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

Addressing the Problem of Large Cardinals with Vedic Wisdom
To appear in the first issue of the International Journal of Mathematics and Consciousness. This is a full write-up of the topics discussed in the talk "Recent Progress in the Mathematical Analysis of the Infinite", see below.

ABSTRACT: Shortly after Cantor's discovery of the existence in mathematics of an endless hierarchy of different sizes of infinite sets, a new challenge concerning the nature of infinity in mathematics arose. Enormous infinities, known as large cardinals, have turned out to be the key to solving many mainstream problems in mathematics, but because of their extraordinarily strong properties, large cardinals cannot be proven to exist at all. The Problem of Large Cardinals is to find a natural way to enrich the standard axioms of set theory so that large cardinals can be derived. To accomplish this goal, a much deeper intuition about the nature of the infinite than has been available so far is needed. We suggest that precisely such intuition can be extracted from the ancient Vedic wisdom. We formulate a new axiom of set theory, strongly motivated both by this ancient wisdom and by mathematical considerations, which provides a solution to the Problem of Large Cardinals.

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. It is also possible to see a video of the talk: Follow this link: video of the talk. This webpage contains several videos. The one that I appear in is 4th from the top, the video labeled "9:00-9:45 AM Morning plenary session", and I am the third speaker; I begin my talk at approimately 1:44 (1 hour 44 mintues) into the recording.

ABSTRACT: 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 is a rough reprint of the transcript of a talk 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 talk appears as a paper in the volume Consciousness Is Primary, Illuminating the Leading Edge of Knowledge, Maharishi University of Management, Fairfield, IA, 2013 (pp. 115--146). The talk 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. 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.

HOME