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)
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 protégés 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 Arroyo’s shoes would be well advised to contemplate St. Mark’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.
June 1st, 2006 at 9:25 am
MY STRATEGY FOR CAPTURING FLT.
I wondered why FLT remained unresolved for centuries and concluded that its underlying fields –foundations, number theory and the real number system – are defective. Therefore, I embarked on their critique-rectification that yielded the following:
1) There are sources of contradiction in mathematics including ambiguous and vacuous concepts, large and small numbers (depending on context), unbounded or infinite set and self-reference. Here is an example of vacuous concept: A triquadrilateral is a plane figure with three vertices and four edges. The Richard paradox is an example of self-reference: The barber of Seville shaves those and only those who do not shave themselves; who shaves the barber? Incidentally, the indirect proof is flawed, being self-referent.
2) Among the requirements for a contradiction-free mathematical space are the following:
a) It must be well-defined by consistent axioms and every concept must be well-defined by them. A concept is well-defined if its existence, properties and relationship with other concepts are specified by the axioms. A false proposition cannot be an axiom as it introduces inconsistency. For example, this proposition cannot be used as an axiom of any mathematical space: There exists a triangle with four edges.
b) The rules of inference (mathematical reasoning) must be specific to and well-defined by its axioms.
c) Any proposition involving the universal or existential quantifiers on infinite set is not verifiable and, therefore, cannot be used as an axiom for it would not endow certainty to the conclusion of a theorem.
3) The real number system does not satisfy the requirements for a contradiction-free mathematical space. In particular, the trichotomy axiom is false since it is equivalent to natural ordering which the real number system has none because most of its concepts are ill-defined. Therefore, the real number system is ill-defined or nonsense and FLT being fomulated in it is also nonsense. Consequently, to resolve FLT the real number system must be fixed first and FLT must be reformulated in it. Andrew Wiles failed to do this and his work collapses althogether.
4) It is alright to introduce ambiguity provided it is ‘approximable” by certainty. For example, a nonterminating decimal is ambiguous since not all its digits are known but it can be approximated by a segment at the nth decimal digit at margin of error 10^-n.
5) The rectification is to build a new real number system R* with three simple axioms and two operations + and x: 1) R* contains the basic integers 0, 1, …, 9, and the operations + and x are well-defined by 2) the addition and 3) multiplication tables of arithmetic that we learned in primary school. The rest of the elements of R* are the terminating decimals first which are later extended to the nonterminating decimals.
A new real number is well-defined if every digit is known or computable, i.e., there is some rule or algorithm for determining it uniquely.
6) The new elements of the new real number system are the dark number d* = 1 – 0.99… - N – (N–1), N = 0, 1, … (the ordinary integers), and u* the equivalence class of divergent sequences. Then the well-defined real numbers are embedded in R* as terminating decimals and the integers as integral parts of decimals. Then the mapping 0 – > d*, N – > (N–1).99…, the new integers, establishes the similarity between the integers and the new integers.
7) Then the counterexamples to FLT are as follows: Let x = (0.99…)10^T, y = d*, z = 10^T, where T is an ordinary integer, T = 1, 2, … Then x, y, z satisfy Fermat’s equation, for n > 2,
x^n + y^n = z^10.
Moreover, if k = 1, 2, …, is ordinary integer, kx, ky, kz also satisfy Fermat’s equation. They are the counterexamples to FLT. They prove that FLT is false and Wiles is wrong.
The critique-rectification of the underlying fields of FLT, the construction of the counterexamples and applications of this new methodology, especially in physics, are developed in the following articles in renowned refereed international journals and conference proceedings:
[18] Escultura, E. E. (1996) Probabilistic mathematics and applications to dynamic systems including Fermat’s last theorem, Proc. 2nd International Conference on Dynamic Systems and Applications, Dynamic Publishers, Inc., Atlanta, 147 – 152.
[19] Escultura, E. E. (1997) The flux theory of gravitation (FTG) I. The solution of the gravitational n-body problem, Nonlinear Analysis, 30(8), 5021 – 5032.
[20] Escultura, E. E. (1998) FTG VII. Exact solutions of Fermat’s equation (Definitive resolution of
Fermat’s last theorem, J. Nonlinear Studies, 5(2), 227 – 254.
[21] Escultura, E. E. (1999) VIII. Superstring loop dynamics and applications to astronomy and biology, J. Nonlinear Analysis, 35(8), 259 – 285.
[22] Escultura, E. E. (1999) FTG II. Recent verification and applications, Proc. 2rd International Conf.: Tools for Mathematical Modeling, St. Petersburg, vol. 4, 74 – 89.
[23] Escultura, E. E. (2000) FTG IX. Set-valued differential equations and applications to quantum gravity, Mathematical Research, Vol. 6, 2000, St. Petersburg, 58 – 69.
[24] Escultura, E. E. (2001) FTG X. From macro to quantum gravity, J. Problems of Nonlinear Analysis in Engineering Systems, 7(1), 56 – 78.
[25] Escultura, E. E. (2001) FTG XI. Quantum gravity, Proc. 3rd International Conference on Dynamic Systems and Applications, Atlanta, 201 – 208.
[26] Escultura, E. E. (2001) FTG. XII. Turbulence: theory, verification and applications, J. Nonlinear Analysis, 47(2001), 5955 – 5966.
[27] Escultura, E. E. (2001) FTG III: Vortex Interactions, J. Problems of Nonlinear Analysis in Engineering Systems, Vol. 7(2), 30 – 44.
[28] Escultura, E. E. (2001) FTG IV. Chaos, turbulence and fractal, Indian J. Pure and Applied Mathematics, 32(10), 1539 – 1551.
[29] Escultura, E. E. (2002) FTG V. The mathematics of the new physics, J. Applied Mathematics and Computations, 130(1), 145 – 169.
[30] Escultura, E. E. (2003) FTG VI. The theory of intelligence and evolution, Indian J. Pure and Applied Mathematics, 33(1), 111 – 129.
[31] Escultura, E. E. (2003) FTG XVII: The new mathematics and physics, J. Applied Mathematics and Computation, 138(1), 127 – 149.
[32] Escultura, E. E. (2003) FTG XVIII. Macro and quantum gravity and the dynamics of cosmic waves, J. Applied Mathematics and Computation, 139(1), 23 – 36.
[33] Escultura, E. E. (2001) FTG. XIV. The mathematics of chaos, turbulence, fractal and tornado breaker, deflector and aborter, Proc. Symposium on Development through Basic Research, National Research Council of the Philippines, University of the Philippines, 1 – 13.
[34] Escultura, E. E. FTG XIX. Recent results, new inventions and the new cosmology, accepted, J. Problems of Nonlinear Analysis in Engineering System.
[35] Escultura, E. E. FTG XV. The new nonstandard analysis and the intuitive calculus, submitted.
[36] Escultura, E. E. (2002) FTG VI. The philosophical and mathematical foundations of FLT’s resolution, rectification and extension of underlying fields and applications, accepted, J. Nonlinear Differential Equations.
[37] Escultura, E. E. (2002) FTG XXII. Extending the reach of computation, submitted.
[38] Escultura, E. E. (2003) The theory of learning and implications for Math-Science Education, submitted.
[39] Escultura, E. E. (2003) FTG XXIII. The complex plane revisited, accepted, Journal of Nonlinear Differential Equations.
[40] Escultura, E. E. (2002) FTG XXIV. Columbia: the crossroads for science, accepted, J. Nonlinear Differential Equations.
[41] Escultura, E. E. (2003) FTG XXV. Dynamic Modeling and Applications, Proc. 3rd International Conference on Tools for Mathematical Modeling, State Technical University of St. Petersburg, St. Petersburg.
[42] Escultura, E. E. (2004) FRG XXVII – XXVIII. Part I. The new frontiers of mathematics and physics. Part I. Theoretical Construction and Resolution of Issues, Problems and Unanswered Questions.
[43] Escultura, E. E. (2005) FRG XXVII – XXVIII. The new frontiers of mathematics and physics. Part II. The new real number system: Introduction to the new nonstandard analysis, Nonlinear Analysis and Phenomena, II(1), January, 15 – 30.
[44] Escultura, E. E. (2005) FTG XXVI. Dynamic Modeling of Chaos and Turbulence, Proc. 4th World Congress of Nonlinear Analysts, Orlando, June 30 – July 7, 2004.
[45] Escultura, E. E. FTG. XXVII (2005). The theory of everything, Nonlinear Analysis and Phenomena, II(2), 1 – 45.
[46] Escultura, E. E. Escultura (2006) FTG XXXIV. Foundations of Analysis and the New Arithmetic,
Nonlinear Analysis and Phenomena, January 2006.
[47} Escultura, E. E. FTG XXXV (2006) The Pillars of FTG and some updates, Nonlinear Analysis and Phenomena, III(2), 1 – 22.
[48] Escultura, E. E. FTG XXXVI (2006) The New Nonstandard Calculus, accepted, Nonlinear Analysis.
For more info see my website: http://home.iprimus.com.au/pidro/
TAKE IDEAS FROM THE TOP, NOT FROM THE FLAT OF ONE’S FOOT.
E. E. Escultura
June 11th, 2006 at 9:02 am
Correction: Fermat’s equation should read:
x^n + y^n = z^n, n > 2.
E. E. Escultura