The Mathematical Field: Part 2 - Applications

Copyright © 2024 Vincent J Hyde.

All rights reserved. No part of this book may be used or reproduced by any means, graphic, electronic, or mechanical, including photocopying, recording, taping or by any information storage retrieval system without the written permission of the author except in the case of brief quotations embodied in critical articles and reviews.

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ISBN: 978-1-9822-9954-5 (sc)

ISBN: 978-1-9822-9955-2 (hc)

ISBN: 978-1-9822-9953-8 (e)

Library of Congress Control Number: 2024908696

Balboa Press rev. date: 06/25/2024

To the teachers who taught me mathematical applications in my university and working years. In engineering, you have to use mathematical applications to solve all kinds of problems, so I am glad that I listened to my teachers. On some occasions, I felt inspired by some of the great stars—like Newton for his gravitational equation, Boole for his Boolean Logic, and Einstein for his equation relating energy and mass. So this book is also dedicated to the stars and their Fields of Knowledge. It should be noted that the Religious Field is automatically included in the dedication, if one considers that our human consciousness and the stars of Heaven and Earth are all following the rules of the Creator who made them.

ABOUT THE AUTHOR

Vincent J. Hyde was born in September 1954 in Calcutta, India. While living in Calcutta, he studied at Saint Xavier’s College.

He immigrated to Sydney, Australia, in February 1970. While living in Sydney, he completed his secondary education at Marcellin College and Merrylands High School, where he obtained his Higher School Certificate in 1973.

He completed the electrical engineering degree course at the University of New South Wales in 1979. He earned a postgraduate diploma in illumination design at the University of Sydney in 1983.

He worked as an electrical engineer at the New South Wales Public Works from 1979 to 2014 and retired from active engineering duties in 2014. Since 2014, he has been writing books to continue his professional development.

He has written seven books with the publisher Balboa Press, as follows:

1) Heaven and Earth

2) A Journey from Dust to Consciousness

3) A Message from the Neighbours

4) Earth’s Reply

5) The Alien World

6) Fields

7) The Mathematical Field: Part 1—Measurements

He is a current member of the Institution of Engineers Australia (MIEAust), Chartered Professional Engineer (Ret) No. 1387147.

AUTHOR’S NOTES

The Mathematical Field: Part 2—Applications is my eighth book.

I have studied in many Fields of Knowledge and wish to thank my teachers and other authors who may have contributed to the work in the Fields of Knowledge.

The Mathematical Field: Part 2—Applications is linked to my seventh book, The Mathematical Field: Part 1—Measurements, and is a necessary read for the reader who may be interested in that or any of the other books I have written. The purpose of this book is to show how the rules and laws of the Mathematical Field, with its Arithmetic Arm, Algebraic Arm, and Geometric Arm, are applied in many Fields of Knowledge.

In this book, I have solved many specific problems to show how the mathematics mentioned in The Mathematical Field: Part 1—Measurements is applied in The Mathematical Field: Part 2—Applications.

The Mathematical Field has many interesting arithmetic, algebraic, and geometric applications in other Fields. Unfortunately, it was impossible for me to include all the applications, so I included some of the important ones that I came across during the study and working phases of my life. The Mathematical Field has certainly helped in the development of machines, and this has enabled human beings to travel around the Earth and communicate across the Earth via machines.

The Earth’s mass is being automatically transformed into lifeforms and machines by inspired design. Human lives appear to be significant not only from a mass point of view but also from a spiritual point of view.

Machines are energy converters: they transform energy from one form to another. One of the fundamental laws of the Creator is the first law of thermodynamics—that the total energy content of the universe is fixed. Energy cannot be created or destroyed but can only be transformed from one form to another. Since the Creator has given human beings the consciousness to make and understand machines, we have the ability transform energy to do useful work that improves the Fields of Knowledge and our lives.

To make and understand machines requires some knowledge of the Mathematical Field. In this book, we will see that both Heaven and Earth are designed based on many of the rules and laws that are described by the Mathematical Field.

It is significant that our consciousness allows us to understand and apply the Mathematical Field to the other Fields all around us.

EXPLANATION OF THE USE OF CAPITALISATION

Upper case has sometimes been used to make it easy for the reader to follow the text, as follows:

1) A single word might have a vague meaning if considered by itself. However, in the context of the Mathematical Field, certain single words have a particular meaning and hence are capitalised. For example, the word field has a meaning associated with the ground where people play a sport or an area where people grow a crop of food. Field in the context of this book is where people work and develop a particular Field of Knowledge over a long period of time, usually resulting in the formation of many human stars.

2) A two-word phrase might need to be considered as a unit and not as two separate words. For example, the phrase Mathematical Field is associated with people working in and developing the Mathematical Field over a relatively long period of time.

3) The three-word phrase Fields of Knowledge must be considered as a unit.

I hope this information is helpful to the reader.

CONTENTS

About the Author

Author’s Notes

Explanation of the Use of Capitalisation

Chapter 1   Introduction

Chapter 2   The Arithmetic Applications

Chapter 3   The Algebraic Applications

Chapter 4   The Geometric Applications

Chapter 5   Scalar and Vector Applications

Chapter 6   Conclusion

Chapter 7   Symbols Used

1

INTRODUCTION

There are numerous arithmetic, algebraic, and geometric applications associated with the macroscopic world of the galaxies, the microscopic world of the atom, and the living world of plants and animals. Many of these mathematical applications are clearly seen in many of the Fields of Knowledge. Mathematics has given us a clear understanding of many of the Creator’s rules and laws, which can be understood by use of mathematical formulas, equations, and graphs.

In The Mathematical Field: Part 1—Measurements, we saw how the day-and-night cycle and the seasonal yearly cycle are periodic functions. We also saw how the heartbeat in animals is a periodic function necessary to keep human beings and all animals alive.

There are numerous mathematical applications. I will only be writing about the interesting ones that I have come across in my studies. I will also deal with the applications in a simple manner so that many people may understand and make use of these applications, which have been realized by many human stars in many Fields of Knowledge.

In this book, arithmetic applications include the following:

1. Humans and the denary (decimal) system

2. Communicating with machines

3. Machines and the binary system

4. Counting and the chemistry field

5. Exponential growth and decay

6. Arithmetic series applications

7. Geometric series applications

8. Logarithm applications

9. Mean and standard deviation applied to the electrical voltage waveform

10. Normal distributions applied to the macroscopic world

11. Probability applied to the microscopic world

Algebraic applications include the following:

1. Rates of change

2. Displacement

3. Velocity

4. Acceleration

5. Differentiation and integration applications

6. Boolean algebra and programmable logic controllers

7. Kirchhoff’s voltage laws and current laws

8. Energy levels, the atom, and the electromagnetic spectrum

Geometric applications include the following:

1. Electrical power

2. Mechanical systems

3. Light

4. Electrical communications

5. Satellites

6. Escaping from the Earth.

Scalar and vector applications include the following:

1. Scalar applications

2. Vector applications

2.1 Mechanical applications

2.2 Electrical applications

2.3 Vector field applications

2.4 Combined vector field electrical and magnetic applications

All the above show a grand design full of periodic functions and symmetry. As we look at the day sky, we see a spherical sun moving across a dome of the sky, which reflects blue light to our eyes; at night, we see a dark dome-shaped sky full of white stars. Around our houses we see beautiful symmetrical shapes—rectangular walls, floor and ceiling, rooms that are cubic, windows that are rectangular or circular, picture frames that are square or rectangular or circular. The doors to our houses are rectangular. Many of our machines—including washing machines, dishwashers, and refrigerators—are cubic. Straight lines can be seen everywhere around our houses.

Even the living creatures that we see are symmetrical in shape and structure. Many of them can be split into two symmetrical halves. Trees, flowers, vegetables, and fruits are all usually symmetrical in shape. It is interesting to note that some of the bigger items created by human beings—like cars, trains, aeroplanes, trams, bicycles, ships, and motorcycles—are usually symmetrical.

The sun, planets, and moons of our solar system have a spherical symmetry. Even their orbits and the orbits of comets have spherical or elliptical symmetry. This symmetry does not apply to our solar system alone. Telescopic evidence shows that planets and moons orbit other stars, and their appearance and orbits are similar to our solar system. In short, they follow similar rules.

We know that designing things that operate in a regular periodic manner and that are highly symmetrical requires planning and intelligence. Religious people generally believe in a Creator that is responsible for the beautiful creation that we see all around us, and perhaps the Creator has inspired human beings to design and manufacture symmetrical objects. It seems as though the natural and living world are all following rules and laws, and this is necessary to exist in the universe. The creation of beautiful cities with all sorts of machines generated through Fields of Knowledge in which many human beings seem to be inspired is miraculous, when one considers the manner in which the dust of the universe formed all these symmetrical features, including galaxies, solar systems, atoms, living cells, and human beings, so that the whole process could be understood through Fields of Knowledge.

Our consciousness has inspired us to discover the different number systems described in The Mathematical Field: Part 1—Measurements. The binary system is used to communicate with machines. This system, where ones and zeros can be used to represent numbers, words, sounds, and pictures, is remarkable. The fact that the ones and zeros can be used to store and carry information in waves, at the rate of gigabits per second, is like a miracle, inspired by the Creator. Binary is the simplest number system, but it is the most useful for machines, with so many applications.

Imagine that we were able to escape from the Earth and find another world, in another galaxy, that was similar to it. We monitored that world from our spaceship and saw no signs of any life. However, when we landed on a beach near an ocean on this new Earth, we found an instrument that described the time of day on this new planet. We would conclude that some form of intelligence must have existed on the planet in the past; otherwise, the symmetrical instrument with periodic movement could not exist. In other words, the atoms on the beach would not come together to form the gearing or electronics in the instrument necessary for the instrument to show 12:00 noon when the planet’s star was overhead.

In this way, for the energy in the universe to form the mass of the galaxies with billions of star masses, planet masses, and moon masses is remarkable. The existence of the elements on the surfaces of planets