If I'm not mistaken, Dr. Escultura is from UP Los Banos. Nung nag-aaral pa ko dun, maraming mga estudyante (both Math and non-Math majors) ang pinapangarap na maging teacher sya sa Math. Magaling daw talaga kasi sya according to those who undergo Math subjects with him.

Thanks, radicalrey. Lahat na yata ng scientists nasa Los Banos eh. Ang sikat sa Diliman yung mga Eng'g courses, Mass Com and Law.

if you read the article, Wiles (if it really was him) was being SARCASTIC. He did not concede and was even ridiculing Escultura.

Hi pancho! Yup, the news about Escultura seemed too good to be true, and Wiles' letter as published in the Manila Times sounded sarcastic indeed. So there is a good reason to be skeptical.

However, according to another article in the Manila Times, Prof. Escultura himself was the source of information including the letters, and that he published his refutations in many scientific journals. Manila Times did not have any reason to doubt him.

But of course, I still welcome comments, corrections, and crticisms about this news.

Yun lang po.

P.S.: Hindi ako taga-Manila Times ha?

perry, try looking at math.sci group at google and mathforge.net. it seems that dr. escultura is a frequent poster and some mathematicians are actually laughing at his ideas, and at Manila Times mismo! i wish he's correct but from what i've read in his posts (he also claims that the relativity theory of Einstein is not correct!), medyo nagdududa ako. i tried emailing manila times about it but they did not reply.

the reason i'm a little concerned, is i am also from UP taking up my phd here in the us (in a different field) and some1 pointed me to a website na parang mga funny stories on the net which pointed to the manila times article, medyo pinagdududahan tuloy ang UP. i wish some1 looks it up, i mean the manila times is a broadsheet, hindi naman sya tabloid right? it's just right that the reporter who wrote the article look up kung credible talaga yung pinagsasabi ni dr. escultura.

Hi again, pancho! Thanks for the reply.

Mukha ngang alarming yan ah. Hmmm, let me research further. I'll search for Escultura's posts at math.sci and mathforge.net. Baka pumangit pa ang impression ng mga tao sa Manila Times.

Yes, I think Escultura is bound to be ridiculed by his colleagues, because he challenged the very foundations of mathematics. Axioms like the trichotomy axiom are already taught in high school and even in Grade 6 level; they are already time-tested and they have been proven to be useful in everyday life. So it's hard to accept that these axioms are actually false. But then, it's also possible that these axioms will turn out to be like Newtonian physics; Newtonian physics are also time-tested and very useful in everyday life, and scientists of the past even accepted it as fact, only to be supplanted later on by Albert Einstein's theory of relativity, because Newtonian physics do not apply anymore to subatomic and cosmic phenomena and any other phenomena which involve near-light speeds. Let's see how the mathematicians will resolve this issue in the long run.

As for the theory of relativity, well, it would also be alarming if Escultura said that the theory is incorrect. But what I've heard about relativity is that it's still an incomplete theory. Some laws in quantum physics violate the theory of relativity, for instance.

Di bale, I'll research further.

Do check out my post on Inside PCIJ (http://pcij.org/blog/ ) about this. As a journalist, I was compelled to do my own investigation, talked to both Dr. Escultura and Prof. Wiles (via email) even and by all indications, the report isn't true.

do any one have a url for the music video of kiss - because im a girl

please send me the sory line of ONLY YOU or FORBIDDEN LOVE

For more on FLT and physics, surf the internet using the key words: escultura mathematics or escultura physics or escultura paired with any of the following: turbulence, gravitation, superstrings, black hole, nonstandard analysis, nonlinear analysis, quantum gravity, cosmic waves, macro gravity.

Post for Perry

1) I think most bloggers here have reading and comprehension problem. The Manila Times’ subhead of the article on FLT is quite clear: “UP prof proves Princeton man wrong.” The proof consists of counterexamples to FLT that I constructed and PUBLISHED in several renowned refereed international scientific journals since 1998 that prove FLT false and Andrew Wiles “proof” wrong. Three of the papers were listed by the Manila Times. Unless these papers are refuted and the refutation is PUBLISHED in similarly renowned journals my counterexamples and my work on FLT stand.

2) The construction of these counterexamples required an overhaul of mathematics, particularly, the real number system and, together with their applications, they are PUBLISHED in three-dozen scientific papers in such renowned journals.

3) One outcome of the overhaul of mathematics was the discovery of the flaw of the current methodology of physics called mathematical modeling. The remedy is dynamic modeling that explains nature in terms of its laws. This new methodology led to the discovery of 45 laws of nature that that anchor the Grand Unified Theory or the flux theory of gravitation, my submission for my 2005 nomination for the Nobel Prize for physics. For verification of my nomination see these links:

http://www.deccanherald.com/deccanherald/Dec132005/snt1734020051212.asp
http://www.hindu.com/edu/2006/09/18/stories/2006091800760200.htm

A partial listing of my three-dozen scientific publications is found in this link:

http://dg.up.edu.ph/viewtopic.php?p=28252#28252

Nothing at all is embarrasing about my work and achievements. Filipinos should be proud of them. What is quite embarrasing is Alecks Pabico’s promotion of himself across the Internet and disccussing an issue he is totally ignorant of. Even more embarrassing and quite pathetic is the fact that he does not know his article, Anatomy of a Hoax, that still hangs in on his pcij blog, has long been discredited, so discredited that he got only one post for the entire year 2006 from someone similarly in the dark out there in the woods. The smart guys here hide behind their aliases.

The counterexamples to FLT are:

x = (0.99…)10^T,

y = d* = 1 - 0.99…

z = 10^T, where T = 1, 2, … .

They satisfy Fermat’s equation, x^n + y^n = z^n, n> 2.

Moreover, the triple (kx,ky,zk), k = 1, 2, …., also satisfy Fermat’s equation.

They are the countable counterexamples to FLT. They are posted, with explanation, on hundreds of blogs, websites, forums, chatrooms and threads across the internet.

Those who were laughing at my work, especially, on the subjects of FLT and the grand unified theory, must have collapsed from exhaustion. I have the last words on these subjects in the hundreds of blogs, chatrooms, forums, websites and threads across the Internet.

Finally, I appreciate and commend the bloggers who still have confidence in the ability of the Filipino not only in science and mathematics but also in other endeavors such as sports, entertainment, art and music and I congratulate others who have similarly excelled and achieved.

I welcome the new articles, On why 0.999… = 1, and, Pinoy’s feat on Fermat’s Theorem turns out to be fake. Let me offer some comments.

) Regarding the first article, the equation 0.99… = 1 is nonsense because the real number system is ill-defined since at least one of its axioms, the trichotomy axiom, was proven to be false by Felix Brouwer by constructing a counter example to it in the book, Benacerraf, P. and Putnam, H. (1985) Philosophy of Mathematics, Cambridge University Press. Then all the arguments in the article collapse to nonsense also.

2) The second article reveals total ignorance of the issue. What is fake about the counterexamples to FLT PUBLISHED in several renowned refereed international scientific journals noted by the major databases? Until someone refutes the counterexamples and the refutation is similarly published in such renowned journals the “feat” stands as world-class contribution to mathematics. For the information of the viewers one of such articles, Escultura, E. E., The mathematics of the new physics, Applied Mathematics and Computation, Vol. 138, 2002, has been used and cited by the Corporate Mathematical Society of Japan, in the 10,000-page, Encyclopedic dictionary of mathematics (2nd ed.), MIT Press, Cambridge, MA, 1993, edited by Kiyosi Itô.

Another outstanding Filipino we can be proud of is the young current International Chess Olympic champion, 18-year-old Filipino-Australian Arriene Caoili.

Additional key words to be paired with my name to surf more of my work: atlas, new mathematics, new phytsics, astronomy, cosmology, generalized integral, set-valued functions, topology, cosmic sphere, cosmic burst, quasar, galaxy, resonance, big bang, intelligence, fractal, nonlinear phenomena, conservation, number theory, new integers, dark number, matter, discrete calculus, intuitive calculus, quantum mechanics, our universe, evolution, genetics, cancer, cosmological vortices, solar system, dynamic systems, dynamic modelling, laws of nature.

For the interested, the abstract of my keynote address at the Fifth International Confereence on Dynamic Systems, May 29, 2007, 9:00 A. M., Atlanta, GA, is online; surf: escultura, atlas. I’m also giving a keynote address at the Fifth World Congress of Nonlinear Analysts, July 10 - 19, 2008, Orlando, FL, on the topic, Dynamic Modelling and the Grand Unified Theory. For information on this congress, surf: escultura, ifna or escultura wcna.

I also commend perry for this blog that provides a venue for open discussion. Everyone has the right to say something, even nonse.

For the viewers, feel free to ask me questions or debate with me on any subject related to math or science.

Correction: “nonse” should read “nonsense”.

At long last Alecks has removed the title of his long-discredited article, Anotomy of a Hoax, and the lone post for the entire year 2006 on his pcij blog but the nonsense posts for 2005 remain. There is not a single post for the current year 2007. What a journalistic career!!! One can’t build a career on hoaxes.

I would like to acknowledge the well-informed and nicely written article, Pinoy dispel’s proof of Fermat’s theorem. More power to the author.

Here’s the latest on the new real number system:

1) The dark number d* is not only set-valued but also a continuum.

2) The dark number d* joins two adjacent decimals. Adjacent pair of decimals have the forms: 3.4700… and 3.4699… which differ by d*. Note that one can’t insert a decimal between adjacent decimals.

3) Therefore, the new real number system remains a continuum and has natural ordering but the decimals remain countably infinite and discrete (follows from the fact that the union of countable sets is countable).

The previous post by EEE is lifted from his keynote address at the Fifth International Conference on Dynamic Systems and Applicatins, entitled, Dynamic modelling and the new mathematics and physics, May 30 2007, Atlanta

Here’s the latest on the new real number system:

1) A nonterminating decimal is the Cauchy limit of its Cauchy sequence. Thus, the Cauchy limit of the Cauchy sequence, 0.9, 0.99, …, 0.99…9, …, is the nonterminating decimal 0.99…; its limit point or topological limit is 1. They differ by the dark number d* = 1 – 0.99…; in other words, they are consecutive or adjacent decimals. Another example of adjacent decimals is the pair 4.3800… and 4.3799… , they also differ by d* as all adjacent decimals do (the viewer can give his own examples of adjacent decimals).

2) The dark number d* is not only set-valued but also a continuum.

3) The decimals are naturally linearly ordered by its lexicographic ordering consecutively.

4) Since the countable union of countable sets is countable the decimals are countable, hence, discrete (one can see the flaw in Gauss’ diagonal method).

5) Since adjacent decimals are joined linearly by the continuum d* the union of the decimals with d* forms a continuum; this space along with u*, the equivalence class of divergent sequences, is called the new real number system.

6) The we summarize the nature of the new real number system:

The new real number system is a continuum, has natural ordering (the real number system has none) and includes the countably infinite new integers (including d*), terminating and nonterminating decimals (the latter ill-defined in the real number system) and the unbounded number u*. It is also non-Archimedean and non-Hausdorff but the decimals are. The new integer has the form, N.99. . ., N = 0, 1, 2, …; the mapping N –> (N – 1).99…, N = 0, 1, 2, …, and 0–> d* establishes isomorphism between the new integers and the integers, the integral parts of the decimals. Moreover, it has the countably infinite counterexamples to FLT:

x = (0.99…)10^T, y = d*, z = 10^T,

where T > 1 is an integer. The triples (kx,ky,kz), k = 1, 2, …, also satisfy Fermat’s equation;
they are the countably infinite nonzero solutions of Fermat’s equation.

(Excerpted from my keynote address, Dynamic modeling and the new mathematics and physics, 5th International Conference on Dynamic Systems and Applications, Atlanta, May 30, 2007; more advanced results are accommodated in my keynote address at a mini-symposium during the 5th World Congress of Nonlinear Analysts, Orlando, FL, July 2008)

E. E. Escultura

ewn q s inyo!!!!!!!!

Announcement of forthcomeing book.

The Grand Unified Hybrid Theory

by E. E. Escultura and V. Lakshmikantham.

The main chapters are: (1) The mathematics of the grand unified theory and (2) The grand unified theory.

Here’s a sample theorem from (1):

Theorem. In the lexicographic ordering, the decimals consist of adjacent predecessor-successor pairs of decimals each joined by the dark number d* (a continuum) so that the closure R* is a continuum. The decimal form a countably infinite, hence, discrete subset of R*.

The applications of GUT include the following articles:

1) The solution of the gravitational n-body problem.
2)Turbulence: Theory, verification and applications.
3) The physics of the mind.
4) Learning, recollection and creativity.
5) The origin and evolution of biological speies.

Elsevier Science, Ltd., has the first option to publish the book.

E. E. Escultura

Update on the new real number system.

The following is lifted from a keynote address for July 2008, The mathematics of the grand unified theory, at the 5th World Congress of Nonlinear Analysis, July 2 - 9, 2008, Orlando, Florida.

1) The new real number system R* is the closure of the terminating decimals in the g-norm. The g norm of a decimal is the decimal itself, e.g., g-norm of pi = pi.

2) The set-valued d* is a continuum.

3) The decimals consists of adjacent predecssor-sucessor pairs in the lexicographic ordering. Adjacent decimals differ by d*, e.g., 4.3800… and 4.399… are adjacent. The average of adjacent pairs is the smaller one, e.g., the average of 1 and 0.99… is 0.99…

4) R*, the union of these adjacent pairs plus d* is a continuum, non-Archimedean and non-Hausdorff but its subset of decimals is countabbly infinite and discrete, Archimedean and Hausdorff.

5) R* does not contain nondenumerable set.

6) The only set that has cardinality is discrete; the continiuum has none.

7) Nondenumerable set does not exist.

Here is the latest on the new real number system.

Update III.

WELL-DEFINING THE NONTERMINATING DECIMALS FOR THE FIRST TIME

This update is lifted from my lecture at a plenary session (distinct from the keynote) of the 5th World Congress of Nonlinear Analysts, Orlando, Florida, July 2 – 9, 2008, entitled, The terminating decimals and their g-closure.

At this time, only the terminating decimals are well-defined; this is our legacy from the Ancients. A nonterminating decimal is simply a meaningless infinite array of digits. In fact, we compute by cutting segments (which are terminating decimals) from them since they are the only decimals we know. Now, we build them on the terminating decimals R and make the latter our point of reference for any further extensions.

A sequence of terminating decimals of the form,

N.a_1, N.a_1a_2, …, N.a_1a_2…a_n, …, (1)

where N is integer and the a_ns are basic integers, is called standard generating or g-sequence.
Its nth g-term, N.a¬_1a_2…a_n, defines and approximates its g-limit, the nonterminating decimal,

N.a_1a_2…a_n,…, (2)

at margin of error 10n. The nth term of (1) is called the nth g-term, a terminating decimal, and its g-limit a nonterminating decimal provided the nth digits are not all 0 beyond a certain value of n.

THE g-NORM AS NATURAL NORM FOR COMPUTATION WITH ADVANTAGES OVER STANDARD NORM

In Update II we introduced the g-norm of a decimal, i.e., itself. It has several advantages over the standard norm:

(a) It avoids indeterminate forms.

(b) Since the g-norm of a decimal is itself, computation yields the answer directly as decimal, digit by digit, and avoids the intermediate approximations of standard computation. This means significant savings in computer time for large computations.

(c) Computation by the g-norm avoids radicals altogether and yields the result directly, digit by digit.

(d) The value or limit of function f(x) at s or as x  s is a decimal obtained by iterated computation of f(x) along successive refinement of sequence x_j that tends to s, as j tends to infinity; again, it yields the result directly as decimal, digit by digit to any desired level of accuracy measured by the number of digits computed.

(e) Approximation by the nth g-term or n-truncation contains or limits the ambiguity of nonterminating decimals.

(f) Calculation of distance between two decimals is direct, digit by digit, and requires no square root. For example, define the nth distance d_¬n between two decimals a, b as the numerical value of the difference between their nth g-terms, a_n, b_n, and their distance is the g-limit of d_n which does not even require square root. In general, computation by the g-norm does not involve roots or radicals.

Theorem. The tail digits of the nonterminating decimals merges into the continuum d*.

Finally, the closure of R in the g-norm or R* is a continuum, non-Archimedean and non-Hausdorff and includes the nonterminating decimals and the dark number d*. However, the system of decimals is a countably infinite subspace of R*, hence, discrete (digital), Archimedean and Hausdorff.

Announcement

Coming book:

The Grand Unified Theory

E. E. Escultura, Editor-contributor

Contributors: Profs. Alex Kavairainen (Russia-Finland),
Christopher Jesudason (Malaysia) and Vladimir Gudkov (Latvia)

Publishers Bentham Science Publishers

Another coming book:

One-author ebook by E. E. Escultura:

The Mathematics of the Grand Unified Theory.

to be published by Bentham Science Publishers.

The book, The Grand Hybrid Unified Theory, that I co-author with V. Lakshmikantham and S. Leela is being published in Germany by a division of Elsevier Science (North-Holland). It will be marketed by the same marketing organization for Elsevier Science and World Scientific books.

The main chapters in it are Quantum Gravity and Macro Gravity that comprise the Grand Uniified Theory. It is much broader than what Einstein envisioned that sought to unify the sttrong and weak forces of quantum mechanics with gravity. This one unifies the various forces and interactions of nature.

Another book in progress to be published by Bentham Science Publishers is: The Grand Unification of Natural Dynamics. It unifies all natural dynamics and physical systems including cosmic waves, photons, cosmological vortices (e.g., planet, star and galaxy) and the superstring, the basic constituent of matter.

E. E. Escultura

FUNDAMENTALS OF THE GRAND UNIFIED THEORY

1. The first milestone of the theory was the introduction of qualitative or noncomputational modeling that explains nature and natural phenomena in terms of the laws of nature used for the first time to solve the gravitational n-body problem (Nonlinear Analysis, 1997); it was instrumental in the discovery of the superstring, basic constituent of matter, required for the solution.

2. Dark matter is one of the two fundamental states of matter, the other visible or ordinary matter. It is dark because it is not diretly observable with present technology using light as medium and is known only indirectly by its impact on visible matter. It comprises over 95% of our universe.

3. The superstring is generalized nested fractal sequence of superstrings, where the first term is a helical loop like a lady’s spring bracelet. The first term contains a superstring, its toroidal flux, that travels through the helical cycle at the speed of 7 x 10^22 cm/sec. When the cycle length (CL) of its segment is 10^-14, agitated. It is this nested fractal structure that makes the superstring indestructible and qualify as basic constituent of matter. For throrough discussion of its structure see the book, Grand Hybrid Unified Theory; for detailed account of its discovery, see the paper, Qualitative model of the atom, its components and origin in the early universe, in press, Nonlinear Analysis, online at Science Direct website.

4. Cosmic waves. Everything vibrates due to the impact of cosmic waves coming from all directions in the Cosmos. The normal vibration of the atom vibrates its nucleus that generates Type I or basic cosmic or electromagnetic waves. Basic cosmic wave serves as carrier of photon, radio or television signals and thought or signal from the sense organ or the gene, i.e., information encoded by neural vibration or vibration of the receptor of a sense organ or normal vibration of the gene. In general we call brain wave basic cosmic wave superposed by or encoded with the vibration characteristics of a living cell. In the cortex they light up the tips of neural dendrite that send them outward across dark matter in all directions like radio transmitters antenna do with radio signals. A wave of any kind is the synchronized vibration of the the constituents of the medium. The other two types of cosmic waves are type II seismic waves composed from basic cosmic waves at the interface of turbulence and type III seismic waves also composed from basic cosmic waves and generated by powerful explosion such as nuclear explosion and lightning.

5. Nature of superstring. Dark matter consists of non-agitated and semi-agitated superstrings. When a non-agitated superstring is hit by cosmic wave, the first term of its fractal sequence may expand to semi-agitated superstring or be projected to bounce among the other suprestrings in its neighborhood and grinds to a halt when it loses impacted energy or its path forms a loop, by flux-low-pressure complementarity, and stabilizes into a semi-agitated superstring. When a semi-agitated superstring is hit by cosmic wave, its first term may break, its toroidal flux remaining in dark matter as non-agitated superstring or a segment may bulge and become agitated to become a primum, unit or visible matter like the electron or the positive and negative quarks. Left alone (no agitation) the superstring shrinks steadily, by energy conservation; this is a very very long process like what happens in the so-called neutron star.

6. Agitated or non-agitated, the speed of the toroidal flux of the superstring, 7 x 10^22 cm/sec, is constant, a constant of nature, by energy conservation, including electric current as flux of superstrings. Note that this is motion of matter 1012 times the speed of light.

7. The primum. Since the toroidal flux of a primum is being hit by cosmic waves from all directions it is thrust into erratic motion called “spike” in the neighborhood of the helical cycles as it is being pulled by the toroidal flux at the speed of 7  1022 cm/sec. This motion pulls the superstrings around the primum into a vortex flux with eye along the primal axis. We call it the induced vortex flux of the primum. Since the primum cannot be separated from its flux, we shall refer to the superstring and its induced vortex flux as the primum and its vortex flux is part of its dynamics. Being motion of matter it is energy measured as static electricity or charge. By convention, the electron has charge 1, the unit charge. Since its vortex flux is matter in motion it is energy which equals 1.6 × 10−19 coulombs. The other basic prima are the positive and negative quarks; their charges are +2/3 and 1/3, respectively. They are the basic prima being the constituent of every atom. They are produced at rapid rate in the Cosmos and in every cosmological body and are produced by the gene in the cellular membrane of every plant or animal.

8. The eye of the primum. By a natural law called flux-low-pressure complementarity, the eye of a primum sucks non-agitated superstrings, by flux-low-pressure complementarity [11] that steadily accumulate there. They are, in fact, the major source of energy in the nuclues (coupled prima) released in nuclear explosion when they are converted to photons and prima besides the shock waves generated by the explosion. In quantum physics the energy released in nuclear explosion, e.g., atom bomb explosion, is attributed to the difference in mass between the constituent nucleons when the nucleus splits. This difference is due to the loss of negative quarks that binds the protons in the nucleus which is quite minute and does not match the explosive power of the atom bomb. That this binding force is quite small is revealed by the fact that a neutron of very low energy. 0.25 calories, is sufficient to split the nucleus of the uranium 235 atom.

9. The primum as magnet. A simple primum is a magnet, its magnetic field determined by the vortex flux of superstrings around it. We use the right hand rule of electricity and magnetism to determine its polarity. For a positive primum, when the index finger points in the direction of flux the thumb points to the north pole or N-pole. Thus, viewed from the N-pole its induced flux is counterclockwise. We shall refer to this magnet as having positive polarity. Otherwise, the flux is clockwise, the primum negative and the polarity reversed – negative.

E. E. Escultura

UPDATE ON THE NEW REAL NUMBER
SYSTEM

1) In both the real and new real number
systems the only well-defined decimals are
the terminating ones; the nonterminating
decimals are simply arrays of digits
most of which are unknown.

2) In the new real number system the
nonterminating decimals are defined, for the
the first time, in terms of the terminating
decimals R as follows:

a) Consider the sequence of terminating
decimals of the form,

N.a_1, N.a_1a_2, …, N.a_1a_2…a_n, …; (1)

the sequence (1) is called standard
generating or g-sequence. Its nth g-term,
N.a_1a_2…a_n, which is a terminating decimal,
defines and approximates the g-limit, the
nonterminating decimal,

N.a_1a_2…a_n…, (2)

at margin of error (maximum error) 10^–n.

b) If the nth digit of the g-limit (2) is not 0
for all n beyond a certain integer k then (2)
defines a nonterminating decimmal.
Note that the nth g-term repeats all the
previous digits of the decimal in the same
order so that if finite terms of the g-sequence
are deleted, the nonterminating decimal it
defines, i.e., its g-limit, remains unaltered.

c) In analysis we define limit in terms of
some norm. We define the g-norm of a
decimal as the decimal itself so that the
g-limt is also defined in terms of the g-norm.
Computation with the g-norm has advantages
one of which being that the result is obtained
directly as a decimal digit by digit so that the
intermediate steps of approximation is avoided.

3) Consider the sequence of decimals,

(d^n)a_1a_2…a_k, n = 1, 2, …, (3)

where d is any of the decimals,
0.1, 0.2, 0.3, …, 0.9, and a_1, …, a_k
finite basic integers (not all 0 simultaneously).
For each combination of d and the a_js,
j = 1, …, k, in (3) the nth term, which
we now refer to as the nth d-term of
this nonstandard d-sequence, is not a
decimal since the digits are not fixed.
As n increases indefinitely it traces the
tail digits of some nonterminating
decimal (note that the nth g-term recedes
to the right with increasing n), becomes
smaller and smaller until it becomes
indistinguishable from the tail digits of the
other decimals. We call the sequence (3)
nonstandard d-sequence since the nth term
is not a standard g-term but has a standard
limit, i.e., limit in the standard norm, which
is 0. Like the g-limit, the d-limit exists since
it is defined by its nonstandard d-sequence
of terminating decimals; we call it a dark
number d, the d-limit of the nonstandard d-
sequence (3). Moreover, while the nth term
becomes smaller and smaller with increasing
n it is greater than 0 no matter how large n is
so that if x is any decimal, 0

Two Fatal Defects in Andrew Wiles’ Proof of FLT

1) The field axioms of the real number system are inconsistent; Felix Brouwer and this blogger provided counterexamples to the trichotomy axiom and Banach-Tarski to the completeness axiom, a variant of the axiom of choice. Therefore, the real number system is ill-defined and FLT being formulated in it is also ill-defined. What it took to resolve this conjecture was to first free the real number system from contradiction by reconstructing it as the new real number system on three simple consistent axioms and reformulating FLT in it. With this rectification of the real number system, FLT is well-defined and resolved by counterexamples that proving that it is false.

2) The other fatal defect is that the complex number system that Wiles used in the proof being based on the vacuous concept i is also inconsistent. The element i is the vacuous concept: the root of the equation x^2 + 1 = 0 which does not exist and is denoted by the symbol i = sqrt(-1) from which follows that,

i = sqrt(1/-1) = sqrt 1/sqrt(-1) = 1/i = i/i^2 = -i or

1 = -1 (division of both sides by i),

2 = 0, 1 = 0, I = 0, and, for any real number x, x = 0,

and the entire real and complex number systems collapse. In general, any vacuous concept yields a contradiction.

References

[1] Benacerraf, P. and Putnam, H. (1985) Philosophy of Mathematics, Cambridge University Press, Cambridge, 52 - 61.
[2] Brania, A., and Sambandham, M., Symbolic Dynamics of the Shift Map in R*, Proc. 5th International
Conference on Dynamic Systems and Applications, 5 (2008), 68–72.
[3] Escultura, E. E. (1997) Exact solutions of Fermat’s equation (Definitive resolution of Fermat’s last theorem, 5(2), 227 – 2254.
[4] Escultura, E. E. (2002) The mathematics of the new physics, J. Applied Mathematics and Computations, 130(1), 145 – 169.
[5] Escultura, E. E. (2003) The new mathematics and physics, J. Applied Mathematics and Computation, 138(1), 127 – 149.
[6]. Escultura, E. E., The new real number system and discrete computation and calculus, 17 (2009), 59 – 84.
[7] Escultura, E. E., Extending the reach of computation, Applied Mathematics Letters, Applied Mathematics Letters 21(10), 2007, 1074-1081.
[8] Escultura, E. E., The mathematics of the grand unified theory, in press, Nonlinear Analysis, Series A:
Theory, Methods and Applications; online at Science Direct website
[9] Escultura, E. E., Lakshmikantham, V., and Leela, S., The Hybrid Grand Unified Theory, Atlantis (Elsevier
Science, Ltd.), 2009, Paris.
[10] Counterexamples to Fermat’s last theorem, http://users.tpg.com.au/pidro/
[11] Kline, M., Mathematics: The Loss of Certainty, Cambride University Press, 1985.

E. E. Escultura
Research Professor
V. Lakshmikantham Institute for Advanced Studies
GVP College of Engineering, JNT University

Summation of the Debate on the New Real Number System and the Resolution of Fermat’s last theorem – by E. E. Escultura

The debate started in 1997 with my post on the math forum SciMath that says 1 and 0.99… are distinct. This simple post unleashed an avalanche of opposition complete with expletives and name-calls that generated hundreds of threads of discussion and debate on the issue. The debate moved focus when I pointed out the two main defects of Andrew Wiles’ proof of FLT and, further on, the discussion shifted to the new real number system and the rationale for it. Naturally, the debate spilled over to many blogs and websites across the internet except narrow minded ones that accommodate only unanimous opinions, e.g., Widipedia and its family of websites, as well as websites that cannot stand contrary opinion like HaloScan and its sister website, Don’t Let Me Stop You. SciMath stands out as the best forum for discussion of various mathematical issues from different perspectives. There was one regular who did debate me online but through e-mail. We debated for about a year and I learned much for him. The few who only had expletives and name-calls to throw at me are nowhere to be heard from.

There was one unsigned feeble attempt from the UP Mathematics Department to counter my arguments online. But it wilted without a response from the science community because it lacked grasp of what mathematics is all about.. It is posted on this message board.

The most recent credible challenge to my positions on these issues was registered by Bart van Donselaar in the online article, Edgar E. Escultura and the Inequality of 1 and 0.99…, to which I responded with the article, Reply to Bart van Donselaar’s article, Edgar E. Escultura and the inequality of 1 and 0.99…; a website on the Donselaar’s paper has been set up:

http://www.reddit.com/r/math/comments/93n3i/edgar_e_escultura_and_the_inequality_of_1_and/

and the discussion is coming to a close as no new issues are being raised. Needless to say, none of my criticisms of my positions on Wiles’ proof of FLT or my critique of the real and complex number systems have been challenged successfully on this website or across the internet. In peer reviewed publications there is not even a single attempt to refute my positions on these issues.
We highlight some of the most contentious issues of the debate.
1) Consider the equation 1 = 0.99… that almost everyone accepts. There are a number of defects here. Among the decimals only terminating decimals are well-defined. The rest are ill-defined or ambiguous. In this equation the left side is well-defined as the multiplicative identity element while the right side is ill-defined. The equation, therefore, is nonsense.
2) The second point is: David Hilbert already knew almost a century ago that the concepts of individual thought cannot be the subject matter of mathematics since they are unknown to others and, therefore, cannot be studied collectively, analyzed or axiomatized. Therefore, the subject matter of mathematics must be objects in the real world including symbols that everyone can look at, analyze and study collectively provided they are subject to consistent premises or axioms. Consistency of a mathematical system is important, otherwise, every conclusion drawn from it is contradicted by another. In order words, inconsistency collapses a mathematical system. Consider 1 and 0.99…; they are certainly distinct objects like apple and orange and to write apple = orange is simply nonsense.
3) The field axioms of the real number system is inconsistent. Felix Brouwer and myself constructed counterexamples to the trichotomy axiom which means that it is false. Banach-Tarski constructed a contradiction to the axiom of choice, one of the field axioms. One version says that if a soft ball is sliced into suitably little piece and rearranged without distortion they can be reconstituted into a ball the size of Earth. This is a topological contradiction in R^3.
4) Vacuous concept generally yields a contradiction. For example, consider this vacuous concept: the root of the equation x^2 + 1 = 0. That root has been denoted by i = sqrt(-1). The notation itself is a problem since sqrt is a well-defined operation in the real number system that applies only to perfect square. Certainly, -1 is not a perfect square. Mathematicians extended the operation to non-negative numbers. However, the counterexamples to the trichotomy axiom show at the same time that an irrational number cannot be represented by a sequence of rationals. In fact, a theorem in the paper, The new mathematics and physics, Applied Mathematics and Computation, 138(1), 127 – 149, says that the rationals and irrationals are separated, i.e., the union of disjoint open sets.
At any rate, if one is not convinced of the mischief that vacuous concept can play, consider this:
i .= sqrt(-1) = sqrt1/sqrt(-1) = 1/i = -i or i = 0. 1 = 0, and both the real and complex number systems collapse.

5) With respect to Andrew Wiles’ proof of FLT it has two main defects: a) Since FLT is formulated in the inconsistent real number system it is nonsense and, naturally, the proof is also nonsense. The remedy is to first remove the inconsistency of the real number system which I did and reformulate FLT in the consistent number system, the new real number system. b) The use of complex analysis deals another fatal blow to Wiles’ proof. The remedy for complex analysis is in the appendix to the paper, The generalized integral as dual to Schwarz Distribution, in press, Nonlinear Studies.

6) By reconstructing the defective real number system into the contradiction-free new real number system and reformulating FLT in the latter, countably infinite counterexamples to it have been constructed showing the theorem false and Wiles wrong.

7) In the course of making a critique of the real number system some new results have been found: a) Gauss diagonal method of proving the existence of nondenumerable set only generates a countably infinite set; b) as of this time there does not exist a nondenumerable set; c) only discrete set has cardinality, a continuum has none..

8) The new real number system is a continuum, countably infinite, non-Hausdorff and Non-Archimedean and the subset of decimals is also countably infinite but discrete, Hausdorff and Archimedean. The g-norm simplifies computation considerably.

E. E. Escultura

Correction: There was one regular at SciMath who did not debate me online but through e-mail. We debated for about a year and I learned much from him. E. E. Escultura

CLARIFICATION ON THE COUNTEREXAMPLES TO FERMAT’S LAST THEOREM
By E. E. Escultura

Although all issues related to the resolution of Fermat’s last theorem have been fully debated worldwide since 1997 and NOTHING had been conceded from my side I have seen at least one post expressing some misunderstanding. Let me, therefore, make the following clarification:

1) The decimal integers N.99… , N = 0, 1, …, are well-defined nonterminating decimals among the new real numbers [8] and are isomorphic to the ordinary integers, i.e., integral parts of the decimals, under the mapping, d* -> 0, N+1 -> N.99… Therefore, the decimal integers are integers [3]. The kernel of this isomorphism is (d*,1) and its image is (0,0.99…). Therefore, (d*)^n = d* since 0^n = 0 and (0.99…)^n = 0.99… since 1^n = 1 for any integer n > 2.

2) From the definition of d* [8], N+1 – d* = N.99… so that N.99… + d* = N+1. Moreover, If N is an integer, then (0.99…)^n = 0.99… and it follows that ((0.99,..)10)^N = (9.99…)10^N, ((0.99,..)10)^N + d* = 10^N, N = 1, 2, … [8].

3) Then the exact solutions of Fermat’s equation are given by the triple (x,y,z) = ((0.99…)10^T,d*,10^T), T = 1, 2, …, that clearly satisfies Fermat’s equation,
x^n + y^n = z^n, (F)

for n = NT > 2. The counterexamples are exact because the decimal integers and the dark number d* involved in the solution are well-defined and are not approximations.

4) Moreover, for k = 1, 2, …, the triple (kx,ky,kz) also satisfies Fermat’s equation. They are the countably infinite counterexamples to FLT that prove the conjecture false [8]. They are exact solutions, not approximation. One counterexample is, of course, sufficient to disprove a conjecture.

The following references include references used in the consolidated paper [8] plus [2] which applies [8]

References

[1] Benacerraf, P. and Putnam, H. (1985) Philosophy of Mathematics, Cambridge University Press, Cambridge, 52 - 61.
[2] Brania, A., and Sambandham, M., Symbolic Dynamics of the Shift Map in R*, Proc. 5th International
Conference on Dynamic Systems and Applications, 5 (2008), 68–72.
[3] Corporate Mathematical Society of Japan , Kiyosi Itô, Encyclopedic dictionary of mathematics (2nd ed.), MIT Press, Cambridge, MA, 1993
[4] Escultura, E. E. (1997) Exact solutions of Fermat’s equation (Definitive resolution of Fermat’s last theorem, 5(2), 227 – 2254.
[5] Escultura, E. E. (2002) The mathematics of the new physics, J. Applied Mathematics and Computations, 130(1), 145 – 169.
[6] Escultura, E. E. (2003) The new mathematics and physics, J. Applied Mathematics and Computation, 138(1), 127 – 149.
[7] Escultura, E. E., The new real number system and discrete computation and calculus, 17 (2009), 59 – 84.
[8] Escultura, E. E., Extending the reach of computation, Applied Mathematics Letters, Applied Mathematics Letters 21(10), 2007, 1074-1081.
[9] Escultura, E. E., The mathematics of the grand unified theory, in press, Nonlinear Analysis, Series A:
Theory, Methods and Applications; online at Science Direct website
[10] Escultura, E. E., The generalized integral as dual of Schwarz distribution, in press, Nonlinear Studies.
[11] Escultura, E. E., Revisiting the hybrid real number system, Nonlinear Analysis, Series C: Hybrid Systems, 3(2) May 2009, 101-107.
[12] Escultura, E. E., Lakshmikantham, V., and Leela, S., The Hybrid Grand Unified Theory, Atlantis (Elsevier Science, Ltd.), 2009, Paris.
[13] Counterexamples to Fermat’s last theorem, http://users.tpg.com.au/pidro/
[14] Kline, M., Mathematics: The Loss of Certainty, Cambridge University Press, 1985.

E. E. Escultura
Research Professor
V. Lakshmikantham Institute for Advanced Studies
GVP College of Engineering, JNT University
Madurawada, Vishakhapatnam, AP, India
http://users.tpg.com.au/pidro/

Being a newcomer in mathematics and science (my first publication is “The solution of the gravitational n-
body problem”, Nonlinear Analysis, Series A, 30(8), Dec. 1997, 521 – 532), I was an underdog in contending ideas with the heavy weights of science and mathematics. Therefore, I had to disseminate my ideas broadly as quickly as possible. The first forum I posted my message in was SciMath, 1997, and the topic was the equality 1 = 0.99… I said that this was really nonsense and I’ll explain why later.

There was a howl of protest and hundreds of messages were posted in protest during the year. Some called me crackpot, lunatic, moron, etc. One even wrote my colleague (who sort of discovered me in mathematics), Prof. V. Lakshmikantham, a famous mathematician who founded the only rapidly expanding field of mathematics today, Nonlinear Analysis, founder and editor-in-chief of several scientific journals, and president and founder of the International Federation of Nonlinear Analysts, to tell him that he was a lunatic for associating with me. There were at least five such guys in SciMath. However, in due course they pulled enough rope to hang themselves with academically and are all quiet now.

Going back to 1 = 0.99…, it was David Hilbert who recognized almost a century ago that the concepts of individual thought, being inaccessible to others, are ambiguous and cannot be discussed, studied and analyzed collectively. Therefore, they cannot be the subject matter of mathematics. The proper subject matter of mathematics must be objects in the real world, e.g., symbols that we also call concepts that everyone can look at provided they are subject to consistent premises or axioms. Clearly, 1 and 0.99… are distinct objects like apple and orange and to say apple = orange is simply nonsense.

As it will turn out SciMath is the best forum in this category in terms of open participation and, naturally, diversity of ideas. The worst in this category, however, is Wikipedia along with its sister website Wikia. Wikipedia requires consensus on posted topic. In other words, it requires uniformity of thought. Wikia specifically bars original research. In effect, they block the progress of science and mathematics which do not thrive on consensus and their progress stands on original research. Between these two extremes the blogs and websites range from good to excellent in terms of diversity of ideas with the only exception of HaloScan and its sister website, DLMSY, which cannot stand contrary opinion. Consequently, they lose bloggers. I identify a few excellent ones in the category of in-betweens: False Proofs, MathForge, WorldPress and Faces of the Moon. I add Knowledgerush in terms of ease in posting – no no username and password which are easy to forget.

However, there is a forum that is a class by itself in terms of the quality and level of intellectual discussion: ISCID (International Society for Computing and Intelligent Design (?)). I recommend experts to visit this website.

E. E. Escultura
Research Professor
Lakshmikantham Institute for Advanced Studies and Departments of Mathematics and Physics
GVP College of Engineering, JNT University, Visakhapatnam, AP, India
E-mail: escultur36@gmail.com * URL: http://users.tpg.com.au/pidro/

Sorry, I missed to append the the title of the above article; it should be:

THE BEST AND THE WORST

E. E. Escultura

What is the difference between music and mathematics?

Answer: Classical music is a treasure but classical mathematics is a trash.

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CALL FOR A GRAND UNIFIED JOINT CELEBRATION

Materialist philosophers of all cultures must have pondered this question: what are the basic constituents of matter? The Greeks answered it with four constituents they found in nature: earth, water, fire and air. The Chinese added one more item – wood. Of course, they were not satisfactory and since then the search for the basic constituent of matter was in limbo for 5,000 years until in the 1950s inspired by the exciting developments in quantum physics particle physicists renewed the search with vigor by smashing the nucleus of the atom in pursuit of the basic irreducible elementary particles or building blocks of visible matter (since dark matter was unknown then). By the 1990s the search was a complete success with the discovery of the +quark (up quark) and quark (down quark) and, earlier, the electron discovered by J. J. Thompson in 1897. They comprise every atom; a heavy isotope has at least one more additional stable elementary particle – the neutrino. Particle physicists have, indeed, found what they were looking for – the irreducible building blocks of visible matter – and whatever they have found beyond this discovery is a bonus for natural science and its applications, a bonus for mankind.

In the 1980s dark matter came to the fore with overwhelming evidence of its existence [6,7,8] and, using the new methodology of qualitative modeling that explains nature and its appearances in terms of natural laws [1,5], was established in 1997 [4] as one of the two fundamental states of matter the other ordinary or visible matter [2,5]. That same year the building block of dark matter, the superstring, was discovered as the crucial factor in the solution of the gravitational n-body problem [4] and development of the grand unified theory (GUT). The latter has been established in a series of papers since 1997 and consolidated in [2]. There is only one basic constituent in view of the non-redundancy and non-extravagance natural principles [3] just as there is only one electron since all electrons have identical structure, properties, behavior and functions and differ only in locations. Moreover, it has been established that the superstring coverts to the basic elementary particles as agitated superstring [1,2,3]. In effect, this proves the superstring as the basic constituent of matter, dark and visible [1,2,3,4,5 ].

This happy turn of events came without notice and fanfare but it is an important milestone for science that calls for a grand unified joint celebration by particle and theoretical physicists to mark these monumental achievements and the threshold of a new epoch for natural science and its applications. Perhaps, a world congress of particle and theoretical physicists is appropriate on this momentous occasion.

References

[1] Escultura, E. E., The mathematics of the grand unified theory, Nonlinear Analysis,
A-Series: Theory: Methods and Applications, 71 (2009) e420 – e431.
[2] Escultura, E. E., The grand unified theory, Nonlinear Analysis, A-Series: Theory:
Methods and Applications, 69(3), 2008, 823 – 831.
[3] Escultura, E. E., Qualitative model of the atom, its components and origin in the
early universe, Nonlinear Analysis, B-Series: Real World Applications, 11 (2009),
29 – 38.
[4] Escultura, E. E., The solution of the gravitational n-body problem, Nonlinear
Analysis, A-Series: Theory, Methods and Applications, 38(8), 521 – 532.
[5] Escultura, E. E., Superstring loop dynamics and applications to astronomy and
biology, Nonlinear Analysis, A-Series: Theory: Methods and Applications, 35(8),
1999, 259 – 285.
[6] Astronomy (a) August 1995, (b) January 2001, (c) June 2002.
[7] Science, Glow reveals early star nurseries, July 1998.
[8] Science, (a) Starbirth, gamma blast hint at active early universe, 282(5395),
December, 1998, 1806; (b) Gamma burst promises celestial reprise, 283(5402),
January 1999; (c) Powerful cosmic rays tied to far off galaxies, 282(5391), Nov.
1998, 1969 – 1971.

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BOOK REVIEW AND PROPOSED REMEDY FOR THE PROBLEMS OF PHYSICS

By E. E. Escultura

The book: THE TROUBLE WITH PHYSICS, Penguin Books, 2008

By Lee Smolin

The book is the most objective and comprehensive assessment of contemporary physics I have read. It assesses where physics is in the search for the grand unification of the forces and interactions of nature and identifies five great problems that must be resolved towards unification. They are stated below with this Reviewer’s comments.

Problem 1. Combine general relativity and quantum theory into a single theory that can claim to be the complete theory of nature.

Reviewer’s comment. By building a theory based on general relativity and quantum theory, it brings in their weakness and inadequacy and other limitations in the search for unification. There is a lot of ambiguity in their basic physical concepts such as matter, energy, charge and gravity. To know matter, for instance, we must know what matter consists of and this requires the discovery of the basic constituent of matter which contemporary physics has not done.

Problem 2. Resolve the problems in the foundations of quantum mechanics either by making sense of the theory as it stands or by inventing a new theory that does make sense.

Reviewer’s comment. I agree with this formulation. However, I would broaden it to the problems of the foundations of natural science and mathematics, the latter being the language and tool of science.

Problem 3. Determine whether or not the various particles and forces can be unified in a theory that explains them all as manifestations of a single fundamental entity.

Reviewer’s comment. I fully agree with this formulation.

Problem 4. Explain how the values of the free constants in the standard model of particle physics are chosen in nature.

Reviewer’s comment. I agree with this formulation with some modification as follows: Explain how the constants of nature, e.g., the Planck’s constant h and the Hubble’s constant, by providing details on how they were determined.

Problem 5. Explain dark matter and energy. Or, if they don’t exist, determine how and why gravity is modified on large scales. More generally, explain why the constants of the standard model, including dark energy, have the values they do.

Reviewer’s comment. I would retain only the first sentence of the formulation since the rest of it is already moot and academic [42].

The author proceeds to lay out in great detail the theories and models proposed so far with a graphic account of the twists and turns in the search for a complete theory. The proposed theories and models range from general relativity and quantum theory through the standard model of elementary particle physics, string theories, a number of dimension theories, quantum gravity, gauge theory and superstring theory. In the end, he concluded that physics today is in total confusion, has accomplished nothing towards unification in almost three decades and a complete theory is nowhere in sight. He bewailed the fact that string theorists have almost exclusive access to research grants and top academic positions in physics for which he should be commended for being able to rise above the confines of this group to which he belongs.

Now, he welcomes the seers to tell us what is wrong with physics and point the way towards unification. This will require, in my view, a critique of its foundations and the foundations of mathematics including its present methodology of quantitative modelling that describes the appearances of nature without providing insights into how nature works. This allows, at best, reasoning by analogy which has an obvious flaw: a bird that walks like a duck and quacks like a duck is not necessarily a duck.

Reviewer’s comment on rectification.

1) We need to clarify physical concepts and distinguish them from mathematical concepts. The former have physical referents – physical objects – that exist in nature and are subject to its laws. Mathematical concepts are man-made that comprise its vocabulary as the language of science; they have no physical referents and are, therefore, not subject to natural laws, e.g., time, distance, dimension, function and equation. Among the physical concepts are matter, energy and physical systems such as the electron, light, electromagnetic wave, atom and galaxy; their existence are verifiable. For example, to clarify what matter is we need to know what it consists of which requires the discovery of its basic constituent.

2) We need to improve the present sense of unification from being descriptive of the appearances of nature in terms of common physical concepts to explanation of how nature works in terms of its laws. This should include explanation of what the forces and interactions of nature and their nature and what physical systems or natural phenomena are.

3) In view of the inadequacy of the present methodology of quantitative modelling of physics that describes the appearances of nature, we need the new methodology of qualitative modelling that explains nature and natural phenomena in terms of natural laws. Its main tool is qualitative mathematics, the complement of computation and measurement. It includes axiomatic systems and abstract mathematics and the search for the laws of nature.

4) We need to clarify that mathematical physics, a collection of mathematical descriptions of nature and natural phenomena, is not theoretical physics. A physical theory is an axiomatic system where the axioms or basic premises are laws of nature and scientific reasoning is based on its axioms – laws of nature – that define it and conclusions drawn from them. This way of reasoning belongs to rational thought. Definition of physical concepts is based solely on its axioms. When the laws of nature that define a physical theory apply to the various disciplines of natural science it is called grand unified or complete theory. For sources and elaboration of the ideas the viewer is referred to the following references.

[1] Escultura, E. E., Diophantus: Introduction to Mathematical Philosophy (With probabilistic solution of Fermat’s last theorem), Kalikasan Press: Manila, 1993.
[2] Escultura, E. E. Probabilistic mathematics and applications to dynamic systems including Fermat’s last theorem, Proc. 2nd International Conference on Dynamic Systems and Applications: Atlanta, May 27 – 31, 1999, pp. 147 – 152.
[3] Escultura, E. E. Bhaskar, T. G.; Leela, S., Laksmikantham, V., Revisiting the hybrid real number system, J. Nonlinear Analysis, C-Series: Hybrid Systems, May 2009, 3, 2, pp. 101 – 107.
[4] Escultura, E. E. Extending the reach of computation, J. Applied Mathematics Letters, 2008, 21, 10, pp. 1074 – 1081.
[5] Escultura, E. E. Exact solutions of Fermat’s equation (A definitive resolution of Fermat’s last theorem, J. Nonlinear Studies, 1998, 5, 2, pp. 227 - 254.
[6] Escultura, E. E. Recent verification and applications, Proc. 2rd International Conference on Tools for Mathematical Modeling, St. Petersburg, 1999, 4, pp. 116 - 29.
[7] Escultura, E. E. The generalized integral as dual of Schwarz distribution, invited paper, J. Nonlinear Studies.
[8] Escultura, E. E. Set-valued differential equations and applications to quantum gravity, J. Mathematical Research, 2000, 6, St. Petersburg, pp. 221 - 224.
[9] Escultura, E. E. The new real number system and discrete computation and calculus, J. Neural, Parallel and Scientific Computations, 2009, 17, pp. 59 – 84.
[10] Escultura, E. E. Introduction to Qualitative Control Theory, Kalikasan Press: Manila, 1991.
[11] Escultura, E. E. The new mathematics and physics, J. Applied Mathematics and Computation, 2003, 138, 1, 145 – 169.
[24] Escultura, E. E. Chaos, turbulence and fractal, Indian J. Pure and Applied Mathematics, 2001, 32,10, pp. 1539 – 1551.
[25] Escultura, E. E. The mathematics of the grand unified theory, Proc. 5th World Congress of Nonlinear Analysts, J. Nonlinear Analysis, A-Series: Theory: Method and Applications, 2009, 71, pp. e420 – e431.
[26] Escultura, E. E. The mathematics of the new physics, J. Applied Mathematics and Computations, 2002, 130, 1, pp. 149 - 169.
[27] Escultura, E. E. Dynamic Modeling and the new mathematics and physics, J. Neural, Parallel and Scientific Computations (NPSC), 2007, 15, 4, PP. 527 – 538.
[28] Escultura, E. E. The theory of intelligence and evolution, Indian J. Pure and Applied Math., 2003, 33, 1, PP. 111 – 129.
[29] Escultura, E. E. The physics of the mind, accepted, J. Science of Healing Outcomes.
[30] Escultura, E. E. The origin and evolution of biological species, J. Science of Healing Outcomes, 2010, 6-7, pp. 17 - 27.
[31] Escultura, E. E. The Unified Theory of Evolution, invited, International Journal of Biological Sciences and Engineering.
[32] Escultura, E. E. Genetic Alteration, Modification, Sterilization With Applications to the Treatment of Genetic Diseases, accepted , J. Science of Healing Outcomes.
[33]Escultura, E. E. Superstring loop dynamics and applications to astronomy and biology, J. Nonlinear Analysis, A-Series: Theory: Methods and Applications, 1999, 35, 8, pp. 259 – 285.
[34] Escultura, E. E., From macro to quantum gravity, J. Problems of Nonlinear Analysis in Eng’g Systems, 2001, 7, 1, pp. 56 – 78.
[35] Escultura, E. E. Turbulence: theory, verification and applications, J. Nonlinear Analysis, A-Series: Theory, Methods and Applications, 2001, 47, 8, pp. 5955 – 5966.
[36] Escultura, E. E., Vortex Interactions, J. Problems of Nonlinear Analysis in Engineering Systems, 2001, 7, 2, pp. 30 – 44.
[37] Escultura, E. E. Dynamic Modeling of Chaos and Turbulence, Proc. 3rd World Congress of Nonlinear Analysts, J. Nonlinear Analysis, A-Series: Theory: Method and Applications, 2005, 63, 5-7, pp. e519-e532.
[38] Escultura, E. E. Global geology and oceanography, invited, International J. Earth Sciences and Engineering.
[39] Escultura, E. E., Dynamic Modeling and Applications, Proc. 3rd International Conference on Tools for Mathematical Modeling, 7, State Technical University of St. Petersburg, St. Petersburg, 2003, pp. 103 - 114.
[40] Escultura, E. E. The Pillars of the new physics and some updates, J. Nonlinear Studies, 2007, 14, 3, pp. 241 – 260.
[41] Escultura, E. E. The solution of the gravitational n-body problem, J. Nonlinear Analysis, A-Series: Theory, Methods and Applications, 2007, 30, 8, pp. 5021 - 5032.
[42] Escultura, E. E. The grand unified theory, contribution to the Felicitation Volume on the occasion of the 85th birth anniversary of Prof. V. Lakshmikantham, J. Nonlinear Analysis, A-Series: Theory: Method and Applications, 2008, 69, 3, pp. 823 – 831.
[43] Escultura, E. E. Qualitative model of the atom, its components and origin in the early universe, Proc. 5th World Congress of Nonlinear Analysts, J. Nonlinear Analysis, B-Series: Real World Applications, 2009, 11, pp. 29 – 38.
[44] Escultura, E. E. Dynamic and mathematical models in physics, Proc. 5th International Conference on Dynamic Systems and Applications, June 30 – July 5, 2007, Atlanta.
[45] Escultura, E. E. The basic concepts and dynamics of quantum gravity with applications, invited, J. Nonlinear Studies.
[46] Escultura, E. E. The trajectories, reachable set, minimal levels and chain of trajectories of a control system, Ph. D. thesis, University of Wisconsin, 1970.
[47] Escultura, E. E. Qualitative modeling for complex systems, Proc. 23rd EURO Conference, July 5 – 8, 2009, Bon, Germany.

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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 signatures 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 arguments but this time focusing on my resolution of Fermat’s last theorem.

Now there is a post in WikiPilipinas, again, addressed to me and attacking my work by repeating the same arguments that I have already resoundingly demolished on many websites. WikiPilipinas, by the way, publishes outright lies about Filipino inventors who have long passed away. It made a blunder, however, by publishing lies about me, the Manny Pacquiao of Science and Mathematics with Teflon world academic stature.

These online articles by IM 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 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 the latest punches can be viewed at these websites:

Cheers,

E. E. Escultura
(continued)

Putting the Institute … (ccontinued)

This “apology” is, of course, fake. I NEVER posted it and I NEVER CLAIMED that I disproved FLT. I did something greater: I DISPROVED IT by counterexamples published in my papers in several renowned peer reviewed scientific journals. A partial list of my publications with abstracts is given in one of my websites, The Grand Unified Theory, http://edgareescultura.wordpress.com/ (see also my old website, Grand Unification of Natural Dynamics, http://users.tpg.com.au/pidro/). Most of my papers are being sold online (for instance, search: escultura science direct elsevier). The latest confirmation of my nomination for the Nobel Prize for Physics in 2005 is the announcement 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 slot among best sellers in July, 2009. For the information of the Institute these are my major achievements recorded and etched in internet archives:

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; formerly North-Holland).
3. Solved the turbulence problem, Nonlinear Analysis, A-Series: Theory, Methods and Applications 47(2001), pp. 1539 – 1551, 5032 (published by Elsevier Science, Ltd).
4. Discovered the superstring, basic constituent of matter, Nonlinear Analysis, C-Series: Theory, Methods and Applications, 30(8), 1997 (it is the foundation of the solution of the gravitational n-body problem).
5. Developed the grand unified theory in a series of papers since 1997 and consolidated in the paper, The Grand Unified Theory, Nonlinear Analysis, C-Series: Theory, Methods and Applications,:69(3), 2008, pp. pp. 823 – 831 5032 (published by Elsevier Science, Ltd).
6. Developed the new real number system, Neural, Parallel and Scientific Computations, 17(2009), 59 – 84 (Published by Dynamic Publishers).
7. Proved Goldbach’s conjecture, Applied Mathematics and Computation, 138(2003), 127 – 14
(published by Elsevier Science, Ltd).
8. Developed the generalized integral for set-valued functions, Proceedings of International Conferences on Tools for Mathematical Modelling, June 2000, St. Petersburg, Russia, pp. 221 - 224.
9. Developed the generalized integral as dual of Schwarz distribution, Nonlinear Studies, invited paper by Nonlinear Studies, in press.
10. Developed the Complex Vector Plane which rectifies the present defect of the complex number system in the appendix to: The generalized integral as dual of Schwarz distribution, invited paper, Nonlinear Studies.
11. Gave a keynote address on the topic, The mathematics of the grand unified theory, and addressed a plenary session on the topic, The new real number system as the g-closure of the terminating decimals, at the 5th World Congress of Nonlinear Analysts, Orlando, Florida, July 2 – 9, 2008 (Sponsored by the International Federation of Nonlinear Analysts).
12. Gave a keynote address at the 4th International Conference on Dynamic Systems and Applications, Atlanta, USA, April 30 – May 2, 2007.
13. 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.
14. Made the first qualitative model of the atom, Qualitative model of the atom, its components and origin in the early universe, Proc. 5th World Congress of Nonlinear Analysts, Nonlinear Analysis, B-Series: Real World Applications, 2009, 11, pp. 29 – 38 (published by Elsevier Science, ltd).

Now, I have been invited to keynote the 6th International Conference on Dynamics Systems and Applications, Atlanta, Georgia, May 25 – 28, 2011, on the topic, Our fractal universe and applications. The abstract will be online shortly at Atlas Conferences website.

Cheers,

E. E. Escultura
(continued)

Putting the Institute … (continued)

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 IM stooped to ground level by posting this fake apology. The brief history of the Institute below and its present status explain this unusual behaviour.

(1) In 1986 I returned from the US after an absence of 15 years due to the political turmoil during that period and re-joined the Department 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 focus 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 mathematics.
(c) There are about 12 papers by the junior faculty on the applications of mathematics to other fields such as biology and computer science. They are also commendable contributions to the fields of applications of mathematics but not mathematics papers.

The last item 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 because the Institute’s website is viewed worldwide. Rather, it is a call for the College to do something with the only Institute that rides on the prestige of the College but refused to join the ranks of its world-class other Institutes.

If I had a glass roof over my head I would keep away from trouble.

Cheers,

E. E. Escultura

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This missing portion of the article, PUTTING THE INSTITUTE …, split into several parts, should be inserted after the paragraph, “These online articles …”:

(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) New Approach to Physics, under ISCID topic Brainstorms (5 pages):
(a) http://www.iscid.org/boards/ubb-get_topic-f-6-t-000607-p-5.html
(b) http://www.iscid.org/boards/ubb-get_topic-f-6-t-000607.html

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

Please note:

The last six paragraphs starting with “(1) False Proofs, http://falseproofs.blogspot.com/2006/06/e-e-escultura.html …” between the paragraph starting with, “These online articles …”

and the paragraph starting with, “This “apology” is, of course, fake.”

Sorry, for the inconvenience.

Cheers,

E. E. Escultura

After several years of publishing outright lies about Filipino inventors and scientists most of whom are long gone and triggerred by a malicious post from the Institute of Mathematics distorting and attacking my work in mathematics, the website WikiPilipinas: Pinoy Science Hoaxes, has been blocked. The entry on the homepage says:

User is blocked

From WikiPilipinas: The Hip ‘n Free Philippine Encyclopedia
Jump to: navigation, search
Your user name or IP address has been blocked.

The block was made by Wikimercky. The reason given is Intimidating behaviour/harassment.
===============
There’s, after all, ethics in cyberspace.

Cheers,

E. E. Escultura

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CONGRATULATIONS TO THE COLLEGE OF SCIENCE, UNIVERSITY OF THE PHILIPPINES!

I have seen the College website only very recently and am pleasantly surprised and quite happy that the College of Science has established itself as a Center of Excellence. Both the Marine Science Institute and the National Institute of Physics have hundreds of scientific papers in peer reviewed scientific journals since their founding in the early eighties with the much newer Institute of Biology having substantial publications as well. The other institutes of the college do not have publications pages in their websites although I know well published colleagues from some of them.

More power and greater achievements for the College!

E. E. Escultura

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By E. E. Escultura

1. On the nuclear crisis in Japan

Several countries along the Northwestern Pacific Rim have expressed concern over the possibility of contamination by airborne radioactive materials coming from the partial meltdown of the nuclear reactors in Fukushima, Japan. I offer some insights based on references [1], [2], [3], [4], [5], [6] below.

There is an elliptical wind cycle called the Northern Pacific Wind Cycle [5], [6], [7] that starts with the Trade Winds originating off the Coast of Ecuador [1], [2], [7] and going west along the Pacific edge of the Southern Hemisphere to the Southern Seaboard of the Philippines. It sweeps across the Philippines and curves North then Northeastward and grates Vietnam and the South and Southeast Coastal Regions of China and Korea. It crosses Japan and becomes the jet stream south of the Siberian Coast that crosses the Bearing Sea. Then it crosses the Alaskan Coast, curves southward and crosses Canada and the Tornado Belt of the US that extends from the Midwest to Texas. Then it and to complete the Northern Pacific Wind Cycle. (For full explanation of this phenomenon see [1], [2], [5])

Airborne radioactive materials ride in and follow the course of this cycle. By the time they reach the Northern American Continent considerable amount of it would have dissipated downwards into the Sea and upwards into the upper atmosphere rendering the radiation considerably weakened there. By the time the radioactive materials reach the Philippines, if any, radiation will be minimal and harmless.

2. More serious problems

However, nuclear meltdown is not the only problem posed by nuclear reactors that include the thorium reactors to be built in India under a US-Indian bilateral agreement. Thorium 232 is a radioactive material three times more abundant than the uranium isotope presently used in nuclear reactors and has a longer half-life than uranium. Though rarely discussed, the most serious problem posed by nuclear reactors in the long term is waste disposal because these nuclear fuels have half-life of at least 1800 years. Presently, nuclear wastes are dump into the ocean. Their containers are bound to erode and leak radiation sooner than their half life. There are known dump sites off the Eastern Coast of Africa that have already caught the attention of environmental groups, particularly, the Green Parties.

The nuclear disaster in Japan is bound to ruin the fishing industry that depends on fisting off the Eastern Coast of Japan. Since some fish species travel across oceans contaminated fish in this region are bound to contaminate the nearby coastal waters of the Pacific Ocean and China Sea. In fact, contaminated fish has been reported caught in Hong Kong just a couple of weeks after the disaster. This is of serious concern for the Philippines and I would recommend that Philippine authorities begin to monitor fish caught in the region.

3. Averting nuclear meltdown

Can a meltdown be avoided? Yes, but it will require rectification of present defective design of nuclear reactors. There should be no power shut off for a reactor to keep the water cooling system running and prevent overheating and meltdown. Installation of appropriate UPS (uninterrupted power service) will insure it. Moreover, there should be an automatic nuclear reaction shut off to suppress further heat generation and prevent meltdown in case the UPS fails. This can be accomplished by installing neutron absorbers (neutron of sufficiently low energy – 0.25 calories – split the uranium core nuclei causing nuclear fission that releases nuclear energy) such as cadmium or graphite rods that can be inserted suitably into the uranium core to choke off nuclear fission. (For the underlying physical explanation, see [3], [5])

Note on the PNRI research reactor in the Philippines

It should be noted that the nuclear disaster in Japan was caused not by the tsunami triggered by the earthquake that occurred there but by that earthquake itself. Therefore, the same disaster could occur at the Philippine Nuclear Research Institute research reactor in Diliman, Q.C., especially, since it is close to a branch of the Marikina Faults that passes under the University of the Philippines Library. I don’t know the power of the research reactor (it should be considerably less than that of a power reactor) but it should be an issue to worry about. I am recommending not a shutdown of the reactor but an automatic “choke” mechanism that would turn off the reactor in the event of an earthquake. Then it can be restarted again.

4. Safe alternatives

There are, of course, safe alternatives to nuclear and fossil fuels for generating energy. Under traditional power generation, we mention the following:

(1) Geothermal power plant with suitable design that recycles the geothermal steam and avoids release of sulfur that causes acid rain as well as damage to the topography of the ground due to distortion of ground surface.
(2) The use of ethanol for internal combustion engine. Ethanol comes from common crops such as cassava and sugar cane. More than 50% of idle land in the Philippines is suitable for growing cassava.
However, this would eat up that can be allotted food production.

(3) A new emerging technology uses the cold underground water for air conditioning and refrigeration. This is, of course, more environment friendly than conventional air conditioning and refrigeration. I have a friend in India who is venturing into this new technology. However, its usefulness as energy source is quite limited.

We now have a new category, GUT technology, that uses the clean, inexhaustible dark matter comprising over 95% of and abundant everywhere in the cosmos [3], [4], [5], [6]. GUT means grand unified theory [3], the basis of the design and construction of such technology [5], [6]. This technology uses the natural engine of the vortex flux of superstrings provided by the magnet. Among the existing GUT technology are the following [5]:
(a) The magnetic train. It uses two magnetic vortex fluxes of opposite spins that push each other and the train, one fixed magnet on the track and the other underneath the train. Such vortex fluxes are natural engines in dark matter.

(b) Another GUT technology which is at the design and prototyping phase is the electromagnetic car which I introduced in India in collaboration with colleagues there. It also uses similar natural engines.

(c) The present electric power plant is only partial GUT technology for it uses other source of energy side by side with the natural dark engine (magnetic vortex flux) such as gasoline, geothermal steam, tidal energy, river current and water falls.

There is a potential for building an electromagnetic power plant using magnets alone. I have received an invitation from an industrialist in India interested in its research and development.

Another electromagnetic engine based on GUT, specifically, the principles that account for magnetic levitation, can provide power to space vehicle that travels through the gravitational field of the Earth that extends far beyond the Moon or any cosmological body such as the Sun and any galaxy. This can revolutionize travel around Earth. Research and development for travel around Earth can be started now but for general space travel that is still way into the future.

References

[1] Escultura, E. E. Turbulence: theory, verification and applications, J. Nonlinear Analysis, A-Series: Theory, Methods and Applications, 2001, 47, 8, pp. 5955 – 5966.
[2] Escultura, E. E. The Pillars of the new physics and some updates, J. Nonlinear Studies, 2007, 14, 3, pp. 241 – 260.
[3] Escultura, E. E. The grand unified theory, contribution to the Felicitation Volume on the occasion of the 85th birth anniversary of Prof. V. Lakshmikantham, J. Nonlinear Analysis, A-Series: Theory: Method and Applications, 2008, 69, 3, pp. 823 – 831.
[4] Escultura, E. E. The mathematics of the grand unified theory, Proc. 5th World Congress of Nonlinear Analysts, J. Nonlinear Analysis, A-Series: Theory: Method and Applications, 2009, 71, pp. e420 – e431.
[5] Scientific natural Philosophy, an ebook in Press, Bentham Science Publishers.
[6] Lakshmikantham, V.; Escultura, E. E.; Leela, S. The Hybrid Grand Unified Theory, Atlantis (World Scientific): Paris, March 2009.
[7] (a) The Earth Atlas; (b) The Oceans Atlas, Dorling Kindersley: London, 1994.

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The order of the psot, Putting the Institute of Matheatics in its Place, has been missed up because of the limitatiion of post length. I am, therefore, posting, an improved and expanded version of the article as a series of posts in the right orfer below.

PUTTING THE INSTITUTE OF MATHEMATICS IN ITS PLACE

By

E. E. Escultura
Research Professor
GVP – Professor V. Lakshmikantham Institute for Advanced Studies
and Departments of Mathematics and Physics, GVP College of Engineering
JNT University, Madurawada, Visakhapatnam 540041, AP, India

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:

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 DDID 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: Methods
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”.

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 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.

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. It appears that Dr. Balmaceda is a new comer to internet mathematics forums where I have posted many, many responses to hundreds of bloggers.

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.

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.
============
I welcome any response to mt post - EEE

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Additonal section to the post, Putting the Instute of Mathematics in its Place:

Response to the Other Points Raised by the WikiPilipinas Article

(1) He (Dr. Escultura) has become infamous as a result of his claim to have disproved the longstanding mathematical problem known as Fermat’s Last Theorem (FLT).

Response: I did not simply claim: I published several papers in per reviewed international journals where I disproved FLT by way of countably infinite counterexamples (although only one counterexample is needed). Among my papers that carry my disproof of FLT are (mathematicians can distinguish prestigious journals and publishers from unupdated ones):

(a) Exact solutions of Fermat’s equation (A definitive resolution of Fermat’s last theorem, Nonlinear Studies, 1998, 5, 2, pp. 227 – 254 (published the by International Federation of Nonlinear Analysts).

(b) The new real number system and discrete computation and calculus, Neural, Parallel and Scientific Computations, 2009, 17, pp. 59 – 84 (published by Academic Publishers).

(c). The new mathematics and physics, Applied Mathematics and Computation, 2003, 138, 1, 145 – 169 (Published by Elsevier Science, Ltd, formerly North-Holland).

(d) The mathematics of the grand unified theory, Nonlinear Analysis, A-Series: Theory: Method and Applications, 2009, 71, pp. e420 – e431 (Elsevier Science, Ltd).

There are also two books that include my counterexamples to FLT:

(e) The Hybrid Grand Unified Theory, Atlantis (a division of Elsevier Science, Ltd; the book is distributed by World Scientific; co-authored with V. Lakshmikantham and S. Leela), March 2009. This book was a best seller in 2009 among all books in all disciplines of natural and social sciences distributed by World Scientific worldwide; it made it to No. 2 spot in the list for July that year.

(f) Natural Scientific Philosophy, Bentham Science Publishers (the leading ebook publisher today). This book is now, completed, edited and will be online anytime now.

Both books (e) and (f) were invited and peer reviewed.

(2) Dr. Escultura’s infamy is a result of not only his incorrect methods, but also his strange behavior.

Response: The only arbiter of scientific merit is the network of peer reviewed international scientific journals, not e bloggers, and in science and mathematics the test of the pudding, so to speak, is in the
publication. This “infamy” exists only in thee wishes of this anonymous blogger.

(3) (a) Dr. Escultura has been widely discredited and has remained silent when asked to support his
Ideas against specific criticism.

(b) Escultura also claims to have resolved other long standing problems in both physics and
mathematics, all of which, again, have been discredited.

(c) Dr. Escultura (claims) that he was nominated for a Nobel Prize in physics.

Response (a) The “criticisms” are based on blog posts; the blog sites cited have had no visitors during
the last 6 years after I responded to ALL of the online criticisms of mmy work (search escultura mathematician, escultura physicist, e. e.escultura).

(b(1)) My resolution of FLT is already documented above (section 1 of my full ressponse. The proof of the 250-year-old Goldbach’s conjecture is done and reproduced in 1(b) – 1(e).

(b(2)) The solution of the 200-year-old gravitation n-body and turbulence problems are in the papers,

(i) The solution of the gravitational n-body problem, Nonlinear Analysis, A-Series: Theory, Methods and Applications, 1997, 30, 8, pp. 5021 - 5032. (Elsevier Science Ltd)

(ii) Turbulence: theory, verification and applications, Nonlinear Analysis, A-Series: Theory, Methods and Applications, 2001, 47, 8, pp. 5955 – 5966 (Elsevier Science, Ltd).

b(2)(i) and b(20(II) are also quoted 1(b) – 1(e).

(c) The most recent verification of my nomination for the Noble Prize for Physicsin 2005 is the announcement by World Scientific, wworldwide distributor of my book, (item 1(e)) which specifically mentions it (search escultura hybrid grand unified theory). To-date NO ONE HAS
FOUND A SINGLE EVIDENCE THAT MY NOMINATION WAS A HOAX.

(4) (a) Dr. Escultura is far from being counted among the greatest mathematicians, and is not known
internationally.

(b) Dr. Escultura is apparently unaware that peer review and a critique of ones work is something to be welcomed as it only serves to call attention to errors that may be correctable and otherwise strengthen the body of knowledge known as mathematics.

Response: (a) When one has over 50 peer reviewed international publication and gets invited to keynote international conferences and world congresses and edit and write books, what would you call him? (By the way, I have just been invited by the German publisher, LAP LAMBERT
Academic Publishing GmbH & Co, to submit my Ph. D. thesis at the University of Wisconsin for publication, a very rare invitation, indeed. At this time, I publish books and papers only by invitation.
Moreover, NOT A SINGLE MATHEMATICIAN OR PHYSICIST HAS EVER REFUTED OR
DISMISSED ANY PART OF MY WORK, only anonymous bloggers
.
(b) Apparently, the blogger cannot distinguish mathematicians from bloggers and mathematics from blog posts; ; nor does he know that reviewers of mathematics and physics papers are mathematicians and physicists, not bloggers.

Cheers,

E. E. Escultura

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