Dr. E. E. Escultura is a world-class mathematician with over fifty technical publications in renowned refereed international journals and conference proceedings. He graduated Ph. D. in mathematics from the University of Wisconsin. His advisor is the famous British mathematician, L. C. Young whose parents, W. H. and G. C. Young, were themselves famous mathematicians. He was a former Mathematics Professor at the University of the Philippines. Now, he is a Research Professor at Lakshmikantham Institute for Advanced Studies and at Departments of Mathematics and Physics, GVP College of Engineering, Jawaharlal Nehru Technical University, Kakinada Campus Madurawada, Visakhapatnam, India.

"THE HYBRID GRAND UNIFIED THEORY by V Lakshmikantham (Florida Institute of Technology, USA), E Escultura (Lakshmikantham Institute for Advanced Studies, India), & S Leela (Florida Institute of Technology, USA). In this book, an attempt is made to provide a hybrid grand unified theory to understand the universe, both in its micro/quantum aspects as well as macro/galactic aspects. The book describes a truly hybrid theory as it encompasses both the modern and ancient theories of the universe, together with its functioning at all levels of human comprehension. One of its authors,

**Dr Escultura**, was nominated in 2005 for a Nobel Prize for his flux theory of gravitation. From then on this theory has been improved, clarified and is now known as the hybrid grand unified theory. This book deals with this new bold theory, unifying mathematics and physics, and answering some open fundamental questions and paradoxes in these disciplines. The book also describes what the ancient scientists knew about these matters."

https://www.worldscibooks.com/mathematics/l009.html

“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!”Here are the Abstracts and Summary of Publications on GUT, its Mathematics and Applications of Dr. Edgar E. Escultura

This series of publications are the basis of the Grand Unified Theory (GUT) and its much broader extension, Grand Unification of Natural Dynamics (GUND). GUND encompasses macro and quantum gravity and unites all physical systems from dark to visible and organic to inorganic.

(1) The Mathematics of Singularities. Trans. National Academy of Science and Technology (Philippines), Manila, 1992, pp. 141 - 153.

Abstract. This is the initial development of the generalized fractal that

provides the essential mathematics for the study of matter and its dark and

visible components. It shows how a curve of any length can be shrunk into

an infinitesimal neighborhood of a point with its length preserved, the

essence of black hole formation. The paper paves the way for the

development of the superstring as a physical concept and the basic

constituent of dark matter. Its axial projection is a rapid sinusoidal curve.

Shrinking it towards infinitesimal neighborhood enhances its frequency and

raises its latent energy indefinitely. A black hole is massive concentration of

non-agitated superstrings that accumulates in the eye of cosmological and

atomic vortices.

(2) Probabilistic Mathematics and Applications to Dynamic Systems Including Fermat's Last Theorem, Proc. 2nd International Conference on Dynamical Systems and Applications, Dynamic Publishers, Inc., Atlanta, 1996, pp. 147 - 152.

Abstract. The paper characterizes undecidability and establishes that

Fermat's last theorem is undecidable. It proposes probabilistic proof for

undecidable propositions. Moreover, the paper has an introduction to the

solution of the gravitational n-body problem presented at the World

Congress of Nonlinear Analysts, that same year and published in Nonlinear

Analysis, A-Series: Theory, Methods and Applications the following year.

(3).Exact Solutions of Fermat's Equation (Definitive Resolution of Fermat’s Last Theorem (FLT). Nonlinear Studies, 5(2), 1998, pp. 227 - 254.

Abstract. The inability to resolve this problem for 360 years is attributed to

the inadequacy of the underlying fields of FLT, namely, foundations, number

theory, the real number system and analysis. Their critique is undertaken

with special focus on Wiles' 127-page proof of this conjecture that bears all

the weakness of classical mathematics. The first major findings are: (1) FLT

is undecidable in arithmetic, the reals, and Rn, n > 1, (2) its underlying fields

are ill-defined and, therefore, FLT itself is ill-defined, and (3) the

characterization of undecidable propositions. It follows that FLT is not just

undecidable, it does not make sense in these spaces. Rectification includes

reconstruction of the real number system without the trichotomy and

completeness axioms. The new space, called the new real number system,

yields countable counterexamples to FLT proving that it is false. It resolves

all the problems, paradoxes, contradictions and unanswered questions of the

underlying fields except the Bieberbach conjecture and the Riemann

hypothesis.

(4) The Solution of the Gravitational n-Body Problem. Presented at the 2nd World Congress of Nonlinear Analysts, Athens, 1996 and published in the special issue of Nonlinear Analysis, A-Series: Theory, Methods and Applications, 30(8), Dec., 1997, pp. 5021 – 5032.

Abstract. The existence of long-standing unsolved problem reveals the

inadequacy of the underlying fields, in this case, mathematics and physics. A

thorough critique of both is undertaken. The main weakness of mathematics

lies in its foundations stemming from lack of insights coming from recent

discoveries such as the sources of ambiguity and lack of clarity regarding its

subject matter. Its critique led to the reconstruction of the contradiction-free

new real number system with new elements that models basic physical

concepts such as the superstring, the basic constituent of matter, the concepts

of time and distance and our universe as a super…super galaxy. The main

critique of physics is the inadequacy of quantitative or computational

modeling (previously called mathematical modeling) that simply describes

the appearances of nature. Consequently it has left long-standing problems

unsolved and fundamental questions unresolved such as what the basic

constituent of matter and the structure of the electron are. The remedy is the

introduction of qualitative modeling (formerly called dynamic modeling) that

explains nature in terms of its laws. This was the crucial factor in the solution

of the n-body and turbulence problems and resolution of fundamental

questions. Their solution and resolution required the discovery of the initial

11 laws of nature that anchored the early formulation of GUT called the flux

theory of gravitation.

(5) Superstring loop dynamics and applications to astronomy and biology. Nonlinear Analysis, Series A: Theory, Methods and Applications, 35(8), (1999); pp. 959 - 985.

Abstract. The paper refines the fundamental physical principles of (4),

includes four biological principles and introduces (a) dark number as the

qualitative model of the superstring, (b) the mathematics of its conversion to

visible matter, (c) matter-anti-matter dynamics, (d) applications to astronomy

and biology and (e) the new nonstandard analysis. It provides, for the first

time, explanation of two recent spectaculars from space made possible

nascent stars and galaxies and (ii) the "cannibalizing" activity of giant

galaxies, including our Milky Way, that prey on their smaller satellite

galaxies. Also, for the first time, the paper links brain waves to dark matter,

provides insights on the functions of the brain, including learning, memory

and intelligence, and proposes therapy for control of brain malfunctions like

autism.

(6) Set-valued differential equations and applications to quantum gravity, Proc. 1st International Conference on Tools for Mathematical Modeling; published in: Mathematical Research, Vol. 6, 2000, St.Petersburg, pp. 58 – 69.

Abstract. The paper starts with the practical problem of solving differential

equation of the form

dy/dx = f(x), where f(x) has the forms,

f(x) – sinn1/x, f(x) = cosn1/x, f(x) = (sinn1/x)cosm1/x,

and n and m are positive integers and the functions have set-valued limits at

the origin. The notions of probability distribution over the set-values and the

integral with respect to it are introduced to devise the generalized integral for

set-valued functions. Then the integral is applied to calculations on prima

and photons whose axial projections are set-valued.

(7) Recent verifications and applications, Proc. 1st International Conference on Tools for Mathematical Modeling, State Technical University of St. Petersburg, St. Petersburg, July 1999, pp. 74 – 89.

Abstract. The paper reviews present verification of the flux theory of

gravitation in quantum physics and astronomy and applies qualitative

modeling (formerly called dynamic modeling) to derive the structure of the

superstring and prima.

[8] Dynamic Modeling and Applications, Proc. 3rd International Conference on Tools for Mathematical Modeling, State Technical University of St. Petersburg, Russia.

Abstract. The paper summarizes recent verification and applications of the

then flux theory of gravitation to the study of the Cosmos, the solar system

and other applications but adds a new element to it: the role of the brain in

the control of cancer.

(9) Quantum Gravity. Proc. Third International Conference on Dynamic Systems and Applications, 26 ‒ 29 May 1999, released 2001, pp. 201 – 208.

Abstract. Quantum gravity is the dynamics of vortex flux of superstrings

induced by primal flux spin. It is distinguished from macro gravity as

dynamics of fluxes of superstrings. Quantum gravity encompasses quantum

physics and extends its domain to dark matter. It explains the genesis of the

atom where the toroidal fluxes of the protons in the nucleus induce coherent

flux around it; the latter draws electrons into orbit, by flux-pressure

complementarity. Quantum gravity explains all forces and interactions of

nature at the biological, molecular, atomic and primal levels including

electromagnetism, matter-anti-matter interaction, surface tension, osmosis

and capillary action in the cells of living organisms as well as primal

coupling and formation of the atom. The main laws of nature governing

quantum gravity are energy conservation, flux compatibility and flux-lowpressure

complementarity.

(10) Turbulence: Theory, Verification and Applications. Proc. 3rd World Congress of Nonlinear Analyst, Catania, 2000, published in the special issue of Nonlinear Analysis, Series A: Theory, Methods and Applications, 47(2001), pp. 5955 – 5966.

Abstract. The paper poses the turbulence problem: given the standard

dynamics find a model that has predictive capability with respect to its

internal and external dynamics and future state. The desired model is the

theory of turbulence, as subtheory of FTG, anchored on 12 of its

fundamental principles. The theory is applied to the study of earthquake,

volcanic activity, tornado, typhoon and lightning. The major results are as

follows:

(1) Solves the turbulence problem and explains the dynamics of earthly

turbulence.

(2) Establishes correlation between solar eclipse, earthquakes and volcanic

activity.

(3) Provides the basis for generating the technology to terminate tornado,

control typhoon partially and monitor seismic and volcanic activity that can

be the basis for prediction.

(4) Establishes the dynamic relationship between under-ocean volcanic

activity, El Niño, typhoon and drought.

(11) Chaos, Turbulence and Fractal. Indian J. Pure and Applied Mathematics, 32(10), pp. 1539 – 1551. (In the original paper this article is incorrectly titled, The flux theory of gravitation IV: The theory of intelligence and evolution).

Abstract. The turbulence problem in (9) is generalized to the modeling

problem: find a model for a physical system that has predictive capability on

its internal, external and future states. The paper starts with a criticism of

computational modeling namely:

(1) Computational model is static and unaffected by and not sensitive to

emerging boundary conditions including interaction with other dynamic

systems;

(2) It simply describes superficial dynamics but lacks predictive capability;

(3) Computation on the model simply reveals behavior of the mathematical

space the model belongs to and has nothing to do with the physical dynamic

system it models; in general computation, provides insights on differential

equations and the real numbers;

(4) Local behavior, especially, at micro scale has no causal relationship with

global behavior; for instance, the second law of thermodynamics that

predicts increasing entropy for closed physical system is valid only locally;

our universe has moved from the chaos of the Big Bang to the high level of

order we now enjoy including biological order; therefore, the first law of

thermodynamics is reversed globally.

(5) A differential equation which is indispensable in quantitative modeling

and its solution have only local validity, a basic principle in the theory of

differential equations. Conventional modeling is inadequate for dealing with

ambiguous sets including chaos, turbulence and fractal; it is shown also that

the real line is chaos. This paper identifies ambiguous sets and their common

thread of uncertainty and identifies appropriate approaches for dealing with

them. Among the ambiguous sets are large and infinite sets (being large and

small depending on context), small and large numbers, micro component of

turbulence, chaos and limit set of fractal. Deterministic mathematics does not

apply to ambiguous sets. This paper proves, for the first time, that the real

line is chaos. The alternative to computational modeling is qualitative

modeling, i.e., physical theory anchored on the laws of nature at both

fundamental states – dark and visible. Physical theory is not developed by

computation alone but is based on synthesis of the collective human

experience and accumulated scientific knowledge. The main tool for

qualitative modeling is qualitative or non-quantitative mathematics defined

broadly as the complement of computational mathematics. The paper also

summarizes the new mathematics required by FTG that, together with some

computational mathematics, e.g., Pontrjagin maximum principle, constitutes

its mathematical component.

(12) Theory of intelligence and evolution. Indian Journal of Pure and Applied Mathematics, 33(1), 2003, 111 – 129.

Abstract. Ten laws of thought are discovered to explain such capability of

the mind as learning and creativity. It explains how values are formed

including mathematical reasoning.

(13) The mathematics of the new physics. Applied Mathematics and Computation, 130(1), 145 – 169.

Abstract. With the terminating decimals as base space subject to the axioms

of the so-called complete ordered field, R*, +, ×, without the axiom of choice

or its variants, the standard topology is introduced. The space is extended

and completed to what is called the new real line with the standard topology.

The reconstructed new real line, R*, +, ×, has two new elements called dark

and unbounded numbers. The domain of the additive and multiplicative

operations is also extended to the new real line, R*, +, ×. The new real line is

further extended to the new nonstandard analysis. The paper refines and

extends the counterexamples to FLT to a combination of countable integers

and new integers (now called decimal integers). The new arithmetic is also

introduced as well as basic arithmetic of twin naturals, new integers and new

nonstandard analysis. The integers and new integers are shown to be

isomorphic; in this isomorphism 0 corresponds to the equivalence class of

dark numbers represented by d*. This isomorphism establishes that both the

integers and the new integers are Peano naturals. It is from this class of

numbers that the counterexamples to FLT are constructed.

(14) From macro to quantum gravity. Problems of Nonlinear Analysis in Engineering Systems, 7(1) 2002; pp. 56 – 78.

Abstract. The paper summarizes the work that starts with the solution of the

gravitational n-body problem and proceeds to develop gravitation in the

large, that is, gravitation at the astronomical scale. It is extended to gravity at

the atomic and biological scales called quantum gravity to form the flux

theory of gravitation (now GUT); it explains surface tension in liquids as

gravity at the molecular scale. The laws of nature are refined and some of the

mathematics of the superstring and black hole excerpted from [14,15} are as

follows:

Theorem 1. A curve of any length can be deformed continuously into an

oscillation in an infinitesimal neighborhood of a point with length preserved

or even enhanced.

Theorem 2. Given oscillatory curve K of any length, real number e > 0 and

line segment AB, there exists continuous deformation of K into a fine

oscillatory curve inside some neighborhood of a line segment which

preserves its length k.

Theorem 2 generalizes Theorem 1 since the segment AB can be confined to

an arbitrary neighborhood.

Theorem 3. Given any oscillatory curve K, there exists continuous

deformation of K, with length preserved, into an arbitrarily small

neighborhood.

Theorem 4. Let K be oscillatory curve of any length k and let b > 0, e = b/2

< K/2. One can shrink oscillatory curve K into arbitrarily small

neighborhood its length and amplitude satisfying │K│/2n+2 < │K│/2n+1 ≤

│K│/2n.

This theorem captures the behavior of superstrings and is the mathematical

basis of black hole formation. Since the energy of an oscillatory motion (e.g.,

superstring flux) is proportional to frequency and infinitesimal oscillation has

great frequency this deformation is energy enhancing and there is no upper

bound for the amount of latent energy in a superstring.

Finally, the paper has graphics of the well known prima, simple and

composite, including the quark, proton, and neutron, nucleus, basic cosmic or

electromagnetic waves and cosmic waves of Types I, II and III. It has also

graphics of generalized fractal.

The paper summarizes all previous papers by the author on gravitation. It

notes, for the first time, that the theory unites the three principal dynamics of

our universe, namely, macro and quantum gravity and cosmic waves where

the last dynamics spans the first two, and thermodynamics. It explains all

interactions of matter at the primal, atomic and biological scales including

electromagnetism, matter-anti-matter interaction, surface tension, osmosis

and capillarity action in the cells of living organisms. The paper also explains

all forms of clustering including the genesis of the atom and molecules and

stellar and galactic formation. It introduces three kinds of cosmic shock

waves: (1) Type I that includes brain waves, i.e., basic cosmic waves

encoded with information from neural cluster, (2) Type II cosmic waves,

e.g., shock waves from grinding of tectonic plates, stellar storms, stellar and

galactic core turbulence and hot volcanic lava flow (used in predicting

eruption) and (3) Type III cosmic waves, e.g., shock waves from nuclear and

thermonuclear explosions and cosmic explosions such as collisions of stars

called supernova and the Big Bang. Types II and III cosmic waves have the

same internal fractal structure but differ in orientation with respect to their

respective radius of propagation. The latter’s axis is normal to the radius of

propagation. The paper also formulates the nested fractal model of our

universe from the super…super galaxy through the superstring.

(15) Vortex interaction. Problems of Nonlinear Analysis in Engineering Systems, 7(2) 2002; pp. 30 –44.

Abstract. The paper develops the fractal-reverse-fractal algorithm that

allows one to locate, from any cosmological body, any other cosmological

body belonging to any cosmological vortex of our universe and, conversely,

from a vortex at any scale to the super…super galaxy, our universe.

(16) The new mathematics and physics. Applied Mathematics and Computation, 138(1), 2002, 127 – 149.

Abstract. The paper summarizes the new mathematics and FTG and some

astonishing results of mathematics. It has detailed critique of J. M. Henle’s

non-nonstandard analysis (Mathematics Intelligencer, 1999) and includes the

resolution of the unsolved problems, paradoxes, contradictions, puzzles,

contradictions and unanswered questions of mathematics, physics, astronomy

and cosmology except the Bieberbach conjecture and Riemann hypothesis.

Among the more notable problems, paradoxes and counterexamples resolved

and summarized here are: FLT, Goldbach’s conjecture, Brouwer’s

counterexample to the trichotomy axiom, Banach-Tarski paradox and the

natural or linear ordering of the new real line.

(17) Macro and quantum gravity, cosmic waves and applications. Applied Mathematics and Computation, 139(1), 2003, 23 – 36.

Abstract. The paper summarizes all previous results on the subject in the

Series on the subject and extends them as follows:

(a) Explanation of the accelerated rapid radial expansion of our universe

from FTG’s viewpoint.

(b) Verification of Hubble’s law in terms of the accelerated radial expansion

of our universe including an explanation of this phenomenon.

(c) Counterexamples to Einstein’s and Newton’s law of gravitation, namely,

cosmic debris such as asteroids and the thin rings of the larger planets of the

solar system.

(d) Lays down the cosmological history and destiny of our universe.

(e) Explains the primordial black hole that exploded as Big Bang as the

destiny of the core of previous universe and points to evidences of the

existence of universes other than ours.

(18) Dynamic (now qualitative) Modeling and Applications. Proceedings, 4th International Conference on Tools for Mathematical Modeling, St. Petersburg, 2003, 167 – 182.

Abstract. Axiomatizes turbulence using dynamic modeling (now qualitative

modeling) that explains gravity as part of its dynamics. It includes a

comprehensive explanation of why the Columbia Space Shuttle crashed on

February 1, 2003.

(19) Foundations of Analysis and the New Arithmetic. Nonlinear Analysis and Phenomena, 3(2), 2003, 13 pages.

Abstract. The paper reconstructs the real number system as decimals into the

new real number system without the trichotomy and completeness axioms

using the basic integers as building blocks (taking this as one of the axioms)

and well-defined by two more axioms – the addition and multiplication

tables of basic arithmetic. Taking the constructivist requirement that a real

number is well-defined only by its digits, that is, when they are known or

computable, we are able to build the new real number system without

contradictions and paradoxes. Among the findings are: the standard real

numbers (the decimals) are finite but unbounded (precise definition of

countably infinite), therefore, discrete, free from contradictions, have natural

ordering and enriched by the unique dark and unbounded numbers d* and u*,

respectively. This new construction suits the needs of computing, especially,

computer simulation, and physics since nature is discrete in view of the

recent discovery of the basic constituent of matter, the superstring.

(20) Dynamic Modeling (now qualitative) of Chaos and Turbulence. Plenary lecture at the 4th World Congress of Nonlinear Analysts, Orlando, 2004, Nonlinear Analysis, 63(5-7), 2005, e519-e532.

Abstract. Applies dynamic modeling to chaos and turbulence as part of the

standard dynamics and builds up the flux theory of gravitation as a general

theory of turbulence. It uses Hubble’s law to compute the present rate of

radial expansion of our universe which is 840 km/sec and its acceleration of

10−10.km/secsec. This is the rate at which matter in our universe, including

the galaxies is radially dispersing outward. The paper also explains the black

hole as massive cluster of non-agitated infinitesimal superstrings collected by

the eye of a macro vortex such as star or galaxy. Left alone, a superstring,

which is nested fractal fluxes of superstings, shrinks towards infinitesimal

superstring. This dynamics occurs in the calm, low-pressure region of the eye

of a macro vortex. It explains that a black hole does not suck matter; it is the

eye that nurtures and builds it up that does. Gravitational attraction itself is

due to the suction by vortex eye. The opposite dynamics is: when a semiagitated

superstring is hit by cosmic shock wave of suitable energy, it

converts to visible matter called primum, e.g., quark, electron and positron.

Furthermore, the paper reveals prototypes of technology that converts dark

matter to useful kinetic energy, electricity and magnetic repulsion presently

used to power magnetic train. (The values obtained here are based on the

corrected age of our universe – the original estimate of 8 billion years instead

of the current estimate of the age of our universe of 14.7 billion years.

(21) The New Frontiers of Mathematics and Science, Part I. Theoretical Construction and Resolution of Issues, Problems and Unanswered Questions, Nonlinear Analysis and Phenomena, Vol I, January 2004,1 – 26.

Abstract. The paper has the most detailed elaboration to-date of dynamic

modeling that led to the development of quantum and macro gravity. It welldefines

and explains ill-defined physical concepts and phenomena such as

quark, atom, black hole, dark matter and supernova.

(22) The pillars of the new physics and some updates. Nonlinear Studies, 14(3), 2007, pp 241 – 260.

Abstract. This paper summarizes the pillars of FTG, updates and uses FTG

to identify and rectify the errors of physics and highlights new applications

and explains the disastrous finite flight of the Columbia Space Shuttle. It

explains many puzzles of physics such as metal fatigue and corrects present

misinterpretation of certain phenomena such as thermonuclear explosion.

(23) The physics of the mind, accepted, The Science of Healing Outcomes.

Abstract. This paper explores the physics behind thought and sensation and

its implications for mathematics and physics and science education. It

explains telekinesis and other amazing capability of the mind such as that

displayed by what psychologists call moronic genius who computes huge

numbers without knowing how that happens. Most of all, it describes how

information is encoded, how they are recalled to the creative-integrative

region for thought and creativity.

its implications for mathematics and physics and science education. It

explains telekinesis and other amazing capability of the mind such as that

displayed by what psychologists call moronic genius who computes huge

numbers without knowing how that happens. Most of all, it describes how

information is encoded, how they are recalled to the creative-integrative

region for thought and creativity.

(24) The New Frontiers of Mathematics and Science, Part II. The new real number system: Introduction to the New Nonstandard Analysis. Nonlinear Analysis and Phenomena, Vol. II, January, 2005, pp. 15 – 30.

Abstract. This is the first formal construction of the new real number system

R*, +, ´, using only three simple axioms: (1) R* contains the additive and

multiplicative identities, 0, 1; and (2) the addition and (3) multiplication

tables of basic arithmetic, and its extension to the new nonstandard analysis.

Limit in Bolzano-Weierstras sense (which is ill-defined) is replaced by

intuitive limit, that is, representation of a decimal by its standard Cauchy

sequence and approximating any decimal to any level of accuracy by the kth

term of its Cauchy sequence. The new real number system is finite but

unbounded (countably infinite) and, therefore, discrete, has no contradiction,

has natural ordering and is enriched by the unique dark number d* and

unbounded number u* and the new integers (now called the decimal

integers). The integers are embedded in R* which rectifies the fundamental

flaw of number theory, that of having no valid axiomatization of the integers.

In the new nonstandard analysis, every function is discrete. This suits the

needs of computing, especially, computer simulation.

(25) Dynamic Modeling (now qualitative) and the new mathematics and physics. Neural, Parallel and Scientific Computations, 15(4), 527 – 538.

Abstract. Surveys the classical and new mathematics involved in the new

physics, i.e., GUT, and highlights the role of the new mathematics.

(26) The origin and evolution of biological species. accepted, The Science of Healing Outcomes (a medical journal).

Abstract. The paper identifies brain waves as the medium for the replication

of the genetic content of biological species. It illustrates intelligence and

organization and division of labor in lower species and their further

advancement and defense against predators and ruminants that pasture on

them in the case of plant species, e.g., plant species that produce toxins. It

points to sensation as the basis of intelligence that allows a biological species

to respond to the environment, survive and advance itself. It illustrates, with

many examples, how species protect itself from other species that feed on it.

It also points out that instinct is genetically determined and explains how it is

actualized in plants and animals.

(27) Extending the reach of computation. Applied Mathematics Letters, 21(10), 2008, 1074 - 1081.

Abstract. The paper applies the new real number system to discrete

computation and quantum algebra.

(28) The theory of everything. Journal of Nonlinear Analysis and Phenomena, Volume II, No. 2, July, 2005, 44 pages (the author’s submission for his nomination for the Nobel Prize for Physics, 2005).

Abstract. This is an expository paper that summarizes and consolidates the

new physics developed in the flux theory of gravitation. The theory unifies

all the forces and interactions of nature from dark matter through quantum

and macro gravity and cosmology. (This was this host’s submission for his

nomination for the Nobel Prize for Physics, 2005)

(29) Dynamic (now qualitative) and mathematical models of physics. Proceedings of the 6th International Conference of Dynamics Systems, 2008; pp. 164 – 169.

Abstract. It provides dynamic and mathematical models of basic physical

concepts, particularly, the photon, quark, neutrino, electron, proton, neutron

and the nucleus.

(30) Basic physical concepts of the Hybrid Grand Unified Theory. Proc. International Conference on Recent Developments in the Mathematical Sciences and Applications, Dec. 25 – 28, 2009, GVP College of Engineering, JNT University, Vishakhapatnam, AP, India, 8 pages.

Abstract. Introduces the other inhabitants of our universe starting with the

superstrings and moving on to the prima, atoms, cosmological vortices and

black holes.

(31) By-passing Chaos With a Theory of Turbulence and Development. An article in the book, Finance Stochastics, World Scientific, London, 2001, edited by E. Perez, D. Bonzo (Eds.).

Abstract. This is the first axiomatic treatment of a new area of social

science, namely, development science. It uses the same technique in the

axiomatization of physics undertaken in the Series. Fundamental social

principles are identified to anchor development science. Based on this theory,

strategic positioning employed for the purpose of establishing scientific,

trade, economic and technological equity between the Third World and the

developed world, particularly, the developed countries. This is the strategy

for generating and accumulating tremendous accumulation of value to reach

the threshold for industrial development.

(32) Probability Distribution In Mathematics, The Philippine Statistician. 40. 1-2 & 3-4. 1991, pp. 47 – 56.

Abstract. Introduces probability distribution as a tool for integrating setvalued

functions.

(33) Qualitative model of the atom, its components and origin in the early universe, Nonlinear Analysis, C-Series: Real World Problems. 11(2009), pp. 29 – 38.

Abstract. This paper is the first qualitative model of the atom and its

components as well as its origin in our early universe. The atom’s

components – proton, neutron (with its neutrino) and electron – are built on

the prima, units of visible matter. Their qualitative models are obtained using

some laws of nature. They yield new information such as the mass of the

neutrino and how heavy isotopes of an atom form as well as the arrangement

of the nucleons. It clarifies some presently unresolved issues such as what

happens in thermonuclear explosion and whether it can be controlled to

generate energy. It also explains the wave-particle duality of the primum and

photon, metal fatigue, matter-anti-matter interaction and brittle and malleable

materials and reviews the early phase of the development of our universe up

to the formation of the first atom.

(34) Qualitative modeling for complex systems, Proc. 23rd International Conference on Operations Research, September 2009, Bonn, Germany, 10 pages (appears also in Problems of Nonlinear Analysis in Engineering Systems, in press).

Abstract. The paper introduces qualitative modeling for analyzing complex

systems and solving complex problems and explaining natural phenomena in

terms of natural laws. Its power is demonstrated by its role in the discovery

of the basic constituent of matter, the superstring, the key to the solution of

the gravitational n-body and turbulence problems. Qualitative modeling is

applied to the equally difficult problem of development using a similar

approach: discovering the relevant laws of society and production. The latter

includes laws governing creation, accumulation and distribution of value and

accumulation and utilization of surplus value. Then a theory of development

is devised for formulating a strategy for development of underdeveloped

countries. It notes that while the problem of underdeveloped countries is

underproduction, i.e., scarcity of social surplus, the problem of developed

countries is just the opposite: overproduction of commodities that cannot be

marketed leading to periodic disruption in the global economy called

recession or depression in its worst form. These opposites provide basis for

symbiotic relationship between the underdeveloped and developed countries

and devising a strategy beneficial to both based on advanced scientific

knowledge provided by the Grand Unified Theory to generate appropriate

technology as the principal component of development.

(35) The mathematics of the grand unified theory. Keynote address at the 5th World Congress of Nonlinear Analysis, July 2 – 9, Orlando, Florida, Nonlinear Analysis, A-Series: Theory, Methods and Applications, 71 (2009) e420 – e431.

Abstract. This paper surveys the mathematics of the Grand Unified Theory,

classical and new, and focuses on the construction of the new real number

system R*.

(36) The new real number system and discrete computation and calculus. Neural, Parallel and Scientific Computation, 17 (2009), 59 – 84.

Abstract: The paper points out the inconsistency and ambiguity of the field

axioms of the real number system and notes that the only clearly defined and

consistent mathematical model of the real numbers is the set of terminating

decimals. Inconsistency collapses a mathematical system since every

statement in it is contradicted by another. The inconsistence in the real

number system comes from the trichotomy and competeness axioms to

which counterexamples have been found To remove the inconsistency and

ambiguity the real numbers are built on the additive and multiplicative

identities 0, 1 and addition and multiplication tables of elementary arithmetic

as its axioms that define the operations addition and multiplication,

respectively. Then using 0 and 1 the terminating decimals are defined on

which the nonterminating decimals are defined for the first time (prior to this

the nonterminating decimals were simply arrays of digits most of which

unknown). The g-norm is introduced where the g-norm of a decimal is itself.

Then the g-closure of the terminating is the new real number system R* that

includes the nonterminating decimal and the set-valued nonstandard number

d* called dark number which is a continuum. Then the decimals are joined

together by the continuum d* so that R* is a continuum It is non-

Archimedean and non-Hausdorf but its subset of decimals countably infinite,

hence, discrete, Archimedean and Hausdorff. Highlighted in this paper are

the counterexamples to FLT that prove it false and the proof of Goldbach’s

conjecture.

(37) The grand unified theory. Nonlinear Analysis, Series A: Theory, Methods and Applications 69(3), 2008, 823 – 831. The paper is a contribution to the felicitation volume, special issue of Nonlinear Analysis on the occasion of 85th birth anniversary of Professor V. Lakshmikantham, founder of the broad and rapidlyexpanding field of nonlinear analysis and Editor-in-Chief of many renowned scientific journals.

Abstract. The paper is the first formal formulation and presents an overview

of the Grand Unified Theory, introduces the ten most important natural laws

and surveys the mathematics related to GUT’s development and applications

with more detail on the author’s recent contribution, the new real number

system.

of the Grand Unified Theory, introduces the ten most important natural laws

and surveys the mathematics related to GUT’s development and applications

with more detail on the author’s recent contribution, the new real number

system.

(38) The generalized integral as dual of Schwarz distribution, in press, Nonlinear Studies.

Abstract. The paper develops the generalized integral and derivative of setvalued

function called wild oscillation using rapid oscillation for

approximation and deriving the probability distribution of wild oscillation as

set-valued function for purposes of generalized integration. It applies the

generalized integral to calculation on the photon

.

(39) Global geology and oceanography. Invited paper, International Journal of Earth Sciences and Engineering, in press

Abstract. The paper develops the theory based on GUT and applies it to lay

down the cosmological history of Earth. It explains the reversal of the

Earth’s magnetic flux during its 25,000-year cycle and the regular reversal of

Indian Ocean current with the summer and Winter Solstices.

(40) Revisiting the hybrid real number system, Nonlinear Analysis: Hybrid Systems, 3(2) May 2009, 101-107 (co-authored with Bhaskar, T. G., Kovak, D., Lakshmikantham V.).

Abstract. The new real number system is combined with Ancient Indian

thought to develop the hybrid real numbers.

(41) The unified theory of evolution, invited paper, International Journal of Biological Sciences and Engineering, in press

Abstract. Eleven laws of nature are discovered to update the theory of

evolution. Among the latest findings are:

evolution. Among the latest findings are:

[42] Genetic alteration, modification and sterilization and applications to the treatment of genetic diseases, accepted, The Journal of the Science of Heaibg Outcomes; 11 paages.

Abstract. The paper formulates the theory behind genetic alteration, modification

and sterilization based on the theory of evolution updated by the grand unified theory

(GUT). The key element in the updated theory is the discovery that the medium for

both the brain and the gene for doing their functions are brain waves, i.e., basic

cosmic waves encoded with the vibration characteristics of a living cell such as the

neuron or the cell of any tissue of living organism. The principal component of brain

wave is the vibration characteristic of the gene. It is established that the gene projects

brain waves that agitate and convert the superstrings in the cellular membrane to

molecules that form the tissues of living things. The gene is turned on to do this task

at the right place on cue from the environment there in accordance with the

biological law, genetic activation.

Then appropriate technology is proposed for treatment of genetic diseases such

as cancer, systemic lupos erythematosus, diabetes, muscular dystrophy and mental

disorder, e.g., depression, without injury to normal cells. The methodology is called

genetic modification; it uses a neutralizer gene to form a composite with the

defective gene that removes its symptoms. The neutralizer gene resonates with the

defective gene so that the brain waves it projects superperpose on the brain waves

projected by the defective gene to produce composite brain waves that do not show

the symptoms of the defective gene. In effect, a composite gene is produced without

the harmful symptoms. For cancer, however, a more appropriate and effective

treatment is genetic sterilization to prevent it from spreading to normal cells. Then

the sterilized cancer cells become harmless; they die in the normal turnover of cells.

Genetic alteration involves introduction of a gene that produces desirable

physical qualities such as the developed muscle of the weight lifter through the

beneficial application of the induced alteration law that says: the possible sources of

genetic alteration are: radiation (including the so called background radiation which

are cosmic waves), direct exposure to foreign gene, frequent, consistent and

sustained use of body part, chemical irritation and concentrated thought about and

pre-occupation with or craving for an object, living or not, during pregnancy.

Again, as in the previous papers, the methodology employed is qualitative

modeling.

(43) Extended Geometrical and Generalized Fractals, Chaos and Applications, a chapter in the ebook, Fractal Classification and Applications, in press, Nova Science Publishers.

Abstract. Starting with classical geometrical fractal in the plane we extend

present classical technique of affine transformation for generating fractal by

admitting other self-similar transformations, e.g., taking mirror image of

generator, sliding over a curve and rotation, where finite generators are

allowed. Such fractal is called extended geometrical. Geometrical fractal is a

sequence of composite affine transformations of a geometrical figure. Affine

transformation is a composite of contraction and translation. We further

extend geometrical fractal by broadening self-similarity to apply to general

properties beyond geometrical such as branching property and circular,

sinusoidal and vortical motion with applications to quantum and macro

gravity and thermodynamics of the grand unified theory (GUT). We focus on

generalized fractal and its applications to quantum and macro gravity and

thermodynamics of GUT.

Since general properties are not always amendable to computation, the

main tool of the present methodology of natural science – quantitative

modeling that relies solely on computation and measurement – the

appropriate methodology for GUT is qualitative modelling that relies on

qualitative mathematics. Our universe is a nested generalized physical fractal

with itself as the first term down through its fractal sequences that end up as

tail sequences of superstrings in dark matter.

In view of the updated scientific knowledge provided by GUT, we

reorient the priority in verifying validity of physical theory. We take as

primary criterion for validity its ability to explain natural phenomena and,

secondarily, invention of technology that works which requires prediction.

Moreover, we clarify some natural phenomena and make some predictions.

(44) Mathematical Models on the way from Superstring to Photon (Coauthored with V. V. Gudkov, Professor of Mathematics, Department of Computer Science and Mathematics, University of Latvia). Nonlinear Analysis, 3(2002), pp. 375 - 382.

Abstract. The paper applies FTG to the physical dynamics of prima

(elementary particles of quantum mechanics) and their clusters and

interactions. The prima considered are the electron, up and down quarks (the

second author uses right and left quarks, respectively, to stress the invariance

of toroidal flux spin and induced flux under radial deformation, translation

and rotation) and coupled prima like the neutrino, proton, neutron and the

nucleus of an atom. The basic mathematical model of a segment of

superstring is the helix as solution of the harmonic wave equation. Any

primal cluster and interaction can be modeled by suitable combination of

deformation, translation, rotation, reflection and attachment. The paper has

data on the tremendous latent energy of dark matter. For example, a cubic

meter of dark matter (vacuum of quantum mechanics) has latent energy

content of 1018 kilograms that is convertible to kinetic energy using

Einstein’s mass-energy equivalence equation. A fundamental physical

principle FTG is utilized here to suite the requirement of quantum gravity,

namely, the flux compatibility principle that governs primal clustering and

interaction.

(45) The Helix and Other Optimal Configurations of Matter and Applications (Co-authored with V. V. Gudkov). Nonlinear Analysis and Phenomena Vol. III, No. 2, 2006.

Abstract. The paper provides both qualitative and computational models of

the common prima like the proton and neutron.

(46) Sustainable Economic-Industrial Development for Underdeveloped Countries (co-authored with Chandra Prakash Kamana, first author, and V.S.R.S. Sarma Salagrama), Proceedings, International Conference on “Accelerating Economic Revival Through Innovation and Reform” Feb. 5, 6, 2010, organized by the Department of Commerce and Industry, Corporate Economics and Management Studies and Women’s Christian College, Chennai, India.

Abstract. Proposes Strategic Positioning as the only strategy for sustainable

development of the Third World in the present situation (see the article,

Primer on Strategic Positioning on this website)

(47) Building Green to Attain Sustainability (co-authored with Chandra Prakash Kamana, first author, andV.S.R.S. Sarma Salagrama), Proceedings, International conference on "Emerging Trends in Engineering (ICETE-2010)”, 20 – 21 February 2010, organized by Dr.J. J. Magdum College of Engineering (JJMCOE) in technical collaboration with Cafet-Innova Technical Society, in Dr. J. J. Magdum College of Engineering, Jaysingpur, Kolhapur District, Maharashtra, India.

Abstract. Points the way to find the lynchpin technologies for Strategic

Positioning that can partake of the enormous global resources into a Third

World Country for its sustainable development.

(48) Building Green – Practices and Challenges (co-authored with Chandra Prakash Kamana, first author and V.S.R.S. Sarma Salagrama). Proceedings of the International Conference on Environmental Sustainability with Green Building Technology (ICESGBT-10), 15 – 17 March 2010, organized by the Department of Civil Engineering, Meenakshi Sundararajan Engineering college, Chennai, India.

Abstract. Identifies the advantages of green building technology with

respect to energy consumption, and comfort and convenience.

(49) Geometrical and Generalized Fractals, Chaos and Turbulence and Applications, chapter contribution to the book, Fractal Classification and Applications, in press, Nova Science Publishers, 53 pages.

Abstract. Starting with classical geometrical fractal in the plane we extend

present classical technique of affine transformation for generating fractal by

admitting other self-similar transformations, e.g., taking mirror image of

generator, sliding over a curve and rotation, where finite generators are

allowed. Such fractal is called extended geometrical. Geometrical fractal is a

sequence of composite affine transformations of a geometrical figure. Affine

transformation is a composite of contraction and translation. We further

extend geometrical fractal by broadening self-similarity to apply to general

properties beyond geometrical such as branching property and circular,

sinusoidal and vortical motion with applications to quantum and macro

gravity and thermodynamics of the grand unified theory (GUT). We focus on

generalized fractal and its applications to quantum and macro gravity and

thermodynamics of GUT.

Since general properties are not always amendable to computation, the main

tool of the present methodology of natural science – quantitative modeling

that relies solely on computation and measurement – the appropriate

methodology for GUT is qualitative modeling that relies on qualitative

mathematics. Our universe is a nested generalized physical fractal with itself

as the first term down through its fractal sequences that end up as tail

sequences of superstrings in dark matter.

In view of the updated scientific knowledge provided by GUT, we reorient

the priority in verifying validity of physical theory. We take as primary

criterion for validity its ability to explain natural phenomena and,

secondarily, invention of technology that works which requires prediction.

Moreover, we clarify some natural phenomena and make some predictions.

(50) The Big Bang and What it Was, Chapter Contribution to the ebook, The Big Bang: Theory, Assumptions and Problems, in press, Nova Science Publishers. 56 pages

Abstract. The paper takes as its premise the occurrence of the Big Bang, a

colossal explosion that gave rise to the birth of our universe. Then through

sequences of mathematical and scientific reasoning called rational thought

using the methodology of qualitative modeling the grand unified theory

(GUT) is developed on laws of nature which establishes what it was that

exploded. This is a new approach. In earlier development both the

occurrence of the Big Bang and what caused it were taken as premises.

In its present development GUT builds its pillars – quantum and macro

gravity and thermodynamics. Through the discovery of appropriate laws of

nature, GUT well defines its fundamental physical concepts such as the

superstring, basic constituent of matter; matter and energy; dark matter; and

charge and gravity. It also well-defines and explains other physical concepts:

primum, photon, matter-anti-matter interaction, atom, cosmic waves, brittle

and malleable materials, metal fatigue, turbulence, galaxy, black hole and

supernova along with the conversion of dark to visible matter.

The cosmology of our universe is traced from its birth at Cosmic Burst 1.5

billion years from the start of the Big Bang through its evolution to the

present as a super…super galaxy 1010 billion light years across and a local

bubble in the timeless boundless Universe and predicts its destiny as black

holes back in dark matter. The existence of universes other than ours is

established from available evidences. Then it is deduced from this

cosmology what the Big Bang was and what caused it.

(51) Our Fractal Universe and Applications. Invited keynote address at the 6th International Conference on Dynamic Systems and Applications, May 25 – 28, Atlanta, USA, to appear in the proceedings. 8 pages.

Abstract. The generalized nested fractal structure of our universe is

described with itself as the common first term. A common feature of every

cosmological vortex is the family of spiral trajectories that simply covers it

along which visible matter falls through and spins around its eye. The

Integrated Pontrjagin Maximum Principle is applied to find the equation of

such a trajectory and solve practical problems.

II. Books and Monographs

(52) Introduction to Qualitative Control Theory. Kalikasan Press, Manila, 1991, 151 pages.

Abstract. This is the first development of qualitative or noncomputational

mathematics applied to control theory. It focuses on the properties of relaxed

trajectories and makes slight improvement of L. C. Young’s integrated

Pontrjagin maximum principle.

(53) On the undecidability of Fermat’s last theorem, monograph published by the Press Center, University of the Philippines Los Baños, 1993. 40 pages

Abstract. The first broad sweep of the partial resolution of this problem

which establishes its undecidability, reformulates it as a problem in R3

and

provides the probabilistic solution to the reformulated problem. The question

of truth of FLT is not considered here.

(54) Introduction to Qualitative Control Theory, Kalikasan Press, Manila, 1991.

Abstract. Adapts qualitative mathematics and modeling (introduced and the

main contribution of this author’s Ph.D. thesis, The Trajectories, Reachable

Set, Minimal Level and Chain of Trajectories in a Control Systme, at the

University of Wisconsin) to control theory. It has also a slight improvement

of L. C. Young’s Integrated Pontrjagin Maximum Principle.

(55) Diophantus: Introduction to Mathematical Philosophy (With Resolution of Fermat and Other Applications). Kalikasan Press, Manila, 1993, 156 pages.

Abstract. The resolution referred to here is probabilistic solution that says:

with probability 1, FLT is true when n > 2. The book makes a thorough

critique-rectification of mathematics including lack of awareness of the loss

of certainty in infinite and very large spaces in mathematical and scientific

pursuit. It introduces a totally new mathematical perspective. Several

counterexamples to the axiom of choice are given. The calculus of set-valued

functions is more fully developed and applied to oscillatory differential

equations. A general theory of fractal provides some of the basic

requirements towards the solution of the gravitational n-body problem. The

book has the first partial resolution of Fermat's last theorem as undecidable

in arithmetic, the reals and the Euclidean plane and the probabilistic solution

of the reformulated problem in R3. It points the way for dealing with

undecidable proposition (proposition having no deterministic proof): the use

of probabilistic mathematics. A critique of Wiles' initial offering of 1993

made it to the appendix while the book was in press. It is the first to point out

that Wiles' main error is lack of insights from recent discoveries in

mathematics such as characaterization of undecidable propositions and the

loss of certainty in infinite or very large spaces.

(56) The Hybrid Grand Unified Theory, co-authored with V. Lakshmikantham and S. Leela and published by Atlantis (a division of Elsevier Science, Ltd.), 2009; 185 pages. (Currently on the World Scientific

best sellers list since May 2009; got on the #2 spot on the list in July in all categories; #1 on the best sellers list in mathematics as of October 3, 2009)

Abstract. The book updates the foundations of mathematics and applies the

new real number system to develop the hybrid real number system. The main

chapter, The Grand Unified Theory, formulates builds GUT on macro and

quantum gravity using the new methodology of qualitative modeling. Then

both qualitative mathematics and GUT are applied to develop the theory of

turbulence and physics of the mind. The book concludes with an overview of

the grand unified hybrid system that combines modern and ancient scientific

thought.

(57) Scientific Natural Philosophy, an ebook in press, Bentham Science Publishers, 2010, 305 pages.

Abstract. The aim of philosophy is to provide a total view of an aspect of

reality, for our present pursuit, nature, the domain of natural science.

Naturally, that view is relative to the level of advancement of the field of

science concerned. The most important component of philosophy is

methodology for it determines the nature of knowledge that can be achieved.

For example, the current methodology of physics – quantitative modeling –

describes the appearances of nature mathematically in terms of numbers,

equations, functions or statistical trends. Thus, the knowledge it provides is

only descriptive. In biology species are classified on the basis of their

appearances, e.g., anatomical structure. However, this methodology has

limitations and left long standing problems of physics unsolved and

fundamental questions unanswered such as the gravitational n-body problem

and what the basic constituent of matter and the structure of the electron are.

The introduction of qualitative or non-quantitative modeling that explains

nature in terms of its laws not only solves and answers the long standing

problems and fundamental questions but also deepens our knowledge beyond

the appearances. It tells us how nature works and allows us to explain the

internal dynamics and interactions of physical systems. It also allows us to

devise technology guided by theory instead of appearances and properties of

materials. At the core of both methodologies are mathematics, qualitative

mathematics for qualitative modeling and computation and measurement for

quantitative modeling. Therefore, mathematics is not only a language of

sciences but also its indispensable tool for analysis. Consequently,

mathematics plays a major role in philosophy as part of methodology and we

shall devote a major part of this book to it.

Scientific natural philosophy is an updated philosophy of natural science

different from and an improvement of all previous ones because it is based

on major scientific development, innovations and discoveries during the last

12 years among which are the following:

(1) First and foremost was the introduction of qualitative modeling (formerly

called dynamic modeling) in 1997 to solve the 200-year old gravitational nbody

problem posed by Simon Marquiz de Laplace at the turn of the 18th

Century. It explains nature and its dynamics, appearances, properties and

motion in terms of its laws (natural laws). It is the complement of

quantitative modeling (formerly called mathematical modeling). The main

tool of qualitative modeling is qualitative mathematics and that of

quantitative modeling its complement, the combination of computation and

measurement. Qualitative mathematics includes this daily activity of the

mathematician or scientist: making conclusions, visualizing, trial and error,

thinking backwards, thought experimenting, engaging in creative activity,

intuition and imagination, negating what is known to find an opening into the

unknown, altering premises to draw out new conclusions and any technique

that yields results. It liberates the mind from unnecessary constraints and is

the key to productive research. Abstract mathematical systems such as

foundations, topology and the search for the laws of nature are qualitative

mathematics. It is based on rational thought and analysis, quantitative

mathematics on intuition. Consequently, qualitative modeling is also based

on rational thought and analysis, quantitative modeling on intuitions.

(2) Since qualitative mathematics has liberalized the search for information

for purposes of knowing nature and explaining its behavior and appearances

it also increases the chance of error creeping into physical theory. Error

includes contradiction, ambiguity, inadequacy and self reference. Therefore,

to avoid error we tighten the filter of admissibility in the choice of concepts

and axioms in the development of physical theory. In particular, we identify

the sources of error to avoid them.

(3) To solve a long-standing problem or resolve unanswered question we

find out why it defies solution or resolution and the first to check are its

underlying fields. Therefore, we go through their critique-rectification to

clear them of errors. This was the crucial first step in both the resolution of

Fermat’s last theorem [and the solution of the gravitational n-body problem.

(4) Qualitative modeling led to two important developments: (a) the

discovery of the existence of two fundamental states of matter, dark and

visible or ordinary matter, where the latter is directly observable and the

former is not and known only by its effect on visible matter and (b) the

discovery of the basic constituent of matter, the superstring.

(5) Qualitative modeling has also led to important discoveries in biology

aside from the biological laws. One is the discovery that the brain and the

gene have the same medium for doing their functions, namely, brain waves,

i.e., basic cosmic waves encoded with the vibration characteristics of living

cells. The main function of the brain is to control all body processes and its

secondary function is providing the venue for thought processes. The gene’s

main function is to produce the tissues of plants and animals in the cellular

membranes through the agitation of dark matter by the brain waves it

projects and their conversion, first to prima, then to atoms and molecules and

finally to the atoms and molecules of the tissues.

(6) Physical theory is a qualitative model of reality, in particular, nature. It is

a mathematical system whose basic premises or axioms are laws of nature.

Being so, any theoretical error is ultimately mathematical. While

mathematics, erroneous or not, is totally harmless and essentially useless in

the mind or its representation, mathematical error may have catastrophic

impact in the real world through the application of erroneous or absence of

theory. Therefore, we have given considerable effort to avoid mathematical

error by identifying its sources and avoiding them or providing remedy. We

cite disastrous failures in applications due to theoretical error.

(a) The disastrous final flight of the Columbia Space Shuttle, February 1,

2003 as being due to inadequate theory. In fact, in trying to explain why the

disaster occurred three new laws of nature were discovered. In particular, the

recurrent peeling of the insulation panels from the Shuttle when the

Columbia Space Shuttle Program was resumed after two and a half years of

suspension was never explained because there was no theory to do so. The

program was scrapped for this reason [34].

(b) The failure to make a breakthrough in plasma research towards

controlling thermonuclear reaction. After over half a century of this research

no significant breakthrough has been made.

(c) Research in particle physics in search of the basic constituent of matter.

Physicists have steadily raised the energy of the collider but they have not

found even a candidate for basic constituent of matter since all they found

are unstable elementary particles with half-life of split second. The basic

constituent of matter must be indestructible otherwise our universe would

have collapsed a long time ago. The large hadron collider in Cerne,

Switzerland was supposed to have been turned on last summer but there has

been no report on it so far. Like thermonuclear research this has been going

on for over half a century. Actually, the superstring has been staring at the

physicists since 1811 when Ernest Rutherford discovered the electron, an

agitated superstring.

(d) Cancer research. Geneticists and oncologists have been trying to

understand this genetic disease for the purpose of developing the most

effective treatment with the least side effect; this has been going on for a

long time but no significant breakthrough has been registered so far, a case of

lack of appropriate theory.

In each of these cases the culprit is theoretical error that includes erroneous,

inadequate and absence of theory to guide the research.

Although 6(b), 6(c) and 6(d) are not as catastrophic as 6(a), the enormous

amount resources, human and material, allotted to such failed research could

have alleviated the desperate conditions in much of the Third World.

(7) The 11 laws of nature discovered in 1997 required to solve the

gravitational n-body problem served as the initial axioms of the flux theory

of gravitation which was later corrected and named the grand unified theory

(GUT).

These are innovations, discoveries and advancement that distinguish the

grand unified theory, which we now summarize and call the new physics,

from all previous physical theories. It is much broader and more general than

what Albert Einstein envisioned which was to describe gravity and

electromagnetism by equations of the same form although this was modified

by quantum physicists who joined in to include the strong and weak forces of

physics in the unification. The grand unified theory that we now have is

stronger and much broader for it explains the forces and interactions of

nature and its appearances and, therefore, unifies as well the entire fields of

natural science. It raises the quality of scientific knowledge from description

of appearances of nature to knowledge of how nature works that includes

explanation of its appearances. Research is in progress to broaden GUT

beyond its pillars – macro and quantum gravity and thermodynamics – and

into the grand unification of natural dynamics where natural dynamics

includes interactions between physical systems and the latter broadened to

include all motions of matter such as cosmic waves, the synchronized

vibration of dark matter. This will not qualitatively alter scientific natural

philosophy based on GUT for there is no change in perspective and

methodology, only extension of domain.

All these developments are synthesized and integrated into scientific natural

philosophy. It is distinguished from all previous philosophies of science

because it is scientific in contrast to being speculative where the former rests

on scientific knowledge. In particular cosmology is no longer speculative but

knowledge provided mainly by macro gravity. Moreover, it is complete as it

provides a full account of the evolution of our universe from its birth at

Cosmic Burst to its destiny as cluster of black holes back in dark matter.

Every application of GUT to solve a scientific problem requires the

discovery of appropriate laws of nature to provide the solution. Thus, the

application of GUT to explain the disastrous final flight of the Columbia

Space Shuttle added three more natural laws to the theory of turbulence [23]

to advance it to the enriched theory of turbulence. In trying to understand the

role of the gene in the evolution of biological species and how it produces

the tissues of a living thing 11 biological laws were discovered to develop

the theory of evolution based on GUT. Five learning principles were also

discovered in the applications of GUT to investigate the brain’s functions.

This is an aspect of innovation in scientific methodology. In traditional

methodology existing knowledge is applied to solve some problems. Here,

given a scientific problem a theory is devised to provide the solution.

Therefore, in this new methodology a scientific problem serves as catalyst

for the advancement of science. It is clear that physical theory is the

embodiment of our knowledge of the domain of a field of natural science and

that without a theory we have, at best, a collection of information about it.

We have some new knowledge that enriches scientific natural philosophy:

(1) The laws of nature are transitory and their manifestation is simultaneous

with the respective emergence of physical systems or natural phenomena that

reveal them. For example, the biological laws that we now enjoy were nonexistent

immediately after the cosmic burst when only simple prima (a

primum is unit of visible matter) existed. They will all vanish as our universe

reaches its destiny as cluster of black holes.

(2) Our universe is a local bubble in the boundless and timeless Universe of

dark matter and there is ample evidence of the existence of other local

universes like ours. There are two kinds of local universes: ordinary resulting

from the steady shrinking of the superstrings that gives rise to nested fractal

sequences of regions of depression that, in turn, evolve into nested fractal

sequences of cosmological vortices of superstrings like the galaxies and

stars, and special universes like ours whose birth was triggered by a big

bang. A big bang is explosion of a black hole, the destiny of a previous

universe. Our universe was due to the explosion of a black hole, the destiny

of the core of a previous universe that created a super…super depression in

dark matter that evolved into a super…super galaxy 1010 light years across.

(3) GUT has brought us to the threshold of a new technological Epoch, the

epoch of GUT technology that runs on dark matter directly or indirectly.

Examples of the former are the magnetic train and the electric power plant

both of which run on fluxes of superstrings. Like the steam engine which

was invented before the development of the science of thermodynamics they

were invented before the development of GUT based on knowledge of the

property of the material used, mainly magnet. Therefore, they are considered

conventional. An example of GUT technology is the electromagnetic engine

for mass transit system. Its invention which is still at the research and

development phase is directly guided by GUT (the invention can only be

announced; details cannot be discussed at this time). Another example which

is still at the research stage (not even at research and development) is the

appropriate technology for genetic alteration, modification and sterilization

for the treatment of genetic diseases.

We provide selective theoretical applications of GUT and its methodology of

qualitative modeling that spill over into several fields of natural science and

its boundary with psychology – physical psychology.

Finally, scientific natural philosophy is materialist and focuses on

explainable physical reality.

In the Pipelines: An ebook, Symposium on the Grand Unified Theory, for

Nova Science Publishers; probable completion: 2012.

******* ******* *******

The following is an article made by Dr. Escultura which you can download in pdf format at http://users.tpg.com.au/pidro/Putting%20The%20Institute%20Of%20Mathematics%20In%20Its%20Place.pdf

**PUTTING THE INSTITUTE OF MATHEMATICS IN ITS PLACE**

In 2005 the Philippine Collegian published the article, STATEMENT FROM THE UP

MATHEMATICS DEPARTMMENT, attacking me personally for my work in mathematics and

physics the argument based on wrong information and ignorance of mathematics and physics.

Fortunately, the Philippine Collegian which adheres to journalistic ethics published my reply, TOTAL

IGNORANCE OF FUNDAMENTALS. This cannot be said of the UP Newsletter which published

the same statement but did not publish my reply revealing itself as a gossip sheet after all. My mole at

the Department told me that the Chairman tried to solicit signatures for the statement from its over

100 faculty members but got only 7 the reason it was published anonymously.

Then in March 2008 another online article, Personal Statement from UPD, was addressed to me,

again, attacking my work by repeating the same old futile arguments but this time focusing on my

resolution of Fermat’s last theorem.

Now, there is a post on a page in the WikiPilipinas website, again, addressed to me and my work that

repeats the same old arguments which I have already resoundingly demolished on many websites.

WikiPilipinas, by the way, has published online on the same webpage outright lies about Filipino

inventors and scientists who are long gone and cannot defend themselves. It labelled as hoax the

inventions of Agapito Flores, Eduardo San Juan and Fe de Mundo without any documentation

whatsoever. It made a blunder, however, by also publishing on the same webpage lies about me, the

Manny Pacquiao of Science and Mathematics with Teflon world academic stature. When I posted this

message in reply the administrator, J. Maguddayao, deleted the entire entries and blocked my

username.

These online articles by the Institute of Mathematics amount to a tiny squeak behind the thousands of

articles, posts and commentaries on my work on several dozen websites not to mention my over 50

scientific papers in many world renown peer reviewed international scientific journals, keynote

addresses at world congresses and international conferences, books and chapters of some books. My

work has been extensively debated across cyberspace since 1997 and not a single hole has been

punched on it. All arguments against my work have been thoroughly demolished including these

feeble attempts by the Institute. Samples of my latest punches can be viewed at these sites:

(1) False Proofs, http://falseproofs.blogspot.com/2006/06/e-e-escultura.html

(2) Free Library, http://www.thefreelibrary.com/E.+E.+Escultura/Contributed-a274787

(3) http://scientopia.org/blogs/goodmath/2011/02/10/e-e-escultura-and-the-field-axioms/#comment-

27520

(4) New Approach to Physics, under ISCID topic Brainstorms (5 pages):

(a http://www.iscid.org/boards/ubb-get_topic-f-6-t-000607.html

(b) http://www.iscid.org/boards/ubb-get_topic-f-6-t-000607-p-2.html

(c) http://www.iscid.org/boards/ubb-get_topic-f-6-t-000607-p-3.html

(d) http://www.iscid.org/boards/ubb-get_topic-f-6-t-000607-p-4.html

(e) http://www.iscid.org/boards/ubb-get_topic-f-6-t-000607-p-5.html

If these feeble attempts by the Institute are a tiny squeak, why take notice? One reason is to take note

of a new trick proudly discovered by the Institute: creating the link,

http://en.wikipilipinas.org/index.php?title=User:Eescultura, to my article in WikiPilipinas with this

message (quoted verbatim including grammatical errors):

To whom it may concern;

I Edgar Escultura formally renounce my claims to have disproven Fermat’s Last Theorem (FLT), my

claims that the real number system is flawed, and my claim that the complex number i is not well

defined. I also retract my claim that Dr. Wiles acknowledged my work was correct and my claim to

have been nominated for the Nobel Prize in physics, I have discovered that these were both cruel

tricks being played on me by people signing a guestbook on my website.

I would like to acknowledge the efforts of various bloggers and their readers for taking the time to

demonstrate the flaws in my arguments. Were it not for their genuine care and patience I would still

be defending indefensible claims. I also apologize to any people who spent considerable time trying to

understand my writing, I was wrong and am man enough to admit it.

I would also like to inform the mathematics community that the journal that published my work,

Nonlinear Studies, did a grave disservice to you all in allowing work so peppered with errors to ever

be printed. I apologize for myself and the irresponsible behaviour of Nonlinear Studies.

Finally to Dr. Wiles, I offer you my sincerest apologies. Your proof is and always was correct, there

were no “fatal flaws” in it as I so often asserted. I also apologize to you for trying to pass off obvious

forgeries as your writings. Most importantly I would like to apologize to you for ever attacking your

stature as a mathematician, my claims were not only false but also inconsiderate, I acted foolishly and

can only hope you can forgive me.

E. E Escultura Research Professor V. Lakshmikantham Institute for Advanced Studies and

Departments of Mathematics and Physics GVP College of Engineering, JNT University

=================

This “apology” is, of course, FAKE. I NEVER POSTED IT and I DID SOMETHING MUCH

GREATER THAN SIMPLY MAKE A CLAIM: I ACTUALLY DISPROVED FLT by

counterexamples published in my papers in several renowned peer reviewed scientific journals. It is

also discussed in my recent books, Scientific Natural Philosophy (Bentham Science Publishers) and

Hybrid Grand Unified Theory (Atlantis, a division of Elsevier Science, Ltd) .When I posted this reply

on WikiPilipnas website it was deleted but the fake apology was retained although edited and toned

down a bit. Still, it is even worse than libel. Moreover, my username has been blocked from that link

and I cannot post my replies. Only the administrator, J. Maguddayao, could have done these changes

in connivance, of course, with the Institute.

The abstracts and summary of my publications are posted on one of my websites, Grand Unified

Natural Dynamics, http://users.tpg.com.au/pidro/ (see also my other website, Grand Unified Theory,

http://edgareescultura.wordpress.com/) Most of my papers are being sold online (for instance, search:

escultura science direct elsevier) and several of my papers have made it to the top 25 most

downloaded papers published by Elsevier Science Ltd in its several scientific journals. The latest

confirmation of my nomination for the Nobel Prize for Physics in 2005, which was dismissed by the

message from the Institute in WikiPilipinas, is the announcement online of my new book, Hybrid

Grand Unified Theory, co-authored with V. Lakshmikantham and S. Leela, published by Atlantis in

March 2009 and distributed by World Scientific which specifically mentions the nomination. This

book was a best seller in 2009 among books of all categories in natural and social sciences distributed

by World Scientific. It made it to the #2 spot on the best sellers list in July, 2009. For the information

of the Institute some of my major achievements recorded and etched in internet archives are as

follows:

1. Disproved Fermat’s last theorem by countably infinite counterexamples, Nonlinear Studies, 5(2),

1998, pp. 227 – 254 (published by the International Federation of Nonlinear Analysts).

2. Solved the gravitational n-body problem, Nonlinear Analysis, A-Series: Theory, Methods and

Applications, 30(8), 1997, pp. 5021 – 5032 (published by Elsevier Science, Ltd).

3. Solved the turbulence problem in, Turbulence: Theory, Verification andAapplications, Nonlinear

Analysis, A-Series: Theory, Methods and Applications 47(2001), pp. 1539 – 1551.

4. Discovered the superstring, basic constituent of matter, Nonlinear Analysis, A-Series: Theory,

Methods and Applications, 30(8), 1997 (this discovery is the foundation of the solution of the

gravitational n-body problem and the grand unified theory).

5. Developed the grand unified theory in a series of papers since 1997 and consolidated in the paper,

The Grand Unified Theory, Nonlinear Analysis, A-Series: Theory, Methods and Applications,:69(3),

2008, pp. 823 – 831 5032.

6. Developed the new real number system in a series of papers and consolidated in the paper, The new

real number system and discrete computation and calculus, Neural, Parallel and Scientific

Computations, 17(2009), 59 – 84 (Published by Dynamic Publishers).

7. Proved Goldbach’s conjecture, Applied Mathematics and Computation, 138(2003), pp. 145 - 169

(published by Elsevier Science, Ltd).

8. Developed the generalized integral for set-valued functions, Proceedings of the International

Conference on Tools for Mathematical Modelling, June 2000, St. Petersburg, Russia, pp. 221 - 224.

9. Developed the generalized integral as dual of Schwarz distribution, in press, Nonlinear Studies,

invited paper.

10. Developed the Complex Vector Plane which rectifies the present defects of the complex number

system in the appendix to: The generalized integral as dual of Schwarz distribution, in press,

Nonlinear Studies, invited paper; it is also summarized in the ebook, Scientific Natural Philosophy.

11. Gave a keynote address at the 5th World Congress of Nonlinear Analysts, Orlando, Florida, July 2

– 9, 2008 (Sponsored by the International Federation of Nonlinear Analysts); on the topic, The

mathematics of the grand unified theory, published in Nonlinear Analysis, A-Series: Theory: Method

and Applications, 2009, 71, pp. e420 – e431.

12. Gave another keynote address at the 7th International Conference on Dynamic Systems and

Applications, on the subject: Our Fractal Universe and Applications, May 25 – 28, 2011, Atlanta (the

abstract is published online).

13. Addressed a plenary session of the 5th World Congress of Nonlinear Analysts on the topic, The

new real number system as the g-closure of the terminating decimals, Orlando, Florida, July 2 – 9;

this paper was integrated in the original paper, The new real number system and discrete computation

and calculus (see item 6 above).

14. Gave a keynote address at the 4th International Conference on Dynamic Systems and Applications,

on the topic, Dynamic and mathematical models in physics, Atlanta, USA, April 30 – May 2, 2007

(the abstract is online).

15. Gave a keynote address at the 5,th International Conference on Neural, Parallel and Scientific

15. Introduced the new scientific methodology of qualitative modelling as the main contribution of

my Ph.D. Thesis, The trajectories, reachable set, minimal levels and chains of trajectories of a control

system, at the University of Wisconsin, 1970; it was applied to physics for the first time to solve the

gravitational n-body problem, 1997.

16. Made the first qualitative model of the atom in the paper, Qualitative model of the atom, its

components and origin in the early universe, Proc. 5th World Congress of Nonlinear Analysts, and

published by, Nonlinear Analysis, B-Series: Real World Applications, 2009, 11, pp. 29 – 38

(published by Elsevier Science, Ltd).

17. Developed the generalized fractal in the paper, Extended geometrical and generalized fractal,

chaos and turbulence, a chapter to an ebook, Fractal Classification and Applications, in press, Nova

Science Publishers.

18. Provided the first full explanation of the Big Bang in the paper, The Big Bang and What It Was, a

chapter in the ebook, The Big Bang: Theory, Assumptions and Problems, in press, Nova Science

Publishers.

The other reason for this article is to identify the sources of frustration that led to this futile and

desperate action by the Institute and provide insights on why the Institute stooped to ground level by

posting the fake apology quoted above. The brief history of the Institute below and its present status

sheds light on this strange behaviour.

(1) In 1986 I returned from the US after an absence of 15 years due to the political turmoil in the

Philippines during that period and re-joined the Department of Mathematics as Associate Professor.

(2) Eager to advance mathematics in the country I proposed in 1988 the conversion of the Department

from a purely teaching department to an Institute with stress on research.

(3) This proposal did not sit well with the leadership for obvious reason: no one else was doing

research at that time and the cloud of insecurity loomed large over it. The fall out: my dismissal from

the Department by denying tenure followed by sustained campaign of vilification that continues to

this day.

(4) What is the score? The Institute’s website reveals the following information:

(a) The Institute has 10 full professors, 7 associate professors, 9 assistant professors, one adjunct

professor, 56 instructors and many lecturers.

(b) NONE OF THE FULL, ASSOCIATE AND ASSISTANT PROFESSORS HAS ANY

PUBLICATION IN MATHEMATICS. The adjunct professor has publications in applied mathematics

which is commendable but not in mathematics.

(c) There are 20 papers by the adjunct professor and graduate students (with co-authors abroad) on the

applications of mathematics to other fields such as biology and computer science. They are also

commendable contributions to the fields of application of mathematics but not to mathematics. In

other words, after having enjoyed generous research grants as an institute, the Institute of

Mathematics has not produced even a single paper in mathematics during all those years. (It would be

more appropriate for this unit of the University to call itself a Department of Applied Mathematics;

ironically, it tries to train mathematicians and claims to be the leader in mathematical research)

In contrast, both the Marine Science Institute and the National Institute of Physics have hundreds of

publications each in per reviewed scientific international journals followed by the Institute of Biology

that has also substantial publications. The other institutes do not have publications pages on their

websites but I know some well published colleagues there except the Institute of Mathematics.

Item (4) above explains why the Institute has all the time to carry on this vilification campaign during

the last 23 years.

This candid look at the Institute is not washing dirty linen in public since the Institute’s website is

viewed worldwide. Rather, it poses a challenge for the College: What can be done to lift the only

Institute that rides on its prestige but failed to deliver?

If I had a glass roof over my head I would not push my luck but keep away from trouble.

(When this article was first published online the Institute website’s publications page closed down

with the sign, “Under Construction”.

ЖЖЖЖЖЖЖ

The Institute of Mathematics is at it Again

The Institute of Mathematics has posted its 4rth anonymous statement since 2005 (URL:

http://en.wikipilipinas.org/index.php?title=Edgar_Escultura) attacking me personally and my work based

on misinformation and ignorance of mathematics, physics and mathematical issues. The statement

must have been authorized by its Director, Dr. Jose Balmaceda, if he himself is not its author. At any

rate, he takes full responsibility for it as IM director. The message replaces an earlier one in this

website of WikiPilipinas that labelled as hoaxes the inventions and scientific discoveries of Agapito

Flores, Eduardo San Juan, Fe de Mundo and my scientific discoveries without any documentation

whatsoever. It was deleted and replaced by this 4rth IM statement only after I pointed out its libellous

nature. The 3rd anonymous IM statement has likewise been deleted as well as a fake apology linked

to this website.

The reason for the anonymity is quite obvious: Dr. Balmaceda is not a mathematician (i.e., he has no

publication in any of the peer reviewed international scientific or mathematical journals whatsoever)

but pretends to know mathematics by commenting on mathematical issues he does not understand

(e.g. he thinks peer review is done by bloggers, view URL:

http://en.wikipilipinas.org/index.php?title=Edgar_Escultura). Thus, he is, objectively, an impostor

and a discredit to the University of the Philippines where he occupies such a high position.

I could have ignored this message since it does not make a dent on my stature as a mathematician and

physicist of world renown based on my over fifty peer-reviewed scientific articles, books and keynote

addresses at international scientific conferences many of which monumental such as (1) the solution

of the 200-year-old gravitational n-body problem, (2) The development of the grand unified theory (a

project that Albert Einstein proposed over 70 years ago but failed to carry out), (3) disproof of the

360-year-old Fermat’s conjecture known as Fermat’s last theorem, (4) my proof of the 250-year-old

Goldbach’s conjecture (the proof is in my article, The new real number system and discrete

computation and calculus, Neural, Parallel and Scientific Computations, 2009, 17, pp. 59 – 84) and

my ebook, Scientific Natural Philosophy (my publications are listed on my website,

http://users.tpg.com.au/pidro/, under the article Abstracts and Summary of Publications) but I

responded to all challenges across cyberspace including those raised by the IM statements to share the

discussion with amateurs and mathematics and physics teachers. (This opens up a new era in

mathematics where mathematical and scientific results are discussed openly so that hoaxes can no

longer stand or errors hide for a long time). Not a single mathematician or physicist has ever refuted

my work.

The Nonsense of Dr. Jose Balmaceda

An excerpt from a webpage of WiikiPilipinas,

http://en.wikipilipinas.org/index.php?title=Edgar_Escultura,

says:

A Proof that d* = 0

Dr. Escultura defines his 'dark number' d* as d* = 1 - .9999999... (where .999999.... is a never ending

string of 9's after the decimal place). He also claims that d* > 0, so this 'dark number' is NOT zero

accordind to Escultura. So we will begin with two simple legal equations, then subtract the second

equation from the first and examine the result. So as not to confuse the * in (d*) with the

multiplication sign (*), in the following equations we will write D in place of d*, that is D = d* = (1 -

.999999...)

(1) 10*(D) = 10*(1 - .999999..) = 10 - 9.999999...

(2) 1*(D) = 1*(1 - .999999...) = 1 - .999999...

Now we subtract equation (2) from equation (1):

10*(D) - 1*(D) = (10 - 9.999999...) - (1 - .999999...)

= 10 - 9.999999... - 1 + .999999...

= (10 - 1) - (9.999999... - .999999...) = 9 - 9.000000... = 0

Also we have

10*(D) - 1*(D) = (10 - 1) * D = 9*D.

So now we have,

9*D = 0 (by equating the results of the above two equations)

D = 0/9 = D = 0

Thus we have proven that in fact if we accept this 'dark number' d*, then it must be the case that d* =

0. However, Escultura explicitly claims that d* > 0.

A Proof that .999999... = 1

It is possible that some people may not be comfortable with the fact that .999999.... = 1. It may seem

at first that .999999... is strictly less than 1, however this is a peculiarity of how we write out numbers,

and I assure you it is true. As above we will start with two perfectly legal equations and again subtract

one from the other to see where it leads.

(1) 10*(.999999...) = 9.999999...

(2) 1*(.999999...) = .999999...

Now we subtract equation (2) from equation (1)

10*(.999999...) - 1*(.999999...) = 9.999999... - .999999... = 9.000000...

Also we have,

10*(.999999...) - 1*(.999999...) = (10 - 1)*(.999999...) = 9*(.999999...).

So now we have,

9*(.999999...) = 9.000000... (by equating the results above two),

(.999999...) = (9.000000...)/9

.999999... = 9/9 (clearly 9.000000... = 9)

.999999... = 1

Thus .999999... may appear at first to be a number smaller that 1, it is in fact equal to 1. There is

nothing 'wrong' with this, it is just a quirk of the decimal system we use to write our numbers. This

allows us to quickly show that d* = 0, as in the following proof:

d* = (1 - .999999...) = (1 - 1) (since we now know that .999... = 1) = 0.

=======

Let me just comment on two of the many nonsense of these "proofs".

1) Proof of d* = 0.

The equation D = d* = (1 - .999999...) is ill -defined, nonsense, IN THE REAL NUMBER SYSTEM

because all nonterminating decimals including .99... is ill-defined there and do not belong to it (they

are well defined in the new real number system). Therefore, the equations,

(1) 10*(D) = 10*(1 - .999999..) = 10 - 9.999999...

(2) 1*(D) = 1*(1 - .999999...) = 1 - .999999...

are nonsense because they apply multiplication and subtraction, the inverse of the addition, which are

binary operations of the real number system, to numbers that do not belong to it. Consequently, the

whole "proof" is total nonsense.

In particular, one cannot apply addition and multiplication (as binary operations IN THE REAL

NUMBER SYSTEM) precisely because they are ill-defined in the real number system. Try, for

instance, adding sqrt2 and sqrt3 and I’ll bet my life that no one can do it. It can be approximated by

some real number but that is not the sum. However, it can be done in the new real number system

because nonterminating decimals are well defined.

2) A Proof that .999999... = 1

The comment in 1) applies as well to the equations,

(1) 10*(D) = 10*(1 - .999999..) = 10 - 9.999999...

(2) 1*(D) = 1*(1 - .999999...) = 1 - .999999...,

which combine a mix of elements NOT BELONGING TO THE REAL NUMBER SYSTEM in a set

of binary operations IN THE REAL NUMBER SYSTEM. Thus, the proof is also nonsense.

Such sloppy mathematics could not have come from a true mathematician. Both errors are quite basic

and reveal utter ignorance of the fundamentals of mathematics. This is a problem peculiar to amateurs

who know only mechanical manipulation of symbols but are ignorant of precise mathematical

reasoning and deep analysis. Moreover, it appears that Dr. Balmaceda is a new comer to internet

mathematics forums where I have posted many, many responses to hundreds of bloggers including my

responses to ALL the points being raised here..

I could have referred Dr. Balmaceda to my original work but, not being a mathematician, i.e., having

no publication in any peer reviewed international journal, he would neither understand my work nor

know such journals. He does not even know which journals are peer reviewed and who the

mathematicians are and that is understandable.

This tit-for-tat with me is an exercise in futility for Dr. Balmaceda, although it wastes my time, and

works to his disadvantage. For, it only reveals more and more (1) my achievements as a

mathematician and physicist of world renown and (2) his true status as an impostor parading as a

mathematician. Remember that there is a light year of difference between a mathematician and a

mathematics teacher.

ЖЖЖЖЖЖЖ

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