Bending Dimensions to eliminate infinities
1st March 2014 copied 27th October 2018
Private & Confidential Copyright © Mr A Pépés
Bending Dimensions to eliminate infinities.
Concept One.
A one dimensional line.
You can only travel or move along a one dimensional line, if you could travel or move along the line in either direction along that line, you would be unaware of the existence of any other dimension. I.e. As far as you are concerned nothing else exists.
Let us start with a one dimensional line.
Let us also say that we do not know how long this line is, and that we believe that it is a finite line.
Which implies we want to eliminate the possibility of having infinities at either end of this line so that these infinities did not actually exist.
How do we do this?
Simple. We bend the line in the next dimension (up), by putting a curve in it.
How much do we bend it by?
Simple. We bend each end by π.
In other words if we were travelling along this line in one direction we would end up at the other end of the line. We have simply made a circle.
The length of the line is just 2π, and it does not mater what the actual length is at this stage.
All circles have a perimeter of 2πr (where r = to the radius of the circle), and only when we specify r (the scale) will we know the true length of this one dimensional line.
I.e. The scale is important.
Theoretically :- now there is no possibility of infinities of length on this line. Only the possibility of travel along this line infinitely (and this involves another dimension, which we will come to later).
Now we have eliminated infinities on a one dimensional line, we can use the same exact process to eliminate each and every other infinity for all the other dimensions in the same manner, one by one. I.e. We bend them to form circles that come back on themselves.
Concept Two.
A two dimensional line. In addition to the first dimension we can move along, if we could move along in two dimensions, we would have a choice of which dimension we wish to move along.
This implies that the two dimensions are linked together and are not totally independent.
In other words you could chose to stay on the path of the one dimensional line, even though the second dimension exists, or visa versa.
Now that we know that these two dimensions are linked, how are they linked?
And how can we move from one to the other?
The answer is we move at right angles to the dimension we are on (or half way between the two ends π/2). If you draw a normal horizontal line on a piece of paper you would just go straight up or down vertically.
Now before we bend the second dimension what do we have?
We have a one dimensional circle in the plane of the second dimension.
This you can represent as a circle on your piece of paper, the one dimensional circle is finite (if you move along it), but your paper can theoretically go to infinity in two directions.
We know we have to move at right angles to this circle to move along in the second dimension.
But what is at right angles to the circle?
You have two choices. The end result must be the same, that we want to eventually bend the second dimension into the third so that which ever direction we chose in the two dimensions there will be no infinities.
What are your two choices?
One choice is the easier one, in which you assume the circle is still a straight line going across the entire piece of paper (draw your line exactly along the middle of your sheet of paper). Bend the paper into a tube so that the two ends of the line join. You have now bent the first dimension. You have a tube with your one dimensional circle in it, right angles to the line is simply anywhere along the tube of your piece of paper.
If you stay in the first dimension you just go round and around the tube (no infinities by design).
If you move along the second dimension, you can go to infinity in either direction along the tube (remember we have not bent the second dimension yet, so infinity in either direction is still a theoretical possibility).
Now if we look closer at the details, you will notice that for every point along the one dimensional line, you have a line along the tube (which is at right angles to the line). Imagine you only had ten points on your circle, you would have ten lines along the tube (all parallel to each other).
Now let us get rid of the infinities in the second dimension.
You again have two choices, ideally you have to bend each and every line along this tube back on itself to create circles, very messy if you are trying to visualise it.
The other easier method (and the result is the same) is to stand well back and look at the tube as a whole from a distance.
What does it look like?
It looks like a line, that goes to infinity at both ends if we were to extend the tube (if you didn't know it was a tube) it would look like our original one dimensional line.
We know how to eliminate infinities, just bend it by π at each end and make a circle 2π in length (again we do not need to know the true length at this stage, until we specify r, later).
What do we now have?
We have a ring that is tubular (not solid) the true (bending) two dimensional plane is this surface on the ring.
You could now if you wish move anywhere on this two dimensional surface in any direction and never reach any infinity (infinities of length do not exist on this surface, only travel or movement to infinity, again this is a different dimension as expressed before, and I will explain later).
[Notice carefully that it is not the surface of a sphere, I will explain what a sphere is later].
Now back to the other choice where we had our circle on our flat piece of paper (the first dimension has already been bent) and we now want to move at right angles to this circle.
You are now yet again presented with two options. You guessed it, the easier option or the more detailed harder to visualise second option.
Let us look at the easier option first (remember the end results are the same).
Let us assume that you are on the one dimensional line (circle) and are unaware of the sheet of paper.
Now pick up your paper and turn it at right angles to yourself so that you just see the edge of the paper. The circle would appear as a straight line from this viewpoint, imagine again that there were points on this circle (10 will do) it will look like a straight line because you can not see the depth of the circle, unless you tilt it slightly. Anyway right angles to this line (circle) is simply lines at every point on the circle away from the paper on either side (again all parallel to each other).
What do you end up with?
Again you end up with a tubular surface, (this time going through the paper), you know how to bend it as before. Result: - the same tubular ring 2D surface with no infinities possible.
Now the more complicated last option. We have our bent one dimensional circle on our piece of paper and we wish to move at right angles to this line.
But this time we want to move in the plane of the paper!
What is now considered at right angles?
Difficult to visualise so we need to break it down. (I know you have two options again, but I am going to just go with the one, the results are always the same).
Let us put in our 10 points on our circle.
We have to move at right angles to each and every point.
If the line was straight then it would be easy, the problem is that the line is curved.
If we look at one point at a time, then the answer becomes a little easier. We could get the mathematicians to explain it, but I think it would confuse things even more.
Simply put, we have to divide the difference between the two extremes and we get a ray coming off the circle, and a ray going to the imaginary centre of the ring (outside the circle) in the opposite direction.
[When you construct a right angle off a straight line with a compass you just divide the angle (180/2 = 90⁰), you do the same with the bent line, you put your compass point on the curve at equal distances on either side of each point and divide, you end up with rays].
Now theoretically we could move to infinity along these rays (because we have not bent the second dimension yet).
We don't want to do that, we want to bend these lines into circles to eliminate all infinities.
If you do this one line (ray) at a time you end up bending the second dimension into a curved tube above your piece of paper!
To best visualise this, imagine that your original line was like a spine curved into a circle, and that each vertebra (the spine bones) were your 10 points and from each point the rays had one rib coming off each side, and the ribs were curved back on themselves to form circles.
You would see a ribbed cage in the shape of a tubular ring. Now finish the job and put a skin on it (the surface).
You end up with a tubular 2D surface along which if you could travel in any direction, you would never come to the end, and yet there is no actual theoretical infinity of length possible.
So far so good.
Remember we have only bent two dimensions.
Now the bending of the third dimension.
This is where things get complicated.
Concept Three.
In line with the previous two concepts we need to travel in a third dimension that is at right angles to the other two dimensions. If this 2D surface was on a sphere, then it would be equivalent to joining rays going from this surface (the skin of the sphere) out to infinities in all directions to the other ends of the rays going into the centre of the sphere?
But as mentioned earlier, this surface although 2D, and you can move to infinity in any direction without coming to an end, it is not the true bending to eliminate infinities.
Why is it not the true bending?
As explained before you need to bend each and every 'one dimensional line' in the 2D plane to itself at the opposite end. I.e. Join each opposing infinity.
Let us look at the details again just before we bend the second dimension. We have our 'one dimensional line' (circle) let us leave our 10 points that each have a line at right angles to it, to create our, at this juncture, a straight tube like structure with ten lines that go to infinity in opposite directions (all parallel to each other).
What we did before, was to take each line in turn and join it to itself at the other opposite side (opposite infinities). We ended up with ten circles (one for each point). Correct. This is not a sphere!
Now what is a sphere?
A sphere is where instead of joining all opposite infinities together, you join all positive infinities together, and all negative infinities together!
In effect you are jumping from one infinity on one line and joining it to another infinity on another line in the same direction, in effect you are joining all ten (positive) infinities at one end, and all the opposite 10 (negative) infinities at the other end.
It is equivalent at looking at your tubular structure and deciding not to bend the whole lot, just crunching the ends together.
Crunching the ends is not the same as bending.
A sphere is topologically the same as a closed tube, you can stretch a sphere and it will look like a tube. [The ends of the tube are closed].
If you stretched it towards infinity in both directions, then traveled along it to one end you would get to the end and you would then turn around at that end and come back on yourself in the opposite direction until you got to the centre, then you would go to the other end and turn around and come back again in the opposite direction until you got back to the centre again.
The two ends of the tube are not joined to each other. (The two opposite infinities are not joined to each other).
In the true bending you do not reverse direction (at what would appear to be infinity), you truly end up at the opposite end and just keep going in the same direction to get back to the beginning, a real loop.
Now you should see a pattern, a one dimensional line needs one bend, (one circle a loop back to the beginning), a two dimensional plane needs two bends, (two loops), a three dimensional volume will need three bends (three loops). And the pattern will continue for each dimension you TRUELY want to bend and eliminate infinities.
End of Concept Three.
So what is a three dimensional volume?
Let us look at our two dimensional surface and try to bend it. It is the surface on our tubular ring.
To avoid stressing the brains or minds of everyone, let us just look at the simplest way of doing this, the end results end up the same (as in all the options of the two dimensional bend).
If we stand back and look at the tube as a whole, side ways (like a doughnut side on), (similar to the circle on our paper sideways) now extend the tube at right angles, you get a solid tube on either side. The original circle created a surface on the tube, the doughnut creates a tube that has solid walls and empty inside extending to infinity on either side.
Now bend the whole lot joining opposite infinities together.
You end up with a bigger doughnut, that has hollow bits inside.
Difficult to visualise, but if you think topologically, you can squeeze it into a spheroid shape and make it look like a sphere, except that the sphere has a tiny hole at the North and South Pole that join together, so you can travel through the sphere without breaking the surface.
Now things get more complicated still when we try to bend the fourth dimension.
I mentioned at the beginning when we were going to bend the first dimension, I said 'if we could travel along the line to infinity'. We obviously can not travel along a one dimensional line, because we are not one dimensional, nor two, three, four, five, etc. until we get to our true dimensional nature. So therefore up until now we have been talking and explaining things in terms of total Abstraction.
So let us start to explain things in more 'Realistic' terms.
We have to add a bit more reality by adding time, but not just any time.
We need to add 'Real' time.
What is 'Real' time?
Believe it or not it has to be something real that can be measured at least in theory.
Something has to 'Exist' to move along the one dimensional line. Time just measures the movement of this existence.
3rd May 2014
Private & Confidential Copyright © Mr A Pépés
Now Existence normally refers to a measure of time. Eg. How long (time) does something exist for?
So it may appear that time is measuring time. I.e. If something exists for no time, then it doesn't exist!
There appears to be a paradox. But this can easily be removed by defining two different dimensions of time. The first dimension (or property) of time is 'does something exist?' If it does, then this something has Existance (notice the spelling, not existence, existence is a transitory thing that can cease). Existance on the other hand is permanent (it never ceases to exist).
When we normally measure time, we are measuring a different dimension (property) of time. This other dimension of time is merely measuring the change of Existance or Existence of 'something'.
In other words if this other dimension of time is zero the 'something' still exists, it just means that nothing has changed.
[Please re-read the previous paragraph and understand it properly].
If the first dimension of time is Existance, then why did I say the other dimension of time and not the second dimension of time?
I said this because there are more dimensions of time. I will explain.
If we go back to our original one dimensional line, I said if we could travel along it. To travel along it we would have to measure time. Which now means we would first have to exist (have Existance) then measure our change of existance along that line. (Two dimensions of time).
Stopping time means we just exist at one point along that line somewhere.
Now let us look at two dimensional lines (the plane). The same thing applies again, but this situation is different. We still have to exist, but we have a choice of which dimension to travel in.
We could travel in time along just the path of the one dimension infinitely, or stop somewhere along that line and then travel along the second dimension.
Now notice what has happened, I said earlier stopping time means we just exist at one point along that line somewhere, in other words the coordinate along that one dimension is constant, doesn't change. But we are now moving along a second dimension.
What is happening to time?
Is it moving or not?
Well the answer is yes and no. What?
Let me explain. There are three options.
First we could have stopped at some point along the one dimension, and did nothing else. (Time stopped).
Or we could have stopped at some point along the one dimension, and started moving in the second dimension.
Or we could have not stopped moving along the first dimension and we started moving in the second dimension as well.
There is a difference between the second and third options. To be able to measure this difference accurately we must be able to measure the existence of time in each dimension. I.e. We can define another dimension (property) of time (one for each dimension).
So in the first option when we stopped, both dimensions of time stopped (became zero).
In the second option one dimension of time stopped (became zero) and the other dimension carried on.
In the third option both dimensions of time carried on.
You should be able to see that if we have 3 dimensions, you could stop anywhere on the 2D plane and travel along the 3rd dimension, or move in all 3 directions simultaneously, therefore there is another dimension of time for the 3rd dimension as well.
Time is not just one dimension but 3 dimensions (4 with Existance).
Things start to get interesting.
What is going backwards in time?
This now gets complicated as you will be able to guess, you can move backwards along one dimension and forwards in the other two!
I will tackle this in another Tea Break Book, as we are still bending dimensions back on themselves.
Are there any more dimensions other than time and space?
Yes the missing elusive 5th dimension. I still call it the 5th dimension for conventional reasons (even though I have made time 4 dimensional so far).
What is the missing 5th dimension?
It is the dimension of Density.
Why density?
Most people think of things (separately) in space and time, but I will show you (explain) that density is a dimension (property) of space and time.
Because everything 'Real' that exists (Existance) be it energy or matter (whether vacuum, dark, light or Ch'i etc.) has a density.
So if we go back again to our original one dimensional line, we would exist at some point with a density of some sort and move along it in time. Stopping time in this context does not change the dimension of density, we still exist.
If density is a dimension then it must be able to increase in one direction and decrease in the opposite direction, and if we are to eliminate infinities we must bend it so that the two ends join (like the normal 3 dimensions of space). We have to make it cyclic.
How do we do that?
Let us break it down.
You can increase the density of something by packing more of it into the same space.
You can decrease the density of something by packing less of it into the same space.
What space?
The Euclidean space that we know. But is this not what most people think of things already, that I said I would explain differently.
Yes and no. I will explain.
If we think of things in the conventional way, then things with density occupy space.
But I said that density is a property of space and time itself.
How can that be?
Well we have to go back to the drawing board and re-examine space itself.
What is space?
Conventionally it is defined by points, lines, planes, and volumes. All points being equal.
Now imagine that all points are not equal. Some points ('Real' points) have a density and some do not.
What is space now?
Well we can define it in the same manner as before except now points, lines, planes and volumes can have different densities (that they did not have before). Things are not superimposed in an empty space anymore, they are the space.
Now we have to look at things in more detail.
How is this density distributed?
If there were a flow along any dimension i.e. A movement along a line then there would be a time that could be measured along that line.
24th July 2014
Private & Confidential Copyright © Mr A Pépés
Let us look at a one dimensional line first. In a time interval one could move past many points, some of which would have a density (let us make it simple and say each point has the same constant density) and some not (let us assume for now that the spacings between our points is constant). That line that you travelled along would have a density of the density points divided by the total points in the line.
This same principle can apply to the other space dimensions. You end up with volumes of space with different densities existing for specified time intervals.
Now if you were to put two equal volumes together to occupy the same space, so that the 'Real' points do not overlap, you end up with a volume that has twice the density.
If space is quantised (explained in another Tea Break Book) it can be considered that each piece of space can have the properties of these bent dimensions (we are effectively specifying a very small r for our circles) and making a little Universe in itself (I call an 'APE'), it would have it's own density. The 'APE' moves in a certain fashion (explained in another Tea Break Book) such that it increases and decreases it's own Secondary volume and it's own density. (I.e. It has it's own inbuilt (minimum and maximum) dimensions of space, time and density).
Now our Universe (the big Universe) is just constructed from the sum of these quantised bits of space, whereby any volume and any density can be constructed.
How do we now bend this dimension?
[We can bend it on the quantised level (in another Tea Break Book)].
We can only bend density in our 3 dimensions (I.e. Using Secondary volumes).
We bend it by using these quantised bits of space ('APE's).
The process is what I call 'the inversion of space'.
Density has a built in minimum and a built in maximum, the two opposite ends, on a quantum level.
It also has a built in minimum and a built in maximum at our level also.
Density is proportional to volume
When we add volumes of 'APE's together we can either keep the same density and increase the volume or we can compact the two volumes and increase the density.
9th June 2015
Private & Confidential Copyright © Mr A Pépés
After reading the above, it appears to end abruptly. I obviously did not finish it. Anyway I think I will write another Tea Break Book on the mechanism of the 'inversion of space'.
Morph your mind with Morphological at
apepes.com
Private & Confidential Copyright © Mr A Pépés
Bending Dimensions to eliminate infinities.
Concept One.
A one dimensional line.
You can only travel or move along a one dimensional line, if you could travel or move along the line in either direction along that line, you would be unaware of the existence of any other dimension. I.e. As far as you are concerned nothing else exists.
Let us start with a one dimensional line.
Let us also say that we do not know how long this line is, and that we believe that it is a finite line.
Which implies we want to eliminate the possibility of having infinities at either end of this line so that these infinities did not actually exist.
How do we do this?
Simple. We bend the line in the next dimension (up), by putting a curve in it.
How much do we bend it by?
Simple. We bend each end by π.
In other words if we were travelling along this line in one direction we would end up at the other end of the line. We have simply made a circle.
The length of the line is just 2π, and it does not mater what the actual length is at this stage.
All circles have a perimeter of 2πr (where r = to the radius of the circle), and only when we specify r (the scale) will we know the true length of this one dimensional line.
I.e. The scale is important.
Theoretically :- now there is no possibility of infinities of length on this line. Only the possibility of travel along this line infinitely (and this involves another dimension, which we will come to later).
Now we have eliminated infinities on a one dimensional line, we can use the same exact process to eliminate each and every other infinity for all the other dimensions in the same manner, one by one. I.e. We bend them to form circles that come back on themselves.
Concept Two.
A two dimensional line. In addition to the first dimension we can move along, if we could move along in two dimensions, we would have a choice of which dimension we wish to move along.
This implies that the two dimensions are linked together and are not totally independent.
In other words you could chose to stay on the path of the one dimensional line, even though the second dimension exists, or visa versa.
Now that we know that these two dimensions are linked, how are they linked?
And how can we move from one to the other?
The answer is we move at right angles to the dimension we are on (or half way between the two ends π/2). If you draw a normal horizontal line on a piece of paper you would just go straight up or down vertically.
Now before we bend the second dimension what do we have?
We have a one dimensional circle in the plane of the second dimension.
This you can represent as a circle on your piece of paper, the one dimensional circle is finite (if you move along it), but your paper can theoretically go to infinity in two directions.
We know we have to move at right angles to this circle to move along in the second dimension.
But what is at right angles to the circle?
You have two choices. The end result must be the same, that we want to eventually bend the second dimension into the third so that which ever direction we chose in the two dimensions there will be no infinities.
What are your two choices?
One choice is the easier one, in which you assume the circle is still a straight line going across the entire piece of paper (draw your line exactly along the middle of your sheet of paper). Bend the paper into a tube so that the two ends of the line join. You have now bent the first dimension. You have a tube with your one dimensional circle in it, right angles to the line is simply anywhere along the tube of your piece of paper.
If you stay in the first dimension you just go round and around the tube (no infinities by design).
If you move along the second dimension, you can go to infinity in either direction along the tube (remember we have not bent the second dimension yet, so infinity in either direction is still a theoretical possibility).
Now if we look closer at the details, you will notice that for every point along the one dimensional line, you have a line along the tube (which is at right angles to the line). Imagine you only had ten points on your circle, you would have ten lines along the tube (all parallel to each other).
Now let us get rid of the infinities in the second dimension.
You again have two choices, ideally you have to bend each and every line along this tube back on itself to create circles, very messy if you are trying to visualise it.
The other easier method (and the result is the same) is to stand well back and look at the tube as a whole from a distance.
What does it look like?
It looks like a line, that goes to infinity at both ends if we were to extend the tube (if you didn't know it was a tube) it would look like our original one dimensional line.
We know how to eliminate infinities, just bend it by π at each end and make a circle 2π in length (again we do not need to know the true length at this stage, until we specify r, later).
What do we now have?
We have a ring that is tubular (not solid) the true (bending) two dimensional plane is this surface on the ring.
You could now if you wish move anywhere on this two dimensional surface in any direction and never reach any infinity (infinities of length do not exist on this surface, only travel or movement to infinity, again this is a different dimension as expressed before, and I will explain later).
[Notice carefully that it is not the surface of a sphere, I will explain what a sphere is later].
Now back to the other choice where we had our circle on our flat piece of paper (the first dimension has already been bent) and we now want to move at right angles to this circle.
You are now yet again presented with two options. You guessed it, the easier option or the more detailed harder to visualise second option.
Let us look at the easier option first (remember the end results are the same).
Let us assume that you are on the one dimensional line (circle) and are unaware of the sheet of paper.
Now pick up your paper and turn it at right angles to yourself so that you just see the edge of the paper. The circle would appear as a straight line from this viewpoint, imagine again that there were points on this circle (10 will do) it will look like a straight line because you can not see the depth of the circle, unless you tilt it slightly. Anyway right angles to this line (circle) is simply lines at every point on the circle away from the paper on either side (again all parallel to each other).
What do you end up with?
Again you end up with a tubular surface, (this time going through the paper), you know how to bend it as before. Result: - the same tubular ring 2D surface with no infinities possible.
Now the more complicated last option. We have our bent one dimensional circle on our piece of paper and we wish to move at right angles to this line.
But this time we want to move in the plane of the paper!
What is now considered at right angles?
Difficult to visualise so we need to break it down. (I know you have two options again, but I am going to just go with the one, the results are always the same).
Let us put in our 10 points on our circle.
We have to move at right angles to each and every point.
If the line was straight then it would be easy, the problem is that the line is curved.
If we look at one point at a time, then the answer becomes a little easier. We could get the mathematicians to explain it, but I think it would confuse things even more.
Simply put, we have to divide the difference between the two extremes and we get a ray coming off the circle, and a ray going to the imaginary centre of the ring (outside the circle) in the opposite direction.
[When you construct a right angle off a straight line with a compass you just divide the angle (180/2 = 90⁰), you do the same with the bent line, you put your compass point on the curve at equal distances on either side of each point and divide, you end up with rays].
Now theoretically we could move to infinity along these rays (because we have not bent the second dimension yet).
We don't want to do that, we want to bend these lines into circles to eliminate all infinities.
If you do this one line (ray) at a time you end up bending the second dimension into a curved tube above your piece of paper!
To best visualise this, imagine that your original line was like a spine curved into a circle, and that each vertebra (the spine bones) were your 10 points and from each point the rays had one rib coming off each side, and the ribs were curved back on themselves to form circles.
You would see a ribbed cage in the shape of a tubular ring. Now finish the job and put a skin on it (the surface).
You end up with a tubular 2D surface along which if you could travel in any direction, you would never come to the end, and yet there is no actual theoretical infinity of length possible.
So far so good.
Remember we have only bent two dimensions.
Now the bending of the third dimension.
This is where things get complicated.
Concept Three.
In line with the previous two concepts we need to travel in a third dimension that is at right angles to the other two dimensions. If this 2D surface was on a sphere, then it would be equivalent to joining rays going from this surface (the skin of the sphere) out to infinities in all directions to the other ends of the rays going into the centre of the sphere?
But as mentioned earlier, this surface although 2D, and you can move to infinity in any direction without coming to an end, it is not the true bending to eliminate infinities.
Why is it not the true bending?
As explained before you need to bend each and every 'one dimensional line' in the 2D plane to itself at the opposite end. I.e. Join each opposing infinity.
Let us look at the details again just before we bend the second dimension. We have our 'one dimensional line' (circle) let us leave our 10 points that each have a line at right angles to it, to create our, at this juncture, a straight tube like structure with ten lines that go to infinity in opposite directions (all parallel to each other).
What we did before, was to take each line in turn and join it to itself at the other opposite side (opposite infinities). We ended up with ten circles (one for each point). Correct. This is not a sphere!
Now what is a sphere?
A sphere is where instead of joining all opposite infinities together, you join all positive infinities together, and all negative infinities together!
In effect you are jumping from one infinity on one line and joining it to another infinity on another line in the same direction, in effect you are joining all ten (positive) infinities at one end, and all the opposite 10 (negative) infinities at the other end.
It is equivalent at looking at your tubular structure and deciding not to bend the whole lot, just crunching the ends together.
Crunching the ends is not the same as bending.
A sphere is topologically the same as a closed tube, you can stretch a sphere and it will look like a tube. [The ends of the tube are closed].
If you stretched it towards infinity in both directions, then traveled along it to one end you would get to the end and you would then turn around at that end and come back on yourself in the opposite direction until you got to the centre, then you would go to the other end and turn around and come back again in the opposite direction until you got back to the centre again.
The two ends of the tube are not joined to each other. (The two opposite infinities are not joined to each other).
In the true bending you do not reverse direction (at what would appear to be infinity), you truly end up at the opposite end and just keep going in the same direction to get back to the beginning, a real loop.
Now you should see a pattern, a one dimensional line needs one bend, (one circle a loop back to the beginning), a two dimensional plane needs two bends, (two loops), a three dimensional volume will need three bends (three loops). And the pattern will continue for each dimension you TRUELY want to bend and eliminate infinities.
End of Concept Three.
So what is a three dimensional volume?
Let us look at our two dimensional surface and try to bend it. It is the surface on our tubular ring.
To avoid stressing the brains or minds of everyone, let us just look at the simplest way of doing this, the end results end up the same (as in all the options of the two dimensional bend).
If we stand back and look at the tube as a whole, side ways (like a doughnut side on), (similar to the circle on our paper sideways) now extend the tube at right angles, you get a solid tube on either side. The original circle created a surface on the tube, the doughnut creates a tube that has solid walls and empty inside extending to infinity on either side.
Now bend the whole lot joining opposite infinities together.
You end up with a bigger doughnut, that has hollow bits inside.
Difficult to visualise, but if you think topologically, you can squeeze it into a spheroid shape and make it look like a sphere, except that the sphere has a tiny hole at the North and South Pole that join together, so you can travel through the sphere without breaking the surface.
Now things get more complicated still when we try to bend the fourth dimension.
I mentioned at the beginning when we were going to bend the first dimension, I said 'if we could travel along the line to infinity'. We obviously can not travel along a one dimensional line, because we are not one dimensional, nor two, three, four, five, etc. until we get to our true dimensional nature. So therefore up until now we have been talking and explaining things in terms of total Abstraction.
So let us start to explain things in more 'Realistic' terms.
We have to add a bit more reality by adding time, but not just any time.
We need to add 'Real' time.
What is 'Real' time?
Believe it or not it has to be something real that can be measured at least in theory.
Something has to 'Exist' to move along the one dimensional line. Time just measures the movement of this existence.
3rd May 2014
Private & Confidential Copyright © Mr A Pépés
Now Existence normally refers to a measure of time. Eg. How long (time) does something exist for?
So it may appear that time is measuring time. I.e. If something exists for no time, then it doesn't exist!
There appears to be a paradox. But this can easily be removed by defining two different dimensions of time. The first dimension (or property) of time is 'does something exist?' If it does, then this something has Existance (notice the spelling, not existence, existence is a transitory thing that can cease). Existance on the other hand is permanent (it never ceases to exist).
When we normally measure time, we are measuring a different dimension (property) of time. This other dimension of time is merely measuring the change of Existance or Existence of 'something'.
In other words if this other dimension of time is zero the 'something' still exists, it just means that nothing has changed.
[Please re-read the previous paragraph and understand it properly].
If the first dimension of time is Existance, then why did I say the other dimension of time and not the second dimension of time?
I said this because there are more dimensions of time. I will explain.
If we go back to our original one dimensional line, I said if we could travel along it. To travel along it we would have to measure time. Which now means we would first have to exist (have Existance) then measure our change of existance along that line. (Two dimensions of time).
Stopping time means we just exist at one point along that line somewhere.
Now let us look at two dimensional lines (the plane). The same thing applies again, but this situation is different. We still have to exist, but we have a choice of which dimension to travel in.
We could travel in time along just the path of the one dimension infinitely, or stop somewhere along that line and then travel along the second dimension.
Now notice what has happened, I said earlier stopping time means we just exist at one point along that line somewhere, in other words the coordinate along that one dimension is constant, doesn't change. But we are now moving along a second dimension.
What is happening to time?
Is it moving or not?
Well the answer is yes and no. What?
Let me explain. There are three options.
First we could have stopped at some point along the one dimension, and did nothing else. (Time stopped).
Or we could have stopped at some point along the one dimension, and started moving in the second dimension.
Or we could have not stopped moving along the first dimension and we started moving in the second dimension as well.
There is a difference between the second and third options. To be able to measure this difference accurately we must be able to measure the existence of time in each dimension. I.e. We can define another dimension (property) of time (one for each dimension).
So in the first option when we stopped, both dimensions of time stopped (became zero).
In the second option one dimension of time stopped (became zero) and the other dimension carried on.
In the third option both dimensions of time carried on.
You should be able to see that if we have 3 dimensions, you could stop anywhere on the 2D plane and travel along the 3rd dimension, or move in all 3 directions simultaneously, therefore there is another dimension of time for the 3rd dimension as well.
Time is not just one dimension but 3 dimensions (4 with Existance).
Things start to get interesting.
What is going backwards in time?
This now gets complicated as you will be able to guess, you can move backwards along one dimension and forwards in the other two!
I will tackle this in another Tea Break Book, as we are still bending dimensions back on themselves.
Are there any more dimensions other than time and space?
Yes the missing elusive 5th dimension. I still call it the 5th dimension for conventional reasons (even though I have made time 4 dimensional so far).
What is the missing 5th dimension?
It is the dimension of Density.
Why density?
Most people think of things (separately) in space and time, but I will show you (explain) that density is a dimension (property) of space and time.
Because everything 'Real' that exists (Existance) be it energy or matter (whether vacuum, dark, light or Ch'i etc.) has a density.
So if we go back again to our original one dimensional line, we would exist at some point with a density of some sort and move along it in time. Stopping time in this context does not change the dimension of density, we still exist.
If density is a dimension then it must be able to increase in one direction and decrease in the opposite direction, and if we are to eliminate infinities we must bend it so that the two ends join (like the normal 3 dimensions of space). We have to make it cyclic.
How do we do that?
Let us break it down.
You can increase the density of something by packing more of it into the same space.
You can decrease the density of something by packing less of it into the same space.
What space?
The Euclidean space that we know. But is this not what most people think of things already, that I said I would explain differently.
Yes and no. I will explain.
If we think of things in the conventional way, then things with density occupy space.
But I said that density is a property of space and time itself.
How can that be?
Well we have to go back to the drawing board and re-examine space itself.
What is space?
Conventionally it is defined by points, lines, planes, and volumes. All points being equal.
Now imagine that all points are not equal. Some points ('Real' points) have a density and some do not.
What is space now?
Well we can define it in the same manner as before except now points, lines, planes and volumes can have different densities (that they did not have before). Things are not superimposed in an empty space anymore, they are the space.
Now we have to look at things in more detail.
How is this density distributed?
If there were a flow along any dimension i.e. A movement along a line then there would be a time that could be measured along that line.
24th July 2014
Private & Confidential Copyright © Mr A Pépés
Let us look at a one dimensional line first. In a time interval one could move past many points, some of which would have a density (let us make it simple and say each point has the same constant density) and some not (let us assume for now that the spacings between our points is constant). That line that you travelled along would have a density of the density points divided by the total points in the line.
This same principle can apply to the other space dimensions. You end up with volumes of space with different densities existing for specified time intervals.
Now if you were to put two equal volumes together to occupy the same space, so that the 'Real' points do not overlap, you end up with a volume that has twice the density.
If space is quantised (explained in another Tea Break Book) it can be considered that each piece of space can have the properties of these bent dimensions (we are effectively specifying a very small r for our circles) and making a little Universe in itself (I call an 'APE'), it would have it's own density. The 'APE' moves in a certain fashion (explained in another Tea Break Book) such that it increases and decreases it's own Secondary volume and it's own density. (I.e. It has it's own inbuilt (minimum and maximum) dimensions of space, time and density).
Now our Universe (the big Universe) is just constructed from the sum of these quantised bits of space, whereby any volume and any density can be constructed.
How do we now bend this dimension?
[We can bend it on the quantised level (in another Tea Break Book)].
We can only bend density in our 3 dimensions (I.e. Using Secondary volumes).
We bend it by using these quantised bits of space ('APE's).
The process is what I call 'the inversion of space'.
Density has a built in minimum and a built in maximum, the two opposite ends, on a quantum level.
It also has a built in minimum and a built in maximum at our level also.
Density is proportional to volume
When we add volumes of 'APE's together we can either keep the same density and increase the volume or we can compact the two volumes and increase the density.
9th June 2015
Private & Confidential Copyright © Mr A Pépés
After reading the above, it appears to end abruptly. I obviously did not finish it. Anyway I think I will write another Tea Break Book on the mechanism of the 'inversion of space'.
Morph your mind with Morphological at
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