Articles on Maharishi Vedic Science and Mathematics
These articles have been published in P. Corazza (Ed.), Consciousness-Based Education:
A Foundation for Teaching and Learning in the Academic Disciplines: Vol. 5. Consciousness-Based Education and Mathematics, 2009, MIU 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 MVS 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.
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Articles on Maharishi Vedic Science and Computer Science
These articles have been published in P. Corazza (Ed.), Consciousness-Based Education:
A Foundation for Teaching and Learning in the Academic Disciplines: Vol. 8. Consciousness-Based Education and Computer Science, 2009, MIU 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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