Advanced
Study
Excerpt From Chapter 22
Proto
and Eleah (God's Math)
The Infinite yet fully
Definite Plane of Symmetry Math
The nature of infinity is very much an unresolved mystery in both physics and
mathematics, but there are a few tolerated infinities, such as electrons and
black holes. And there are infinite series equations which mathematicians say
are defined because they express Convergence. For example, .999... is said to be
equal to 1, even if the universe’s fastest computer would never be able to
appreciate the .999…as a single definite value.
Other examples of convergence include:
The sequence: 1/1, 1/2, 1/3, 1/4 ...
is converging toward 0.
The equation: 4  2  1  1/2  1/4 
1/8  ... is converging to 0 also.
The equation: 1/2 + 1/4 + 1/8 +
1/16 ... is converging toward a limit of one.
And the equation: 1 + 1/2 + 1/4 + 1/8
+ 1/16 + ... is converging toward 2.
Obviously (1 + 1 + 1 + ...) is not a convergent series, it has an increasing
value, so there is never a completed sum. There is no convergence. In ordinary
math we think of the set of positive or negative numbers as continuous and
indefinite.
In
symmetry math there is one ultimate value which contains all other numbers and
on either side of Omega Zero other values decrease. As we count into ever larger
numerals, the symmetry value decreases toward an infinitely small value.
Consequently, the values of larger numerals converge toward two outer extreme
points. This clearly visible convergence allows positive infinity and negative
infinity to have definite values. So they can be represented as two numbers.
Consider what a relief this model is to the anxiety of indefiniteness in
ordinary math.
Unlike our present finite system of values,
which definitely does not consider positive or negative infinity to be a
number, in symmetry math we can define two final numbers on either side of
zero. In symmetry math, if we add ones endlessly (1+1+1+ ...), there is still
always a next greater numeral, but the value of the sum is decreasing and
converging toward a point of infinitely small value. That point is a last
number. I call the convergent sum for positive numbers Proto,
which means first in time. Proto is a numeric representing positive infinity,
here written +∞. I call the ultimate negative number
Elea, the sum of all negative numbers. Obviously I derived the names from the
proton and electron.
In treating a positive and a negative infinity as numbers, we then can write
this simple equation:
+∞ + ∞
= ∞ = 0
All of symmetry math is defined and whole, bounded by extremes, just as
pattern space is defined and whole. The symmetry plane is infinite but
bounded. As a result, we can begin from Proto or Elea and count toward zero.
Figure 22.1: In symmetry math
the whole mathematical
number line is a spectrum of infinities extending out
from a whole infinity toward two half infinities.
In ordinary math the nothing of zero cannot relate to positive or negative
infinity in the way convergence allows the extreme values of this symmetry
mathematical plane to relate. Unlike ordinary math, in symmetry math we can
say both sides of the plane are perfectly balanced around zero and not
balanced around any other number, simply because Proto and Elea are definite
and absolute values. They are definable as numbers, where in ordinary math
there aren’t ultimate positive and negative numbers, since we can never reach
the end value of a nonconverging series.
Three Different Answers
We
can now reconsider the issue of there being three incompatible answers when
summing all reals or integers. If we keep in mind that in symmetry math we have
boundaries, zero in the middle, and Proto and Elea on opposite ends, we then
again consider the equation:
(1
+ 0) + (2 + (1)) + (3 + (2)) + (4 + (3)) + ...
Since positive infinity is a number in symmetry math, we can count away from
positive infinity toward zero, and so we can consider an end to this equation.
As shown below, now the equation ends definitively with the same displacement
that it began with, and since the equation is a sum of all numbers, the
equation ends by also summing the number Elea into the final sum, causing the
equation to equal zero, as shown below:
Figure 22.2: Notice that Proto
can be subtracted from or reduced, but not added to. Elea can be added to but
not subtracted from. Also note that in symmetry math the addition of ∞ and +∞
is actually a combining of
both sets into an ‘everything’, rather than a cancellation of positive and
negative which creates nothing.
Math and Order
One of the surprising and elegant features of symmetry math is that although
the two smallest numbers, Proto and Elea, are points of infinitely small
value, each number still represents half of the whole. What do I mean by half
of the whole? Where the symmetry value of the number one includes all numbers
except (1), the symmetry value of Proto equals all numbers except all the
negative numbers. All the negative numbers must be made separate, just as
grouping order separates the game pieces of checkers. All we can do is remove
all the negative numbers, or all the positive numbers, from the fullness of
zero, which makes Proto and Elea the two smallest possible values in this
system. Consequently we don’t have a value of nothing in this system. Proto
and Elea are as small as any values can become. So even though Proto contains
the infinity of all positive numbers, relative to all other values, it is
infinitely small.
Obviously the infinitely small value of Proto (and Elea) can be related to the
infinitely small size of the Alpha state of the big bang. Just as spacetime
collapses in our past to a smallest possible size, Proto and Elea are
equivocally the smallest possible values in symmetry math. Then just as the
Omega zero of symmetry math is infinitely large and contains all numbers, the
expanding universe ultimately becomes a space that extends infinitely in all
directions. Symmetry math is essentially a mathematical model of the Universe.
Symmetry math provides a great deal of insight into the properties of the
Alpha state from which time originated. Proto is all positive numbers grouped
apart and unified into a positive singularity. Proto is a positive oneness, an
ultimate one that is positive, like the 1 byte of computers. Some of Alpha’s
properties such as "uniformity" are similar to Omega’s properties. The
greatest difference is energy content. Since the very nature of being positive
or negative is imbalance, the extreme positive of Alpha is naturally a very
energetic state, a probabilistic energy all aimed at moving toward balance.
Some big bang theorists describe time originating from a false vacuum, which
is an empty space that for some reason isn't stable.
Symmetry
Math and Space
In the same way that we live caught between two kinds of order, in
terms of space we live in between a three dimensional (3D) space and a four
dimensional space (4D), so we live in a fractional 3.x space. We might guess
that we live in a 3.7304572 dimensional universe, that is expanding and so
moving ever nearer to the complete 4D universe. Further, I believe a negative
curvature is properly understood as being identical to an expanding space, and
a positive curvature is identical to gravitational contraction (both are
necessarily temporal). A negative curvature is time moving forward. A positive
curvature is time moving backwards.
Relative to our expanded 3.x space, the Alpha space in our past, which
is only a 3D space, is infinitely curved (and hot). Even though Alpha is a
simple flat and empty infinitely extended space, that space is the smallest
space possible and appears infinitely small relative to our much larger 3.x
expanded space. So for example, a contracting universe (big crunch) could only
reduce to a 3D space which we perceive from within spacetime to be a point.
This explains why some physicists see a vacuum at the beginning of time while
others see an infinitely dense singularity. They are the same state.
Inversely, an expanding space ultimately becomes a 4D space (after a big rip
type of ending), which is an absolutely full 4D space, meaning it contains all
possible curvatures, or all 3.x fractional states (same as superposition of
all possible universes).
An expanding universe is the result of a single 3D (positive) space colliding
with a single 3D (negative) space, i.e., Proto and Elea, which causes the big
bang. A summing of the two spaces results in a perfectly flat, fully inflated
4D space, i.e., the absolutely stable true vacuum, which is the absolute zero
of all physics (a neutral space). Brett McInnes (2002 big smash paper) and
Robert Caldwell (2002 big rip paper) have both referred to the end of time as
the "final" and "ultimate singularity". Time ends as the ultimate 4D
singularity. And this 4D singularity is the native state of reality, i.e., the
default setting. It is the nothing that is everything. The two 3D spaces
(positive and a negative) are inevitable components of a 4D space, two perfect
halves of the 4D whole. A Euclidean 3D space can only expand, contracting
toward a 2D or 1D space violates conservation of the eternal 4D whole
(although we can understand the components of a 3D space as built from lesser
dimensions. I prefer Rob Bryanton's model where a one dimensional line, and a
two dimensional split, and a third dimensional fold, produce a three
dimensional space that is seen as a point from higher dimensions. Note that in
Bryanton's model we can more clearly recognize the full space (Omega) in our
future to actually be 6 dimensional, 3D + 3D = 6D, i.e., time equals 3
dimensions of space).
In summary we can appreciate the consistency of structure between symmetry
math and the two kinds of order. Symmetry math produces the same structure as
the SOAPS model explained in earlier chapters. All possible curvatures (all
possible states) exist between an empty Euclidean 3D space and a full 4D
space, like slices of a whole pie. All fractions are embedded in the 4D whole.
Conservation of the 4D whole is always enforced (the ultimate global
symmetry). In the distant past, the electromagnetic energy of a 3D space, the
false vacuum, is infinite. A 3D space is a false vacuum because
electromagnetically it is either positive or negative in reference to a full
and neutral 4D space, and so temporally or probabilistically a 3D space is
like a pendulum swung to one side. A 4D space is a state of balance. In the
distant future, the end result of accelerating expansion causes any two points
to expand away from one another at the speed of light, therein not allowing
virtual particles or quantum fluctuations. The dark energy density becomes
infinite, which is simply nature enforcing the absolute stability of the
perfect vacuum and perfect symmetry. This 4D space exists in our future,
although it also exists now, or it is the now.
Always
Infinitely Extended
Hopefully it is obvious that symmetry math relates so much more gracefully to
the largescale evolution of our spacetime than does ordinary math,
particularly so since the WMAP anisotropy probe soundly determined the
largescale cosmos is geometrically flat. Most astrophysicists recognize that
if the overall cosmos is geometrically flat presently, then even the Alpha
state had to have been flat, which means that it extended infinitely in all
directions. A cosmos that is flat in its present is always flat in its present
state, even at the very beginning of time. This seems to lead to a paradox,
since we see Alpha as a point, and a singularity, but it is simply a matter of
perspective. Everything is relative, meaning everything is intimately related
and interdependent. Even though we view Alpha as an infinitely small point at
our beginning of our time, we can see from symmetry math that Alpha is still
half of the infinite whole.
Just as Proto is an infinity of numbers, the positive density of our Alpha is
an infinity of positive space, it is just not the larger whole infinity of
Omega. Viewed internally positive Alpha or Proto would extend infinitely in
all directions as a universe within itself. It would be flat and infinitely
extended because it has infinite content (I will now sometimes refer the Alpha
states as Proto and Elea).
In comparison to other states, Proto is a very simple state that is not
further defined than itself, much like the word something. It is all the
positives divided apart from all the negatives, and that creates a seamless
union of all positives. Semantically Proto relates to the basic idea conveyed
by the word ‘somethingness’. Alternatively we necessarily perceive anything
beyond that somethingness to be a ‘nothingness’, when it is actually the flip
side of the coin, or the negative Alpha or Elea. The other side of the balance
doesn’t seem as real or valid to us, because it isn’t here. We can’t see it.
We can’t detect it.
We also sometimes conceptually deny the reality of Proto in our past. It is
said the laws of physics break down at Alpha. We deny Proto because we can’t
imagine how time could have begun from a single point in time, or from an
extremely ordered state. We only view Proto from the outside, because we view
Proto relative to the much larger expanded space of our own cosmos. In fact
our entire sense of dimension or size is ultimately relative to both Proto and
Omega.
Our most basic sense of scale originates with Proto perceived as the smallest
physical size possible in nature, half of the whole, and ends with Omega Zero
as the largest physical size. It seems a little strange but we ourselves can
seem larger than the infinite extension of Proto. Keep in mind that in science
we already know or imagine our physical bodies to be larger than the tiny
point of the big bang, which has been described as being as small as a pea,
smaller than a proton, small enough to fit under one’s fingernail. We don’t
relate to the internal dimensions of Proto, we are of the larger dualistic
world, where positives and negatives combine into something larger, so
naturally our world is comparatively larger in comparison to the vast inner
Proto universe.
Finally, the size or volume of Proto and our own cosmos are both viewed
relative to the much larger absolute fullness of Omega, which is one of two
reasons why the expansion of the universe is presently accelerating. We see a
absolute zero future as a hyper expanded space, with every spatial direction
traveling away from every other spatial direction, therein creating the most
extreme state of spatial inflation imaginable; which also happens to be the
largest Universe imaginable, and naturally so. Due to the basic principle of
relativity, we are naturally physically connected to both the bottomup and
the topdown of reality. We are invariably connected to the big picture.
Conclusions
Everyone unconsciously thinks in accordance with a logical framework. That
framework is greatly supported by a highly successful mathematical system, one
primarily based on the gain and debt of countable things. We see the world
either as a thing, or as an accumulation of things, and can't help but imagine
the many parts or the whole to be arisen above the backdrop of nothingness.
This standard view of zero as nothing (meaning no distinct things or objects)
is a valid system of understanding. Our ordinary math is based upon a
perspective derivative of grouping order, or thingness. But a view where “the
total summation of things equals zero” is also a valid system of
understanding. There are two logical frameworks to utilize in order to
understand nature, the bottomup and the topdown. They are not independent.
They are complementary. This new and unique mathematical system is derived
from symmetry order, with its foundational axiom reflecting the innate
singleness and wholeness of existence. As a perspective it doesn't see
isolated or individual things. All its values are definitive but infinite, so
it cannot divide up or count the world of objects. It sees geometric fields,
patterns, curvatures in space, that extend outward infinitely, that always
remain enfolded in the whole.
In ordinary math we count upward into an endless staircase of numbers, with no
finality or boundary, and thus reality modeled by such a system has no
ultimate sum. In that ordinary math fundamentally counts things, there is
naturally a number that represents no things, while no number can represent
everything. If we instead switch into a mathematical mode that is able to
represent everything as a whole, then naturally we find that the system
represents reality in an entirely different way. We haven’t merely reversed
values, we have changed the very nature of our system of understanding.
In symmetry math, infinity is no longer constrained to a never ending process,
but rather the infinity of mathematical values is whole, bounded only by
infinite extremes. Engulfing the finite, the entire symmetry mathematical
plane is real, complete, and consequently quiescent and timeless. In symmetry
math, zero represents everything, and because the smallest values of this
system still represent half of the whole, we no longer confuse the nothings in
this system with nonexistence. Nothings in this system are singularities. In a
purely philosophical study of the three fundamental states, Omega is of course
denoted as everything while interestingly the positive and negative outer
poles can be related to ultimate illusory concepts of something and nothing;
two singularities annotated the simplest of any two meanings, concepts which
are certainly real, but which eventually break down in an ultimate perception
of reality.
In considering the new axioms of this system, we would not expect the values
of the symmetry plane to be derived from an elementary first thing somehow
emerging from nothing or an empty set, as is imagined of ordinary math. All is
not magically arisen above nothing. In fact there is no axiom of nothing in
symmetry math to imply a nonexistence, from which we question the existence of
the rest. Not surprisingly I hope, this new system feels more like the primary
system, while the axiomatic structure of ordinary math now seems more to be an
abstract representation of reality. We just need to keep in mind the
underlying lesson we have just learned from this math, that there cannot be a
greater infinite without the finite, and there cannot be a finite world of
things without the infinite whole.
Part
Five: Designing the Multiverse
Book
Contents Part
l The Beginning of Timelessness Ch1 Time is Imaginary
Ch2
Why the Universe Exists Timelessly
Ch3 The Great
Cosmic Boundaries Ch4 Describing the Realm of All Possibilities Ch5 Caught Between Two Kinds of Order Part
II The Governing Dynamics Ch6 Natural Order Ch7 Enfolded Symmetry Ch8 Beautiful
Diversity Ch9 Something from Nothing? Part III The Comprehensibility Of All Ch10 Infinity
Means What? 10.1 A Branching Out of ManyWorlds 10.2 The Multiverse 10.3 Many Realms 10.4
Absolute Chaos 10.5 Perfection Ch11 Time is a Direction in Space Part IV The Great Cosmic
Attractor
Ch12 The Shape of All Conceivables
Ch13
Everything Moves Towards Balance Ch14 Equilibrium Ch15 Convergence Ch16 The Big Bloom Part
V The Second Law is Too Simple Ch17 Away from Order toward Order Ch18 Multiple Arrows of Time Ch19 A
Matter of Space Ch20 Built in From the Beginning Part VI Cosmic Psyche Ch21 God’s
Math Ch22 Proto and Elea Ch23 Our Basic Natures Ch24 Cosmic Lovers Part VII
Spiritual Science Ch25 Becoming Aware Ch26 The White World Ch27 God, Infinity, and Nature As One
This
page last updated
May 11th, 2007
