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 !
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
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
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
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
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
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
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
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
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
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
"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
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.
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.
Lawless ~ November 26th, 2007