Ray Donner - Planet Master: Under the Double Integral

By Stan Burns

Under The Double Integral is the second in a series of novels by Stan Burns. It is a sequel to Stans first novel, Extraordinary Space, The Integral.

Under The Double Integral is a work of science fiction that blends everyday life activities of a family from a moderately sized Midwestern community with various other intriguing activities, known only to a few, mainly that of exploring the vastness of space.

In the novel, an ordinary teen is given the means to travel to distant planets and back. His explorative curiosity of the planets is first sparked while in high school and this curiosity continues well into his college years.

While Ray Donners extra-planetary adventures are intended to be kept secret from his younger siblings, their antics are nevertheless evident throughout the novel. Amazingly, Ray reaches a breakthrough that could have astounding implications for all mankind, a second chance if you will, for mankind to get it right.

Ray Donner (Planet Master) Under The Double Integral, and Beyond the Final Frontier.

• Language: English
• Publisher: AuthorHouse
• Release date: Feb 16, 2010
• ISBN: 9781449068868

Stan Burns

Stan Burns started his work career as a cartographer. After working as a cartographer for two years, his intent was to teach high school mathematics for just one year. Instead, he spent 32 years teaching high school the final 22 of which as Mathematics Department Chairman. Stan has also taught mathematics at a Jr. College for four years and at a Four Year College for nine years. Stan has a wife and three children and has now retired from teaching. Prior to this literary work, Stan authored a 754 page mathematics text book.

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© 2010 Stan Burns. All rights reserved.

No part of this book may be reproduced, stored in a retrieval system, or transmitted by any means without the written permission of the author.

First published by AuthorHouse 2/12/2010

ISBN: 978-1-4490-6886-8 (ebk)

ISBN: 978-1-4490-6885-1 (sc)

ISBN: 978-1-4490-6884-4 (hc)

Library of Congress Control Number: 2010900294

Printed in the United States of America

Bloomington, Indiana

Contents

Chapter 1

Ray Comes of Age

Chapter 2

Transitive Knowledge

Chapter 3

An Integral Encounter of

Ordinality One

Chapter 4

A Tensor Solo

Chapter 5

Entry of the Double Integral

Chapter 6

Post Ball of a Lunar Flair

Chapter 7

Days of Initial Matriculation

Chapter 8

The Mysterious Toboggan

Chapter 9

Arcane Resolutions in Space and Sea

Chapter 10

The Solar Basis

Chapter 11

Journey to Orthodise

Acknowledgements

Special thanks should be given to Mrs. Jeanne Faulkner, one of my former teachers, one of my former co-workers, and a friend for many years, for her direction and assistance in reviewing the manuscript. Her recommendations and suggestions have been invaluable to the project.

Secondly, I would like to thank fellow author and friend Mr. Freddie Lambert for his critique and error analysis regarding the manuscript. His assistance has been extremely helpful for the project.

Last but certainly not least, I would like to thank my wife Angela for her role in reviewing the manuscript and making some critical suggestions.

Without the help of these individuals, it is likely that this writing project would still be limping along the road to completion. Their work, efforts, and contributions are greatly appreciated.

Chapter 1

Ray Comes of Age

Ray Donner, the first born to the union of Lyte and Jaseta Donner, was in the eve summer of his senior year of high school. Ray was an academically excellent student at the high school and a member of the varsity baseball team. Altogether, there are four children in the Donner family. Lyte Donner, a Professor Emeritus of Mathematics at the Local University, lives with his family in Dodecaville, a moderately sized Midwestern community. Lyte Donner is the owner of a chain of retail stores located in the Dodecaville area. The stores are called Electric Air and are geared to radio controlled model aircraft related items for hobbyists, general electrical devices associated with consumer electronics, including CD players, MP3 players, DVD players, amplifiers, receivers, home theater, some electronic kits, and the like.

In a year previous to the current, Lyte Donner discovered the existence of a remarkable phenomenon, an extension to our ordinary space. Lyte and Jaseta referred to this extension of ordinary space as ExtraOrdinary Space. Lyte perfected a vehicle for traveling in the ExtraOrdinary Space which he referred to as the INTEGRAL. Lyte was led to this discovery by examining mathematical models. Mankind lives in a three dimensional world. For our globe, man has developed various systems designed to pinpoint locations on the globe. One common system in wide use today involves the notions of longitude and latitude, a two dimensional system used to simplify positional descriptors of our three dimensional globe. Also in use are three dimensional systems designed to pinpoint any position in space relative to a base or an origin. It is quite common to measure the location of a position from the base as movements or displacements along three lines of reference, lets say for simplicity, an east-west line, a north-south line, and an up-down line. It is easier to refer to these three lines as the x, y, and z lines or preferably as the x, y, and z axes. Actually, the x, y, and z axes are situated in a plane tangent to the Earth at the base point or origin.

In the past and still now for most, it is generally thought that mortal man’s existence is limited to or trapped in just three dimensions. Indeed it is difficult for man to visually perceive anything beyond three dimensions. Through mathematics however, man can conceive various models that extend well beyond three dimensions. Lyte Donner’s discovery adds a fourth line of reference for movement available to mankind. Typically in mathematics, the fourth line of reference is called the w-axis and certainly Lyte refers to this movement away from the ordinary three dimensions as movement relative to the w-axis and the space associated with such movement as w-space, which is of course four dimensional space and Lyte now refers to movement in our normal 3-dimensional space as movement in xyz. Lyte would caution one from being to hasty and bringing in current biases and accepted theories about the fourth dimension to his discovered extension. The new direction of movement is the result of extending the rules of 3-dimensional Euclidean space to 4-dimensional space. It is Euclidean Four Space. As mentioned, Lyte perfected a device called the INTEGRAL to move into the new space. Lyte reasoned that a derivative, a concept from the annals of analytic mathematics, decreases the degree of a polynomial function. An antiderivative on the other hand increases the degree of a polynomial function. A fundamental theorem of analytical mathematics shows that an integral is the same as an antiderivative. An integral thus increases degree. Increasing the degree is akin to increasing dimension. That is why Lyte refers to his remarkable vehicle as the INTEGRAL. Lyte would further caution that it would be a mistake to perceive the INTEGRAL as a teleportation device. The INTEGRAL simply moves into extended space. Nothing is teleported anywhere. Nothing is disassembled and then reassembled as the INTEGRAL moves from point to point as would be the case in teleportation.

Because Lyte had strong concerns about the personal safety of those with knowledge of the INTEGRAL project, and among other issues, he delayed turning the project over to the government. The INTEGRAL project got underway well before the Donner children came onto the scene. Lyte thought the INTEGRAL project was so profound that it should be put to work for the benefit of all mankind and not just a few power hungry individuals seeking to control a population and not for a few greedy businessmen that would exploit the people and make windfall amounts of money. The question then and still remains: Is the INTEGRAL going to be put to work for all mankind? During Ray’s childhood, Lyte decided that if Ray continued on a positive academic path and if he continued to be a responsible individual, then somewhere around age 18, Lyte would school him on the issues involved. When Lyte was satisfied that the issues were clearly understood, Ray would be introduced to INTEGRAL Science and the exploration of the Extraordinary Space which is the travel domain of the INTEGRAL. Before that could be done however, Ray must have already demonstrated a responsibility in operating a motor vehicle as a teen. Ray must also have demonstrated a responsibility in handling tasks at Electric Air ranging from routine at first to managerial at a later time. With all these things in place, Lyte would present the INTEGRAL to Ray somewhere around 21 years of age or sooner. The ball would then be in Ray’s court. He would be the one to decide if INTEGRAL Science should be entrusted to humans and if the INTEGRAL could be put to work to benefit all mankind. Ray would be encouraged to seek his brother’s and sisters’ advice on the issue at the right time. Ray would determine when the time was right.

The time had now come to begin to school Ray in Integral Science. Up to this point, Ray had met all of Lyte’s previously determined prerequisites. Ray puts a lot of time in at Electric Air, He basically manages the original store during the summer season with occasional help from Lyte and Jaseta and he coordinates operations between the other stores in the Electric Air chain. Ray has demonstrated that so far, he is a responsible teenaged driver.

In the past, Lyte and Jaseta Donner had some remarkable adventures with the INTEGRAL. The INTEGRAL was used for intercontinental travel. Lyte and Jaseta have flown the INTEGRAL in w-space at speeds in excess of 1,800 miles per second, basically speeds equal to about 1% of the speed of light. It is Lyte’s belief that the INTEGRAL is capable of flying at a speed approaching 100% the speed of light. Lyte has never tested this belief at least not yet.

Ray has one brother and two sisters. The second Donner child born was a girl. They named her Wave J. Donner. Jaseta thought that was cute. She said it had a nice flow to it from Lyte’s name, Lyte Wave. Wave’s middle name is Jaseta. Ray is slightly more than two years older than Wave. The third Donner child born was also a girl. They named her Dawn J. Donner. . Dawn’s middle name is Jane. The fourth Donner child born was a boy. Lyte said that was perfect because each of the siblings now had a brother and a sister. They named their fourth child Laser Joseph Donner. The Donner children are each spaced about two years apart.

Lyte knew there are a lot of frontiers the INTEGRAL must face. Lyte always wanted to explore some of those frontiers. It was Lyte’s belief that the INTEGRAL could be used for efficient space travel. Lyte has now tested the INTEGRAL on unmanned space flights. He has already sent the INTEGRAL to the Moon in w-space but has not entered xyz there yet. A tensor was set for the Moon and the trip took about two minutes moving at the INTEGRAL’s best tested speed to date. From the vantage point of w-space and through the view port inside the INTEGRAL, pictures of the Lunar surface have been taken from a location just a foot or two inside w using the technology Lyte developed years before. Lyte used this technology to see into xyz space while safely in w. Lyte is still unsure of the flight range of the INTEGRAL. He reasons the range could be virtually unlimited because the INTEGRAL would be able to see its base on a straight line vector. The INTEGRAL has most often flown on a straight line path in w, but relative to xyz, much curvature may have been involved. The INTEGRAL could fly 360 degrees around the globe, but in w, the flight could amount to a straight line. Lyte reasons, Surely we are able to view stars and objects in the sky several light years from Earth because the light they emit travels to Earth on a straight line. The INTEGRAL flies on a straight line in w. The range of the INTEGRAL could be therefore virtually unlimited. It even gets better than this. The INTEGRAL’s flight to a planet could be on a straight line in w not being influenced and bounded by gravitational forces in the solar system. This would lessen the distances thought necessary to travel in order to reach another planet. Lyte postulated that traveling in xyz space is the same as traveling on the surface of a hypersphere. The analogy is simply this. Traveling in xyz is akin to traveling along an arc of a circle, but traveling in w is akin to traveling along the chord of the circle joining the endpoints of the arc. Obviously the distance along a straight line chord is shorter than the distance along an associated arc and thus straight line distances between the planets would be much less in w. This, coupled with the INTEGRAL’s great speed, would eliminate the need for ionic propulsion and other plasma propulsion engines for deep space travel in xyz. Lyte planned to test the INTEGRAL with unmanned interplanetary flights at a future point provided his near space and Moon ventures were successful. He would be able to explore the climate and surfaces on the planets with crystal clarity all from a screen inside his Inner Cube. The question was, would Lyte dare to venture to these places himself and even reenter xyz there? Much testing had to be done first.

The Donners are living peacefully in Dodecaville. Looking in on the Donners on a summer day, a typical blazing hot July summer day in Dodecaville it was to be more exact, finds Lyte over at Electric Air running the show there. Jaseta, Ray, Dawn, and Wave were at home recreating under the air and in the pool. The time was about 5 PM. Jaseta thought Laser should also be at home at that time and sent Ray out to look for him. Ray was told that Laser Joe had ridden his bicycle over to his friend Carl’s home and that’s where Ray was headed in his car. It turns out that Laser Joe, Carl, and two other boys had ventured away from Carl’s home riding their bikes. Without adult approval, the four 11 year old lads had ridden their bikes over to the old Dodecaville Passenger Rail Station. The old passenger rail station still had its waiting room and station building standing but it had been closed for passenger service for several years. The tracks were still being used however but mostly for freight trains. A few Amtrak trains also used the tracks daily. The Amtrak Rail Passenger Station in Dodecaville was at another location in the city. In the old days, the Dodecaville Passenger Rail Station had four tracks to serve rail passengers. An underground walkway was provided for passengers to move from one track to another and back and forth to the terminal waiting room. It seemed that the boys were playing a game. They wanted to see who was brave enough to walk the underground walkway solo.

The boys stopped the bicycles at the old terminal building. One boy at a time then would start on foot, go underground, and resurface after having passed underneath all four tracks. After that, the boy would return to the terminal at surface level walking across each of the four tracks. Carl was first. He disappeared down the steps to the underground walkway. In about one minute he could be seen coming up the last stairwell at which time he returned to the terminal and declared, That walk was a piece of cake. Paul was next. His walk was successful too. It was now Laser Joe’s turn. He disappeared down the steps into the underground walkway. Laser was thinking, Man this odor down here is GROSS! The walkway was partially illuminated but only by the light coming in from the five stairwells. Laser Joe had passed the second stairwell and was headed towards the third. He passed the third and was headed towards the fourth. Midway to the fourth, Da Deeeeeeeeeeeee, Boom Boom Ba Boom, squealed two high pitched and frightening notes from a violin followed by the heartbeat rumbling of a timpani, or so it seemed. Laser Joe had unexpectedly encountered a big figure at the bottom of the fourth stairwell, a giant of a man standing with his hands on his hips, beckoning with his finger for Laser Joe to come to him, and then verbally ordering Laser Joe to do just that. Come here boy! said the man in a deep gruff scary tone. Laser Joe nervously but quickly sized the situation up. It was too far for him to turn around and try to run back to the third stairwell, He would probably be easily caught. He said OK to the man and started to approach the man. He slowly approached the man but was careful enough to stay just out of arms reach. Then all of a sudden, swoosh, Laser Joe turned on the speed eluding the man, dashing past the man, and zipping up the fourth stairwell frantically skipping two and three steps at a time. The man turned around but could not react quickly enough. Laser Joe dashed across the tracks to his bicycle. At that time, the other three boys saw the man emerge from the stairwell. Laser Joe speaking in an alarming tone explained, Let’s get out of here. That man is trying to catch us. They all got on their bicycles and anxiously sped away from the scene at maximum speed all the time hollering and carrying on with fright.

In a little while and just two blocks away from the railroad facility, Ray was in his car stopped at a red traffic light when the four boys sped from left to right past him. Ray made a right turn, caught up with Laser Joe and his group, and then stopped the bicycle cavalcade. Ray pulled over to the curb. The bicycles were all on the sidewalk. They began to explain to Ray, A big man is chasing us! A man is chasing us! said two or three of the boys trying to speak in confusion at the same time. Ray wanted to know where. He did not see anyone chasing the boys. After the boys talked for a while, Ray suggested that the man in question was probably a railroad policeman. His duty is to maintain safety and security around the tracks and the terminal area, explained Ray. This explanation seemed to ease the tension among the boys. When asked, the boys all said they did not see any NO TREAPASSING signs. Things were calm at this point. Ray then instructed the other three boys to carefully ride their bicycles to their homes. He put Laser Joe’s bicycle in the trunk of his car. Laser got into Ray’s car and Ray drove the both of them home.

A person meeting Laser Joe for the first time through this bicycle riding railroad terminal experience would probably agree that the introduction was somewhat of a bombastic one and might have the opinion that Laser Joe was an adventurous and maybe a troublesome child. Actually, Laser Joe was a good lad, sometimes adventurous though, and sometimes dangles around in malicious mischief. Upon the lad’s arriving home, Jaseta Donner evaluating the afternoon experience, immediately warned Laser Joe that one more incident of that type would ground him for the balance of the summer. At the Donner home, all the family members were present except Lyte. Wave Donner, now 15 years of age, was preparing dinner and her sister Dawn Donner, 13 years of age was assisting. Things otherwise seemed normal at the Donners’. Later, it was a normal dinner and after that, leisure time with the family was also normal.

It was the next day. Another blazing hot day in Dodecaville it was. The telephone rang. It was one of Laser Joe’s friends. He said he had a new baseball and was headed over to the school yard to play. He wanted Laser Joe to meet him there. Laser Joe sought and received clearance to go over to the school grounds to play baseball with his friend. Just as Laser Joe was arriving, four or five other boys were also arriving. There were not enough boys to form teams so they decided to just practice hitting and fielding. One of the boys commented, This ball is brand new and it should last for the rest of the summer if we do not hit it on top of the school building. In the past, Laser Joe and one other boy would occasionally climb the gutter pipe to retrieve lost balls from atop the school building. Jaseta Donner got wind of this and prohibited Laser Joe from continuing this activity. She cited obvious danger as the reason. The other boy’s mom also got wind of this and stopped her son. There was now no one that could climb the building or at least there was no one willing to attempt the climb, so a ball hit atop the building would be basically a lost ball.

The new ball looked really clean and it was the only ball they had. Laser Joe took a position in the outfield about 30 feet from the fence at the school ground boundary. The fence was a wire fence about four feet high. A homeowner on the other side of the fence yelled out to the boys, Don’t hit that ball in this direction towards my home. You might break a window and if the ball comes in my yard, I am going to keep it. None of the boys had the power to hit the ball over the fence from where home plate was located anyway so there was little worry besides, the fence would keep the ball on the school grounds. Laser Joe spotted a small hole at the bottom of the fence. Laser sized the situation up. There was no worry because the hole was too small for a ball to fit through besides no one could hit it or even throw it accurately enough to exactly target the hole even if they tried all day. It was the very first pitch. KaPop went the ball as it left the bat clearing the infield and eluding Laser Joe in the outfield. The ball was headed for the fence. It looked as if it were headed