A post submitted by CGI member ScienceTruth.

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The Winnemucca Institute for Advanced Studies presents

A Comparative Study of the Differing Mathematical Disciplines
Used in the Analysis of Interstellar Astrophysical Phenomena Observation

Abstract

The purpose of this Paper is to elucidate and illustrate how Mathematics can be used as a tool, just like the different 'octaves' of the EM Spectrum, so that we can 'see through' the intervening 'obscurity' of a large data set, so that the 'noise' of the data can be 'quieted' and a 'clearer picture' will emerge of our observations. Like the center of our Milky Way Galaxy for example; when viewed in the visible-light wavelength we cannot see it due to the overwhelmingly obscuring dusty material, but when viewed in the 3.2 cm, 5.6 cm, or 7 cm wavelengths, we can clearly see many structures at the center of our galaxy exceedingly well, because that wavelength of the EM Spectrum easily passes through the intervening obscuring dust without being absorbed or changed. Herein we propose to use differing mathematical disciplines to 'see through' the obscuring 'noise' of unneeded data to see the important data, and then view what the Universe will now show us.

The differing tools in the Mathematical Spectrum

Base 10 Number System The Concept of Zero Imaginary Numbers
Geometry Algebra Tensors Spinors Vectors

Cartesian Graph Degrees of a circle Radians of a circle
Logarithms Scalars and Scalar Fields
Functions Transforms Operators Matrix and Matrix Fields
Differential Equations Partial Differential Equations
Wavelets Wave Functions Energy Density Functions
Solitons Loop Quantum Gravity Theory
Gauge Theory Group Theory Lie Theory String Theory
Classical Mechanics Quantum Mechanics Quantum ElectroDynamics
The Electric Universe Theory
Dobsonian Cosmology : Adviata Vedanta & Modern Physics

This is a pursuit to develop additional tools from the ones above for new perspectives of seeing things better and more clearly. As Scalars and Vectors see the same event differently, so do the other mathematical disciplines listed above, and as tools we use one over another for the specific analysis we desire, for example; Radians are more useful at times than are Degrees, in certain circular calculations.

We very much need to develop new 'perspectives' to correctly 'see' the Universe and its interstellar activities, and new mathematical disciplines are one way to do this. This 'comparative analysis' is a way of cataloging the tools we have now. It is also a springboard to see what voids in our perspectives persist, how to recognize those voids, and how to fill them in the future by inventing new mathematical tools. For Example: What would be the result of using a different number base other than base 10, to say calculate Pi, Phi, Planck's Constant, etc etc. Is there a number base that would result in Pi being a whole number instead of a number that goes on and on ? Maybe base 10 is cumbersome, and some other number base would make things simple ! In that case we need to calculate, say, 25 important 'numbers' in Physics, in base 2 through base 27 and see what we find, or even through base 121 ! This particular exercise may prove fruitless, but it needs to be done to be sure. Regardless, other new math 'disciplines' will be very helpful, just as the ones we have now are very helpful in the certain instances for their best use. Could the new development of AI do 'the heavy lifting' through Base 121 !! It might be quicker than using a circular slide rule !

New Tools are needed for Mathematicians

In which, like the differing octaves of the EM Spectrum, as per Low Frequency, Radio, Infrared, Visible, Ultraviolet, X-ray, Gamma-ray, and how those differing 'octaves' of the EM Spectrum interact with, or pass-thru, the intervening material medium of 'matter', as in the ISM of outer space, or even here on Earth, and we receive differing 'information' from those differing octaves, depending on how they interact with the matter they are passing through (like ground penetrating radar), or the matter they are reflecting off of (like LIDAR), or what matter those varying wavelengths of the EM Spectrum are traversing without interacting (like viewing our galactic center). The goal is to glean what information is being carried by those differing wavelengths, and what they are telling us about what we are observing. The wavelengths are each telling us, and giving us, a differing view into the world that they are 'seeing'. Each octave organizes their information differently so that we 'see thru' a large set of data, or we may view what that data is 'reflecting off of,' and we then reorganize that data into a graph, or a chart, or a field, and by the differing method of 'organization' of the data by the differing 'octave' of the Mathematical Spectrum we use, we see things differently, and subsequently much more clearly, or calculate our results more easily, and that is because of the resulting 'simplification' that this 'specific mathematical spectrum' has. That is the power of organizing the data from its differing perspective.

e.g. - Reason for the “ultraviolet divergence” according to Bjorken and Drell *

Commenting on the fact that contemporary theories about quantum scattering of fundamental particles grew out of application of the quantization procedure to classical fields that satisfy wave equations, Bjorken and Drell [1] pointed out the following facts about such a procedure which are still as relevant today as in 1965: The first is that we are led to a theory with differential wave propagation. The field functions are continuous functions of continuous parameters x and t, and the changes in the fields at a point x are determined by properties of the fields infinitesimally close to the point x. For most wave fields (for example, sound waves and the vibrations of strings and membranes) such a description is an idealization which is valid for distances larger than the characteristic length which measures the granularity of the medium. For smaller distances these theories are modified in a profound way. The electromagnetic field is a notable exception. Indeed, until the special theory of relativity obviated the necessity of a mechanistic interpretation, physicists made great efforts to discover evidence for such a mechanical description of the radiation field. After the requirement of an "ether" which propagates light waves had been abandoned, there was considerably less difficulty in accepting this same idea when the observed wave properties of the electron suggested the introduction of a new field. Indeed there is no evidence of an ether which underlies the electron wave. However, it is a gross and profound extrapolation of present experimental knowledge to assume that a wave description successful at "large" distances (that is, atomic lengths ≈10-8 cm) may be extended to distances an indefinite number of orders of magnitude smaller (for example, to less than nuclear lengths ≈ 10-13 cm). In the relativistic theory, we have seen that the assumption that the field description is correct in arbitrarily small space-time intervals has led—in perturbation theory—to divergent expressions for the electron self-energy and the bare charge. Renormalization theory has sidestepped these divergence difficulties, which may be indicative of the failure of the perturbation expansion. However, it is widely felt that the divergences are symptomatic of a chronic disorder in the small-distance behaviour of the theory. We might then ask why local field theories, that is, theories of fields which can be described by differential laws of wave propagation, have been so extensively used and accepted. There are several reasons, including the important one that with their aid a significant region of agreement with observations has been found. But the foremost reason is brutally simple: there exists no convincing form of a theory which avoids differential field equations."

[1] - J.D. Bjorken, S. Drell (1965). Relativistic Quantum Fields, Preface. McGraw-Hill. ISBN 0-07-005494-0.

* This is a prime example of how the Winnemucca Institute is seeking a 'new paradigm' in mathematics so as to make our calculations more correct, and more expeditious. A 'new perspective' into the 'ultraviolet divergence' as provided by a 'new math discipline' would be a prime example of how developing 'new math tools' is what the Winnemucca Institute is all about, and would be working towards as one of their prime agendas. All other groups of investigators are also welcomed and encouraged to explore these ideas as well.

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