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TreeIncarnation.com
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TreeIncarnation

Tree of Life, branching
through time with us
as it's leaves. [Intro]

Preface

Science
of Meaning

The Cubed IO-Sphere

Oscillating the Universe

Mirror Mind World
more soon

Guest
Interviews
 

Milo Wolff Dec 18th, '06
A Universe of Waves


Audio
Presentations


Episode 1 Jan 3rd, '06
The Looking Glass Key

Episode 2 Jan 9th, '06
Floating on Nothing

Episode 3 Jan 15th, '06
Universe in Your Hands

Episode 4 Feb 2nd, '06
Cracking The Matrix

Episode 5 June 23rd, '06
Mind Over Matter

Episode 6 Dec 12th, '06
The Immortal You

Episode 7 Jan 5th, '07
Bucky Fuller &
The Hidden Nature
of Space


Episode 8 Jan 17th, '07
Immortal
ReMemberance
How Immortality works


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Last Updated
18 Jan 2007


Ever been on a space walk ?

It's a silly question. Of course you have. Wherever you go, you get there by walking through space.

We never give this much thought, despite the fact that we are always moving through space at great speed, all the while surrounded by our own advanced life-sustaining biosphere.

Now we're going to do something even easier than a space walk. Without going anywhere, we're simply going to spin !

Spin of Space

Observing the Observation

The current quantum scientific interpretation of the properties of an electron show that a 720° rotation is required in order to observe the electron making one complete cycle. Whereas in 'normal' space 360° is one complete rotation. But we will show, that this seeming curiousity is nothing more than the result of a misinterpretation of the very nature of space.

The anomalous 720° property of quantum systems seems to tell us that the behavior of the 'quantum world' differs from that of our everyday experience. But, however counter-intuitive it might seem, this 720° rotation is a phenomena which we too can experience.on a 'macroscopic' scale. You can test this out for yourself!

First you will need to be able to spin freely on the spot, you could be standing or sitting. To do this you could use a swivel chair. Then, while standing/sitting and facing a particular direction, make one full rotation of yourself - either clockwise or anti-clockwise. Now, something very odd has just happened. It seemed like you made one rotation, but believe it or not, two simultaneous counter rotations have just occurred!

Don't believe it ? Well, seeing is believing. So,.... what did you see?

The effect which you saw with your own eyes and the effect which is observed from some outside frame of reference were not the same. There are two rotational perspectives! One the inverse of the other!

Let's say that you start off facing 12 o'clock and begin to rotate clockwise. As you see it from your perspective, the landscape around you is moving opposite to the direction in which you intended your body to move. From your perspective, the landscape is moving from right to left, i.e. counter-clockwise. But why is it that, at the same time, you somehow 'know' that you are 'really' moving from left to right i.e. clockwise ?

In effect, you have accepted that you are moving with respect to your surroundings. We tend to think that this external fame of reference is more true than what our eyes are telling us. But perhaps not! Maybe this is a misconception. Perhaps both reference frames are equally true, and furthermore, perhaps neither one can exist independently!

Drawing on the points raised in this simple experiment, we can now begin to re-interpet the properties of space. Let's explore how we can model these complimentary rotational properties, by examining simple spherical rotations.


The Hidden Rotation from Within

The sphere is the epitome of perfect symmetry. In other words, whichever way you look at a sphere from the outside, it always looks the same. But, if we apply some sort of rotation to a sphere - in any direction, this simultaneously creates an 'axis of rotation'. This axis is an implicit result of applying a rotation to the sphere. and note that we 'spin' the sphere in one direction but the resulting 'axis of rotation' describes a different direction.

This rotation breaks the symmetry which once existed, because now we no longer have something which is identical when viewed from different directions. Now what we see is differenent from various angles, and there are definite northern and southern poles at either 'end' of the rotational axis.

Lets say that when we rotated that sphere from it's symmetrical state, you spun it 360°. This initial rotation formed the polar axis, which didn't exist prior to us spinning it. So when rotating the sphere by 360° angularly, we simultaneously created not just an axis, but an axis which is actually another angle! The polar axis is an angle. It's a 180° angle. We call this a straight line. But take care. This so-called 'straight line' is really a 180° angle!

And if we fail to realize that our initial rotation implicitly created a definite axial angle of 180°, we overlook an key intrinsic property of space.

We cannot ignore the effects which this angle produces on objects as we rotate them. So, instead of simply rotating the sphere by 360° and thinking nothing of it, we must include this additional polar angle of 180° in our understanding of spherical rotation. By so doing, we add a crucial element which we will now explore in further detail.

Adding the effects of this angle as a rotation on the sphere may not seem intuitive at first, but a perfectly aligned rotation -with no other influences- is impossible to observe in reality. All observed motions are continuously being acted upon by outside forces. A body in motion is acted upon by effects which are precessional, these effects are characterized by having a perpendicular orientation in respect to the initial direction. The 180° axial angle we've just been describing is at a right angle to the direction which defined the initial rotation. The fact is, there are no isolated events. All events are in motion and all events act upon each other precessionally. Now let's consider how to include the effect of this axial angle on the rotation of the sphere.

We can simply include this 180° axial angles effect to the total rotation of the sphere by rotating the sphere 180° in an axis which is perpendicular to itself. Now, the Cartesean 'X,Y, Z' axis are themselves perpendicular to each other, so whichever axis we assume for the 360° rotation we are left with two other axes which are both perpendicular to this. If, for example, our initial 360° rotation corresponded to a rotation in the 'Y' axis, then either the 'X' or 'Z' axis will carry the 180° axial rotation. Let's apply the 180° rotation to the 'Z' axis.

Due to the effect of the 180° 'tilt', the seemingly straightforward 360° rotation contains an additional angular component and thus the rotation of the sphere is no longer a complete cycle. The inherent axial 180° tilt causes an inversion of the sphere and in fact causes the poles to actually swap places - in the very process which created them!

If we place an arrow on the sphere as we begin the rotation, the arrow points in a particular direction. We can see that when the arrow comes back to the where it started, it is now orientated 'upside down'.

This simple demonstration shows the inherent mirroring property of space. This axial angle of 180° (produced from one circular rotation) appears like a straight line inside a circle. (There is a lot of symbolism appearing here, but let's not go into it just yet.)

Extending upon these initial observations we can go further to explore some of the underlying patterns made by spatial rotations. The initial rotation of 360° produced a 180° angle which was half of 360°. So the ratio was 2 to 1. But as the marker we placed on the sphere never completed a full cycle and was inverted when it returned, we would need to double our initial rotation to complete a single cycle.

Here, instead of 360°, we rotate by 720°. Therefore using the same ratio of 2 to 1, we must include an axial angle of 360° instead of 180°. Now, after two rotational cycles in one axis and one rotational cycle in the other, the marker returns to it's original position and orients in the initial direction again. This is the true nature of a quantum systems rotation. Where, in order to make one rotation and return to it's initial position, an electron rotation of 720° must occur (not 360°).

This suggests that our understanding of the basic properties and dynamics of space is incomplete. We are only aware of these properties and dynamics because the unavoidable nature of space reveals itself fully at the atomic quantum level. There is a clear connection between the spatial analysis which we have been exploring here and the 720° 'anomaly' which manifests in quantum mechanical systems. In fact, this experiment with spherical rotations may be the most accurate description of what really happens in an electron orbital.

The real world spinning chair demonstration with which we opened this article, shows that the two rotations comprising the 720° are the result of observation from an inside frame of reference and from an outside frame of reference. Two 'inverted' rotations have occurred. This process becomes unavoidably clear at the quantum mechanical scales, where only whole units of energy (and action) can occur. At the quantum level the effects of both the observed and the observer must be accounted for fully.

These simple demonstrations suggest that the spatial dynamics which apply to the quantum scales are the same as those which apply to our everyday experience. The rotations of electrons have been experimentally observed to have an intrinsic 720° rotation. Now you can experimentally test and prove that in your everyday experience, one full 'spinning chair' rotation requires a minimum of 720° in all. When we rotate ourselves around once, we find that achieving this requires a simultaneous clockwise and anti-clockwise rotation. (one from our perspective and the other from an outside perspective).

Even though we conceptually think of one single rotation having occurred, there is no getting away from the fact that two counter-rotations must have taken place. In this way, it becomes clear that the single 360° rotation only had status in a conceptual sense, i.e. it was a notional rotation. It may well be that the notion of an apparent single 360° rotation has a relationship to our concept of a linear passage of time.

All of this hints at the underlying reason for the confused 'special case' nature of quantum space. The bias of pre-quantum classical science was not to account for the subjective experiences of the observer, as if the observer was 100% uninvolved. But when it came to the unavoidable properties of quantum systems, the effects of 'observation' and the 'observer' suddenly cropped up. Now we see that a basic misunderstanding of the nature of space is why quantum space seemed to have propeties fundamentally different than the space of our day to day experience. We have exposed the hidden assumptions which gave rise to this confusion.

Continuing with the spherical rotations in more detail, we can see even more evidence which confirms that we are on the right track. If we trace the motion of the marking pointer by drawing the path of it's motion, we see that the pointer is outlining a very familiar form.

It may not look obvious at first glance, but take a closer look.....

It's a tetrahedron!

The opened areas correspond to the faces of the tetrahedron, the areas where the path overlaps are congruent with the polar edges of the tetrahedron, while the peaks of the curves line up with vertices. This spherical rotation is describing a tetrahedron in 'waveform' !

Surely no mere coincidence. The 'simplest' of all space-occupying polyhedra is a tetrahedron. A tetrahedron has four triangular faces, where each triangle has 180°, giving the tetrahedron a total 'angular value' of 720°. So our method of rotating a sphere, which fully accounts for the effects of it's precessional axis, has defined the shape of the primal polyhedra.

Just for curiosity, suppose that the tetrahedral path that we have described here, was the 'path' describing an electron in the 'S' orbital of a hydrogen atom. Then what would we see if another electron were to complete the shell and stabilized the atom ?. Due to the Pauli Exclusion Principle, if the initial electron had the property of "spin up" then the second would have to be "spin down". To model this we could assume that this corresponds to two polar points on the sphere. If we now use two markers instead of one, and position them at opposite sides of the sphere, we will see the formation of new structure.

The effect of one tetrahedron interlocking with another of opposite orientation, is called a duo-tetrahedron or 'star tetrahedron'. And within the duo-tetrahedron is an octahedron. In order to highlight what the spherical rotations are describing, we've made the duo-tetrahedron more visible. Here it is colored yellow, while the octahedron is colored red.


The blue dotted path's follow two points
on either side of the sphere

Just as a hydrogen atom with two electrons instead of one will create a more stable atom, the octahedron we see here is a more stable structure than the tetrahedron. Notice how the paths which make up the edges of each tetrahedron overlap to add strength to the structure. In addition, the poles of the octahedron add stability through the formation of an x pattern - where the paths 'cross-over'. This is reminiscent of the structural stability of a hen egg. We know the enormous strength in the polar areas of the eggshell. Holding an egg with the index and thumb on each pole, it's nigh impossible to crack the egg by applying pressure to these areas. So there is a consistency between our spatial explorations and real world structures.

Deeper explorations using this methology reveals a complex numerical and harmonic relationship arising from these simple spherical rotations. The nature of the polyhedra is revealed as the result of spherical rotations due to precession. This technique describes some of the fundamental platonic solids.

Untying the Doughnut

Have you ever noticed that when you spin a coin or a spinning top, the faster it spins, the less wobble there is - and the more noticeable the overall pattern. Leaving aside the physics involved, it's clear that when the coin spins fast, the visual effect resembles a sphere. The faster it goes, the more stable is that spherical pattern. But as rotation slows, a wobble begins. The previously upright vertical axis starts to lean. And as rotation slows the shape starts to look like a doughnut - or torus.

This is an indication that hidden rotational relationships exist between the sphere and the torus. The torus is composed of two radial components. One radius defines the 'thickness' of the ring of the torus, while the other radius defines the torus ring's distance from it's center (this radius defines how much of a 'hole' the torus has). Notice that if both radii were the same length, then the resulting torus will have an infinitely small hole at it's center.

But, if the radius which defines the ring's distance from the torus center is zero and the ring's 'thickness' remains, then the surface of the torus would overlap with itself and it's shape would be indistinguishable to that of a sphere. This is like the effect we see with a spinning coin. It was analysis of this structure which initiated my own explorations of spheres and their axial rotations.

Here we can see how two 'kissing' spheres rotating extremely fast around each other form a torus. Overlapping the two spheres as they rotate gives the effect of the torus 'growing' from the sphere (much like the spinning coin).


Just like with a coin;
the faster the spin - the more spherical the pattern.

Extending upon this method, I noticed that if you imagine that the resulting torus is rotating infinitely fast on some other perpendicular axis, the result would be spherical again. Not only that, but the interior of this structure shows some surprising visual properties.


The 'vortex' at the center of the torus has rotated to
define a plane with two spheres implied on either side.

Note that a pattern shows up when viewing the structure from 'side on' which seems to suggest Fibonacci spirals. This model ties into our earlier exploration of simple spherical rotations. Even without the spheres showing, there are two spheres implied within the interior of this toroidal model. If we take those spheres and rotated them 720° around the Y (vertical) axis, the motion would describe the initial torus structure from the previous example. And if we then were to rotate by 360° through another axis, we would be describing the full model shown here. The underlying motion which these two spheres go through are the same as those which we saw when we rotated the single sphere by 720° and 360°. So, we can place two spheres into the torus structure and rotate them as described.


The tetrahedral pattern as described by two spheres
rotated by 720 and 360 degrees.


The two-sphere toroidal structure is helpful in visualizing how rotating a sphere along these precessionary axes can form a tetrahedral pattern. But there is another pattern which emerges from these same basic movements. When we applied rotational values to two axes, assigning 720° rotation to the 'Y'axis and 360° to the 'Z' axis, the resulting pattern was tetrahedral.

Suppose we 'flip' the rotations around, so that the axis which had the 720° rotation (Y), is assigned 360° and the axis which rotated 360° (Z), now rotates by 720°. This will invert -or mirror- the rotational values between the two axis. Surprisingly, the result is a new pattern!

Now instead of a tetrahedron, we see a 'double knot' type pattern. When viewed from various positions, this pattern reveals many interesting forms.


The same rotations applied to two spheres
producing the double loop pattern.

This new pattern arises through simply mirroring the number of rotations between the two axis, and is an extension of the mirroring nature of space seen before. The dual nature of these spherical rotations corresponds to the relationship between the observer and the observed.

The formation of these two patterns relates to the two frames of reference required for an event to take place. Just as when you spin on the spot creating two opposite rotations for a total of 720°. A similar process is at work here, creating both the tetrahedron and 'double knot' pattern. Depending on the axes to which you chose to apply the rotations, you get one or the other of these two patterns.

When you look at a clock face, obviously, you would see a clockwise rotation of the hands. If you imagine looking at that same clock face from behind, you would see an anti-clockwise rotation of the hands. Again, this is the difference between observing the clock from the outside and observing from the inside. The same happens when you look at a clock face in a mirror. It seems to advance anti-clockwise. These counter rotations are implicit, and create the tetrahedral and 'double knot' patterns. The same rotations are used, but the axes are mirrored.

Pysicists describing a rotation with vectors use a technique called the 'right hand rule'. This allows determination of the direction of rotation. If you hold your right hand out with your thumb pointing up (this will be the same direction as the associated vector), then when you curl your fingers, the direction in which your fingers curl will be a description of the direction which the vector is 'rotating'. This rule holds true only as long as your coordinate system remains 'right handed'. Technically, what has happened with this new double knot pattern, is that from our perspective, one of the rotations became inverted and went from an anti-clockwise rotation to a clockwise. You could even say that, with this inversion, we crossed over from a right-handed coordinate system into a left handed one (though technically we haven't changed coordinate systems).

This duality fits the minimum of two rotations which we have shown are needed to fully describe spatial events. So, if one pattern (the tetrahedron for example) relates to an inside frame of reference, then the other (double knot) pattern is the same structure viewed from the 'outside'.

So if one pattern is inside and the other is outside, perhaps these two might turn out to be descriptions of the nucleus and the electron of the atom! And as we delve further into the inner constituents of the atom, we find that the 720° property still present, showing that the two reference frames of 'observer' and 'observed' are omnipresent. Wouldn't this have consequences for theories dealing with the origins of life?

Summary
Not everything that can be counted counts,
and not everything that counts can be counted.

~ A. Einstein ~

Looking back at the history of modern science, the Copernican Revolution stands out as a major turning point. The fact that a heliocentric model of the solar system gave correct predictions for the motion of the planets had the effect of replacing the geocentric models of Ptolemy and disproving religious interpretations of the time.

"Nicolaus Copernicus, in his 'On the Revolutions of the Heavenly Spheres' (1543), demonstrated that the motion of the heavens can be explained without the Earth being in the geometric center of the system, so the assumption that we are observing from a special position can be dispensed with."

The success of this new model allowed Kepler, Galileo and Newton to make lasting contributions to modern science. But adopting the new heliocentric model and disposing of the old geocentric view was not without consequences.

The motion of the 'heavenly bodies' could now be elegantly and accurately explained without the Earth being at the geometric center of the solar system, but this implied that we are not observing planetary motions from some special, central position.

That the Earth rotates around the sun is objectively verifiable, but equally so that each individual observer is always experiencing its local environment from a unique central point of view. Every observer experiences it's unique viewpoint as the center of it's environment, and no two observers can ever experience that same frame of reference simultaneously.

However, from the surface of the Earth we each contribute to a collective point of view, which in itself constitutes a unique center. Collectively we have a frame of reference with the Earth at it's center. From here, we can see the sun and moon traverse the sky. And only from here can it be seen that a total eclipse causes lunar and solar disks to align perfectly - matched in apparent size. From here, we feel the immensely hot solar radiation as a mild heat on our skin and are protected from the inhospitabe cold of deep space.

Einstein's theory of relativity is a theory of motion as observed by different observers. But
what we have been describing here differs significantly. For a start, what we've described violates one of the fundamental rules of relativity: the constancy of the speed of light and it's upper speed limit. If we were to take the objective method of measuring speed and apply it to our example, we would end up with some very odd results.

In our real world example, when the observer makes a rotation, he/she observes the environment moving at great speed - even the slightest movement of the head results in the observer seeing the entire environment moving. But if we were to objectively account for the distances and velocities at which this environment is moving, we would end up in awkward situation. Imagine calculating the total mass of your environment and then accounting for it's observed movement in terms of distances traveled as you tilt your head. If you scan your eyes across the night sky, you will witness the stars moving faster than the speed of light!

The problem here is one of approach. It's not possible to objectively measure the unique experiences of the observer. There are two fundamentally different frames of reference. One is as seen (and experienced) from the inside and the other is as seen from the outside. The later of the two is governed by the objective method. But the unique experience of the observer can never be objectively known.

Think of it as akin to a poker player's hand which remains concealed from the rest of the players throughout the play. It's this aspect which is unknowable to the other players and which gives the player the freedom to bluff strength or weakness. Using this it is possible for the player to gain an advantage over the deterministic odds of the game. But more than this, the game would not exist without this privacy. It's this same privacy of each observer's unique experience that gives life the ability to leverage itself beyond the predicteable rules. It is through this freedom that life gains an edge over the deterministic and probabilistic laws of physics.

At this stage you might ask.... "What kind of physics is this?"
Well, who said it was all about the physical?


We can take another key perspective on the two counter-rotating movements, as described in the real world spinning chair experiment, to see what this implies about entropy and energy transactions. In the experiment, we noted the two points of view (POV) which produced the counter- rotating movements. One POV was from the perspective of the outside environment. Let's call this 'O-POV'. Then there was you, the inside, or the individual observer perspective, which we'll call 'I-POV'.

So, in brief, here is what happened. From the O-POV, the environment did not move, only the individual moved - clockwise. On the flip-side, from the I-POV, the individual did not move, while the environment did move - anti-clockwise. Notice that the sum total of this positive and negative action is a canceling out. The O-POV results in a plus one rotation for the individual, while the I-POV has a minus one rotation for the environment. The sum of the two is zero. It is 'normalized'. This is true for all motion. But if so, then what's the whole point of motion? Has anything been gained ? A lot has been gained, but before we get to that, let's fill in some extra details about the two transactions that have taken place.

In the experiment, the O-POV is the objective perspective. Fom here we can see that the energy required to make the individual rotate, started in chemical reactions within the individual's body. Food, water, air, etc. were converted into energy to be transported into the cells of the muscles. The energy was then used by the muscles to achieve the rotation. The end result was a dissipation of energy into the surrounding environment, in the form of friction and heat. This is in line with the well known mechanisms of entropy, i.e. the tendency for energy to dissipate from stored up (ordered) states.

Inversely, the internal I-POV had another kind of energy transaction which can be seen as a gain in ordered energy, but of a kind which is not easily quantifiable or measurable. If we trace the information (i.e. energy) which the individual received from the environment, we will find that the light from the environment has triggered impulses in the eye, which in turn causes a chain reaction of impulses which will end up as information relayed to the brain. This is as far as we can trace the physical forms of energy. The sensing mechanisms of the brain is where the trail ends.

But, we haven't said anything about the value which this information carried. It was the experiential knowledge of the environment which was of real value to the individual. It was the meaning the information portrayed which was important. The value of this kind of experiential knowledge is priceless to the individual yet is not measurable in terms of an energy gain. Even if we say that this information was merely transferred into memory, we still cannot disregard it's value to the individual. This is negative entropy, a gain which can not be physically detected. The value is what the information means to the individual's unique situation.

It's clear to me that the two counter rotations can be related to entropy and negentropy. There is an accumulation of order through a gain in experience and meaning, while a simultaneous dissipation of stored energy takes place in the environment. On the surface, it may seem that perhaps the sum total would be that the two processes simply cancel each other out and that nothing is really gained. But due to the constant 'non-physical' (metaphysical) increase of experience, there is always a gain. And even in purely physical terms, the dispersal of energy via entropy means that nothing is really ever lost.

Perhaps this means that time, instead of being a measurable linear phenomenon, repeating forever without change, can best be understood as experienced. Constantly changing and growing.

Appendix I
Rotational Ratios

There is one last 'twist' to the kinds of patterns which this method creates. If we increase the number of rotations upon each axis by equal amounts we get a faster moving sphere, but one which creates the same pattern. For example, to get the tetrahedral pattern we applied two rotations to the Y axes and one rotation to the Z. If we double the values to four rotations for the Y and two for the Z, we would still be using the same ratio of 2 to 1. The result would be the same shape, but at a higher frequency -so two identical tetrahedral patterns will be created over the same period of time.

It is only when we change the ratios of the rotational values that we will see new patterns emerging. Below are a few examples of some basic ratios, starting from the left, we see the original 2 to 1 ratio creating the tetrahedral pattern. Next is a pattern which has the ratio of 3 to 1, then next we see the 4 to 1 ratio, etc.



From left to right;
The ratios 2:1, 3:1, 4:1, 5:1, 6:1, 7:1


The patterns created from each of these ratio's reflect some of the interesting behaviors of number. We can see here that the even numbered ratios (2 to 1, 4 to 1, 6 to 1 etc.) have a lot in common. They all display spiraling paths, the number of which is double the number of their ratio. Four spirals from a ratio of 2 to 1, eight spirals from 4 to 1 and so on.

Conversely the odd numbered ratios had an different quality. The number of spirals associated with each odd ratio match perfectly. The 3 to 1 ratio has three spirals, the 5 to 1 has five, and so on. Notice how this comes about. Each ratio has the effect of either causing the spirals to re-trace their original path (add to each other), or to form only unique paths (separated). The result is that the odd numbered ratios have doubled-up spirals (where the path has re-traced itself), while the even ones have separated out spirals, where only a single path is created for each spiral.

These are not the only relationships we find here. When we flip the rotational values between the axes (where the ratio of 2 to 1, becomes 1 to 2 etc.) we get the 'double-knot' pattern instead of a tetrahedron. This holds true for all ratios and each ratio type produces unique double loops which themselves have even and odd properties. Needless to say, there is vast complexity within these relationships, but for brevity's sake, we only touch on a fraction of them here and unfortunately haven't yet applied this to harmonic ratios.

Justin Lawless ~ November 26th, 2007

     

Top graphic based on Menger Sponge by Paul Bourke. Copyright applies. Use only with permission.

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