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 and 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 “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 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 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 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 – 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 Wiles’ 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 Wiles’ supporters have done massive promotion of his proof including publication of some books about it. Unless they address point blank my specific criticisms of the proof, it will not prosper.

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 or 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/