Reality has changed, jed; wake up!!!

E. E. Escultura

Reply to Bart van Donselaar’s article, Edgar E. Escultura and the inequality of 1 and 0.999…

1) The reason Bart van Donselaar cannot see why 1 and 0.99… are distinct is he looks at them as concepts in one’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. The right subject matter for mathematics are objects in the real world everyone can see, e.g., symbols. 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 “claim” that FLT is false and Wiles’ 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 Wiles’ proof of FLT, posted in several blogs and websites.

3) He relies on dictionary definitions of concepts which is quite inappropriate for 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 Brouwers’ 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 – 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 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 – 532; the journal is a publication of Elsevier Science Ltd. based there in
Amsterdam.

7) He claims he can compute with nonterminating decimals. Try adding sqrt2 and sqrt3 and write the precise sum. I would like to see how he does this impossible feat. His claim is based on imprecise thinking.

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. My book co-authored with Profs. V. Lakshmikantham and S. Leela released last March that applies the new real number system to mathematics, physics and other fields has now made it to #2 on World Scientific’s best sellers list in July from #48 last June. I really doubt if people buy books they don’t understand. Therefore, the problem of understanding the new real number system is elsewhere not in my work.

10) I notice lately, that Wiles’ 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 and posting it on blog 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.

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., Lakshmikantham, V., and Leela, S., The Hybrid Grand Unified Theory, Atlantis (Elsevier Science, Ltd.), 2009, Paris.
[11] Counterexamples to Fermat’s last theorem, http://users.tpg.com.au/pidro/
[12] 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
http://users.tpg.com.au/pidro/