, 1 November 2005, Pages 601-617
Bai, D.; Xu, Y.
20. Multiple positive and sign-changing solutions for a singular Schrodinger equation with critical growth • Article
Nonlinear Analysis, Volume 64, Issue 3, 1 February 2006, Pages 381-400
Chen, J.
21. Strong convergence of the CQ method for fixed point iteration processes • Article
Nonlinear Analysis
Martinez-Yanes, C.; Xu, H.-K.
22. Nonlinear analysis of arterial blood flow-steady streaming effect • Article
Nonlinear Analysis, Volume 63, Issue 5-7, 1 November 2005, Pages 880-890
Jayaraman, G.; Sarkar, A.
23. Existence and exponential stability of periodic solution for impulsive delay differential equations and applications • Article
Nonlinear Analysis, Volume 64, Issue 1, 1 January 2006, Pages 130-145
Yang, Z.; Xu, D.
24. Uniqueness results for nonlinear elliptic equations with a lower order term • Article
Nonlinear Analysis, Volume 63, Issue 2, 1 October 2005, Pages 153-170
Betta, M.F.; Mercaldo, A.; Murat, F.; Porzio, M.M.
25. Positive solutions of a second-order singular ordinary differential equation • Article
Nonlinear Analysis, Volume 61, Issue 8, 1 June 2005, Pages 1383-1399
Bonheure, D.; Gomes, J.M.; Sanchez, L.
View this website at: http://top25.sciencedirect.com/index.php?subject_area_id=16&journal_id=0362546X
Paper No. 8, Dynamic Modelling of Chaos and Turbulence, presented by the author at a plenary session of the 4th World Congress of Nonlinear Analysts, Orlando, FL, July 5, 2004, provides, for the first time, the most comprehensive explanation of gravity as part of the dynamics of turbulence, specifically, vortex flux of superstrings (the superstring is the basic constituent of matter), such as galaxy, star, planet and moon. Dynamic modelling (an off-shoot of the resolution of FLT), the new methodology introduced by the author as an alternative to the present methodology of physics called mathematical modelling (that describes nature in terms of numbers, equations, functions, etc.) explains nature in terms of its laws. To-date 43 laws of nature have been discovered using this new methodology.
E. E. Escultura
For those wanting to pursue a career in mathematics and physics I’d like to offer some tips:
1) There are two math departments in the country that have entries in renowned refereed international journals, i.e., they have effective programs of research and the capability to train mathematicians who can contribute significantly to the advancement of the field and the development of the country. They are the Departments of Mathematics at LaSalle and Ateneo.
2) The UP Math Department has the distinction of being the largest mathematics department in the country with over 100 members of the faculty.
3) The National Institute of Physics at UP has several entries in renowned refereed international journals. The Ph.D.s it has trained have distinguished themselves in physics.
E. E. Escultura
I met Dr. Escultura when I was a consultant for the Clark Development Corporation in Clark Field, Pampanga in 1999. We became friends and have extensive discussion of his work, especially, when he visits Sydney. I followed his many posts and articles in several blogs, websites and forums, especially, Sci Math, Mathforge ISCI (International Society for Compexity, Information and Design). I even tried to read his original work, Exact solution of Fermat’s equations (Definitive resolution of Fermat’s last theorem (Nonlinear Studies, Vol. 5, No. 2, 1998) pp. 227 – 254). Last May when he visited Australia I asked him to summarize his work on Fermat’s last theorem. He agreed and sent me the article below:
MY STRATEGY FOR CAPTURING FLT.
I wondered why FLT remained unresolved for centuries and concluded that its underlying fields –foundations, number theory and the real number system – are defective. Therefore, I embarked on their critique-rectification that yielded the following:
1) There are sources of contradiction in mathematics including ambiguous and vacuous concepts, large and small numbers (depending on context), unbounded or infinite set and self-reference. Here is an example of vacuous concept: A triquadrilateral is a plane figure with three vertices and four edges. The Richard paradox is an example of self-reference: The barber of Seville shaves those and only those who do not shave themselves; who shaves the barber? Incidentally, the indirect proof is flawed, being self-referent.
2) Among the requirements for a contradiction-free mathematical space are the following:
a) It must be well-defined by consistent axioms and every concept must be well-defined by them. A concept is well-defined if its existence, properties and relationship with other concepts are specified by the axioms. A false proposition cannot be an axiom as it introduces inconsistency. For example, this proposition cannot be used as an axiom of any mathematical space: There exists a triangle with four edges.
b) The rules of inference (mathematical reasoning) must be specific to and well-defined by its axioms.
c) Any proposition involving the universal or existential quantifiers on infinite set is not verifiable and, therefore, cannot be used as an axiom for it would not endow certainty to the conclusion of a theorem.
3) The real number system does not satisfy the requirements for a contradiction-free mathematical space. In particular, the trichotomy axiom is false since it is equivalent to natural ordering which the real number system has none because most of its concepts are ill-defined. Therefore, the real number system is ill-defined or nonsense and FLT being fomulated in it is also nonsense. Consequently, to resolve FLT the real number system must be fixed first and FLT must be reformulated in it. Andrew Wiles failed to do this and his work collapses altogether.
4) It is alright to introduce ambiguity provided it is 'approximable" by certainty. For example, a nonterminating decimal is ambiguous since not all its digits are known but it can be approximated by a segment at the nth decimal digit at margin of error 10^-n.
5) The rectification is to build a new real number system R* with three simple axioms and two operations + and x: 1) R* contains the basic integers 0, 1, ..., 9, and the operations + and x are well-defined by 2) the addition and 3) multiplication tables of arithmetic that we learned in primary school. The rest of the elements of R* are the terminating decimals first which are later extended to the nonterminating decimals.
A new real number is well-defined if every digit is known or computable, i.e., there is some rule or algorithm for determining it uniquely. Note that the periodic decimals including the terminating decimals are well-defined new real numbers and the real numbers, the terminating decimals, are embedded in the new real number system. The integers are embedded isomorphically into the integral parts of the decimals and are, therefore, well-defined by the axioms of R*. This remedy’s the major flaw of number theory, namely, the fact that the integers have no adequate axiomatization.
6) The new elements of the new real number system are the dark number d* = 1 – 0.99… - N – (N–1), N = 0, 1, … (the ordinary integers), and u* the equivalence class of divergent sequences. The mapping 0 – > d*, N – > (N–1).99…, where N = 1, 2, …, maps the integers isomorphically into the new integers which means that they have almost identical behavior, the only difference being that d* > 0.
7) Then the counterexamples to FLT are as follows: Let x = (0.99...)10^T, y = d*, z = 10^T, where T is an ordinary integer, T = 1, 2, ... Then x, y, z satisfy Fermat's equation, for n > 2,
x^n + y^n = z^n.
Moreover, if k = 1, 2, ..., is ordinary integer, kx, ky, kz also satisfy Fermat's equation. They are the counterexamples to FLT. They prove that FLT is false and Wiles is wrong.
8) The mapping of the integers to the integral parts of the decimals embeds the former into the new real numbers subject its axioms. This rectifies a major flaw in number theory, that the integers, its subject matter, has inadequate axiomatization.
The critique-rectification of the underlying fields of FLT, the construction of the counterexamples and applications of this new methodology, especially in physics, are developed in the following articles in renowned refereed international journals and conference proceedings:
[18] Escultura, E. E. (1996) Probabilistic mathematics and applications to dynamic systems including Fermat's last theorem, Proc. 2nd International Conference on Dynamic Systems and Applications, Dynamic Publishers, Inc., Atlanta, 147 – 152.
[19] Escultura, E. E. (1997) The flux theory of gravitation (FTG) I. The solution of the gravitational n-body problem, Nonlinear Analysis, 30(8), 5021 – 5032.
[20] Escultura, E. E. (1998) FTG VII. Exact solutions of Fermat's equation (Definitive resolution of
Fermat's last theorem, J. Nonlinear Studies, 5(2), 227 – 254.
[21] Escultura, E. E. (1999) VIII. Superstring loop dynamics and applications to astronomy and biology, J. Nonlinear Analysis, 35(8), 259 – 285.
[22] Escultura, E. E. (1999) FTG II. Recent verification and applications, Proc. 2rd International Conf.: Tools for Mathematical Modeling, St. Petersburg, vol. 4, 74 – 89.
[23] Escultura, E. E. (2000) FTG IX. Set-valued differential equations and applications to quantum gravity, Mathematical Research, Vol. 6, 2000, St. Petersburg, 58 – 69.
[24] Escultura, E. E. (2001) FTG X. From macro to quantum gravity, J. Problems of Nonlinear Analysis in Engineering Systems, 7(1), 56 – 78.
[25] Escultura, E. E. (2001) FTG XI. Quantum gravity, Proc. 3rd International Conference on Dynamic Systems and Applications, Atlanta, 201 – 208.
[26] Escultura, E. E. (2001) FTG. XII. Turbulence: theory, verification and applications, J. Nonlinear Analysis, 47(2001), 5955 – 5966.
[27] Escultura, E. E. (2001) FTG III: Vortex Interactions, J. Problems of Nonlinear Analysis in Engineering Systems, Vol. 7(2), 30 – 44.
[28] Escultura, E. E. (2001) FTG IV. Chaos, turbulence and fractal, Indian J. Pure and Applied Mathematics, 32(10), 1539 – 1551.
[29] Escultura, E. E. (2002) FTG V. The mathematics of the new physics, J. Applied Mathematics and Computations, 130(1), 145 – 169.
[30] Escultura, E. E. (2003) FTG VI. The theory of intelligence and evolution, Indian J. Pure and Applied Mathematics, 33(1), 111 – 129.
[31] Escultura, E. E. (2003) FTG XVII: The new mathematics and physics, J. Applied Mathematics and Computation, 138(1), 127 – 149.
[32] Escultura, E. E. (2003) FTG XVIII. Macro and quantum gravity and the dynamics of cosmic waves, J. Applied Mathematics and Computation, 139(1), 23 – 36.
[33] Escultura, E. E. (2001) FTG. XIV. The mathematics of chaos, turbulence, fractal and tornado breaker, deflector and aborter, Proc. Symposium on Development through Basic Research, National Research Council of the Philippines, University of the Philippines, 1 – 13.
[34] Escultura, E. E. FTG XIX. Recent results, new inventions and the new cosmology, accepted, J. Problems of Nonlinear Analysis in Engineering System.
[35] Escultura, E. E. FTG XV. The new nonstandard analysis and the intuitive calculus, submitted.
[36] Escultura, E. E. (2002) FTG VI. The philosophical and mathematical foundations of FLT’s resolution, rectification and extension of underlying fields and applications, accepted, J. Nonlinear Differential Equations.
[37] Escultura, E. E. (2002) FTG XXII. Extending the reach of computation, submitted.
[38] Escultura, E. E. (2003) The theory of learning and implications for Math-Science Education, submitted.
[39] Escultura, E. E. (2003) FTG XXIII. The complex plane revisited, accepted, Journal of Nonlinear Differential Equations.
[40] Escultura, E. E. (2002) FTG XXIV. Columbia: the crossroads for science, accepted, J. Nonlinear Differential Equations.
[41] Escultura, E. E. (2003) FTG XXV. Dynamic Modeling and Applications, Proc. 3rd International Conference on Tools for Mathematical Modeling, State Technical University of St. Petersburg, St. Petersburg.
[42] Escultura, E. E. (2004) FRG XXVII – XXVIII. Part I. The new frontiers of mathematics and physics. Part I. Theoretical Construction and Resolution of Issues, Problems and Unanswered Questions.
[43] Escultura, E. E. (2005) FRG XXVII – XXVIII. The new frontiers of mathematics and physics. Part II. The new real number system: Introduction to the new nonstandard analysis, Nonlinear Analysis and Phenomena, II(1), January, 15 – 30.
[44] Escultura, E. E. (2005) FTG XXVI. Dynamic Modeling of Chaos and Turbulence, Proc. 4th World Congress of Nonlinear Analysts, Orlando, June 30 – July 7, 2004.
[45] Escultura, E. E. FTG. XXVII (2005). The theory of everything, Nonlinear Analysis and Phenomena, II(2), 1 – 45.
[46] Escultura, E. E. Escultura (2006) FTG XXXIV. Foundations of Analysis and the New Arithmetic,
Nonlinear Analysis and Phenomena, January 2006.
[47} Escultura, E. E. FTG XXXV (2006) The Pillars of FTG and some updates, Nonlinear Analysis and Phenomena, III(2), 1 – 22.
[48] Escultura, E. E. FTG XXXVI (2006) The New Nonstandard Calculus, accepted, Nonlinear Analysis.
For more info see my website: http://home.iprimus.com.au/pidro/
E. E. Escultura
MY STRATEGY FOR CAPTURING FLT.
I wondered why FLT remained unresolved for centuries and concluded that its underlying fields –foundations, number theory and the real number system – are defective. Therefore, I embarked on their critique-rectification that yielded the following:
1) There are sources of contradiction in mathematics including ambiguous and vacuous concepts, large and small numbers (depending on context), unbounded or infinite set and self-reference. Here is an example of vacuous concept: A triquadrilateral is a plane figure with three vertices and four edges. The Richard paradox is an example of self-reference: The barber of Seville shaves those and only those who do not shave themselves; who shaves the barber? Incidentally, the indirect proof is flawed, being self-referent.
2) Among the requirements for a contradiction-free mathematical space are the following:
a) It must be well-defined by consistent axioms and every concept must be well-defined by them. A concept is well-defined if its existence, properties and relationship with other concepts are specified by the axioms. A false proposition cannot be an axiom as it introduces inconsistency. For example, this proposition cannot be used as an axiom of any mathematical space: There exists a triangle with four edges.
b) The rules of inference (mathematical reasoning) must be specific to and well-defined by its axioms.
c) Any proposition involving the universal or existential quantifiers on infinite set is not verifiable and, therefore, cannot be used as an axiom for it would not endow certainty to the conclusion of a theorem.
3) The real number system does not satisfy the requirements for a contradiction-free mathematical space. In particular, the trichotomy axiom is false since it is equivalent to natural ordering which the real number system has none because most of its concepts are ill-defined. Therefore, the real number system is ill-defined or nonsense and FLT being fomulated in it is also nonsense. Consequently, to resolve FLT the real number system must be fixed first and FLT must be reformulated in it. Andrew Wiles failed to do this and his work collapses althogether.
4) It is alright to introduce ambiguity provided it is 'approximable" by certainty. For example, a nonterminating decimal is ambiguous since not all its digits are known but it can be approximated by a segment at the nth decimal digit at margin of error 10^-n.
5) The rectification is to build a new real number system R* with three simple axioms and two operations + and x: 1) R* contains the basic integers 0, 1, ..., 9, and the operations + and x are well-defined by 2) the addition and 3) multiplication tables of arithmetic that we learned in primary school. The rest of the elements of R* are the terminating decimals first which are later extended to the nonterminating decimals.
A new real number is well-defined if every digit is known or computable, i.e., there is some rule or algorithm for determining it uniquely.
6) The new elements of the new real number system are the dark number d* = 1 – 0.99… - N – (N–1), N = 0, 1, … (the ordinary integers), and u* the equivalence class of divergent sequences. Then the real numbers are embedded in R* by the mapping 0 – > d*, N – > (N–1).99…, to well-define them.
7) Then the counterexamples to FLT are as follows: Let x = (0.99...)10^T, y = d*, z = 10^T, where T is an ordinary integer, T = 1, 2, ... Then x, y, z satisfy Fermat's equation, for n > 2,
x^n + y^n = z^10.
Moreover, if k = 1, 2, ..., is ordinary integer, kx, ky, kz also satisfy Fermat's equation. They are the counterexamples to FLT. They prove that FLT is false and Wiles is wrong.
The critique-rectification of the underlying fields of FLT, the construction of the counterexamples and applications of this new methodology, especially in physics, are developed in the following articles in renowned refereed international journals and conference proceedings:
[18] Escultura, E. E. (1996) Probabilistic mathematics and applications to dynamic systems including Fermat's last theorem, Proc. 2nd International Conference on Dynamic Systems and Applications, Dynamic Publishers, Inc., Atlanta, 147 – 152.
[19] Escultura, E. E. (1997) The flux theory of gravitation (FTG) I. The solution of the gravitational n-body problem, Nonlinear Analysis, 30(Cool, 5021 – 5032.
[20] Escultura, E. E. (1998) FTG VII. Exact solutions of Fermat's equation (Definitive resolution of
Fermat's last theorem, J. Nonlinear Studies, 5(2), 227 – 254.
[21] Escultura, E. E. (1999) VIII. Superstring loop dynamics and applications to astronomy and biology, J. Nonlinear Analysis, 35(Cool, 259 – 285.
[22] Escultura, E. E. (1999) FTG II. Recent verification and applications, Proc. 2rd International Conf.: Tools for Mathematical Modeling, St. Petersburg, vol. 4, 74 – 89.
[23] Escultura, E. E. (2000) FTG IX. Set-valued differential equations and applications to quantum gravity, Mathematical Research, Vol. 6, 2000, St. Petersburg, 58 – 69.
[24] Escultura, E. E. (2001) FTG X. From macro to quantum gravity, J. Problems of Nonlinear Analysis in Engineering Systems, 7(1), 56 – 78.
[25] Escultura, E. E. (2001) FTG XI. Quantum gravity, Proc. 3rd International Conference on Dynamic Systems and Applications, Atlanta, 201 – 208.
[26] Escultura, E. E. (2001) FTG. XII. Turbulence: theory, verification and applications, J. Nonlinear Analysis, 47(2001), 5955 – 5966.
[27] Escultura, E. E. (2001) FTG III: Vortex Interactions, J. Problems of Nonlinear Analysis in Engineering Systems, Vol. 7(2), 30 – 44.
[28] Escultura, E. E. (2001) FTG IV. Chaos, turbulence and fractal, Indian J. Pure and Applied Mathematics, 32(10), 1539 – 1551.
[29] Escultura, E. E. (2002) FTG V. The mathematics of the new physics, J. Applied Mathematics and Computations, 130(1), 145 – 169.
[30] Escultura, E. E. (2003) FTG VI. The theory of intelligence and evolution, Indian J. Pure and Applied Mathematics, 33(1), 111 – 129.
[31] Escultura, E. E. (2003) FTG XVII: The new mathematics and physics, J. Applied Mathematics and Computation, 138(1), 127 – 149.
[32] Escultura, E. E. (2003) FTG XVIII. Macro and quantum gravity and the dynamics of cosmic waves, J. Applied Mathematics and Computation, 139(1), 23 – 36.
[33] Escultura, E. E. (2001) FTG. XIV. The mathematics of chaos, turbulence, fractal and tornado breaker, deflector and aborter, Proc. Symposium on Development through Basic Research, National Research Council of the Philippines, University of the Philippines, 1 – 13.
[34] Escultura, E. E. FTG XIX. Recent results, new inventions and the new cosmology, accepted, J. Problems of Nonlinear Analysis in Engineering System.
[35] Escultura, E. E. FTG XV. The new nonstandard analysis and the intuitive calculus, submitted.
[36] Escultura, E. E. (2002) FTG VI. The philosophical and mathematical foundations of FLT’s resolution, rectification and extension of underlying fields and applications, accepted, J. Nonlinear Differential Equations.
[37] Escultura, E. E. (2002) FTG XXII. Extending the reach of computation, submitted.
[38] Escultura, E. E. (2003) The theory of learning and implications for Math-Science Education, submitted.
[39] Escultura, E. E. (2003) FTG XXIII. The complex plane revisited, accepted, Journal of Nonlinear Differential Equations.
[40] Escultura, E. E. (2002) FTG XXIV. Columbia: the crossroads for science, accepted, J. Nonlinear Differential Equations.
[41] Escultura, E. E. (2003) FTG XXV. Dynamic Modeling and Applications, Proc. 3rd International Conference on Tools for Mathematical Modeling, State Technical University of St. Petersburg, St. Petersburg.
[42] Escultura, E. E. (2004) FRG XXVII – XXVIII. Part I. The new frontiers of mathematics and physics. Part I. Theoretical Construction and Resolution of Issues, Problems and Unanswered Questions.
[43] Escultura, E. E. (2005) FRG XXVII – XXVIII. The new frontiers of mathematics and physics. Part II. The new real number system: Introduction to the new nonstandard analysis, Nonlinear Analysis and Phenomena, II(1), January, 15 – 30.
[44] Escultura, E. E. (2005) FTG XXVI. Dynamic Modeling of Chaos and Turbulence, Proc. 4th World Congress of Nonlinear Analysts, Orlando, June 30 – July 7, 2004.
[45] Escultura, E. E. FTG. XXVII (2005). The theory of everything, Nonlinear Analysis and Phenomena, II(2), 1 – 45.
[46] Escultura, E. E. Escultura (2006) FTG XXXIV. Foundations of Analysis and the New Arithmetic,
Nonlinear Analysis and Phenomena, January 2006.
[47} Escultura, E. E. FTG XXXV (2006) The Pillars of FTG and some updates, Nonlinear Analysis and Phenomena, III(2), 1 – 22.
[48] Escultura, E. E. FTG XXXVI (2006) The New Nonstandard Calculus, accepted, Nonlinear Analysis.
For more info see my website: http://home.iprimus.com.au/pidro/
E. E. Escultura
Correction: Fermat's equation should be,
x^n + y^n = z^n, n > 2, and the counterexamples are:
x = (0.99...)10^T, y = d*, z = 10^T, where T is an ordinary integer, T = 1, 2, ..., d* = 1 - 0.99... = N - (N - 1).99... Then x, y, z satisfy
Fermat's equation, for n > 2, x^n + y^n = z^n. Moreover, the triple kx, ky, kz, k = 1, 2, ..., also satisfy Fermat's equation.
E. E. Escultura
WHAT IS THE TAKE ON FLT?
Since 1997 my work in Math and Physics, especially, FLT, has been widely discussed and debated across the Internet in various fora, websites and newsgroups. In the math forum Sci Math I have several threads on topics related to FLT. One of the earliest was the thread, Is 1 = 0.99…? This alone generated about 700 posts and has been resolved in my favour. Since January I posted in Sci Math the thread, Contradiction-Free Mathematical Space, The Adics and Other Nonsense, My Strategy for Capturing the Basic Constituent of Matter and The State-of-the-Art in Mathematics. The first thread alone generated 153 posts and all of them were resolved in my favour. They are all quiet now and consigned to the archives with me having the last words. All threads in Sci Math since 1997 have generated over 2,000 posts. I also have several threads in Mathforge that generated about 700 posts and another in ISCID (International Society for Complexity, Information and Design), New Approach to Physics, covering 5 pages. Now, all is quiet not just in the Western Front but in all Fronts for these threads and websites because the issues have all been resolved in my favour with me having the last words.
When the Manila Times carried the news story, UP Prof Proves Princeton Man Wrong, Blogs and threads sprouted like mushrooms attacking my work as a hoax, calling me names and chastising me for taking the Manila Times for a ride. None of them knew the issues involved and they all blurted nonsense all along. Unfortunately, I knew about them only last April. Now that I have responded to them, except the “monologues” or blogs that disallow posts of contrary opinions, they are also quiet now. But their booh-boohs have come home to roost and one of the bloggers, Alex of pcij, with Roy Choco, after having slandered me for over a year, cried, “moTHERRRR…….!!!!!” and threatened to sue me for slander. I told his lawyer, Atty. D'Campanilla, to send the subpoena immediately so that I can tell it to the Marines. His threat is posted on my Message Board at http://home.iprimus.com.au/pidro/.
But here is the rub:
After more than 9 years of discussion and debate NOT A SINGLE HOLE HAS BEEN PUNCH ON MY WORK. The blog relleck.net reported that my name ranks 4th in successful searches next to the mathematician Leonard Euler and followed by analyst Danzig, a poor 5th, with my share of 1.7%. On top of these, neither Andrew Wiles nor his three supporters, Ribet of UC Berkeley, Mazur of Harvard and Saranak of Princeton, refuted my criticisms of Wiles’ work or challenged my counterexamples to FLT to prove it false and Wiles wrong.
Where, oh, where art thou smart guys from the UP Math Department? Enliven this blog and debate with me. You don’t have to identify yourself if you are embarrassed by your own feeble ideas and empty publication list.
E. E. Escultura
BACKGROUND ON FLT
Since the publication in June 2005
by the Manila Times of the news story, UP Prof Proves Princeton Man Wrong, many threads, blogs and websites appeared attacking me for making up a hoax and taking the Manila Times for a ride. Except for a few, none of them knew what the real issue is all about. Unfortunately, I did not notice these attacks until last January. The issue here is the status of the conjecture by Fermat popularly known as Fermat’s last theorem (FLT) and Wiles’ “proof” of it. My response is quite categorical: FLT is false and Wiles’ “proof” is wrong, which is precisely what the Manila Times article reported. Since then I have explained the issue and documented my resolution of FLT by posting, My Strategy for Capturing FLT (posted also in this blog’s Introduction), in blogs and websites that register contrary opinions and do not delete my posts. I have the last words on the issue there. The exceptions are the website, Wikipedia, and the blog, False Proofs, by Larry Freeman, which have open and substantive discussion of FLT and related issues.
The inability to resolve FLT for 360 years triggered critique-rectification of its underlying fields of foundations, number theory and the real number system. Based on I have summarized beloow the foundational requirements for a
CONTRADICTION-FREE MATHEMATICAL SPACE.
This topic is a thread on many blogs and websites including Sci Math.
1) A mathematical space consists of consistent axioms, well-defined concepts and their consequences called theorems. A mathematical space is consistent if it does not contain or give rise to contradiction.
2) A concept is well-defined if its existence, properties and relationship with the other concepts are specified by the axioms. The negation of 'well-defined' is 'ill-defined' or 'vacuous' or 'ambiguous' or 'nonsense'. Note that a mathematical space in my sense has no room for ambiguity. Note, further, that ambiguity is a source of contradiction. More is required to well-define a real number: every digit is known or computable, i.e., there is some rule or algorithm for determining it uniquely. The rational number pi is well-defined since every digit can be computed from its series expansion. The digits of a normal number are chosen at random from the basic integers, 0, 1, .., 9.
Application
3) I apply these requirements to construct the real number system without the axiom of choice. I take Hilbert's formalist approach that the mathematical objects are simply symbols (not the concepts of thought although we shall refer to them as concepts) well-defined by consistent set of axioms. We specify the symbols as the decimals; they are the new real numbers R* with operations + and x subject to the following axioms: a) R* contains the basic integers 0, 1, …, 9.
b) The operations + and x are well-defined by the addition and
c) multiplication tables, respectively.
Note that, to avoid contradiction stemming from the ambiguity of infinite set (more precisely, unbounded set, i.e., cannot be contained in any finite set) the building blocks of R*, the basic integers, are finite. Out of these basic integers the nonterminating decimals are constructed as standard Cauchy sequences. An example of a well-defined new real number is a normal number. The new real number system has the following properties: finite but unbounded, discrete, non-Archimedian, free from contradiction, has natural ordering (the lexicographic ordering) and enriched by the nonstandard numbers, dark and unbounded numbers d* and u*, respectively, as well as the new integers, i.e., integers of the form, N.99…, where N is the ordinary integer 0, 1, ... The dark number d* = 1 – 0.99... has the property that, given a new real number x, x > d*. Also, given new real number y, y < u*; d* is the counterpart of infinitesimal and u* is the counterpart of the calculus' infinity but they are both well-defined.
This provides just the right discrete mathematics for computer science, especially for simulation, and physics since matter is discrete (consisting of its basic constituent called superstring). R* also contains the countable counter-examples to Fermat's last theorem (shown in the Introduction) and embeds the real numbers, including the integers, as a subspace. This rectifies the major flaw of number theory, that the integers, its subject matter, has no valid axiomatization.
Prescription for Contradiction-Free Mathematical Space
1) Contradiction reduces a mathematical space to nonsense; among the sources of contradiction are the following: ambiguity or uncertainty, ill-defined concepts, vacuous statement, large or small number depending on concept (due mainly to limitation of computation) and self reference, e.g., the indirect proof. Therefore, I enumerate below some of the requirements for avoiding contradiction.
2) The first major step in avoiding contradiction was done by Hilbert a century ago when he recognized that the concepts of individual thought cannot be the subject matter or objects of a mathematical space since they are inaccessible to others and can neither be studied or discussed collectively nor axiomatized.
3) Therefore the mathematical objects must be symbols in the objective world (we call them concepts, too) well-defined by consistent axioms. Now, I require that every concept must be well-defined, i.e., its existence, properties and relationship with other concepts be specified by the axioms. Existence is stressed since vacuous statement or defining expression is inherently contradictory, e.g., the statement: “the solution of the equation x^2 + 1 = 0 is not 0” is quite true but it leads to the contradiction 1 = 0; the reason for it is: the equation is vacuous. That solution has been denoted by i = sqrt(-1) = sqrt(1/-1) = 1/i = -i, from which follows that 2i = 0 or 1 = 0.
4) Since every mathematical space is well-defined only be its own axioms distinct mathematical spaces are independent; therefore, a concept in one is ill-defined in the other and any proposition involving concepts from two distinct spaces is ambiguous or ill-defined.
5) It follows from 4) that the rules of inference must be specific to and well-defined by the axioms of the given mathematical space. In particular, formal logic is flawed because it applies to distinct mathematical spaces.
6) It also follows from 4) that undecidable propositions are those involving ill-defined concepts. In particular, Goedel’s incompleteness theorems are nonsense because they involve concepts from two distinct spaces, the integers and the propositional calculus.
7) A decimal is well-defined only if every digit is known or computable, i.e., there is some rule or algorithm for determining it uniquely. The numbers pi and the logarithmic base e are well-defined since their digits can be computed from their series expansion. So is a normal number whose digits are chosen at random from the basic integers.
8) A mathematical space must be built on finite concepts to avoid the ambiguity of infinite set. Thus, I built the new real number system (the decimals) on the basic integers, 1, 2, …, 9. Then I well-defined the decimals, terminating or nonterminating.
9) Ambiguity may be introduced provided it is “approximable” by certainty; for example, a nonterminating decimal is ambiguous (except in exceptional cases) because not all its digits are known but it can be approximated to any desired margin of error; for example a nonterminating decimal is approximated by its initial segment at the nth decimal digit and the margin of error is 10^-n.
10) Here is an example of self-reference called the Richard paradox: The barber of Seville shaves those and only those who does not shave himself. Who shaves the barber?
E. E. Escultura
Prescription for Contradiction-Free Mathematical Space
1) Contradiction reduces a mathematical space to nonsense; among the sources of contradiction are the following: ambiguity or uncertainty, ill-defined concepts, vacuous statement, large or small number depending on concept (due mainly to limitation of computation) and self reference, e.g., the indirect proof. Therefore, I enumerate below some of the requirements for avoiding contradiction.
2) The first major step in avoiding contradiction was done by Hilbert a century ago when he recognized that the concepts of individual thought cannot be the subject matter or objects of a mathematical space since they are inaccessible to others and can neither be studied or discussed collectively nor axiomatized.
3) Therefore the mathematical objects must be symbols in the objective world (we call them concepts, too) well-defined by consistent axioms. Now, I require that every concept must be well-defined, i.e., its existence, properties and relationship with other concepts be specified by the axioms. Existence is stressed since vacuous statement or defining expression is inherently contradictory, e.g., the statement: “the solution of the equation x^2 + 1 = 0 is not 0” is quite true but it leads to the contradiction 1 = 0; the reason for it is: the equation is vacuous. That solution has been denoted by i = sqrt(-1) = sqrt(1/-1) = 1/i = -i, from which follows that 2i = 0 or 1 = 0.
4) Since every mathematical space is well-defined only be its own axioms distinct mathematical spaces are independent; therefore, a concept in one is ill-defined in the other and any proposition involving concepts from two distinct spaces is ambiguous or ill-defined.
5) It follows from 4) that the rules of inference must be specific to and well-defined by the axioms of the given mathematical space. In particular, formal logic is flawed because it applies to distinct mathematical spaces.
6) It also follows from 4) that undecidable propositions are those involving ill-defined concepts. In particular, Goedel’s incompleteness theorems are nonsense because they involve concepts from two distinct spaces, the integers and the propositional calculus.
7) A decimal is well-defined only if every digit is known or computable, i.e., there is some rule or algorithm for determining it uniquely. The numbers pi and the logarithmic base e are well-defined since their digits can be computed from their series expansion. So is a normal number whose digits are chosen at random from the basic integers.
8) A mathematical space must be built on finite concepts to avoid the ambiguity of infinite set. Thus, I built the new real number system (the decimals) on the basic integers, 1, 2, …, 9. Then I well-defined the decimals, terminating or nonterminating.
9) Ambiguity may be introduced provided it is “approximable” by certainty; for example, a nonterminating decimal is ambiguous (except in exceptional cases) because not all its digits are known but it can be approximated to any desired margin of error; for example a nonterminating decimal is approximated by its initial segment at the nth decimal digit and the margin of error is 10^-n.
10) Here is an example of self-reference called the Richard paradox: The barber of Seville shaves those and only those who does not shave himself. Who shaves the barber?
For the benefit of the UP Community I would like to offer some insights on mathematics education. The failure rate in the mathematics series from basic algebra to calculus at the UP Math Department is well over 50%. This has nothing to do with the quality of the students because the selection process for entrance to the University is quite tough. Nor is it due to incompetence of the teachers because faculty selection is also quite tough. It is not even due to wrong methodology because each discipline determines its own appropriate methodology for teaching. Moreover, this is an international phenomenon although the failure rate abroad is not quite as high. Having been on the faculty of the Department myself I can now assess in hindsight what the problem is: Present mathematics is quite defective. During the last 9 years I have posted hundreds of threads across the internet in dozens of blogs and websites on the status of mathematics and its applications including physics. The discussions have spilled over into several mathematics departments internationally. I would like to share one subject that has been discussed widely on a global scale:
PRESCRIPTION FOR CONTRADICTION-FREE MATHEMATICS
1) Contradiction reduces a mathematical space to nonsense; among the sources of contradiction are the following: ambiguity or uncertainty, ill-defined concepts, vacuous statement, large or small number depending on context (due mainly to limitation of computation) and self reference, e.g., the indirect proof. Therefore, I enumerate below some of the requirements for avoiding contradiction.
2) The first major step in avoiding contradiction was done by Hilbert a century ago when he recognized that the concepts of individual thought cannot be the subject matter or objects of a mathematical space since they are inaccessible to others and can neither be studied or discussed collectively nor axiomatized.
3) Therefore the mathematical objects must be symbols in the objective world (we call them concepts, too) well-defined by consistent axioms. Now, I require that every concept must be well-defined, i.e., its existence, properties and relationship with other concepts be specified by the axioms. Existence is stressed since vacuous statement or defining expression is inherently contradictory, e.g., the statement: “the solution of the equation x^2 + 1 = 0 is not 0” is quite true but it leads to the contradiction 1 = 0; the reason for it is: the equation is vacuous. That solution has been denoted by i = sqrt(-1) = sqrt(1/-1) = 1/i = -i, from which follows that 2i = 0 or 1 = 0.
4) Since every mathematical space is well-defined only be its own axioms distinct mathematical spaces are independent; therefore, a concept in one is ill-defined in the other and any proposition involving concepts from two distinct spaces is ambiguous or ill-defined.
5) It follows from 4) that the rules of inference must be specific to and well-defined by the axioms of the given mathematical space. In particular, formal logic is flawed because it applies to distinct mathematical spaces.
6) It also follows from 4) that undecidable propositions are those involving ill-defined concepts. In particular, Goedel’s incompleteness theorems are nonsense because they involve concepts from two distinct spaces, the integers and the propositional calculus.
7) A decimal is well-defined only if every digit is known or computable, i.e., there is some rule or algorithm for determining it uniquely. The numbers pi and the logarithmic base e are well-defined since their digits can be computed from their series expansion. So is a normal number whose digits are chosen at random from the basic integers.
Cool A mathematical space must be built on finite concepts to avoid the ambiguity of infinite set. Thus, I built the new real number system (the decimals) on the basic integers, 1, 2, …, 9. Then I well-defined the decimals, terminating or nonterminating.
9) Ambiguity may be introduced provided it is “approximable” by certainty; for example, a nonterminating decimal is ambiguous (except in exceptional cases) because not all its digits are known but it can be approximated to any desired margin of error; for example a nonterminating decimal is approximated by its initial segment at the nth decimal digit and the margin of error is 10^-n.
10) Here is an example of self-reference called the Richard paradox: The barber of Seville shaves those and only those who do not shave himself. Who shaves the barber?
E. E. Escultura
Correction: Fermat's equation should read: x^n + y^n + z^n, n > 2.
Correction to #6, My Strategy for Capturing FLT:
d* = 1 - 0.99... = N - (N - 1).99..., where N = 1, 2, ..., is an integer.
Visit the Atlas website:
http://atlas-conferences.com/cgi-bin/abstract/catb-02
for the abstract of my keynote address at the 5th International Conference on Dyanamic Systems and Applications, May 30 - June 2, Atlanta, USA. Mathematicians and Physicists are invited. Click the homepage for information.
Since the Manila Times carried the front-page news story about my resolution of Fermat’s conjecture popularly known as Fermat’s last theorem (FLT) headlined, UP Prof Proves Princeton Man Wrong, in May of last year several threads, blogs and websites rose to attack my work on the wrong issue. All the bloggers, however, are totally ignorant of the issue, especially, Alecks Pabico of PCIJ who advertised his blog across the internet extensively, and someone by the fake name Roy Choco. Moreover, the UP Math Department published an unsigned “Statement from the Math Department” in the Philippine Collegian, student campus publication, the UP Newsletter, faculty publication of the University of the Philippines, Diliman, Q.C., both of which are also ill-informed of the issue. To the credit of the Philippine Collegian, it published my response to the letter but the UP Newsletter never did.
FLT says, for n > 2, the equation,
x^n + y^n = z^n
has no solution in integers.
Andrew Wiles proposed a proof of this conjecture in an article in the Annals of Mathematics, 1995. I criticized his proof in the paper, Probabilistic Mathematics and Application to Dynamic Systems Including Fermat’s Last theorem, I presented at the 2nd International Conference on Dynamic Systems and Applications, Atlanta, GA, USA, which appeared in its Proceedings, 1996. I then criticized his proof in the paper, Exact solution of Fermat’s Equation (Definitive resolution of Fermat’s last theorem), Nonlinear Studies, Vol. 5, No. 2, 1998, published by the International Federation of Nonlinear Analysts, where I proved the conjecture false by constructing countably counterexamples to FLT. I must stress that since then there has been neither a refutation of my counterexamples to FLT nor a rebuttal of my criticisms of Wiles’ proof in refereed journals or internet discussions.
In my previous articles above I have shared with the viewers my strategy for capturing FLT as well as a general scheme for constructing contradiction-free mathematical space. I’m highlighting below major points of contention in the internet discussions.
1) One of the issues that have been discussed extensively across the internet since I raised them in 1997 is the question of whether 1 = 0.99… This was resolved by David Hilbert a century ago when he recognized that the concepts of individual thought cannot be the subject matter of mathematics since they are inaccessible to others and can neither be studied collectively nor axiomatized. It follows that intuition is not valid in mathematical reasoning. Therefore, the objects of a mathematical space must be symbols in the real world that everyone can look at (we call them concepts also) well-defined by consistent axioms. A concept is well-defined if its existence, properties and relationships among themselves are specified by the axioms. Existence is stressed here because vacuous concepts (vacuous defining expressions) are ambiguous and a source of contradiction. An example of vacuous concept is the “triquadrilateral”, a plane figure with four edges and three vertices. An example of a vacuous proposition is: “the greatest integer satisfies the trichotomy axiom”. It is easy to derive an absurdity from it such as: “the largest integer is 1”. BTW, the idea that an axiom is neither true nor false or that it is true by virtue of its being an axiom is nonsense. There are strict requirements for an axiom to avoid contradiction that reduces a mathematical space to nonsense.
2) Since 1 and 0.99… are distinct symbols they cannot be equal; therefore, d* = 1 – 0.99… cannot be zero and the usual that that d* = 0 is false. Thus, the usual proof in elementary algebra that 1 = 0.99… is false.
3) Since every mathematical space is well-defined only by its own axioms, distinct mathematical spaces are independent. Therefore, a concept in one space is ill-defined in another. It follows that any proposition or argument involving concepts from two distinct mathematical spaces is ill-defined. It follows further that Goedel’s incompleteness theorems are flawed because they involve concepts from two distinct mathematical spaces, the integers and the propositional calculus.
4) It follows from 3) that universal rules of inference including those provided by formal logic are not valid mathematical reasoning (since they apply to distinct mathematical spaces). Therefore, the rules of inference must be specific to and well-defined by the axioms of the given mathematical space. Moreover, every term or symbols must be well-defined because the introduction of undefined terms introduces ambiguity.
5) Infinite set has inherent ambiguity since not all its terms can be identified or enumerated or checked for its properties. Therefore, any proposition about the properties of EVERY element of an infinite set is ambiguous or unverifiable. For example, if I want to check that EVERY element of an infinite set has property A I must start with some element x and check that this is so. Then I check another element y, etc. It is clear that this is never completed. The same is true with the use of the existential quantifier, “there exists”. Therefore, the use of an axiom involving the universal or existential quantifier in an infinite mathematical space is inadmissible for it does not endow certainty to a theorem. The remedy: build a mathematical space on finite set; then well-define infinite set when needed.
6) In view of 5) the completeness axiom of the real number system is inadmissible for it introduces uncertainty on the infinite real numbers; this is one of its defects. Another ambiguity of the real number system is that its axioms do not specify the system of symbols they well-define: are they the triadic numbers, decimals, fractions, etc.? They are different systems of symbols having different properties. Therefore, they cannot be well-defined by the same set of axioms.
7) The most serious problem with the real number system is that the trichotomy axiom is false, a counterexample to it having been constructed by Felix Brouwer (Benacerraf and Putnam, Philosophy of Mathematics, Cambridge U Press, 1985). This makes it inconsistent and ill-defined.
8) Even ignoring 7) for the moment, addition and multiplication are well-defined only on terminating decimals because these operations require the last terms to carry out and nonterminating decimals do not have them. We can only approximate the sum and product of nonterminating decimals. Try adding sqrt2 and sqrt3 and you’ll run smack into this problem.
9) The integers do not form a well-defined mathematical space. The Peano postulates are essentially a definition and do not well-define a mathematical space. Other developments of the integers from set theory involve the axiom of choice which, in turn, involves the universal and existential quantifiers on infinite set. A remedy would be to embed them isomorphically into the decimals as their integral parts so they become well-defined as a subspace but this would require fixing the decimals first by well-defining them by consistent axioms.
19) It follows from all of the above items that whether one considers FLT as a problem on the integers or the real numbers, it is ill-defined and does not make sense. The first crucial step in resolving FLT is to specify the real numbers as decimals and construct them as well-defined mathematical space on consistent axioms which I did here previously using three simple axioms. Then I well-defined the nonterminating decimals as standard Cauchy sequences. The resulting mathematical space is the new real number system (consisting of decimals) that contain the new integers d* and nonterminating decimals of the form N.99…, where N = 0, 1, …, are integers. Then I reformulate FLT as a problem on the new real number system. Then the countable counterexamples to it exist and are already posted here proving both FLT and Andrew Wiles” “proof” wrong.
The results here and their applications are published in over two-dozen refereed international journals; leads to references are in my website:
http://home.iprimus.com.au/pidro/
To reiterate my main point that Andrew Wiles’ proof is wrong, his proof is not valid being based on the ill-defined real number system, specifically, the integers, that, at the same time, makes the initial formulation of FLT ill-defined, ambiguous, nonsense.
Finally, despite my over two-dozen publications in renowned refereed international journals and conference proceedings and internet threads, forums, blogs and websites, not a single hole has been punched on my work.
Cheers.
E. E. Escultura.
Deccan Herald » Science & Technology » Detailed Story Dec. 13, 2005
Nobility of the Nobel prize
By B M Hegde
Many who deserved the Nobel prize did not get it.
How noble is the Nobel Prize? I was pleased to read in one of our English dailies an open letter written by ten noted physicists to the Nobel committee protesting the exclusion of Prof EVG (George) Sudarshan from this year’s Nobel in physics while giving it to Prof Glauber. I feel they are fully justified in doing so as Sudarshan richly deserved this honour much before Glauber.
The Nobel tradition has been like that all through if one looked at the history of Nobel Prizes ever since Alfred Nobel, who made his millions by selling dynamite, had a heart transformation following a devastating fire in his own factory. He then realised, for the first time, that it is in giving that one gets. He gave all to establish this great tradition of honouring great brains in several fields. The list got expanded after some years with more money coming in. Respice to prospice — let us look back to look forwards. Mahatma Gandhi, the apostle of peace, never got the Nobel Peace Prize, while some confirmed criminals got the same for their heart transformation in their evening of life (vridda naari pathivritaa).
Wagner Juregg got the Nobel for medicine in 1927. He claimed, in a “scientific” paper that he had invented the fever therapy for successfully treating the most dreaded disease of those days, General Paresis of the Insane (GPI), a miserable complication of the then king of diseases, syphilis. Just as any one worth his salt that “researches” AIDS today gets a large booty of the $ 8 billion of the NIH research grant money, people were venerated when they talked about syphilis those days.
Be that as it may, let us go back to our friend Wagner Juregg. His name came up before the Nobel committee in 1926. Gladius, a physician member of the Nobel committee that year knew that Juregg did not invent anything new. It was Hippocrates, the father of modern medicine, in 100 BC that introduced fever therapy to medicine. Juregg tried to inject malaria parasite into GPI victims in mental hospitals to see if the very high fever that malaria parasites produce could kill the treponema pallidum, the fearsome germ of syphilis, which people normally acquire through sexual intercourse. Six of the one hundred patients thus injected improved clinically and more than fifty of them died (not reported in the paper) of malaria as Europeans do not have racial immunity against falciparum malaria.
Gladius could thus avert a tragedy in 1926. Gladius told the committee that Juregg ought to be tried in a criminal court instead for killing that many patients out of the one hundred that he used for his experiments! There were no ethical committees those days! But read on to know that Wagner Juregg got the Nobel Prize the following year after Gladius died providentially of a massive heart attack in 1926.
There are exceptions and many good deserving people did get the Nobels. One of them was my teacher, Bernard Lown, who deserved the Nobel for his invention — the Lown’s defibrillator — the machine that saves many lives in the emergency room after cardiac arrest. But what he did get was the Nobel Peace Prize instead much later. He founded the Physicians Against Nuclear War (PANW) in 1974 and fought against the might of the US war lords to prevent further nuclear stockpiling and was instrumental in getting the Russian communists to talk to American capitalists. He was mainly responsible for preventing America dumping its plutonium waste in a small island off the west coast of Africa.
The ones left out
The numbers that were cheated in this process are too many to enumerate. However, a few deserve to be mentioned for their great contributions in different fields of human endeavour for which they richly deserved the Nobel.
John OM Bockris is a distinguished Emeritus professor of chemistry at the A&M University in Texas. He is the father of “cold fission” — nuclear fusion occurring in a laboratory test tube! He was ridiculed, persecuted but he survived all that. He was cheated of the Nobel despite several nominations over the decades! Professor Rustom Roy, Evan Pugh Professor of material sciences (and many other professorships) at the Penn State University is the world’s top material scientist. His laboratory is considered the leader. He invented the “sol-gel” technique that is used even today to extract nano-particles. He should be rightly called the father of nanotechnology. He was nominated a dozen times for the Nobel without the committee selecting him. His technique is the one that scientists use even today, though.
Most recent is the case of Professor Eddie Escultura, from the Philippines, a great mathematical brain who contributed something novel in the field of quantum physics. He was considered for the Nobel this year by the committee only to be rejected in favour of Professor Glauber. But the developments following this would reveal the sickness that has afflicted the Nobel committee. Professor Gerholms, an eminent physicist on the Nobel committee resigned from the committee to protest the dropping of Eddie. He goes one step further. In a personal letter to Prof. Escultura, Prof Gerholms wrote as to what went on inside the committee room and named two prominent members of the committee lobbying for their candidates. Gerholms in his resignation letter wrote to the committee that lobbying is highly objectionable inside the Nobel committee. Bold man indeed!
Another distinguished Indian mathematician, Professor Lakshmikantham of the Florida Institute of Technology, whose original work in the field of non-linear analysis has taken him to the top in the world of mathematics also falls into this category of losers. He was rejected several times. One could go on and on. I have come to one conclusion that where there are men manning any organisation, including governments, morality and authenticity would be the casualties. Poor Alfred Nobel did not know that it would have been better to have the Nobel committee of laws rather than of men.
“Men, whether in palace or pad; castle or cottage”, are governed by the same emotions and passions. Winston Churchill was dead right when he said that “it is better to deserve than to get.” All the losers mentioned above and the countless others who have “wasted their sweetness in the desert air” (including the one Indian who keeps telling me that he should have got the Nobel in his field) could take heart from the knowledge that it is better that they deserved the Nobel much more than many around them that managed to bag the prize.
http://www.deccanherald.com/deccanherald/
Dec132005/snt1734020051212.asp
A partial Google search of the topics discussed in my works in the fields of mathematics, physics and the physics of thought (theory of intelligence) yields the results below. This can serve as guide for researchers interested in my work in these fields – E. E. Escultura.
Mathematics:
Results 1 - 10 of about 24,600 for escultura mathematics. (0.14 seconds)
Results 1 - 10 of about 21,700 for escultura number theory. (0.09 seconds)
Results 1 - 10 of about 899 for escultura fermat. (0.11 seconds)
Results 1 - 10 of about 132,000 for escultura analysis. (0.29 seconds)
Results 1 - 10 of about 3,680 for escultura integers. (0.62 seconds)
Results 1 - 10 of about 34,300 for escultura real numbers. (0.10 seconds)
Results 1 - 10 of about 704 for escultura nonlinear analysis. (0.29 seconds)
Results 1 - 10 of about 1,220 for escultura nonstandard analysis. (0.25 seconds)
Results 1 - 10 of about 108 for escultura nonstandard calculus. (0.53 seconds)
Results 1 - 10 of about 221 for escultura non-archimedean. (0.51 seconds)
Results 1 - 10 of about 1,310 for escultura topology. (0.47 seconds)
Results 1 - 10 of about 71,600 for escultura algebra. (0.12 seconds)
Results 1 - 10 of about 15,400 for escultura geometry. (0.34 seconds)
Results 1 - 10 of about 26 for escultura set-valued function. (0.41 seconds)
Results 1 - 10 of about 1,000 for escultura probability. (0.07 seconds)
Results 1 - 10 of about 597 for escultura generalized integral. (0.27 seconds)
Results 1 - 10 of about 95 for escultura generalized derivative. (0.42 seconds)
Results 1 - 10 of about 19,400 for escultura complex numbers. (0.11 seconds)
Results 1 - 10 of about 16,800 for escultura new mathematics. (0.12 seconds)
Results 1 - 10 of about 524 for escultura new arithmetic. (0.56 seconds)
Results 1 - 10 of about 293 for escultura qualitative mathematics. (0.83 seconds)
Results 1 - 10 of about 685 for escultura mathematical foundations. (0.10 seconds)
Results 1 - 10 of about 611 for escultura rules of inference. (0.23 seconds)
Results 1 - 10 of about 232 for escultura axiomatic systems. (0.30 seconds)
Results 1 - 10 of about 276 for escultura cauchy sequences. (0.19 seconds
Results 1 - 10 of about 520 for escultura computation. (0.09 seconds)
Results 1 - 10 of about 17,200 for escultura paradoxes. (0.29 seconds)
Results 1 - 10 of about 4,980 for escultura discrete mathematics. (0.44 seconds)
Results 1 - 10 of about 10,800 for escultura formal logic. (0.25 seconds)
Results 1 - 10 of about 29,000 for escultura natural numbers. (0.41 seconds)
Results 1 - 10 of about 308,000 for escultura nobel. (0.41 seconds)
Physics:
Results 1 - 10 of about 54,900 for escultura physics. (0.09 seconds)
Results 1 - 10 of about 21,500 for escultura new physics. (0.11 seconds)
Results 1 - 10 of about 501 for escultura quantum physics. (0.19 seconds)
Results 1 - 10 of about 285 for escultura quantum gravity. (0.10 seconds)
Results 1 - 10 of about 12,900 for escultura gravity. (0.09 seconds)
Results 1 - 10 of about 229 for escultura superstring. (0.29 seconds)
Results 1 - 10 of about 285 for escultura quantum gravity. (0.10 seconds)
Results 1 - 10 of about 17,500 for escultura black hole. (0.09 seconds)
Results 1 - 10 of about 14,600 for escultura dark matter. (0.09 seconds)
Results 1 - 10 of about 285 for escultura quantum gravity. (0.28 seconds)
Results 1 - 10 of about 24,500 for escultura galaxy. (0.29 seconds)
Results 1 - 10 of about 1,470 for escultura primum. (0.16 seconds)
Results 1 - 10 of about 208 for escultura superconductivity. (0.24 seconds)
Results 1 - 10 of about 306 for escultura cosmic waves. (0.21 seconds)
Results 1 - 10 of about 72 for escultura seismic waves. (0.20 seconds)
Results 1 - 10 of about 9,600 for escultura quark. (0.10 seconds)
Results 1 - 10 of about 139 for escultura electromagnetism. (0.33 seconds)
Results 1 - 10 of about 29,900 for escultura chaos. (0.13 seconds)
Results 1 - 10 of about 1,100 for escultura turbulence. (0.37 seconds)
Results 1 - 10 of about 15,000 for escultura dynamic system. (0.11 seconds)
Results 1 - 10 of about 24,700 for escultura n body problem. (0.23 seconds)
Results 1 - 10 of about 661 for escultura flux theory. (0.23 seconds)
Results 1 - 10 of about 36,800 for escultura big bang. (0.09 seconds)
Results 1 - 10 of about 128 for escultura cosmic sphere. (0.09 seconds)
Results 1 - 10 of about 705 for escultura quasar. (0.05 seconds)
Results 1 - 10 of about 605 for escultura asteroids. (0.23 seconds)
Results 1 - 10 of about 420 for escultura comets. (0.29 seconds)
Results 1 - 10 of about 33,700 for escultura earth lights. (0.11 seconds
Results 1 - 10 of about 695 for escultura balls of fire. (0.22 seconds)
Results 1 - 10 of about 74,500 for escultura new technology. (0.35 seconds)
Results 1 - 10 of about 40,000 for escultura high technology. (0.08 seconds)
Results 1 - 10 of about 32 for escultura magnetic levitation. (0.33 seconds)
Results 1 - 10 of about 682 for escultura free energy converter. (0.10 seconds)
The physics of thought (theory of intelligence):
Results 1 - 10 of about 25,800 for escultura intelligence. (0.17 seconds)
Results 1 - 10 of about 1,170 for escultura sensation region . (0.30 seconds)
Results 1 - 10 of about 660 for escultura creative integrative region. (0.08 seconds)
Results 1 - 10 of about 627 for escultura resonance. (0.07 seconds)
Results 1 - 10 of about 34,500 for escultura laws of nature. (0.18 seconds)
Results 1 - 10 of about 57 for escultura genetic encoding. (0.19 seconds)
Results 1 - 10 of about 271 for escultura genetic activation. (0.42 seconds)
Results 1 - 10 of about 56 for escultura autoimmune system. (0.18 seconds)
Results 1 - 10 of about 20,200 for escultura biology. (0.51 seconds)
Results 1 - 10 of about 35,200 for escultura sensation. (0.77 seconds)
Results 1 - 10 of about 366,000 for escultura cancer. (0.10 seconds)
Results 1 - 10 of about 1,420 for escultura autism. (0.27 seconds)
Results 1 - 10 of about 72,100 for escultura reflex. (0.78 seconds)
Results 1 - 10 of about 11,000 for escultura instinct. (0.10 seconds)
Results 1 - 10 of about 635 for escultura intuition. (0.36 seconds)
Results 1 - 10 of about 152,000 for escultura learning. (0.13 seconds)
Results 1 - 10 of about 117 for escultura birthmark. (0.84 seconds)
Results 1 - 10 of about 81 for escultura genetic replication. (0.28 seconds)
Results 1 - 10 of about 54 for escultura genetic cystic fibrosis. (0.35 seconds)
Results 1 - 10 of about 21,700 for escultura cloning. (0.12 seconds)
Results 1 - 10 of about 21,700 for escultura cloning. (0.12 seconds)
A partial Google search of the topics discussed in my works in the fields of mathematics, physics and the physics of thought (theory of intelligence) yields the results below. This can serve as guide for researchers interested in my work in these fields – E. E. Escultura.
Mathematics:
Results 1 - 10 of about 24,600 for escultura mathematics. (0.14 seconds)
Results 1 - 10 of about 21,700 for escultura number theory. (0.09 seconds)
Results 1 - 10 of about 899 for escultura fermat. (0.11 seconds)
Results 1 - 10 of about 132,000 for escultura analysis. (0.29 seconds)
Results 1 - 10 of about 3,680 for escultura integers. (0.62 seconds)
Results 1 - 10 of about 34,300 for escultura real numbers. (0.10 seconds)
Results 1 - 10 of about 704 for escultura nonlinear analysis. (0.29 seconds)
Results 1 - 10 of about 1,220 for escultura nonstandard analysis. (0.25 seconds)
Results 1 - 10 of about 108 for escultura nonstandard calculus. (0.53 seconds)
Results 1 - 10 of about 221 for escultura non-archimedean. (0.51 seconds)
Results 1 - 10 of about 1,310 for escultura topology. (0.47 seconds)
Results 1 - 10 of about 71,600 for escultura algebra. (0.12 seconds)
Results 1 - 10 of about 15,400 for escultura geometry. (0.34 seconds)
Results 1 - 10 of about 26 for escultura set-valued function. (0.41 seconds)
Results 1 - 10 of about 1,000 for escultura probability. (0.07 seconds)
Results 1 - 10 of about 597 for escultura generalized integral. (0.27 seconds)
Results 1 - 10 of about 95 for escultura generalized derivative. (0.42 seconds)
Results 1 - 10 of about 19,400 for escultura complex numbers. (0.11 seconds)
Results 1 - 10 of about 16,800 for escultura new mathematics. (0.12 seconds)
Results 1 - 10 of about 524 for escultura new arithmetic. (0.56 seconds)
Results 1 - 10 of about 293 for escultura qualitative mathematics. (0.83 seconds)
Results 1 - 10 of about 685 for escultura mathematical foundations. (0.10 seconds)
Results 1 - 10 of about 611 for escultura rules of inference. (0.23 seconds)
Results 1 - 10 of about 232 for escultura axiomatic systems. (0.30 seconds)
Results 1 - 10 of about 276 for escultura cauchy sequences. (0.19 seconds
Results 1 - 10 of about 520 for escultura computation. (0.09 seconds)
Results 1 - 10 of about 17,200 for escultura paradoxes. (0.29 seconds)
Results 1 - 10 of about 4,980 for escultura discrete mathematics. (0.44 seconds)
Results 1 - 10 of about 10,800 for escultura formal logic. (0.25 seconds)
Results 1 - 10 of about 29,000 for escultura natural numbers. (0.41 seconds)
Results 1 - 10 of about 308,000 for escultura nobel. (0.41 seconds)
Physics:
Results 1 - 10 of about 54,900 for escultura physics. (0.09 seconds)
Results 1 - 10 of about 21,500 for escultura new physics. (0.11 seconds)
Results 1 - 10 of about 501 for escultura quantum physics. (0.19 seconds)
Results 1 - 10 of about 285 for escultura quantum gravity. (0.10 seconds)
Results 1 - 10 of about 12,900 for escultura gravity. (0.09 seconds)
Results 1 - 10 of about 229 for escultura superstring. (0.29 seconds)
Results 1 - 10 of about 285 for escultura quantum gravity. (0.10 seconds)
Results 1 - 10 of about 17,500 for escultura black hole. (0.09 seconds)
Results 1 - 10 of about 14,600 for escultura dark matter. (0.09 seconds)
Results 1 - 10 of about 285 for escultura quantum gravity. (0.28 seconds)
Results 1 - 10 of about 24,500 for escultura galaxy. (0.29 seconds)
Results 1 - 10 of about 1,470 for escultura primum. (0.16 seconds)
Results 1 - 10 of about 208 for escultura superconductivity. (0.24 seconds)
Results 1 - 10 of about 306 for escultura cosmic waves. (0.21 seconds)
Results 1 - 10 of about 72 for escultura seismic waves. (0.20 seconds)
Results 1 - 10 of about 9,600 for escultura quark. (0.10 seconds)
Results 1 - 10 of about 139 for escultura electromagnetism. (0.33 seconds)
Results 1 - 10 of about 29,900 for escultura chaos. (0.13 seconds)
Results 1 - 10 of about 1,100 for escultura turbulence. (0.37 seconds)
Results 1 - 10 of about 15,000 for escultura dynamic system. (0.11 seconds)
Results 1 - 10 of about 24,700 for escultura n body problem. (0.23 seconds)
Results 1 - 10 of about 661 for escultura flux theory. (0.23 seconds)
Results 1 - 10 of about 36,800 for escultura big bang. (0.09 seconds)
Results 1 - 10 of about 128 for escultura cosmic sphere. (0.09 seconds)
Results 1 - 10 of about 705 for escultura quasar. (0.05 seconds)
Results 1 - 10 of about 605 for escultura asteroids. (0.23 seconds)
Results 1 - 10 of about 420 for escultura comets. (0.29 seconds)
Results 1 - 10 of about 33,700 for escultura earth lights. (0.11 seconds
Results 1 - 10 of about 695 for escultura balls of fire. (0.22 seconds)
Results 1 - 10 of about 74,500 for escultura new technology. (0.35 seconds)
Results 1 - 10 of about 40,000 for escultura high technology. (0.08 seconds)
Results 1 - 10 of about 32 for escultura magnetic levitation. (0.33 seconds)
Results 1 - 10 of about 682 for escultura free energy converter. (0.10 seconds)
The physics of thought (theory of intelligence):
Results 1 - 10 of about 25,800 for escultura intelligence. (0.17 seconds)
Results 1 - 10 of about 1,170 for escultura sensation region . (0.30 seconds)
Results 1 - 10 of about 660 for escultura creative integrative region. (0.08 seconds)
Results 1 - 10 of about 627 for escultura resonance. (0.07 seconds)
Results 1 - 10 of about 34,500 for escultura laws of nature. (0.18 seconds)
Results 1 - 10 of about 57 for escultura genetic encoding. (0.19 seconds)
Results 1 - 10 of about 271 for escultura genetic activation. (0.42 seconds)
Results 1 - 10 of about 56 for escultura autoimmune system. (0.18 seconds)
Results 1 - 10 of about 20,200 for escultura biology. (0.51 seconds)
Results 1 - 10 of about 35,200 for escultura sensation. (0.77 seconds)
Results 1 - 10 of about 366,000 for escultura cancer. (0.10 seconds)
Results 1 - 10 of about 1,420 for escultura autism. (0.27 seconds)
Results 1 - 10 of about 72,100 for escultura reflex. (0.78 seconds)
Results 1 - 10 of about 11,000 for escultura instinct. (0.10 seconds)
Results 1 - 10 of about 635 for escultura intuition. (0.36 seconds)
Results 1 - 10 of about 152,000 for escultura learning. (0.13 seconds)
Results 1 - 10 of about 117 for escultura birthmark. (0.84 seconds)
Results 1 - 10 of about 81 for escultura genetic replication. (0.28 seconds)
Results 1 - 10 of about 54 for escultura genetic cystic fibrosis. (0.35 seconds)
Results 1 - 10 of about 21,700 for escultura cloning. (0.12 seconds)
Results 1 - 10 of about 21,700 for escultura cloning. (0.12 seconds)
Below is an updated guide ti discussions on EEE's work.
Important websites 1:
My website: http://home.iprimus.com.au/pidro/
On the Nobel in Physics
http://thevelho88.free.fr/bazar/ManilaTimes.pdf#search=%22escultura%20nobel%20physics%22
http://www.deccanherald.com/deccanherald/Dec132005/snt1734020051212.asp
http://kerrycollison.net/index.php?/archives/212-University-of-Philippines-Physics-prof-up-for-Nobel-Prize.html
The thread, New Approach to Physics, under ISCID topic Brainstorms (5 pages)
http://www.iscid.org/boards/ubb-get_topic-f-6-t-000607-p-5.html
http://www.iscid.org/boards/ubb-get_topic-f-6-t-000607.html
Dave Rusin’s
http://www.math.niu.edu/~rusin/known-math/93_back/aaargh
-----------
http://www.ravikiran.com/2005/05/12/proof-of-fermats-last-theorem/
http://www.calmighty.com/?p=76
http://dontletmestopyou.blogspot.com/2005/05/wiles-escultura-and-fermat.html
Two entries here:
http://www.dm.unito.it/personalpages/cerruti/mathnews0704.html
----------
http://ramil.sagum.net/node/102#comment-13592
http://www.mathforge.net/index.jsp?page=seeReplies&messageNum=729
Sassy Lawyer:
http://www.houseonahill.net/index.php/blog/permalink/wiles-escultura-and-pierre-de-fermats-equation/
---
152 entries here:
http://mathforum.org/kb/thread.jspa?threadID=1319346&tstart=945
http://mathforum.org/kb/message.jspa?messageID=4513929&tstart=915
http://mathforum.org/kb/thread.jspa?threadID=1366462&tstart=15
http://mathforum.org/kb/thread.jspa?threadID=1366462&messageID=4645070
Mathforge
http://www.mathforge.net/index.jsp?page=seeReplies&messageNum=729
http://www.mathforge.net/index.jsp?page=seeReplies&messageNum=1236
http://www.mathforge.net/index.jsp?page=seeReplies&messageNum=672
Black hole
http://www.damtp.cam.ac.uk/user/gr/public/bh_home.html
----
http://highfiber.org/content.php?a=&s=threads&ss=3&id=3840&p=&anon=1
http://asiapundit.com/2005/08/26/friday-philippines-roundup/
http://dg.up.edu.ph/viewtopic.php?p=28252#28252
http://dg.up.edu.ph/viewtopic.php?p=24298&sid=4fa596d48178b843e9c4e0ef5f208209
http://www.physicsforums.com/register.php
Faces of the Moon:
http://perryv.i.ph/blogs/facesmoon/index.php?itemid=140#commentform
Left Blank
http://rantingchemist.com/blog/archives/2005/05/fighting_over_f.html
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http://www.grahamkendall.net/Math/Math%20Newsgroups/mm-1558.txt
JSH
http://www.groupsrv.com/science/about67873.html&highlight=
http://www.groupsrv.com/science/about67873-0-asc-15.html
http://www.groupsrv.com/science/about67873-0-asc-30.html:
Math News
http://66.102.7.104/search?q=cache:K0-tFnJtRaoJ:www.dm.unito.it/personalpages/cerruti/mathnews0704.html+escultura+mathematics&hl=en&ct=clnk&cd=55
Batangbaler
http://batangbaler.net/board/index.php?s=53ec30f1196b59e96e8f7f184c804aa9&showtopic=24&st=20
----
http://les-mathematiques.u-strasbg.fr/phorum/read.php?f=2&i=171787&t=171787
EEEscultura #8 among top 25 hotest papers
http://top25.sciencedirect.com/index.php?subject_area_id=16&journal_id=0362546X
------
rellek.net: reports EEE ranks 4th in successful searches. 1.7% share, 565 of the 16,006 tracked key phrases
http://rellek.net/blog/?m=200505
http://batongpatay.blogspot.com/2005/06/escultura-resurrected.html
-------
http://www.manilatimes.net/national/2005/jun/15/yehey/opinion/20050615opi7.html
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http://skyscrapercity.com/archive/index.php/t-145567-p-2.html
http://groups.google.fr/group/sci.math/tree/browse_frm/month/1998-04?hl=fr&_done=%2Fgroup%2Fsci.math%2Fbrowse_frm%2Fmonth%2F1998-04%3Fhl%3Dfr%26&hl=fr
http://www.physicsforums.com/showthread.php?t=82957
GUT:
http://www.manilatimes.net/national/2005/jun/19/yehey/images/front.pdf
----
Berchman’s
http://berchmans99.blogspot.com/
Coprime Numbers
http://www.blogger.com/publish-comment.do?blogID=12535639&postID=111521767845531073&r=ok
nitpicky
http://nitpicky.org/2005/05/sith-happens.html
------
http://en.wikipedia.org/wiki/Talk:Fermat%27s_last_theorem
Larry Freeman:
http://fermatslasttheorem.blogspot.com/
False proof:
http://falseproofs.blogspot.com/2006/06/e-e-escultura.html
New blogs here:
http://www.google.com/search?q=escultura+fermat&hl=en&lr=&start=20&sa=N
http://forums.randi.org/showthread.php?threadid=39117&perpage=40&pagenumber=2
http://forums.randi.org/register.php?a=act&u=10221&i=99017417
http://atlas-conferences.com/cgi-bin/abstract/submit/catb-01
http://atlas-conferences.com/cgi-bin/abstract/catb-02
halo scan: http://www.haloscan.com/comments/abelincoln81/111568869010740680/
A year after my nomination for the Nobel Prize for physics and a year of debate on FLT this blog awards the blog,
http://dontletmestopyou.blogspot.com/
2005/06/escultura-still-riding-
dead-horse.html
the distinction as the only holdout from the Sinister Club for continuing to pursue a lost cause: trying to convince the public that both my nomination for the nobel prize for physics and proof that FLT is false are a hoax. This blog also cries uncle by deleting some of my posts.
Announcing …
Major articles in present and future issues of the journal, Nonlinear Analysis and Phenomena:
Vol. III, No. 2, July 2006:
1) E. E. Escultura, The pillars of the new physics.
2) V. V. Gudkov, The Helix and Other Optimal Configurations of Matter and
Applications.
3) D. Kovach, The functional analysis of non-archimedean numbers.
Vol. IV, No. 1, January 2007:
1) C. G. Jesudason, Evidence of nonlinearity of chemical rate constant expression from
MD simulation.
2) E. E. Escultura, The physics of the mind.
3) D. Kovac and E. E. Escultura, Dialogue on the new mathematics.
Vol. IV, No. 2:
There will be three articles by C. G. Jesudason, V. V. Gudkov and E. E. Escultura. Escultura’s article will have the title, Thought, natural science and the new mathematics.
Abstract of Escultura’s article:
The paper is a sequel to the article, The physics of the mind (Nonlinear Analysis and Phenomena, Vol. IV, No. 1, 2007). It summarizes the nature of our universe and devises appropriate mathematics for computation, measurement and development of physical theory. Appropriate mathematics includes the new real number system based on the rectification of foundations and introduction to discrete calculus. The final section summarizes the novel features of the new mathematics and resolves and explains some of the paradoxes of mathematics
Section 9 of the article:
9. Summary of new features; explanation of some paradoxes
We summarize the new features of the new nonstandard calculus as introduction to the mathematical space of functions over the new real number system. We may also refer to it as discrete calculus.
(1) A terminating decimal is an initial segment of some standard Cauchy sequence.
(2) A nonterminating decimal is the Cauchy limit of its standard Cauchy sequence.
(3) Although a function in the new nonstandard calculus is discrete-valued its graph in the new Cartesian plane (i.e., the Cartesian product R*R* with the standard topology) is the same as its graph in the Cartesian plane since each missing value is a dark number which is not detectable.
(4) In calculus a function is smooth at a point if its derivative exists, i.e., its left and right derivatives are equal. A discrete function is, of course, non-smooth in calculus even if its left and right discrete derivatives are equal. For example, at the vertical cusp of the catenoid the left and right discrete derivatives are both equal to u*.
(5) In calculus the existence of local maximum or minimum requires the existence of the derivative at either point. This is not the case with discrete functions. For example, the vertical cusp of the schizoid is its maximum even if its left and right discrete derivatives there are not equal.
(6) Since the left and right discrete derivatives are independent, we distinguish the left from the right maximum or minimum of a function. If the left derivative at a point is finite and positive then it has a left maximum there; if it is negative, it has a left minimum there. Analogous statement holds for the maximum.
(7) As we noted above a discrete function has both maximum and minimum regardless of the existence of discrete derivative. To find the maximum M and minimum m of f(x) on [a,b] we split the interval into subsegments where f(x) has local maximum or local minimum aside from the end points which are either local maximum or minimum. Unless f(x) is rapidly oscillating there will be finite number of such segments. In each segment there will be at least a left or right maximum or minimum or both. Take a segment, and suppose that its left maximum ML has been computed as a Cauchy sequence in accordance with the scheme devised above. Then the function ML – f(x) is maximum when f(x) is minimum. Simply compute the value of the function along sequence of midpoints that gets closer and closer and using the sequence of truncations of both ML and sequence of values of f(x) corresponding to the midpoints of those segments to find the Cauchy sequence for max(ML – f(x)). Since ML is constant, we can find the Cauchy sequence for the minimum mL. Thus there will be finite local left minima and maxima for the subintervals. Therefore, we can find the absolute maximum and minimum for f(x) on [a,b].
(8) Ref. [31] presents several counterexamples to the generalized Jourdan curve theorem for n-sphere where in each case a continuous curve has points in both the interior and exterior of the n-sphere, n = 2, 3, … . the explanation is: what was thought to be a continuum (continuous image of an arc) is actually discrete and misses the n-sphere.
(9) In [35] Lakatos presents counterexamples at every step in Cauchy’s proof of Euler’s conjecture on the vertices, edges and faces of a polyhedron. This paradox is due to the ambiguity of infinite set, the set of polyhedra being infinite so that there may be an exception to any proposition about it. Another flaw in Cauchy’s proof is the use of mapping of R3 to R2 which are distinct mathematical spaces. It is the same ambiguity of infinite set that yields the Banach-Tarski paradox [34].
Across the Internet, it looks like Abe Lincoln (fake name) of the blog HaloScan is the last surviving member of the Sinister Club who continues to peddle the idea that my counterexamples to FLT that proved the conjecture false and Andrew Wiles proposed proof wrong and my 2005 nomination for the Nobel Prize in physics were hoaxes. At the same time he continued to pose questions to me as of last month but when he did not like my answers he deleted the thread. Now he warns that my posts are banned from his blog.
Announcment. Vol. III, No. 2, July 2006 is now out. The major articles are:
1) E. E. Escultura, The pillars of the new physics and some updates.
2) V. V. Gudkov, The helix and other optimal configurations of matter and applications.
D. Kovach, The functional analysis of nonarchimedean numbers.
Future issues:
Vol. IV, No. 1, January 2007. The major issues are:
1) C. G. Jesudason, Evidence of nonlinearity of chemical rate constant expression from MD simulation.
2) E. E. Escultura, The physics of the mind.
3) D. Kovach, On the nature of nonstandard numbers.
Vol. IV, No. 2, July 2007.
1) E. E. Escultura, Thought, natural science and the new nonstandard analysis.
The other two articles are not yet known.
There is nothing else beyond my Flux Theory of Gravitation or the new physics except verification and applications, especially, to the development of new technology. New technology involves conversion of dark matter or latent energy to visible matter or visible (kinetic) energy, etc., electricity and magnetism. An example of new technology is the magnetic train. It is now possible to build power plants of any megawatts of power based on conversion of dark matter to electricity. De Broglie estimated that the latent energy density of dark matter when convertible to kinetic energy is 10^26 joules/cu. ft.
In this regard, I congratulate George Smoot for winning the 2006 Nobel Prize for physics and appreciate the fact that his discovery of background radiation through the COBE project verifies my theory (FTG). However, I have some questions:
1) Where did that explosion called the big bang come from and how did it happen?
2) Did it conform to or violate the first law of thermodynamics?
3) If it did, prove it; if it didn't does it mean that the birth of our universe violated the first law of thermodynamics?
4) Was the Cosmos empty before the big bang? If it was, how do you account for the explosion? If it wasn't what did it consist of?
5) How do you account for the steady formation of cosmic dust that congeals into stars or even galaxy (scientists discovered last year a nascent galaxy in its early formation).
6) Provide a rough account of the evolution of our universe from the big bang to its present state.
7) Why do cosmological bodies (except debris such as asteroids) spin?
8) It can be derived from Hubble's law that the rate of radial expansion of our universe is of order of magnitude 10^20 km/sec and its acceleration is 10^-10 km/secsec. How do you explain this?
9) How can you prove that the radiation that you detected came from the big bang? Can you rule out present sources?
10) Finally, what is the basic constituent of matter and what is its role in the birth of our universe?
Correction: delete "when" to read "... density of dark matter convertible to kinetic energy is 10^26 joules/cu. ft."
The Big Bang is not a theory but a cosmological event that occurred some 12 billion years ago. The only physical theory that puts the Big Bang in context is the flux theory of gravitation (FTG). What Smooth and Mather verified are cosmic waves that originate at the core of galaxies and stars. The original cosmic waves generated by the Big Bang have been mainly demolished by cataclysmic events such as the Cosmic Burst (second Big Bang) and the more energetic ones that pierced the Cosmic Sphere must have sufficiently weakened to imperceptibility.
Correction: Smoot
Nonlinear Analysis and Phenomena
Volume V No. 1 January 2008
FTG XXXIX. Theory of Evolution
E. E. Escultura
Gayatri Institute of Advanced Studies, Visakhapatname, India
E-mail: escultur36@yahoo.com * URL: http://home.iprimus.com.au/pidro/
General Abstract. This three-part paper is the third major application of dynamic modeling: development of the theory of evolution of our universe from the Big Bang through the emergence, differentiation, advancement, organization and intelligence of biological species. The first major application was the initial development of the Flux theory of gravitation (FTG), required to solve the gravitational n-body problem, and its further development. The second was dynamic modeling of biological phenomena and how the brain works in the three papers, Theory of intelligence and evolution, Indian Journal of Pure and Applied Mathematics, 33(1), 2003, Superstring loop dynamics and applications to astronomy and biology, Nonlinear Analysis, 35(8), 1999, and, The physics of the mind, Nonlinear Analysis and Phenomena, IV(1), 2007.
Part I summarizes the mathematical foundations of FTG and uses dynamic modeling to lay down the origin, evolution and destiny of our universe. It highlights the formation of the carbon atom as the building block of most living things. Part II presents the gene as the crucial factor in the emergence, evolution, development and advancement of biological species and their differentiation. Part III focuses on intelligence and organization of and division of labor in biological species. All of parts I - III uses to the hilt the power and advantages of dynamic modeling and its principal component, qualitative mathematics.
Part I
The origin, evolution and destiny
of our universe
________________________________________________________________
Key words and phrases. Charge, Dimension, Isotope, Primum, Quasar, Superstring, Big Bang, Black hole, Cosmic sphere, Cosmic wave, Cosmological vortex, Dark matter, Dark number, Gravitational flux, Macro Gravity, Olber's paradox, Our universe, Quantum gravity, The Universe, Visible matter. ________________________________________________________________
Abstract. The paper introduces dynamic modeling as the remedy for the inadequacy of mathematical modeling and summarizes the mathematical foundations of the flux theory of gravitation (FTG). Then FTG is applied to nature to trace and summarize the origin and evolution of our universe up to the formation carbon atoms as the base of almost all biological organisms.
Nonlinear Analysis and Phenomena
Volume V No. 2 July 2008
FTG XL. Theory of Evolution
E. E. Escultura
Gayatri Institute of Advanced Studies, Visakhapatname, India
E-mail: escultur36@yahoo.com * URL: http://home.iprimus.com.au/pidro/
Part II
The origin and evolution of biological species
________________________________________________________________
Keywords and phrases. Bases, Gene, Mitosis, Mutant, Mutagen, Cancer, Carcinogen, Instinct, Resonance, Fertilization, Self-fertilization, Brain wave, Genetic activation, Genetic encoding, Genetic alteration, Composite brain wave.
________________________________________________________________
Abstract. A sequel to the papers, Superstring loop dynamics and applications to astronomy and biology, Nonlinear Analysis, 35(8), 1999, The theory of intelligence and evolution, (Indian J. Pure and Applied Mathematics, 33(1)), The physics of the mind, (Nonlinear Analysis and Phenomena, IV(1)), and, The origin, evolution and destiny of our universe, Nonlinear Analysis and Phenomena, V(1), January 2008, this paper applies dynamic modeling to draw out and formulate more biological laws and advance the theory of evolution started in the first paper. It presents the gene as the crucial factor in the development, advancement and differentiation of biological species. Conjectures are raised which can be tested by experimental science and a perspective is put forward on some outstanding and unresolved questions of biological evolution. Research projects are suggested for the development of technology for the treatment of genetic diseases such as cancer and lupus.
Nonlinear Analysis and Phenomena
Volume V No. 1 January 2008
FTG XXXIX. Theory of Evolution
E. E. Escultura
Gayatri Institute of Advanced Studies, Visakhapatname, India
E-mail: escultur36@yahoo.com * URL: http://home.iprimus.com.au/pidro/
General Abstract. This three-part paper is the third major application of dynamic modeling: development of the theory of evolution of our universe from the Big Bang through the emergence, differentiation, advancement, organization and intelligence of biological species. The first major application was the initial development of the Flux theory of gravitation (FTG), required to solve the gravitational n-body problem, and its further development. The second was dynamic modeling of biological phenomena and how the brain works in the three papers, Theory of intelligence and evolution, Indian Journal of Pure and Applied Mathematics, 33(1), 2003, Superstring loop dynamics and applications to astronomy and biology, Nonlinear Analysis, 35(8), 1999, and, The physics of the mind, Nonlinear Analysis and Phenomena, IV(1), 2007.
Part I summarizes the mathematical foundations of FTG and uses dynamic modeling to lay down the origin, evolution and destiny of our universe. It highlights the formation of the carbon atom as the building block of most living things. Part II presents the gene as the crucial factor in the emergence, evolution, development and advancement of biological species and their differentiation. Part III focuses on intelligence and organization of and division of labor in biological species. All of parts I - III uses to the hilt the power and advantages of dynamic modeling and its principal component, qualitative mathematics.
Part I
The origin, evolution and destiny
of our universe
________________________________________________________________
Key words and phrases. Charge, Dimension, Isotope, Primum, Quasar, Superstring, Big Bang, Black hole, Cosmic sphere, Cosmic wave, Cosmological vortex, Dark matter, Dark number, Gravitational flux, Macro Gravity, Olber's paradox, Our universe, Quantum gravity, The Universe, Visible matter. ________________________________________________________________
Abstract. The paper introduces dynamic modeling as the remedy for the inadequacy of mathematical modeling and summarizes the mathematical foundations of the flux theory of gravitation (FTG). Then FTG is applied to nature to trace and summarize the origin and evolution of our universe up to the formation carbon atoms as the base of almost all biological organisms.
Nonlinear Analysis and Phenomena
Volume V No. 2 July 2008
FTG XL. Theory of Evolution
E. E. Escultura
Gayatri Institute of Advanced Studies, Visakhapatname, India
E-mail: escultur36@yahoo.com * URL: http://home.iprimus.com.au/pidro/
Part II
The origin and evolution of biological species
________________________________________________________________
Keywords and phrases. Bases, Gene, Mitosis, Mutant, Mutagen, Cancer, Carcinogen, Instinct, Resonance, Fertilization, Self-fertilization, Brain wave, Genetic activation, Genetic encoding, Genetic alteration, Composite brain wave.
________________________________________________________________
Abstract. A sequel to the papers, Superstring loop dynamics and applications to astronomy and biology, Nonlinear Analysis, 35(8), 1999, The theory of intelligence and evolution, (Indian J. Pure and Applied Mathematics, 33(1)), The physics of the mind, (Nonlinear Analysis and Phenomena, IV(1)), and, The origin, evolution and destiny of our universe, Nonlinear Analysis and Phenomena, V(1), January 2008, this paper applies dynamic modeling to draw out and formulate more biological laws and advance the theory of evolution started in the first paper. It presents the gene as the crucial factor in the development, advancement and differentiation of biological species. Conjectures are raised which can be tested by experimental science and a perspective is put forward on some outstanding and unresolved questions of biological evolution. Research projects are suggested for the development of technology for the treatment of genetic diseases such as cancer and lupus.
Just to let the viewers know...
Of the hundreds of threads, blogs, chatrooms, websites and forums that have open discussion of my works from diverse perspectives, I should point out three monoblogs that have only monologues about my works, i.e., they disallow opposing views. While I have responded to and I have the last words among all the other posts, the monologues have all the attacks that remain unrefuted. They are:
1) Batongpatay,
2) Physics Forum and
3) HaloScan (also known as DLMSY).
E
Just to let the viewers know...
Of the hundreds of threads, blogs, chatrooms, websites and forums that have open discussion of my works from diverse perspectives, I should point out three monoblogs that have only monologues about my works, i.e., they disallow opposing views. While I have responded to and I have the last words among all the other posts, the monologues have all the attacks that remain unrefuted. They are:
1) Batongpatay,
2) Physics Forum and
3) HaloScan (also known as DLMSY).
EEE
I just came across this blog that I lost for a long time. Therefore, I'm providing an update on the new real number system.
UPDATE ON THE NEW REAL NUMBER
SYSTEM
1) In both the real and new real number
systems the only well-defined decimals are
the terminating ones; the nonterminating
decimals are simply arrays of digits
most of which are unknown.
2) In the new real number system the
nonterminating decimals are defined, for the
the first time, in terms of the terminating
decimals R as follows:
a) Consider the sequence of terminating
decimals of the form,
N.a_1, N.a_1a_2, …, N.a_1a_2…a_n, …; (1)
the sequence (1) is called standard
generating or g-sequence. Its nth g-term,
N.a_1a_2…a_n, which is a terminating decimal,
defines and approximates the g-limit, the
nonterminating decimal,
N.a_1a_2…a_n…, (2)
at margin of error (maximum error) 10^–n.
b) If the nth digit of the g-limit (2) is not 0
for all n beyond a certain integer k then (2)
defines a nonterminating decimmal.
Note that the nth g-term repeats all the
previous digits of the decimal in the same
order so that if finite terms of the g-sequence
are deleted, the nonterminating decimal it
defines, i.e., its g-limit, remains unaltered.
c) In analysis we define limit in terms of
some norm. We define the g-norm of a
decimal as the decimal itself so that the
g-limt is also defined in terms of the g-norm.
Computation with the g-norm has advantages
one of which being that the result is obtained
directly as a decimal digit by digit so that the
intermediate steps of approximation is avoided.
3) Consider the sequence of decimals,
(d^n)a_1a_2…a_k, n = 1, 2, …, (3)
where d is any of the decimals,
0.1, 0.2, 0.3, …, 0.9, and a_1, …, a_k
finite basic integers (not all 0 simultaneously).
For each combination of d and the a_js,
j = 1, …, k, in (3) the nth term, which
we now refer to as the nth d-term of
this nonstandard d-sequence, is not a
decimal since the digits are not fixed.
As n increases indefinitely it traces the
tail digits of some nonterminating
decimal (note that the nth g-term recedes
to the right with increasing n), becomes
smaller and smaller until it becomes
indistinguishable from the tail digits of the
other decimals. We call the sequence (3)
nonstandard d-sequence since the nth term
is not a standard g-term but has a standard
limit, i.e., limit in the standard norm, which
is 0. Like the g-limit, the d-limit exists since
it is defined by its nonstandard d-sequence
of terminating decimals; we call it a dark
number d, the d-limit of the nonstandard d-
sequence (3). Moreover, while the nth term
becomes smaller and smaller with increasing
n it is greater than 0 no matter how large n is
so that if x is any decimal, 0 < d < x. The set
of d limits of all nonstandard d-sequences is
the set-valued dark number d*
4) We state some important results:
Theorem. The d-limits of the tail digits of
all the nonterminating decimals traced by
the nth d-terms of the d-sequence (3) form
the continuum d*.
Theorem. In the lexicographic ordering R
consists of adjacent predecessor-successor
pairs of decimals (each joined by d*) so
that the closure R* in the g-norm is a
continuum.
Note that the trichotomy axiom follows
from the lexicographic ordering of R*
which is not defined on the real numbers
since nonterminating decimals are not
well-defined there.
Corollary. R* is non-Archimedean and
non-Hausdorff but the subspace of decimals
are Archimedean and Hausdorff in the
standard norm.
Theorem. The rationals and irrationals are
separate, i.e., they are not dense in their union
(this is the first indication of discreteness
of the decimals).
Whenever d* appears in an equation or expression
it means that the equation or expression holds for
each element d of d*.
Theorem. The largest and smallest elements
of R* in the open interval (0,1) are 0.99… and
d* = 1 – 0.99…, respectively.
The following theorem used to be a conjecture.
It now has a proof in R*.
Theorem. An even number greater than 2
is the sum of two prime numbers.
(This post is excerpted from my keynote
address at the 5th World Congress of
Nonlinear Analysts, The Mathematics of
the Grand Unified Theory, July 5, 2008,
Orlando, Florida, now in press at Nonlinear
Analysis, Series A, Theory, Methods and
Applications) and on-line at Science Direct.
E. E. Escultura
Emeritus Research Professor
GVP Institute for Advanced Studies and
Departments of Mathematics and Physics,
JNT University, Visakhapatnam, India
This comment has been removed by the author.
See my articles:
"Edgar E. Escultura en de ongelijkheid van 1 en 0,999"
and
"Omega-analyse en 0,999"
on
http://wetenschap.infonu.nl/wiskunde/32165-edgar-e-escultura-en-de-ongelijkheid-van-1-en-0999.html
and
http://wetenschap.infonu.nl/wiskunde/35856-omega-analyse-en-0999.html
Regards,
Bart van Donselaar
CALL FOR A GRAND UNIFIED JOINT CELEBRATION
Materialist philosophers of all cultures must have pondered this question: what are the basic constituents of matter? The Greeks answered it with four constituents they found in nature: earth, water, fire and air. The Chinese added one more item – wood. Of course, they were not satisfactory and since then the search for the basic constituent of matter was in limbo for 5,000 years until in the 1950s inspired by the exciting developments in quantum physics particle physicists renewed the search with vigor by smashing the nucleus of the atom in pursuit of the basic irreducible elementary particles or building blocks of visible matter (since dark matter was unknown then). By the 1990s the search was a complete success with the discovery of the +quark (up quark) and quark (down quark) and, earlier, the electron discovered by J. J. Thompson in 1897. They comprise every atom; a heavy isotope has at least one more additional stable elementary particle – the neutrino. Particle physicists have, indeed, found what they were looking for – the irreducible building blocks of visible matter – and whatever they have found beyond this discovery is a bonus for natural science and its applications, a bonus for mankind.
In the 1980s dark matter came to the fore with overwhelming evidence of its existence [6,7,8] and, using the new methodology of qualitative modeling that explains nature and its appearances in terms of natural laws [1,5], was established in 1997 [4] as one of the two fundamental states of matter the other ordinary or visible matter [2,5]. That same year the building block of dark matter, the superstring, was discovered as the crucial factor in the solution of the gravitational n-body problem [4] and development of the grand unified theory (GUT). The latter has been established in a series of papers since 1997 and consolidated in [2]. There is only one basic constituent in view of the non-redundancy and non-extravagance natural principles [3] just as there is only one electron since all electrons have identical structure, properties, behavior and functions and differ only in locations. Moreover, it has been established that the superstring coverts to the basic elementary particles as agitated superstring [1,2,3]. In effect, this proves the superstring as the basic constituent of matter, dark and visible [1,2,3,4,5 ].
This happy turn of events came without notice and fanfare but it is an important milestone for science that calls for a grand unified joint celebration by particle and theoretical physicists to mark these monumental achievements and the threshold of a new epoch for natural science and its applications. Whatever particle physicists have achieved beyond this discovery is a bonus for natural science and its applications, a bonus for mankind. Perhaps, a world congress of particle and theoretical physicists is appropriate on this momentous occasion.
References
[1] Escultura, E. E., The mathematics of the grand unified theory, Nonlinear Analysis,
A-Series: Theory: Methods and Applications, 71 (2009) e420 – e431.
[2] Escultura, E. E., The grand unified theory, Nonlinear Analysis, A-Series: Theory: Methods and Applications, 69(3), 2008, 823 – 831.
[3] Escultura, E. E., Qualitative model of the atom, its components and origin in the early universe, Nonlinear Analysis, B-Series: Real World Applications, 11 (2009),
29 – 38.
[4] Escultura, E. E., The solution of the gravitational n-body problem, Nonlinear Analysis, A-Series: Theory, Methods and Applications, 38(8), 521 – 532.
[5] Escultura, E. E., Superstring loop dynamics and applications to astronomy and biology, Nonlinear Analysis, A-Series: Theory: Methods and Applications, 35(8),
1999, 259 – 285.
[6] Astronomy (a) August 1995, (b) January 2001, (c) June 2002.
[7] Science, Glow reveals early star nurseries, July 1998.
[8] Science, (a) Starbirth, gamma blast hint at active early universe, 282(5395), December, 1998, 1806; (b) Gamma burst promises celestial reprise, 283(5402),
January 1999; (c) Powerful cosmic rays tied to far off galaxies, 282(5391), Nov. 1998, 1969 – 1971.
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