How the Natural Unity
Expressed or Felt
in Humans is the Same
Unity that's Expressed
in Mathematical Language
John L. Waters
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Copyright 2003 by John L. Waters. All Rights
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How the Natural Unity Expressed or Felt in Humans is
the Same Unity that's Expressed in Mathematical
Language.
Revised February 25, 2003
Revised February 26, 2003 after being read and
critiqued by Chris Lee of the HSU Writing Center
Revised Friday, February 28, 2003
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1. This paper presents a precise expression which
helps us integrate our brains, bodies, emotions, and
senses with our reasoning minds.
How can unity be expressed precisely in a way that is
useful to humans who want to cultivate a sense of
unity in their bodies and understand this sense so as
to reinforce the unity between emotions, physical
sensations, and the intellect itself? The following
mathematical expression of unity presents one answer
to this question.
2. In this section and in the following section a
mathematical definition of unity is given.
Observe that for every vibrational frequency w, (no
matter what is vibrating and no matter what the
medium is,) and for every time t the following
mathematical sentence is true:
(Coswt + iSinwt)(Coswt - iSinwt) = 1 = unity
where i is equal to the square root of negative one.
We'll call the equation expressed above "the unity
formula."
3. Here is the proof of the unity formula:
Proof:
Consider the above formula, and multiply the
expressions on the left. Remove the parentheses. We
get
Cos(squared)wt - iCoswtSinwt + iCoswtSinwt +
Sin(squared)wt = 1
But iCoswtSinwt - iCoswtSinwt = 0
so we are left with the sentence
Cos(squared)wt + Sin(squared)wt = 1
But this sentence is an elementary trigonometric
identity that is derived in any textbook on elementary
trigonometry.
Notice that by starting with this established
trigonometric identity, we can argue in the other
direction and obtain the mathematical formula for
unity presented at the beginning.
Hence we have proven the desired result
(Coswt + iSin wt)( Coswt - iSinwt) = 1 = unity.
QED
We'll call this formula "the unity formula."
4. Any repetitive movement enables a person to apply
the unity formula and sense the natural unity that is
the number one.
The unity formula expresses unity in terms of any
vibration over time and relates the presence of
vibrational activity in time to the sense of unity in
time. Note that w=omega is any single vibrational
frequency. Omega is any constant number. This omega
frequency can be a certain color, a certain musical
tone, the constant ticking of a clock, the steady
dripping of a leaky faucet, a shaman's drum beating
steadily, the steady beating of your own heart, or the
rocking of a rocking horse a child plays upon. Some
children even rock themselves and don't need to be
rocked by another person or by some device such as a
wooden horse or a swing.
5. In the unity formula two complementary circular
movements are described: one clockwise, the other
counterclockwise.
Note the circularity in the movement indicated by the
unity formula. As the vibration continues the
movement is clockwise in the factor
Coswt - iSinwt
and counterclockwise in the factor
Coswt + iSinwt.
Note that one circle is traced by a clockwise moving
radius vector and the other circle is traced by a
counterclockwise moving radius vector. Note also that
when a person walks, runs, or pedals a bicycle the
each leg is rotating. One leg rotates clockwise as
the other leg rotates counterclockwise. We observe
these balanced and complementary movements with
respect to a reference frame located at the center of
the pelvic region. Consequently when a person puts a
lot of effort into this physical activity and attains
a level of concentration in which the activity itself
is the focus, this person may have feel the "cosmic"
unity in the same way a mystic does at a "peak"
experience. Why? Because in moving his or her body
in this way the person is actually applying the unity
formula.
6. There are many ways to apply the unity formula.
The claim is that when a person applies the unity
formula, the person experiences more unity, more
comfort, and more peace.
Besides running, walking, or riding a bicycle, a
person can also apply this formula just by lying on
the ground, relaxing, and gazing up into the blue
sky. The vibrations of blue sky light felt in each
eye stimulates both sides of the visual cortex at the
back of the head. One can get the same "cosmic" sense
without having to mount a bicycle and expend all that
energy in pedaling and panting down the road. One can
listen to the steady ringing of a bell or some other
steady vibration and be struck by the same sense of
"cosmic" unity. The sense of unity is sensed in the
body of a person who has discovered the natural or
"mystical" unity, even though he or she might not know
this mathematical formula or have even studied
mathematics at all. A principle of nature is working
whether or not human beings are consciously aware of
it or understand it mathematically.
7. In counting objects or whole numbers, a person
engages in cyclic-repetitive movements but the
attention is focused on naming the numbers, not on
feelings in the body or on the vibratory movement
itself.
In learning to count, a child actually moves in a
cyclic-repetitive manner to point at objects, to touch
objects or to move objects from one place to another.
For example, consider the child who is counting
pennies. First there is a pile of uncounted pennies.
Each time the child counts one penny, the child moves
that penny off to a new pile. At the end of the
counting process the old pile of pennies is gone and
there is a new pile close by. The child knows the
number of pennies in the new pile, and trusts that the
same number of pennies was in the old pile. That is,
the child trusts that by counting the pennies the
counting process itself didn't cause any penny to
appear or vanish. So now we just examine the movement
in the child's body as he or she is counting the
pennies.
8. While counting only part of the body may be
engaged.
We observe that throughout the counting process the
child was rocking back and forth and moving each penny
in the same way each time, so in counting a pile
containing two thousand and fifty nine pennies, the
child repeated the same rocking movement over and over
again. However the child probably used only one hand
to move each penny. This is different from using both
legs and both feet to propel a bicycle.
9. Even when a person is applying the unity formula,
he or she usually isn't attentive to the omega
vibration because one is attentive to something else.
In each case the bicyclist and the penny-counter are
applying the unity formula, and each cycle is a unity.
The bicyclist produces a number of single wheel
rotations in moving from one location to another. The
penny counter produces a number of cycles in his or
her body movement, one cycle for each single penny.
The penny counter, however, is attentive to the names
of the numbers, and the bicyclist is attentive to the
roadway and makes sure he or she doesn't ride off the
road or get hit by a car. Perhaps it's more likely
that a beach bum lying on his back for hours and hours
on a warm sunny day and feeling his heart beating and
his lungs expanding and contracting and just gazing up
into the blue sky letting quadrillions of vibrations
of the color blue stimulate his eyes and brain will
sense the "cosmic" unity a lot more than will the
small child who is concentrating on reciting the names
of the numbers while counting pennies, or the careful
bicyclist who has to concentrate on avoiding potholes
and oncoming trucks, cars, and buses.
10. Many persons have described an unusual experience
that can be explained by applying the unity formula.
For example, consider what Orson Bean wrote about an
experience he had in visiting a Reichian therapist
named Ellsworth Baker. Doctor Baker subjected Orson
Bean to a session of pushing and poking, and then had
the actor lie on his back and move his legs vigorously
as though he was pedaling a bike. This treatment went
on for many minutes until Bean thought his legs would
fall off. He continued moving his legs, though, and
in his book, "Me and the Orgone" Orson Bean wrote
about how, after this session of intense body
movement, the sky looked unusually blue and had little
white points of light in it and the trees looked
unusually green. Bean also wrote that this therapy
had done more for him than dozens of talk sessions
with psychotherapists.
Orson Bean's description of his mystical experience
and altered vision after Doctor Ellsworth Baker's
treatment follows:
"The sky over the East River...was a deeper blue than
any I had seen in my life, and there seemed to be
little flickering pinpoints of light in it. I looked
at the trees. They were a richer green than any I had
ever seen It seemed as though all my senses were
heightened. I was perceiving with greater clarity. I
walked home feeling exhilarated and bursting with
energy."(1)
Bean's description of his heightened perceptions is
compatible with the descriptions of altered vision
that Alan Watts gave of his own mystical experience,
the one he recorded on page 125 of his book entitled
"Nature, Man, and Woman." Watts wrote:
"The sky was in some way transparent, its blue quiet
and clear, but more inwardly luminous than ever at
high noon. The leaves of the trees and shrubs assumed
qualities of green that were incandescent, and their
clusterings were no longer shapeless daubs, but
arabesques of marvelous complexity and clarity...
Flowers-- I remember especially the fuchsias-were
suddenly the lightest carvings of ivory and coral."(2)
11. The unity formula helps us understand
intellectually at least some mystical experiences.
In summary, recall that at the start of this paper a
certain mathematical formula for unity was shown to be
correct for all vibrational frequencies at all times.
It was then shown how this formula has sometimes
inadvertently been applied by different persons to
sense the mystical unity even though they weren't
able to give a clear explanation for their newfound
unitive sense. Lastly we reviewed the reports of
individual persons who in their writings noted an
increased awareness of unity in themselves in
conjunction with their noticing certain vibrations,
particularly certain pure colors in the sky and in
plants.
12. Additional remarks:
Autistic children don't pay as much attention to
people and social interaction and word usage as normal
children do. All or most autistic children show an
intense fascination with gazing and with repeating
certain body movements and/or exposing themselves to
certain vibrational inputs from the physical
environment. For example, an autistic children may
rock their bodies or gaze at a colored wall or
something else that normal people don't consider worth
paying special attention to. This can be interpreted
as another example of humans applying the unity
formula to experience a great peace or at least a
needed relief from a chronic inner tension that normal
people don't feel.
Furthermore, a shaman beating his drum combines the
repetitive body movement of beating the drum with the
hearing of the steady repetitive noise from the drum
head itself. It may be suggested that these two
inputs help the shaman sense the unity of the whole
"Big Holy" (as the Native Americans often call it.)
13. The unity formula helps us a lot.
The unity formula helps us intellecually understand
the sense of joy, fulfilment, tranquillity, serenity,
and peace, the reduction of tension, and the
repetitive physical movements in both autistic
children and in so-called "holy" persons including
chanting, drumming, and spinning in circles that many
persons employ to enable them to cultivate their own
sense of unity and peace. Even tethered circus
elephants have been observed rocking their bodies.
One can ask why an animal would expend all that
physical energy unless it brings the animal some
pleasure or other benefit.
14. The Unity formula enables us to understand the
sublime emotion and feel it more and more.
Now that the source of the sublime emotion is
intellectually understood, more persons can undertake
to cultivate this sense in themselves. This is a good
thing because consciously applying the unity formula
more will bring more comcort and more peace to more
people at a time when billions of human beings are
experiencing more and more negative effects of
socially-sanctioned conflicts and destruction of
nature as well as humanity.
15. Human harmonization and integration is a
progressive next step in human education and culture.
Integration and harmonization of the highest human
emotion with the rational intellect and with human
vision and the other senses helps each conscious and
reasonable human being feel blessed repeatedly and to
eliminate wanton environmental destruction as well as
genocide and other destructive activities which are
still commonplace today.
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References:
1. Wilson, Colin "The Quest for Wilhelm Reich"
(Garden City, New York: Anchor Press/Doubleday, 1981)
p. 165
2. Watts, Alan "Nature, Man, and Woman" (New York:
Pantheon Books, Inc., 1958) p. 125
John L. Waters
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