The Wholeness Axiom “asserts in a mathematical way that the universe arises from transformational dynamics of wholeness that preserve the essential nature of wholeness."
by Maharishi International University, Fairfield, Iowa, USA, Achievements
22 February 2020
A new article, “Indestructibility of Wholeness,” by Maharishi International University (MIU) Professor Paul Corazza will soon appear in the mathematics journal Fundamenta Mathematicae.
The article continues Dr. Corazza’s 30-year project to fine-tune the foundation of mathematics in a way that gives a proper account of the mathematical infinite, drawing on principles of Maharishi Vedic Science.
In this new article, Dr. Corazza proves that once the fundamental axioms of mathematics are enriched in a way that makes them “aware of their own wholeness,’’ the usual manipulations that mathematicians do to transform the mathematical universe in sometimes dramatic ways is incapable of undermining the wholeness known in the original universe.
Regarding the so-called “enrichment” of the fundamental axioms, Dr. Corazza says, “As they are understood today, the foundational axioms are not strong enough to account for the presence of certain kinds of exotic infinities in the mathematical universe – infinities that play a crucial role in many areas of mathematical research.”
Because of this limitation, in 1990 Dr. Corazza formulated the Wholeness Axiom, which he said “asserts in a mathematical way that the universe arises from transformational dynamics of wholeness that preserve the essential nature of wholeness.
Adding the Wholeness Axiom to the list of standard axioms provides the account of mathematical infinities – even the exotic ones – that has been missing for so long.”
Dr. Corazza’s new article addresses a challenge that any new mathematical foundation must face: Does the new foundation survive after modern techniques are applied to create new universes?
An old question, solved by such techniques, was to determine the exact infinite size of the real number line. Stanford professor Paul Cohen showed in the 1960s that for almost any imaginable infinite size, there is a universe in which the real number line has that exact size.
So what happens to the Wholeness Axiom in those new universes? “If this new axiom is as good as expected, the Wholeness Axiom will hold true in all such universes,’’ Dr. Corazza said. “And this is what I was able to prove in my paper. The Wholeness Axiom survives all such transformations of the universe.”
The paper is available for free via the online research network Research Gate at bit.ly/333JfJu.
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