by Ken Renshaw
Appendix:
Canice's Eight-dimensional Movie
(Not Essential to The Story. read only if you are interested in eight-dimensional mathematics.)
Film: Cast: Narrator and historical and contemporary characters.
The show opens with a real person, a commentator who is a well known physics professor (having appeared in PBS scientific programs) who sets up the idea that we will learn how to calculate distances in spacetime and explore other concepts of space and time.
In the first scene we have an animated character, Pythagoras who is a Greek, in a toga, being asked by a Nero-looking character to calculate the distance (d) from the entrance in a Greek temple to the farthest corner. He measures the distance from the door of the temple to the back wall (x) and then measures the distance from there to the corner (y) and then the animation shows him calculating the hypotenuse of the triangle, mumbling his famous formula, 'the square of the hypotenuse is the sum of the squares of the two sides.' He scratches out a formula in the dirt on the ground:
(d)2= (x)2 + (y)2 and continues mumbling to himself.
Then, he decides to calculate the distance from the door to the top of the wall in the far corner. He scratches his head, and then he measures the distance up the wall (z) and then adds it to his formula,
(d)2= (x)2 + (y)2+ (z)2
and then dances around in delight.
Another character who has modern dress, a baggy sweater, tennis shoes and wild hair comes in. It is Einstein. He tells Pythagoras that if we put the temple on a big chariot traveling at a speed of (v), we can calculate the distance from the door now the upper corner where it will be (t) later. All we have to do is add one more term to Pythagoras' formula:
(d)2= (x)2 + (y)2+ (z)2+ (vt)2.
Cut to the temple sitting on a giant chariot. Einstein hits the horse on the rump and it charges off. We see a line connecting the door of the temple before it started moving stretching to the corner of the moving temple as it moves away.
Pythagoras says, "That is interesting, but who would ever do anything with that?"
Einstein is seen scratching his head as the scene fades.
The commentator then adds:
"That is about how far we can go visualizing spacetime. There was no evolutionary advantage for our species to evolve with the ability to visualize more dimensions than we can see. Quite a bit after the time of Pythagoras, mathematicians decided their equations didn't have to limited by what they could see. They can have equations that describe any number of dimensions and geometries. Einstein's mathematics teacher at his college, Herman Minkowski, liked to play around with a higher number of dimensions than four. One of his sets of higher dimensions is now called complex eight-dimensional Minkowski space, which we will call eight-space for short. Mathematicians like to name things after their originators. Pythagoras's theorem is named after Mr. Pythagoras, for instance.
"Like many things in mathematics, the idea of eight-space lay around unused for years. After the turn of this century, a mathematician found eight-space could be used to explain many mysteries in physics and expand the field to explain some no-no topics such as ESP. Until this new explanation came along, most physicists would write you off as crank if you even mentioned ESP, because there was no scientific explanation for it. All psychic phenomena were considered the product of ignorance, superstition, and unscientific thinking. Few credible scientists would touch the subject for fear of being ostracized by their peers.
"Knowledge of eight-space may change the way we think about many things, so lets explore it further. We have to first address the idea of the word 'complex' in eight space, the idea of complex numbers. If you went to k-12 school in the last decade, you know all about complex numbers. However, chances are your parents and surely your grandparents don't know about them In 1545 an Italian mathematician, Geroiamo Cardano was trying to solve an equation but nothing worked. Lets let Geroiamo explain."
Switch to another animation. Our character, Geroiamo, is dressed like the men we see in Shakespearian plays, wearing puffy sleeved shirts, pantaloons, tight pants, pointed toe shoes.
Geroiamo is sitting at a table scribbling away on equations. He keeps muttering and swearing, wadding up his paper and throwing it on the floor, starting over. His cleaning lady comes in to clean up and asks him why he is making this mess. He explains that he is trying to solve this equation, and he keeps ending with an impossible number, the square root of minus one.
The cleaning lady picks up a piece of paper, unwads it and stares at it for a minute. "You mean this number here, minus one that looks as though it is under a table or awning?"
"Yes,'" says Geroiamo. "There can be no number that, if multiplied by itself, can make a minus one. A minus times a minus is always a plus."
The cleaning lady looks at the paper and says, "But the number is right here. Why don't you simply call it a number and stop making such a mess."
We see Geroiamo showing his equations to friends. They all laugh derisively and ridicule him for only being able to solve the equation with a fictitious or imaginary numbers. They say, "Who will ever do anything with that?"
The commentator returns and says:
"As Geroiamo found the imaginary numbers convenient to solve problems, other mathematicians found it convenient to use them. After a while, certainly by the start of the nineteenth century, nobody thought anything bad about using imaginary numbers. Engineers used them in designing and analyzing bridges.
This brings us to Einstein in the early twentieth century:"
In the animation, we see a child Einstein working on a formula. Old Pythagoras is looking over his shoulder. He says, "You are only twelve years old, do you think you can prove my theorem in a new way?" Einstein hands Pythagoras the paper and Pythagoras reads it a while, and then dances around joyfully saying,
"He did it! He did it! It has been a thousand years since anyone did anything original to prove my theorem. But who will ever do anything with that?"
The commentator returns and says, "In 1901 Einstein submitted his doctoral dissertation, an early paper on his theory of relativity. Here, we see what happened."
A young Einstein, recognizable by his not-yet wild grey hair, walks, in a dejected slumping mode, into a room where there is a professor, identifiable by his academic robe.
"Why so glum?" asks the professor.
"Professor Minkowski, my doctoral dissertation on the theory of relativity was rejected because it was too far out. Those old fossils want me to write a paper on old stuff that they will be comfortable with."
Minkowski says, "I read your paper and thought it was quite good. I think you should make time an imaginary number so your theory will fit with other new stuff going on physics."
Then, we see Geroiamo walk in saying, "Good suggestion, imaginary numbers can be used to solve all kinds of problems."
Einstein replies, "In all due respect, I don't like imaginary numbers. I don't know how to visualize them, and particularly imaginary time, and that is how I think."
Minkowski adds, "That's one of the differences between working in math and physics. Mathematics doesn't need to relate to anything you can see. Physics, especially among the old guys on your dissertation committee, has to relate to something you can measure. Your relativity theory doesn't have any experiments to go with it. Why don't you dust off that old paper you did about the size of atoms."
Einstein replies, "That paper has a great amount of measurement data. That should satisfy the old goats."
The commentator returns:
"In 1905, Einstein was awarded his doctorate. Around that time, he was working on a paper about mass and energy."
We see Einstein in a baggy sweatshirt and tennis shoes with his wild uncombed hair. He is scribbling on paper, scratching his head, pulling his hair, getting up and walking around in a circle.
Pythagoras in is toga walks in and asks, "What is the problem?"
Einstein says, "I am working on
a paper about inertia, mass, and energy, and can't get the right formula."
"Why don't you use my old one that you proved as a kid?" advised Pythagoras. He goes to the blackboard and writes:
(d)2= (x)2 + (y)2
Einstein says, "Yes, but I think I will use the one with the three dimensions plus a time dimension."
He goes to the blackboard and writes one more term:
(d)2= (x)2 + (y)2+ (z)2+ (vt)2.
Einstein scratches his head and says, "If I replace dimensions x, y, z with symbols that mean momentum, mumble, mumble, mumble."
Einstein fills the blackboard with symbols, erases, writes again and finally steps back.
(E/c)2= (Mc)2 + (p1)2+ (p2)2+ (p3)2
He steps back and says, 'The p's are momentum: if the mass isn't moving we can make those zero and then reduce the equation to:
E=Mc2
Who will ever do anything with that?" he questions.
The commentator returns and says, "That's the way Physics and Mathematics are. People create or discover things that may not be of much use in their time. Sometimes much later it gets used. Remember, in 1905 when Einstein came up with this famous formula, most people rode in horse-drawn buggies and the airplane had not been invented.
"Now, we will address another idea that was way before its time, higher dimensional spaces, specifically Minkowski's eight–dimensional spaces. We will let Geroiamo help out in the explanation."
We see Professor Minkowski in his academic robes speaking before a class, and drawing on a blackboard."
"Let me introduce you to an eight-dimensional concept of spacetime. The first four dimensions are those of common experience. We can have one dimension of front-back, one of left-right, one of up-down, and another for time that could be before-later.
"Let me illustrate with this three-dimensional checkerboard."
Professor Minkowski goes over to a structure that is four 8 x 8 regular checkerboards, one above the other, separated by plastic legs.
He places a black checker piece at the corner of the bottom board and says,
"Here, we have a three dimensional space. For now, we will let velocity equal zero. The piece can move forward or back, let me call that x, right or left, let me call that y, or up or down, let me call that z. Let's call this corner the zero of all dimensions. Now, I will move this piece up four, to the top layer, forward four spaces, and left four spaces. It is now at z=4, y=4, x=4. How do we figure out how far the piece has moved from the zero corner?"
Pythagoras appears in his toga from the side of the stage. He says, "All you have to do is use my theorem."He writes on the blackboard:
(d)2= (x)2 + (y)2+ (z)2 + (vt)2= 16+16+16+0=48
Minkowski produces a calculator from his pocket and says,"d equals the square root of 48 that is 6.93. If we had moved the whole checkerboard structure through the time dimension such that vt=1, then d would be 7 even."
"In these four dimensions, shown here, all of what you might think of as normal physics taught in our k-12 schools applies."
Minkowski then places another set of four checkerboards, made out of clear plastic, on top of the other four, with the zero corner located where the piece is at 4,4,4. He says, "Here, we are adding four mote dimensions that start from where the piece is in after moving in the first four. Since we used our normal four dimensions in the bottom checkerboards, we have to use imaginary numbers here."
Geroiamo walks in from the side of the stage and says, "Don't worry about the idea of imaginary numbers: they are simply another kind of numbers that are convenient for mathematicians."
Minkowsky continues, "The physical piece, here at location x=4, y=4, z=4, can't move into the imaginary space. That is the law of physics. However, information about the piece can move into all eight dimensions. It can be up here in the imaginary space at ix=4, iy=4, iz=4."
The commentator returns to say, "Here, we have to say that this is a new theory. To prove Pythagoras' theorem, all we have to do is go out and measure a bunch of triangles and see whether it worked. We know that Einstein's E=Mc2 idea behind all our nuclear power plants. Later, we will show you examples of how information travels in eight–dimensional space."
Minkowski returns and continues,
"If our physical piece is at location x=4, y=4, z=4, and has eight-dimensional information about the piece at coordinates of the x=4, y=4, z=4, ix=4, iy=4, iz=4 and t=it=0 (so we don't have to bother with time here) the information then, we can calculate the information distance between the zero corner (on the bottom checkerboard)."
Then, Pythagoras reappears and says, "We can use the eight-dimensional form of my formula." He writes his formula mumbling to himself:
(d)2= (x)2 + (y)2+ (z)2 + (vt)2+ (ix)2 + (iy)2+ (iz)2 + (ivt)2
He says, "Since we are letting t=0.we can rewrite this as:
(d)2= (4)2 + (4)2+ (4)2 + (0)2+ (i4)2 + (i4)2+ (i4)2 + (0)2 "
Geroiamo jumps up and says, "Since (i)2=-1,
(d)2= 16 + 16+ 16 −16 −16 −16 = 0"
Minkowski returns and says, "The eight-dimensional information distance between the starting square on bottom checkerboard and the physical piece is zero."
Einstein returns and says, "When I first learned about all of this I was a little tyke, when the words Pythagoras and hypotenuse were beyond me. My uncle, Herman who lived a few miles away, explained it this way:
To get to my house from your house, you have to go down the highway for four miles, turn left on the crossroad and go three miles, and there you are. Or, you could not go by the road and take the shortcut across the field directly from your house to my house. You calculate how long the shortcut is by squaring the distances on the two roads adding them up and taking the square root. 42+ 32= 25=52. The shortcut to my house is 5 miles.
I like the word shortcut better than hypotenuse."
Minkowski says, "I agree, lets not confuse people. Let's call the distance the shortcut distance."
The commentator returns and says, "What does all this complicated mathematics mean? It means that, in eight-dimensions there is a zero-distance information shortcut from the corner square to where the checker started to where it is on the fourth level. If you were at the starting square and wanted to know some information about the physical piece (if it is heads-up or heads-down) The information could come through the shortcut.
"You don't need to care about or understand all these mathematics. You do need to know that a valid, scientific, paradigm exists for the many kinds of information shortcuts we use and observe.
"We all have something I call the 'Magic Mirror of The Mind.' In fairy tales, some witches, or sorcerers have magic mirrors that they can command to get information for them. You remember, 'Mirror-mirror on the wall, who is the fairest of them all.' Well, the one we all have is more limited. We can say, 'What did I have for breakfast," and our Magic Mirror of The Mind makes an information shortcut in spacetime, from where you are now, to when and where you were having breakfast You might think it is a memory stored somewhere in your brain, but it isn't. Scientists with their MRIs can pinpoint areas in the brain active when you try to recall breakfast. However, they have not found any area that has the possibility of storing all the zillions of bits of information you can recall. This is a new idea so there is not much research on this yet because we think it is simply memory. This idea does not fit the current scientific paradigm.
"Conventional scientists such as physicists, engineers, chemists, medical researchers, and others who believe that reductionist science has all the answers, are reluctant to believe that any psychic phenomenon can be valid, because it doesn't fit any scientific paradigm that they know. They would have heard many anecdotal tales of people experiencing psychic phenomena, but will dismiss it as superstition, ignorance, or lack of education. Many will present an angry response to the mere mention of the idea."
The film now shows interviews of a few people who report of their own psychic experiences.
&
nbsp; The first interviews are with people who made changes in their routines, for no special reason, and avoided accidents. They had a premonition.
One is an executive who refused to board an airliner because of his visions of it crashing. The airliner did crash on takeoff, and everyone was killed;
A second clip is a housewife who, for no apparent reason, decided to pick her daughter up at school. The school bus that her daughter would have ridden was hit by a drunk driver and several children were badly injured.
A third clip is of a farmer who related that, on his way home from town he decided to take an alternate route, that he never used, past a lake. As he arrived at the lake, he saw a car with a woman and child go off a bridge and plunge into the water. He was able to save them.
This is followed by an extended clip of experiments at SRI with people remote sensing targets in the Stanford area.
The commentator returns. He is talking in front of a slide show of people in laboratories involved in psychic research. He says:
"Many university laboratories have done experiments with psychics and other people to test the ability to perceive things in spacetime. Little of that research is highly valued in the academic community. Largely these studies document and make statistics about observable psychic phenomena, stuff that simply happens, that has no scientific basis. It falls into the same general category of studies of UFO sightings. If there is no scientific basis, the subject can be ignored by the scientific community at large. This scientific response is as though science is an ostrich, hiding its head in a four-dimensional sand."
The movie ends with a picture of an ostrich with its head in the sand.
About The Author
I live in Cambria, California, with the love of my life, on the edge of a pine forest, on a hillside, overlooking the Pacific.
I was Chief Scientist and Marketing Manager at a company that manufactured communications satellites.
My job was to sell commercial satellites to companies like AT&T and its foreign counterparts.
The trouble with selling satellites is nobody can see them.
All I had to sell were the beliefs about satellites we could build. My real job was being a "peddler of beliefs" to very technical customers.
I made a lifelong study of recognizing the beliefs and patterns in peoples' lives. This led me to write a book, "The Secret of Your Life Script" about how beliefs make the same things happen to us over-and-over.
I decided that we are entangled in a psychic cloud that guides our everyday existence. I show this in this novel,"Love Story, In The Cloud"