In the recent issue of the International Journal of Mathematics and Consciousness, Dr. Corazza explores the basis of concept of mathematical infinity and looks at the self-interacting dynamics that give rise to large cardinal numbers.
by Maharishi University of Management, Fairfield, Iowa, USA, The Review
24 March 2018
Two years after the inaugural issue of the International Journal of Mathematics and Consciousness, a second issue has been published this fall, featuring a 200-page paper titled "The Magical Origin of Natural Numbers" by Maharishi University of Management (MUM) Professor Paul Corazza.
Dr. Corazza begins the article with the bold claim that the very largest mathematical infinities are not well understood in modern mathematics because the intuition underlying the modern-day concept of mathematical infinity is not sufficiently developed.
"The basic infinite set that everyone knows about is the collection of natural numbers 1, 2, 3, .... But what if we take the viewpoint that these numbers are like particles in space and ask, what is the underlying field that gives rise to this sequence of numbers?" he asked.
The article develops this idea, which is inspired by the way the ancient sages in many traditions viewed the emergence of numbers, and also by the way quantum field theory explains the appearance of particles in the universe.
The paper begins with a brief history of the study of the mathematical infinite. In the mid-20th century, the study of the different sizes of infinite sets eventually led to the discovery of notions of infinite that are so strong they can't be proven to exist at all; these infinities are known as large cardinals.
"A question that has puzzled researchers for decades is how to account for the presence of large cardinals in the universe," Dr. Corazza said. "Some new axiom seems to be needed."
The key to understanding large cardinals, he said, is to understand how the natural numbers arise through self-interacting dynamics of a special kind of transformation. "Studying these dynamics, we can observe how each natural number 1, 2, 3,. . . pops out, one at a time."
In the paper Dr. Corazza goes on to explain how a study of this same kind of special transformation applied to the universe itself can solve the problem of large cardinals. He proposes a new axiom, called the Wholeness Axiom, which postulates a very strong form of this kind of transformation.
"The Wholeness Axiom states that there is a fundamental transformation from the universe to itself, and in its first move, all these extraordinary large cardinals are seen to emerge," he said.
The new issue is available online for free at ijmac.com, or a print version can be purchased in the University Store in the Argiro Student Center at Maharishi University of Management, Fairfield, Iowa, USA.
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