"The scandal-driven effort to shake the Arroyo presidency appears to have fizzled out".and this is because:

"The "revelations" were, in the end really confirmations of what the public knew: jueteng was the basis of the politics of patronage since time immemorial and, as the audiotapes suggest, our electoral process remains flawed and vulnerable."He has this to say about the cheating charge

"Granting that voting outcomes in Lanao del Sur were massaged, could it have altered the final outcomes? The best counter-evidence is that Barbers lost and Biazon won. Therefore, if the numbers were massaged, they were not massaged well enough to alter the outcomes in the closely fought battle for the last slot in the senatorial win column."And on the self appointed saviors of our nation;

"Besides, the "heroes" we were supposed to flock to were flawed characters. Some of them are patently insane. Some are clearly impostors".We had the same reaction to the Estrada offer:

Then comes Joseph Estrada, offering to head a junta.

That is the last nail in the coffin of this chaotic blitz. The whole effort is now doomed to be buried in the shallow grave of utter hilarity.

Some cautionary words for the present administration:

"But taking the wind from the sails of this badly-designed blitz is the easy part.

The more difficult part is climbing out of the hole this whole episode dug for us, restoring credible leadership to a battered nation and restoring a path to a future where institutions work and the economy functions. Although political survival is more or less assured, the integrity issues must be dealt with convincingly".

## 11 comments:

I too am very amused by his excellency Professor Escultura, it's nice to visit his website once in a while to read his guest book..He mentions a 'fallout' in October, I guess this is because the Nobel Prize for Physics will be announced....sana nga manalo na para tumahimik na sya....

Saturday 08/27/2005 3:10:37am

Name: E. E. Escultura

Homepage:

E-Mail:

Referred By: Just Surfed In

City/Country:

Comments: Dear Gareth,

Please tell your friends in the UP Math Department and their writing coach from PCIJ that the ball game is over and the fall out will start coming in October.

Thanks.

E. E. Escultura

--------------------------------------------------------------------------------

Thursday 08/25/2005 6:24:30pm

Name: Gareth

Homepage:

E-Mail:

Referred By: Just Surfed In

City/Country: Australia

Comments: Dr Escultura, your published works would have a greater chance of winning the Nobel Prize for Literature than the Nobel Prize for Physics.

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Thank you for anticipating another Nobel possibility, in literature.

I think your friends at the Math Department will not have any headway because they cannot sign their appeal and so the Academy members would not know who is making the appeal. If they check the Math website there won't be name recognition either. Plus, what they did will haunt them back come October along with the writing coach from PCIJ who misrepresented the Philippine Media.

What do you think of my previous message on my message board?

E. E. Escultura

I can see Alex's blogsite pcij still squeaking behind my posts with new colorful borloloy amd the last post of June 13, 2006, the only post of that year.

E. E. Escultura

It looks like only Mr. Choco and Alex Pabico are still squeaking the echoes of past chaotic thoughts behind the huge volume of discussion of my work on the various blogs and websites across the Internet where I have the last words. Mr. Choco must be seeing things and needs psych attention. I never commented on Alex Magno. If I were to comment now I would congratulate him for taking the summit of Mt. Oppe at no sweat.

Cheers.

E. E. Escultura

Alex must have run out of things to write he fills his column by quoting himself.

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 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.

E. E. Esccultura

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 0.99…, 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.

E. E. Escultura

Needless to say, none of my criticisms of 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 pieces and rearranged without distortion they can be reconstituted into a ball the size of Earth. This is a topological contradiction in R^3.

E. E. Escultura

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.

E. E. Escultura

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..

E. E. Escultura

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.

Finally, we note that all the issues about the new real number system, my critique of Wiles’ proof of FLT and my counterexamples to FLT to prove it falls have been debated thoroughly in cyberspace during the last 12 years and ALL resolved COMPLETELY in my favor. Not a single hole has been punched on my entire work.

E. E. Escultura

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., 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 Fermat’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/

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