PAUL CORAZZA
Articles discussing connections between Maharishi Vedic Science and foundational aspects of mathematics and computer science.
Articles on Maharishi Vedic Science and Mathematics

Mathematics of Pure Consciousness
This paper was presented at the WAVES (World Association for Vedic Studies) July 31 -- Aug 3, 2014, at Maharishi University of Management, Fairfield, IA. Slide presentation available here

Adi Shankara, the foremost exponent of Advaita Vedanta, declared "Brahman alone is real, the world is mithya (not independently existent), and the individual self is nondifferent from Brahman." A fundamental question is, How does the diversity of existence appear when Brahman alone is? The YogaVasistha declares, "The world appearance arises only when the infinite consciousness sees itself as an object." Maharishi Mahesh Yogi has elaborated on this theme: Creation is nothing but the dynamics of pure consciousness, which are set in motion by the very fact that pure consciousness is conscious; being conscious, it assumes the role of knower, object of knowledge and process of knowing. To help clarify these issues, we offer a mathematical model of pure consciousness. We show that in a natural expansion of the universe of mathematics by ideal elements, there is a unique set Ω whose only element is itself, and which is equal to the set of all possible transformations from itself to itself. All "real" mathematical objects can be seen to arise from the internal dynamics of . All differences among numbers, and among all mathematical objects, are seen to be ghostly mirages, hiding their true nature as permutations of one set, Ω.

Magical Origin of the Natural Numbers
The paper was presented at the MUM Faculty Research Seminar, April 26, 2013, at Maharishi University of Management, Fairfield, Iowa. The paper suggests a new version of the Axiom of Infinity that incorporates the intuition that the underlying reality of "the infinite" is self-referral dynamics of an unbounded field. Taking this step, it is shown, leads naturally to a solution to the Problem of Large Cardinals. Original power point slides are here.

Recent Progress in the Mathematical Analysis of the Infinite
This paper was presented at the 2012 faculty symposium with Maharaja Adhiraj Rajaraam, entitled "Maharishi Vedic Science: Illuminating the Cutting Edge of Modern Science," held at Maharishi University of Management, in Fairfield Iowa. The paper surveys the history of the mathematical study of the infinite and how a solution to a modern-day mathematical problem about the infinite has been solved using the principles described in Maharishi Vedic Science. The paper will appear in the proceedings of the conference. Original power point slides are here.

The next two articles have appeared in P. Corazza, A. Dow (Eds.), Consciousness-Based Education: A Foundation for Teaching and Learning in the Academic Disciplines: Vol. 5. Consciousness-Based Education and Mathematics, 2011, MUM Press.

Vedic Wholeness and the Mathematical Universe: Maharishi Vedic Science as a Tool for Research in the Foundations of Mathematics

This is a very detailed discussion of Maharishi Vedic Science and the set theory of the infinite. The article gives a survey of ideas of set theory and the mathematics of the infinite, leading up to the modern-day theory of large cardinals. The article shows how the Problem of Large Cardinals -- the problem of determining how these enormous large cardinals arise and how they can be accounted for (since they cannot be proven to exist from the known foundational axioms) -- can be addressed, and even solved, through an application of Maharishi Vedic Science.

The Wholeness Axiom.

This is a presentation of Maharishi Vedic Science and the mathematical infinite written originally for mathematicians, but is reasonably readable by anyone. The article offered fundamental intuitions about the universe, which expand upon known intuitions derived from the work of Cantor and other more modern researchers, as the basis for introducing a new axiom in mathematics, the Wholeness Axiom. The Wholeness Axiom embodies, in mathematical language, the essential features of the dynamics of wholeness in Maharishi Vedic Science: Wholeness is an all-inclusive totality that moves within itself, knows itself, remains unchanged by its own self-transformations, unfolds on the basis of a collapse of its unbounded nature to its point, and that is present at every point in creation. The paper shows how these principles are given expression in mathematics, and how this expression, in the form of the Wholeness Axiom, solves the Problem of Large Cardinals.

Articles on Maharishi Vedic Science and Computer Science

The next two articles have appeared in K. Levi, P. Corazza (Eds.), Consciousness-Based Education: A Foundation for Teaching and Learning in the Academic Disciplines: Vol. 8. Consciousness-Based Education and Computer Science, 2011, MUM Press.

The Self-Referral Dynamics Of Computation: An Introduction To A Course On Algorithms

This introduction to a graduate course on Algorithms begins with the question "What is computation?" We ask whether Nature's way of computing all that it accomplishes has the same algorithmic character as the mathematical tools that are used in science to model Nature. We review the perspectives offered by Maharishi Vedic Science and recent discoveries in quantum field theory, both of which conclude that Nature's computational dynamics are based on self-referral performance at a hidden, unmanifest level. We then show how the very mathematics of computation has its basis in self-referral dynamics by showing that every computable function may be defined as the fixed point of an operator on a vast (and therefore, in a sense, unmanifest) function space.

Computable Functions In The Theory Of Algorithms: Collapsing Infinity To A Point

This introduction to a graduate course on Algorithms shows how the class of functions that are actually used in Computer Science arises from a much vaster class of number-theoretic functions through a sequence of "collapses" to successively narrower function classes. The vast majority of number-theoretic functions are essentially indescribable. By contrast, it is possible to know in full detail the behavior of the functions belonging to the much more restricted class of definable functions. Restricting further to the class of computable functions, it becomes possible to describe the behavior of each function in terms of a computer program; that is, one can describe how to compute each function in this class. And the narrowest class of functions - the class of polynomial time bounded functions - consists of functions that can be computed in a feasible way, efficiently enough to be of practical value in real applications. We discuss how this sequence of collapses parallels the creative dynamics of pure consciousness itself, as described by Maharishi's Vedic Science, as it brings forth creation through the collapse of the abstract, indescribable infinite value of wholeness to the concrete, specific point value within its nature.

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