tag:blogger.com,1999:blog-3722233.post200078035..comments2023-10-01T07:37:32.894-05:00Comments on Computational Complexity: Counterexample to Fermat's Last Theorem Found!!!Lance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger74125tag:blogger.com,1999:blog-3722233.post-55506037189466267042016-12-21T10:38:31.181-06:002016-12-21T10:38:31.181-06:00E. E. ESCULTURA IS A EXAMPLE TYPICAL OF "CRAN...E. E. ESCULTURA IS A EXAMPLE TYPICAL OF "CRANCKPOT MATHEMATICAL". PATHETICS AND RIDICULOUS ...skoxhttps://www.blogger.com/profile/05170994734879812229noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-91067260636186309702016-03-01T10:27:20.461-06:002016-03-01T10:27:20.461-06:00Is it a generalised proof for all real numbers?Is it a generalised proof for all real numbers?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-2360487154736923962016-03-01T00:48:16.904-06:002016-03-01T00:48:16.904-06:00New Paper: The Resolution of the Great 20th Centur...New Paper: The Resolution of the Great 20th Century Debate in the Foundations of Mathematics;<br />http://www.scirp.org/Journal/PaperInformation.aspx?PaperID=63915 E. E. Esculturahttps://www.blogger.com/profile/09364110851327981518noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-28315799608496832532015-05-18T04:57:19.889-05:002015-05-18T04:57:19.889-05:00To Keven: What a surprise! I left you at the botto...To Keven: What a surprise! I left you at the bottom of a pit five years ago when you failed to sustain your claim that you can add sqrt2 and sqrt3. - E. E. Escultura <br />E. E. Esculturahttp://users.tpg.com.au/pidro/noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-16162105535684930572013-10-05T05:41:30.755-05:002013-10-05T05:41:30.755-05:00See : Finding Numbers satisfying the condition of ...See : Finding Numbers satisfying the condition of fermat<br />http://www.iosrjournals.org/iosr-jm/pages/v7i4.htmlUnnikrishnanhttps://www.blogger.com/profile/10791822713167465854noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-43032265482841877012013-03-04T23:32:29.843-06:002013-03-04T23:32:29.843-06:00The following article debunks every false proof th...The following article debunks every false proof that 0.999... equals 1:<br /><br />https://www.filesanywhere.com/fs/v.aspx?v=8b696686586172b3b0a7<br /><br />John Gabriel<br />http://johngabrie1.wix.com/newcalculusJohn Gabriel New Calculushttps://www.blogger.com/profile/08536758763788584665noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-87950363608054234172011-04-08T03:52:24.702-05:002011-04-08T03:52:24.702-05:00A simple proof of Fermat’s last theorem:
1)Ferm...A simple proof of Fermat’s last theorem:<br /><br /> <br />1)Fermat theorem has this equivalent theorem:<br /> <br />X^n+Y^n ?= Z^n (1) <br /><br />(X, Y, Z :fractional-rational numbers, n: natural number >2) <br /><br />2) Let’s divide (1) by (Z-X)^n, then we can also prove that there exists this equivalent theorem:<br /><br />X’^n+Y’^n ?= Z’^n and Z’ =X’ +1 <br /><br />(X’, Y’, Z’ :fractional-rational numbers, n: natural number >2)<br /><br />3) Please note that a theorem is a mathematical structure, in which the symbols are not important, then we can have this theorem:<br /><br /> X^n+Y^n ?= Z^n and Z =X +1 (*)<br /><br />(X, Y, Z :fractional-rational numbers, n: natural number >2)<br /><br />This is, exactly, the theorem 1) with an additional condition Z=X+1. <br /><br />Then:<br /><br />a)Please check theorem 3) with any X that is an integer and with any Y that is a real fractional–rational number (such as 5/3, 15/7…: they are rational-fractional numbers that cannot be reduced to integers). <br /><br />b)Please check theorem 3) with any X that is a real fractional–rational number and with any Y that is an integer.<br /><br /> This simple proof of Fermat theorem is clear enough.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-26266659378913797852010-11-12T14:13:58.821-06:002010-11-12T14:13:58.821-06:00Unni:
I also ask, what awards and honours? I have...Unni:<br /><br />I also ask, what awards and honours? I have serious doubt that any University or non-fringe mathematical institute or association or whatever would grant any awards to anyone based on counterexamples to FLT, since none can exist. Perhaps if in the course of looking for a counterexample to FLT someone were to discover something new, that might merit some attention. By something new, I mean some 'accidental' discovery that has value in and of itself.<br /><br />I have to ask, what is your mathematics background? Do you know what it means to prove something is impossible, or that something cannot exist?<br /><br />To draw an analogy, in earlier times alchemists searched for the philosphers stone. This stone would somehow turn lead into gold. Now they figured out all sorts of nice properties that this stone would have, but at the end of the day no such stone could exist, so these 'properties' were useless.<br /><br />My advice to you if you want to become a mathematician or want to be taken seriously by them, is to learn as much math as possible. Go to university, or educate yourself, but if you choose to educate yourself do not waste time with the nonsense of people like E Escultura, try cover the standard material from a typical undergrad program. By assuming that every problem can be sovled with just highschool algebra you are making a huge mistake. When all you have is a hammer, everything looks like a nail. If simple algebra were enough to tackle every problem then calculus, differential equations, topology, group theory, etc., would never have been needed or created. By learning as much as possible you allow yourself to bring as many tools as possible to bear on a problem, but you will also understand why this or that tool is inapropriate or not powerful enough to attack certain problems. My point is that simple algebra is to the study of mathematics as spelling is to literature; it is necessary to master, but not enough to produce anything meaningful.kSaugahttps://www.blogger.com/profile/10383064863774679836noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-77954864374267197272010-11-11T15:15:11.080-06:002010-11-11T15:15:11.080-06:00UnnI:
you miss the point. Proving that there is n...UnnI:<br /><br />you miss the point. Proving that there is no integer k satisfying 0<k<1 in no way proves or disproves FLT. <br /><br />THe point I make is that since FLT has be conclusively proven to be true, then any attempt to define criterion for a counterexample is pointless. You could create all sorts of criterion. Even if your criterion were valid, they cannot be satisfied and be a counter examply to FLT since no counter example to FLT can exist. Quite simply you are defining a set of rules that can only be satisifed by the null set. Maybe I didn't explain myself well. If you don't get what I am saying I can explain it further. <br /><br />Proving the criterion don't exist isn't the point. You could find all sorts of interesting facts about x,y,z satisfying FLT if you were to assume that such a solution exists. BUt since such a solution is impossible, the very things you set out to study do not in fact exists, rendering their study pointless.<br /><br />Dear lord, can someone else chime in here and help me?kSaugahttps://www.blogger.com/profile/10383064863774679836noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-84496029591019084502010-11-09T23:21:31.333-06:002010-11-09T23:21:31.333-06:00So proving such criterion doesn't exist will p...So proving such criterion doesn't exist will prove the theorem with much smaller and simpler efforts than Wiles as to prove up to this I need only two A4 sheets using high school algebra. Can u prove such ki doesn't exist like there exist no integers between 0 and 1?Unnikrishnanhttps://www.blogger.com/profile/10791822713167465854noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-19561017224442374712010-11-09T23:17:01.876-06:002010-11-09T23:17:01.876-06:00Then you prove such ki doesn't exist. Then the...Then you prove such ki doesn't exist. Then the proof will be much smaller and simpler than wiles.Unnikrishnanhttps://www.blogger.com/profile/10791822713167465854noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-22661031808169799062010-11-09T19:02:35.239-06:002010-11-09T19:02:35.239-06:00Unni is also nuts. FLT has been proven to be true....Unni is also nuts. FLT has been proven to be true. The proof has been checked nd verfied by hundreds if not thousands of mathematicians. So any criterion for finding a counterexample is pointless, one cannot exist. It's like finding a criterion to find an integer k s.t. 0< k < 1, is can never be done.kSaugahttps://www.blogger.com/profile/10383064863774679836noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-89808306568400768712010-11-09T19:00:34.141-06:002010-11-09T19:00:34.141-06:00Escultura is NUTS!Escultura is NUTS!kSaugahttps://www.blogger.com/profile/10383064863774679836noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-19423933451535843732010-11-09T01:11:31.154-06:002010-11-09T01:11:31.154-06:00I have developed a criteria to get counter example...I have developed a criteria to get counter example to FLT and received various awards and honours during 2000 -2005.<br /><br />The criterion are :<br /><br />1. x = k3^n + nk1h1, y = k2^n + nk1h1, z = k1^n - nk1h1 , if none of x,y,z is a multiple of n.<br />(This can also be written in the simple form<br />x= (k1^n - k2^n + k3^n)/2, y== (k1^n +k2^n - k3^n)/2, z = (k1^n +k2^n + k3^n)/2 )<br /><br />2. x = k3^n + nk2h2, y = k2^n + nk2h2, z = ((k1^n)/n) – nk2h2, if one and only one of x,y,z is a muliple of n<br /><br />where k3<k2<k1 are natural numbersUnnikrishnanhttps://www.blogger.com/profile/10791822713167465854noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-88038551534891376072010-11-09T01:07:27.706-06:002010-11-09T01:07:27.706-06:00I HAVE DEVELOPED A CRITERION TO FIND THE COUNTER E...I HAVE DEVELOPED A CRITERION TO FIND THE COUNTER EXAMPLE TO FLT during 2000 for which I got many awards and honours.<br /><br />The criterion are :<br /><br />1. x = k3^n + nk1h1, y = k2^n + nk1h1, z = k1^n - nk1h1 , if none of x,y,z is a multiple of n.<br />(This can also be written in the simple form<br />x= (k1^n - k2^n + k3^n)/2, y== (k1^n +k2^n - k3^n)/2, z = (k1^n +k2^n + k3^n)/2 )<br /><br />2. x = k3^n + nk2h2, y = k2^n + nk2h2, z = ((k1^n)/n) – nk2h2, if one and only one of x,y,z is a muliple of n<br /><br /><br />where k1, k2 and k3 are positive integers such that k3<k2<k1Unnikrishnanhttps://www.blogger.com/profile/10791822713167465854noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-33488335171097911772010-11-09T01:02:49.593-06:002010-11-09T01:02:49.593-06:00I HAVE FOUND A SIMPLE CRITERION TO GET COUNTER EXA...I HAVE FOUND A SIMPLE CRITERION TO GET COUNTER EXAMPLES TO FLT AND ANY ONE CAN VERIFY MY PROOF<br /><br />1. x = k3^n + nk1h1, y = k2^n + nk1h1, z = k1^n - nk1h1 , if none of x,y,z is a multiple of n.<br />(This can also be written in the simple form<br />x= (k1^n - k2^n + k3^n)/2, y== (k1^n +k2^n - k3^n)/2, z = (k1^n +k2^n + k3^n)/2 )<br /><br />2. x = k3^n + nk2h2, y = k2^n + nk2h2, z = ((k1^n)/n) – nk2h2, if one and only one of x,y,z is a muliple of n<br /><br />where k1,k2,k3 are integers such that k3<k2<k1Unnikrishnanhttps://www.blogger.com/profile/10791822713167465854noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-67882591405473519772010-10-31T05:14:12.714-05:002010-10-31T05:14:12.714-05:00Book Review by E. E. Escultura (continued)
Refere...Book Review by E. E. Escultura (continued)<br /><br />References<br /><br /><br />[1] Escultura, E. E., Diophantus: Introduction to Mathematical Philosophy (With probabilistic solution of Fermat’s last theorem), Kalikasan Press: Manila, 1993.<br />[2] Escultura, E. E. Probabilistic mathematics and applications to dynamic systems including Fermat's last theorem, Proc. 2nd International Conference on Dynamic Systems and Applications: Atlanta, May 27 – 31, 1999, pp. 147 – 152.<br />[3] Escultura, E. E. Bhaskar, T. G.; Leela, S., Laksmikantham, V., Revisiting the hybrid real number system, J. Nonlinear Analysis, C-Series: Hybrid Systems, May 2009, 3, 2, pp. 101 – 107.<br />[4] Escultura, E. E. Extending the reach of computation, J. Applied Mathematics Letters, 2008, 21, 10, pp. 1074 – 1081.<br />[5] Escultura, E. E. Exact solutions of Fermat’s equation (A definitive resolution of Fermat’s last theorem, J. Nonlinear Studies, 1998, 5, 2, pp. 227 - 254.<br />[6] Escultura, E. E. Recent verification and applications, Proc. 2rd International Conference on Tools for Mathematical Modeling, St. Petersburg, 1999, 4, pp. 116 - 29.<br />[7] Escultura, E. E. The generalized integral as dual of Schwarz distribution, invited paper, J. Nonlinear Studies.<br />[8] Escultura, E. E. Set-valued differential equations and applications to quantum gravity, J. Mathematical Research, 2000, 6, St. Petersburg, pp. 221 - 224.<br />[9] Escultura, E. E. The new real number system and discrete computation and calculus, J. Neural, Parallel and Scientific Computations, 2009, 17, pp. 59 – 84.<br />[10] Escultura, E. E. Introduction to Qualitative Control Theory, Kalikasan Press: Manila, 1991.<br />[11] Escultura, E. E. The new mathematics and physics, J. Applied Mathematics and Computation, 2003, 138, 1, 145 – 169.<br />[12] Escultura, E. E. Chaos, turbulence and fractal, Indian J. Pure and Applied Mathematics, 2001, 32,10, pp. 1539 – 1551.<br />[13] Escultura, E. E. The mathematics of the grand unified theory, Proc. 5th World Congress of Nonlinear Analysts, J. Nonlinear Analysis, A-Series: Theory: Method and Applications, 2009, 71, pp. e420 – e431.<br />[14] Escultura, E. E. The mathematics of the new physics, J. Applied Mathematics and Computations, 2002, 130, 1, pp. 149 - 169.<br />[15] Escultura, E. E. Dynamic Modeling and the new mathematics and physics, J. Neural, Parallel and Scientific Computations (NPSC), 2007, 15, 4, PP. 527 – 538.<br />[16] Escultura, E. E. The theory of intelligence and evolution, Indian J. Pure and Applied Math., 2003, 33, 1, PP. 111 – 129.<br />[17] Escultura, E. E. The physics of the mind, accepted, J. Science of Healing Outcomes.<br />[18] Escultura, E. E. The origin and evolution of biological species, J. Science of Healing Outcomes, 2010, 6-7, pp. 17 - 27.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-41913377520932322272010-10-30T19:31:39.197-05:002010-10-30T19:31:39.197-05:00Book review by E. E. Escultura (continued)
Review...Book review by E. E. Escultura (continued)<br /><br />Reviewer's comment. I would retain only the first sentence of the formulation since the rest of it is already moot and academic [42]. <br /><br />The author proceeds to lay out in great detail the theories and models proposed so far with a graphic account of the twists and turns in the search for a complete theory. The proposed theories and models range from general relativity and quantum theory through the standard model of particle physics, string theories, a number of dimension theories, quantum gravity, gauge theory and superstring theory. In the end, he concluded that physics today is in total confusion, has accomplished nothing towards unification in almost three decades and a complete theory is nowhere in sight. He bewailed the fact that string theorists have almost exclusive access to research grants and top academic positions in physics for which he should be commended for being able to rise above the confines of this group to which he belongs. <br /><br />Now, he welcomes the seers to tell us what is wrong with physics and point the way towards unification. This will require, in my view, a critique of its foundations and the foundations of mathematics including its present methodology of quantitative modelling that describes the appearances of nature without providing insights into how nature works. This allows, at best, reasoning by analogy which has an obvious flaw: a bird that walks like a duck and quacks like a duck is not necessarily a duck.<br /><br />Reviewer's comment on rectification. <br /><br />1) We need to clarify physical concepts and distinguish them from mathematical concepts. The former have physical referents – physical objects – that exist in nature and are subject to its laws. Mathematical concepts are man-made that comprise its vocabulary as the language of science; they have no physical referents and are, therefore, not subject to natural laws, e.g., time, distance, dimension, function and equation. Among the physical concepts are matter, energy and physical systems such as the electron, light, electromagnetic wave, atom and galaxy; their existence are verifiable. For example, to clarify what matter is we need to know what it consists of which requires the discovery of its basic constituent.<br /><br />2) We need to improve the present sense of unification from being descriptive of the appearances of nature in terms of common physical concepts to explanation of how nature works in terms of its laws. This should include explanation of what the forces and interactions of nature and their nature and what physical systems or natural phenomena are.<br /><br />3) In view of the inadequacy of the present methodology of quantitative modelling of physics that describes the appearances of nature, we need the new methodology of qualitative modelling that explains nature and natural phenomena in terms of natural laws. Its main tool is qualitative mathematics, the complement of computation and measurement. It includes axiomatic systems and abstract mathematics and the search for the laws of nature.<br /><br />4) We need to clarify that mathematical physics, a collection of mathematical descriptions of nature and natural phenomena, is not theoretical physics. A physical theory is an axiomatic system where the axioms or basic premises are laws of nature and scientific reasoning is based on its axioms – laws of nature – that define it and conclusions drawn from them. This way of reasoning belongs to rational thought. Definition of physical concepts is based solely on its axioms. When the laws of nature that define a physical theory apply to the various disciplines of natural science it is called grand unified or complete theory. For sources and elaboration of these ideas the viewer is referred to the following references.E. E. Esculturahttp://edgareescultura.wordpress.com/noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-11187402932380713722010-10-30T19:25:33.834-05:002010-10-30T19:25:33.834-05:00BOOK REVIEW AND PROPOSED REMEDY FOR THE PROBLEMS O...BOOK REVIEW AND PROPOSED REMEDY FOR THE PROBLEMS OF PHYSICS <br /><br />By E. E. Escultura<br /><br />The book: THE TROUBLE WITH PHYSICS, Penguin Books, 2008 <br /><br />By Lee Smolin<br /><br />The book is the most objective and comprehensive assessment of contemporary physics I have read. It assesses where physics is in the search for the grand unification of the forces and interactions of nature and identifies five great problems that must be resolved towards unification. They are stated below with this Reviewer's comments.<br /><br />Problem 1. Combine general relativity and quantum theory into a single theory that can claim to be the complete theory of nature.<br /><br />Reviewer's comment. By building a theory based on general relativity and quantum theory, it brings in their weakness and inadequacy and other limitations in the search for unification. There is a lot of ambiguity in their basic physical concepts such as matter, energy, charge and gravity. To know matter, for instance, we must know what matter consists of and this requires the discovery of the basic constituent of matter which contemporary physics has not done. <br /><br />Problem 2. Resolve the problems in the foundations of quantum mechanics either by making sense of the theory as it stands or by inventing a new theory that does make sense.<br /><br />Reviewer's comment. I agree with this formulation. However, I would broaden it to the problems of the foundations of natural science and mathematics, the latter being the language and tool of science. <br /><br />Problem 3. Determine whether or not the various particles and forces can be unified in a theory that explains them all as manifestations of a single fundamental entity.<br /><br />Reviewer's comment. I fully agree with this formulation.<br /><br />Problem 4. Explain how the values of the free constants in the standard model of particle physics are chosen in nature.<br /><br />Reviewer's comment. I agree with this formulation with some modification as follows: Explain the constants of nature, e.g., the Planck's constant h and the Hubble's constant, by providing details on how they were determined. <br /><br />Problem 5. Explain dark matter and energy. Or, if they don't exist, determine how and why gravity is modified on large scales. More generally, explain why the constants of the standard model, including dark energy, have the values they do.E. E. Esculturahttp://edgareescultura.wordpress.com/noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-43298758699971735512010-04-29T09:08:42.628-05:002010-04-29T09:08:42.628-05:00In the 1980s dark matter came to the fore with ove...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 ]. <br /><br />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.<br /><br />References<br /><br />[1] Escultura, E. E., The mathematics of the grand unified theory, Nonlinear Analysis,<br />A-Series: Theory: Methods and Applications, 71 (2009) e420 – e431.<br />[2] Escultura, E. E., The grand unified theory, Nonlinear Analysis, A-Series: Theory: Methods and Applications, 69(3), 2008, 823 – 831.<br />[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),<br />29 – 38.<br />[4] Escultura, E. E., The solution of the gravitational n-body problem, Nonlinear Analysis, A-Series: Theory, Methods and Applications, 38(8), 521 – 532.<br />[5] Escultura, E. E., Superstring loop dynamics and applications to astronomy and biology, Nonlinear Analysis, A-Series: Theory: Methods and Applications, 35(8),<br />1999, 259 – 285.<br />[6] Astronomy (a) August 1995, (b) January 2001, (c) June 2002.<br />[7] Science, Glow reveals early star nurseries, July 1998.<br />[8] Science, (a) Starbirth, gamma blast hint at active early universe, 282(5395), December, 1998, 1806; (b) Gamma burst promises celestial reprise, 283(5402),<br />January 1999; (c) Powerful cosmic rays tied to far off galaxies, 282(5391), Nov. 1998, 1969 – 1971.E. E. Esculturahttp://users.tpg.com.au/pidro/noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-135004040084674862010-04-29T09:06:48.889-05:002010-04-29T09:06:48.889-05:00CALL FOR A GRAND UNIFIED JOINT CELEBRATION
Materi...CALL FOR A GRAND UNIFIED JOINT CELEBRATION<br /><br />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.E. E. Esculturahttp://users.tpg.com.au/pidro/noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-70076533925002445612010-04-28T06:31:19.044-05:002010-04-28T06:31:19.044-05:00CALL FOR A GRAND UNIFIED JOINT CELEBRATION
Materi...CALL FOR A GRAND UNIFIED JOINT CELEBRATION<br /><br />Materialist philosophers of all cultures must have pondered this question: what are the basic constituents of matter? The Greeks answered it with four elements 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 development of 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 matter. By the 1990s the search was a complete success with the discovery of the +quark (up quark) and quark (down quark) and the electron (discovered in 1897). They are basic as constituents of every atom; a heavy isotope has at least one more constituent – the neutrino. The particle physicists have, indeed, found what they were looking for – the irreducible building blocks of matter – and whatever they have found beyond these is a bonus for natural science. <br /><br />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 for 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 was also established that the superstring coverts to the basic elementary particles as agitated superstring [1,2,3]. In effect, this established the superstring as the basic constituent of matter, dark and visible [1,2,3,4,5 ]. <br /><br />This happy turn of events came without fanfare and was not even noticed 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. Perhaps, a world congress of particle and theoretical physicists is appropriate on this occasion.<br /><br />References<br /><br />[1] Escultura, E. E., The mathematics of the grand unified theory, Nonlinear Analysis,<br />A-Series: Theory: Method and Applications, 71 (2009) e420 – e431.<br />[2] Escultura, E. E., The grand unified theory, Nonlinear Analysis, A-Series: Theory:<br />Method and Applications, 69(3), 2008, 823 – 831.<br />[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),<br />29 – 38.<br />[4] Escultura, E. E., The solution of the gravitational n-body problem, Nonlinear Analysis, A-Series: Theory, Methods and Applications, 38(8), 521 – 532.<br />[5] Escultura, E. E., Superstring loop dynamics and applications to astronomy and biology, Nonlinear Analysis, A-Series: Theory: Method and Applications, 35(8), 1999, 259 – 285.<br />[6] Astronomy (a) August 1995, (b) January 2001, (c) June 2002.<br />[7] Science, Glow reveals early star nurseries, July 1998.<br />[8] Science, (a) Starbirth, gamma blast hint at active early universe, 282(5395), December, 1998, 1806; (b) Gamma burst promises celestial reprise, 283(5402),<br />January 1999; (c) Powerful cosmic rays tied to far off galaxies, 282(5391), Nov. 1998, 1969 – 1971.E. E. Esculturahttp://users.tpg.com.au/pidro/noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-32993322074564424502009-11-24T04:41:32.625-06:002009-11-24T04:41:32.625-06:00References
[1] Escultura, E. E., The solution of...References<br /><br />[1] Escultura, E. E., The solution of the gravitational n-body problem, Nonlinear Analysis, Series A: Theory, Methods and Applications, 30(8), Dec. 1997, 521 – 532.<br />[2] Escultura, E. E. (1997) Exact solutions of Fermat's equation (Definitive resolution of Fermat’s last theorem, 5(2), 227 – 2254.<br />[3] Escultura, E. E. (1999) Superstring loop dynamics and applications to astronomy and biology, J. Nonlinear Analysis, 35(8), 259 – 285.<br />[4] Escultura, E. E. (1999) Recent verification and applications, Proc. 2rd International Conf.: Tools for Mathematical Modeling, St. Petersburg, vol. 4, 74 – 89.<br />[5] Escultura, E. E. (2001) From macro to quantum gravity, J. Problems of Nonlinear Analysis in Engineering Systems, 7(1), 56 – 78. <br />[6] Escultura, E. E. (2001) Quantum gravity, Proc. 3rd International Conference on Dynamic Systems and Applications, Atlanta, 201 – 208. <br />[7] Escultura, E. E. (2001) Turbulence: theory, verification and applications, J. Nonlinear Analysis, 47(2001), 5955 – 5966.<br />[8] Escultura, E. E. (2001) Vortex Interactions, J. Problems of Nonlinear Analysis in Engineering Systems, Vol. 7(2), 30 – 44.<br />[9] Escultura, E. E. (2001) Chaos, turbulence and fractal, Indian J. Pure and Applied Mathematics, 32(10), 1539 – 1551.<br />[10] Escultura, E. E. (2002) The mathematics of the new physics, J. Applied Mathematics and Computations, 130(1), 145 – 169.<br />[11] Escultura, E. E. (2003) The new mathematics and physics, J. Applied Mathematics and Computation, 138(1), 127 – 149.<br />[12] Escultura, E. E. (2003) Macro and quantum gravity and the dynamics of cosmic waves, J. Applied Mathematics and Computation, 139(1), 23 – 36. <br />[13] Escultura, E. E., (2003) Dynamic Modeling and Applications, Proc. 3rd International Conference on Tools for Mathematical Modeling, State Technical University of St. Petersburg, St. Petersburg.<br />[14] Escultura, E. E., (2004) Problems and Unanswered Questions of physics and their resolution, Nonlinear Analysis and Phenomena, I(1), 1 – 26. <br />[15] Escultura, E. E., The new real number system and discrete computation and calculus, 17 (2009), 59 – 84.<br />[16] Escultura, E. E., (2005) Dynamic Modeling of Chaos and Turbulence, Proc. 4th World Congress of Nonlinear Analysts, Orlando, June 30 – July 7, 2004; Nonlinear Analysis, Volume 63, Issue 5-7, 1 November 2005, e519-e532. <br />[17] Escultura, E. E., (2005). The theory of everything, Nonlinear Analysis and Phenomena, II(2), 1 – 45.<br />[18] Escultura, E. E., (2006) Foundations of Analysis and the New Arithmetic, Nonlinear Analysis and Phenomena, January 2006. <br />[19] Escultura, E. E., The Pillars of the new physics and some updates, Nonlinear Studies, 14(3), 2007, 241 – 260. <br />[20] Escultura, E. E., The physics of the mind, accepted, The Journal of the Science of Healing Outcome. <br />[21] Escultura, E. E., The cosmology of our universe, submitted, Problems of Nonlinear Analysis in Engineering Systems.<br />[22] Escultura, E. E., (2007) Dynamic Modeling and the new mathematics and physics, Neural, Parallel and Scientific Computations, 15(4), 2007, 527 – 538. <br />[23] Escultura, E. E., The grand unified theory, contribution to the Felicitation Volume on the occasion of the 85th birth anniversary of Prof. V. Lakshmikantham: Nonlinear Analysis: TMA, 69(3), 2008, 823 – 831.<br />[24] Escultura, E. E. The mathematics of the grand unified theory, Nonlinear Analysis, A-Series: Theory, Methods and Applications, 71 (2009) e420 – e431.<br />[25] Escultura, E. E. Dynamic and mathematical models in physic, Proc. 5th International Conference on Dynamic Systems and Applications, June 30 – July 5, 2007, Atlanta, 164 – 169. <br />[26] Escultura, E. E. (2004) Dynamic Modeling of Chaos and Turbulence, NA, TBA, 63(5-7), e519 – e532. <br />[27] Escultura, E. E. The basic concepts and dynamics of quantum gravity with applications, in press, Nonlinear Studies<br />[28] Escultura, E. E., Qualitative model of the atom, its components and origin in the early universe, Nonlinear Analysis: C-Series: Real World Applications, 11 (2010), 29 – 38.E E Esculturahttp://users.tpg.com.au/pidro/noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-70191848960613108602009-11-24T04:40:03.884-06:002009-11-24T04:40:03.884-06:00The remedy for this inadequacy of methodology is q...The remedy for this inadequacy of methodology is qualitative or non-quantitative modeling (formerly called dynamic modeling) that explains nature or natural phenomena in terms of the laws of nature. While quantitative modeling describes the appearances of nature mathematically, qualitative modeling explains its internal dynamics and interactions including its appearances in terms of its laws. The former is based on computation, measurement and intuition, the latter on qualitative mathematics, rational thought and analysis. Qualitative mathematics includes the following routine activity of the mathematician or scientist: <br /><br />Making conclusions, visualizing, abstracting, thought experimenting, engaging in creative activity, intuition, imagination and trial and error to sift out what is more appropriate, negating what is known to gain some insights into the unknown, altering premises to draw out new conclusions, thinking backwards and all other techniques that yield results. <br /><br />Qualitative modeling alters the task of the scientist from computation and measurement to the search for the laws of nature. It was used for the first time to solve the gravitational n-body problem in 1997. The solution required the discovery of the basic constituent of matter, the superstring. It required 11 laws of nature to accomplish both. They where the initial laws of nature of GUT known as the flux theory of gravitation then.<br /><br />At present particle physicists are still smashing the nucleus of the atom in search of the basic constituent of matter, the superstring, which has been going on for over half a century. Actually, the superstring has been staring at us since 1811 when Ernest Rutherford discovered the electron. The electron is an agitated superstring. A non-agitated superstring is dark, i.e., its size is less than 10^(-14) meters. It is the basic constituent of dark matter, one of the two fundamental states of matter, the other being visible or ordinary matter. Dark matter is not observable with present technology and is known only by its impact on visible matter. When suitably agitated by cosmic waves the superstring expands to a primum, unit of visible matter such as the electron or positive or negative quark. These three prima are called basic prima because they are constituents of every atom. They are converted from dark matter at staggering rate in the Cosmos and in the cells of living things – plants or animals. In the Cosmos alone the prima form cosmic dust that get entangled into cosmological vortices and collect at their cores at the rate of one star per minute.E E Esculturahttp://users.tpg.com.au/pidro/noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-20713861898857547082009-11-24T04:36:19.714-06:002009-11-24T04:36:19.714-06:00What has FLT to do with GUT? The first major theor...What has FLT to do with GUT? The first major theorem in its resolution was the characterization of undecidable (unprovable) propositions that says, essentially, that a proposition is unprovable if it is ambiguous, i.e., involves ambiguous or ill-defined concepts. Being “ill-defined” is the negation of “well-defined” and a concept in a mathematical system is well-defined if its existence, properties or behavior and relationship with other concepts are specified by its axioms. To avoid ambiguity and contradiction (the latter often hides in the former) every concept in a mathematical space must be well-defined and in its construction the choice of the axioms is not complete until this requirement is achieved. When we have two distinct mathematical spaces every concept in one is ill-defined in the other since each mathematical space is well defined only by its axioms. A physical theory is a mathematical space whose axioms are laws of nature. In a mathematical space the axioms are man-made and have nothing to do with the laws of nature. <br /><br />In the present methodology of physics called quantitative modeling (formerly called mathematical modeling) natural phenomena are described mathematically and a physical problem is modeled by a mathematical problem so that the solution of the latter is attributed to the solution of the physical problem. Reasoning is purely by analogy since there is no causal relation between the physical and mathematical spaces concerned. This is the reason for the existence of long-standing unsolved problems and unanswered fundamental questions of physics like what the basic constituent of matter and the structure of the electron are.E E Esculturahttp://users.tpg.com.au/pidro/noreply@blogger.com