It seems almost like Monty Python. Recall their Spanish Inquisition sketch:

*Chapman: *I* don’t know – Mr Wentworth just told me to come in here and say that there was trouble at the mill, that’s all – I didn’t expect a kind of Spanish Inquisition.*

(*JARRING CHORD) (The door flies open and Cardinal Ximinez of Spain (Palin) enters, flanked by two junior cardinals. Cardinal Biggles (Jones) has goggles pushed over his forehead. Cardinal Fang (Gilliam) is just Cardinal Fang) *

*Ximinez: NOBODY expects the Spanish Inquisition! Our chief weapon is*

suprise…surprise and fear…fear and surprise…. Our two

weapons are fear and surprise…and ruthless efficiency…. Our

*three* weapons are fear, surprise, and ruthless efficiency…and an

almost fanatical devotion to the Pope…. Our *four*…no…

*Amongst* our weapons…. Amongst our weaponry…are such elements as

fear, surprise…. I’ll come in again. (Exit and exeunt)

suprise…surprise and fear…fear and surprise…. Our two

weapons are fear and surprise…and ruthless efficiency…. Our

*three* weapons are fear, surprise, and ruthless efficiency…and an

almost fanatical devotion to the Pope…. Our *four*…no…

*Amongst* our weapons…. Amongst our weaponry…are such elements as

fear, surprise…. I’ll come in again. (Exit and exeunt)

Think of a similar scenario with the announced Philippine Energy Police. “No one expects the Energy Police!”

In other news: it’s springtime, politically, that is, for Senator Juan Ponce Enrile: Newsstand points out what a key player he’s been, and remains. Former senator Ernesto Maceda thinks Enrile, his old chum, is still with the opposition; he also suggests that the withdrawal of Rep. Eulogio Magsaysay was due to the politically-powerful Iglesia ni Cristo. Columnist Armando Doronila takes a more sober look at what the recent actions of the two (Enrile and Magsaysay) really indicate, politically. The Philippine Daily Inquirer simply calls it shenanigans in its editorial.

In the punditocracy, Jarius Bondoc, who has been a strong supporter of the President, now asks, is it all worth it? He points out that,

*[Referring to the President’s announcement in 2003 not to run again for office, because she was a cause for division] Arroyo read right. Not only is the nation deeply divided. So are her own allies, who now are fighting over who should get bigger slabs of pork or more protÃƒÂ©gÃƒÂ©s appointed. In the end, they will not fight for her but for themselves. She will be all alone.*

*Is the Presidency worth all this? Anybody in ArroyoÃ¢â‚¬â„¢s shoes would be well advised to contemplate St. MarkÃ¢â‚¬â„¢s evangelization: “For what shall it profit a man, though he win the world, if he lose his soul?” *

What accounts for Bondoc’s publicly faltering faith?

Patricio Diaz thinks that the President’s creation of a commission to study and propose constitutional changes is actually a thinly-disguised attempt to draft a new charter according to her own wishes, because she doesn’t trust Congress. Australian policy wonk and columnist Peter Wallace pleads for Filipinos to embrace globalism.

The blogosphere has the lawyers all abuzz. Punzi recounts a lunch in which he and some friends bewailed the nitpicking on rules going on in the House. Edwin Lacierda looks at what his fellow lawyers have been saying on TV, and debates some of their points. Other bloggers range from political venting, too -in the case of Gari, against the country’s bloated debt- to more sociological observations, such as Sassy Lawyer’s noticing that cheap DVD player sales are up. Leon Kilat has an update on the gerrymandering attempts in Cebu province (which I wrote about some time ago).

Random Thoughts has a clever idea: the Salen-ga Awards, which he says, are

*In honor of Prof. Edgardo E. Escultura, I am proposing the establishment of the Salen-ga awards. The Salen-ga awards will be given to that exemplary Filipino who has contributed to the development of Filipino’s interest in science through the propagation of their crackpot theories…. I propose that the award be given every 5th of May to commemorate the day when the Manila Times reported that Prof. EEE had disproven Andrew Wiles proof regarding Fermat’s Last theorem. *

The Jason Journals reports the blogger’s experience not once, but twice, with Succubi.

Blogjam dot cow insists even if you get attached to the snails you’ve caught, they make a delicious risotto. From the comments though, it seems eating slugs can be bad for the brain, and that tarantula omelets don’t sound so hot.

And finally, via BuzzMachine, Doc Searls condemns “splogs.”

“(They are also prohibited from using these vehicles) on Sundays, legal holidays, out of regular hours or out of official routes,” he (Angelo Reyes) said. Official routes? What the f*** are official routes?

Also the sign painted on the side of government vehicles reads, “For official use, also”

The energy savings in the OPS has more to do with the fact that Bunye is not allowed to work and say as much as he used to. People in Malacanang bite their nails when the lights are on at his office late at night. Who knows what booboo Bunye is cooking up again. DENR should come in a close second if only someone can muzzle Defensor.

hahahaa kulit

must be a very slow news day. kakabagot na din.

i challenge you to use lumberjack next time. =) i enjoy your reading your blog. keeps me somewhat updated with pinoy politics.

ice breaker:

nothing is more construed more than a weasel who dresses in sheep’s clothing and pretends to be a wolf…ika nga, we are seeing an “ENRONIZATION” of philippine politics…insider-trading inside the politburo where power is the commodity and mud-slinging tactics are basics of climbing the “pyramid”…buti pa nga si Salen-ga kahit di ka sigurado pinagmalaki nya ang Pilipino

Nobody can take seriously a guy who has “Ponce” in his name!

Two Fatal Defects in Andrew Wilesâ€™ Proof of FLT

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 proving that it is false.

The remedy for the real number system is given in the paper, The new real number system and discrete computation

and calculus, Neural, Parallel and Scientific Computation, 17 (2009), 59 â€“ 84. The counterexamples are given in

the article, Exact solutions of Fermatâ€™s equation (Definitive resolution of Fermatâ€™s last theorem), Nonlinear Studies,

5(2), 1998, pp 227 â€“ 254.

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. The remedy is in the appendix to the paper, The generalized integral as dual to Schwarz distribution.. In general, any vacuous concept yields a contradiction.

Reply to Bart van Donselaarâ€™s article, Edgar E. Escultura and the inequality of 1 and 0.999…

1) The reason Bart van Donselaar cannot see why 1 and 0.99â€¦ are distinct is he looks at them as concepts in oneâ€™s mind. He missed what David Hilbert already knew almost a century ago that such concepts are ambiguous being unknown to others. Therefore, they cannot be the subject matter of mathematics. 1 and 0.99.. are distinct objects in the real world like orange and apple and to write the equation orange = apple is simply nonsense.

2) He could not understand why I â€œclaimâ€ that FLT is false and Wilesâ€™ proof is incorrect since he says the proof is admired Worldwide (actually only four or five mathematicians do). Well, an error is an error and I hope he has seen my article, Two fatal defects of Wilesâ€™ proof of FLT, posted in several blogsites and websites.

3) He relies on dictionary definitions of concepts which is quite inappropriate in mathematics. Constructivism in my sense has nothing to do with intuitionism. It simply avoids sources of ambiguity and contradiction.

4) He claims that constructivists have not found hard evidence of defects in standard mathematics. The evidences is just under his nose: Felix Brouwersâ€™ counterexample to the trichotomy axiom, Putnam and Benacerraf, Philosophy of Mathematics, Cambridge University Press, 1985; I also have my own version in, The new real number system and discrete computation and calculus, Neural, Parallel and Scientific Computation, 17(2009), 59 â€“ 84.

5) He thinks mathematicians (he probably means some mathematicians) are happy with traditional mathematics for there is nothing wrong with it. Well, I wish them continued bliss of innocence.

6) He doubts that I have solved the gravitational n-body problem. I did in the paper, The solution

of the gravitational n-body problem, Nonlinear Analysis, Series A: Theory, Methods and Applications,

30(8), Dec. 1997, 521 â€“ 532; the journal is a publication of Elsevier Science Ltd. based there in

Amsterdam.

7) He claims he can compute with nonterminating decimals. Such computation depends on the digits and most of the digits of a nonterminating decimal are unknown. His claim is based on imprecise thinking. At any rate, I would like to see how he did this impossible feat. Can he add sqrt2 and sqrt3 and write the sum precisely? We can only approximate a nonterminating decimal or result of computation with nonterminating decimals.

8) He also cannot understand why it is impossible to verify whether a nonterminating decimal is periodic or nonperiodic. Clue: the digits are infinite and we cannot look at all of them to check.

9) He chastises me for writing difficult mathematics and physical theory. New ideas are initially difficult but if they are correct they will pass the test of time. Initial critics of my work had a hilarious time calling me a crackpot, lunatic, moron, etc., but where are they now? My posts had been picked up by many blogs and websites and my papers have been used by renowned publications such as the Encyclopedic Dictionary of Mathematics and Elsevier Science. A number of them made it to the top 25 most downloaded papers published by Elsevier Science, online at Science Direct archives. Only Wikipedia Encyclopedia have barred my posts entirely because the administrator explains that it requires unanimity of ideas. Therefore, only Wilesâ€™ proof is published there and kept in its archives. HaloScan and DLMSY also have rejected my posts but continue to publish criticisms of my work without my response because they cannot stand contrary opinion.

10) I notice lately, that Wilesâ€™ supporters have done massive promotion of his proof including publication of some books about it. It will not prosper unless they address my specific criticisms of the proof point blank.

Conclusion.

The article is not well thought out and uses rumors and gossips. For example, it quotes Alecks Pabico an amateur journalist who lost his job as a journalist for commenting on an issue he knows nothing about and writing about it which he posted in blogsites and websites across the internet.

Bart is unsure of his ideas, makes claims he cannot verify and resorts to name-dropping which makes me doubt if he, like Alecks, understands what he is writing about.

E. E. Escultura

Research Professor

V. Lakshmikantham Institute for Advanced Studies

GVP College of Engineering, JNT University, Visakhapatnam, India

http://users.tpg.com.au/pidro/

Summation of the Debate on the New Real Number System and the Resolution of Fermatâ€™s last theorem â€“ by E. E. Escultura

The debate started in 1997 with my post on the math forum SciMath that says 1 and 0.99â€¦ 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 Wilesâ€™ 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, Donâ€™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 at SciMath who did not debate me online but through e-mail. We debated for about a year and I learned much from 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.

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 0.99â€¦, to which I responded with the article, Reply to Bart van Donselaarâ€™s article, Edgar E. Escultura and the inequality of 1 and 0.99â€¦; a website on the Donselaarâ€™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 Wilesâ€™ 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 = 0.99â€¦ 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 0.99â€¦; 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 pieces 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 â€“ 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 Wilesâ€™ 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 Wilesâ€™ 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.

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), 68â€“72.

[3] Escultura, E. E. (1997) Exact solutions of Fermat’s equation (Definitive resolution of Fermatâ€™s last theorem, 5(2), 227 â€“ 2254.

[4] Escultura, E. E. (2002) The mathematics of the new physics, J. Applied Mathematics and Computations, 130(1), 145 â€“ 169.

[5] Escultura, E. E. (2003) The new mathematics and physics, J. Applied Mathematics and Computation, 138(1), 127 â€“ 149.

[6] Escultura, E. E., The new real number system and discrete computation and calculus, 17 (2009), 59 â€“ 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., The generalized integral as dual of Schwarz distribution, in press, Nonlinear Studies.

[10] Escultura, E. E., Revisiting the hybrid real number system, Nonlinear Analysis, Series C: Hybrid Systems, 3(2) May 2009, 101-107.

[11] Escultura, E. E., Lakshmikantham, V., and Leela, S., The Hybrid Grand Unified Theory, Atlantis (Elsevier Science, Ltd.), 2009, Paris.

[12] Counterexamples to Fermatâ€™s last theorem, http://users.tpg.com.au/pidro/

[13] 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/

CLARIFICATION ON THE COUNTEREXAMPLES TO FERMATâ€™S LAST THEOREM

By E. E. Escultura

Although all issues related to the resolution of Fermatâ€™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.99â€¦ , N = 0, 1, â€¦, 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.99â€¦ Therefore, the decimal integers are integers [3]. The kernel of this isomorphism is (d*,1) and its image is (0,0.99â€¦). Therefore, (d*)^n = d* since 0^n = 0 and (0.99â€¦)^n = 0.99â€¦ since 1^n = 1 for any integer n > 2.

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

3) Then the exact solutions of Fermatâ€™s equation are given by the triple (x,y,z) = ((0.99â€¦)10^T,d*,10^T), T = 1, 2, â€¦, that clearly satisfies Fermatâ€™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, â€¦, the triple (kx,ky,kz) also satisfies Fermatâ€™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), 68â€“72.

[3] Corporate Mathematical Society of Japan , Kiyosi ItÃ´, 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 Fermatâ€™s last theorem, 5(2), 227 â€“ 2254.

[5] Escultura, E. E. (2002) The mathematics of the new physics, J. Applied Mathematics and Computations, 130(1), 145 â€“ 169.

[6] Escultura, E. E. (2003) The new mathematics and physics, J. Applied Mathematics and Computation, 138(1), 127 â€“ 149.

[7] Escultura, E. E., The new real number system and discrete computation and calculus, 17 (2009), 59 â€“ 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 Fermatâ€™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/