|
By
The Numbers {2/22/2002} |
|
In
the tradition
of the Pythagoreans, the universe is running on integers and
rationing. Numerology, then, was the way of looking at just about
everything. We are not staying with or departing from tradition. Yet,
the picture of the HyperStates is mostly about integers and
near-integers. One hyperstate is a ratio. One other hyperstate,
although it is computable and potentially real, does not seem to
actually form. As of now, there are ten realizable and observed
topologies in the cosmos |
|
There is much
similarity between the colorful dots of hyperstates and the Tetractys
of the Pythagoreans. Verbal interpretations of the Tetractys from the
Pythagorean tradition such as the "universal order" in
literal terms and "nature's spring" in the figurative sense
are indeed close to hyperstates. A new platform, if true, is not the
end but the beginning of the next building phase.
HyperStates
start with Tetractys of Pythagoras
One
(blue) state is added and all eleven states are placed on one facet
of the tetrahedron. We arrive at the triangular pyramid geometry
|
|
If you came here
looking for some good applications of the Pythagorean Theorem, we use
it in the construction of the golden
proportion. Another app is the geometric
mean, which makes a square out of any rectangle and also gives
you a square root of any length.
If you have
questions regarding the story that Pythagoreans feared irrational
numbers, read up on it in this footnote
on free energy. It may be based on the
mysterious applications of irrationals that "they" do not
want you to get into.
Operators also
issue from numbers at the commencement of the realization of the
second dimension because a movement or a measurement is required. Say
hello to the friendly transcendental number
Pi.
As soon as you
constuct the circle [the meaning of a circle takes a while], you may
get an itch to divide
the circle into exact and even segments. This brings the power
of geometry home. Oh, and the stars, too.
Once you know
which numbers can divide a circle, you may want to tackle the squaring
of the circle. Transcendentals and irrationals can be tamed but
this is a new thing where magic becomes a component of geometry. Then
again, atoms do it every day.
We also have a
summary of Pythagoras'
accomplishments on our credits page. |
|
|
Fundamentally,
numbers come first. The Pythagorean Tetractys with 1, 2, 3, and 4
dots also refers to 0, 1, 2, and 3
degrees of independence, because 1 is associated with a dot, 2 with a
line, 3 with an area (plane), and 4 with volume (some say solid).
Degrees of independence are, again, numbers. Degrees of independence
form the fundamental constructs for geometry.
Dots of the
Tetractys plus one (blue) dot form hyperstates.
Hyperstates
are about the creation of the real environment that is tractable (non-chaotic)
and that has its origin in the virtual domain, which is oftentimes
called hyperspace
or ether or "fire." Hyperspace is intangible (invisible)
and is not explicitly shown in the HyperStates picture because
HyperStates is about the one single facet of the triangular pyramid
where all real (visible, hard) topologies manifest. We can represent
the hyperspace as an eye and put it on top, which results in a
triangular pyramid of tetrahedron with the eye at the apex.
Presently, the HyperStates picture includes three axes that project
the real plane from the hyperspace or from one's eye. The projection
from one's eye reveals the individual and the collective way of
building the real world on the real plane because it is our
cumulative knowledge that continues to compute and create the ever
growing and organized universe.
Although
the solutions for the axial parameters converge toward integers, the
integer value is not fully reached — but their sum adds up to
three exactly*.
The sum being integer three stems from the fundamental maxim of the
real domain, which deals with tractability limits. (Tractability is a
subset of computability.)
If we define the
triangle as the "summing triangle," then the outer
hyperstates would be on the triangle's edge. The triangle can also be
defined axially as the "bounding triangle," in which case
the outer hyperstates would be just inside it. In either case, all
hyperstates are in the plane formed by the triangle and that is the
reason for calling the triangle the template of the real
plane.
Technically, each and every point on the real plane is a solution
but because the plane is also a logical plane, there is no
measurement metric associated with it. The creation of realities,
then, has no prescribed size. If we apply integers to the real plane,
the summing of 3 out of 4 numbers (0, 1, 2, and 3) in a way that
results in integer three
yields ten
integer-summing sequences,
which correspond to 10 hyperstates.
The
presentation (orientation, rotation) has no overwhelming preference. The
spherical galaxy hyperstate is at the top corner as magenta. It may
be said that spherical galaxy's organization is closest to the
"harmony of spheres." However, bodies have no independent
movement in hyperstate 3,0,0 because they all move in synchrony.
Orbits also are not purely spherical but have a large degree of
symmetry. Hyperstate 0,3,0 could also claim the top and the sun is
indeed an awesome sight — yet the sun can also go nova.
Hyperstate 0,0,3 is a simple one and, while common and uneventful,
there is opportunity there for new growth because the growth is
mostly localized. In the alchemical tradition a discourse on
orientation would fill many pages. [If your ship is in hyperspace,
you do not want to materialize in 0,3,0. But if you are building a
centralized organization, that is the place to be..] Hyperstate 3,0,0
has periodicity while 0,3,0 does not. Hyperstate 0,0,3 has
translational (linear) repeatability that can be called periodic as
well since the velocity there is constant. In summary, Hyperstates'
triangular plane has neither the "top" state nor a
direction in which it is pointing (up or down or sideways).
Organized
topologies also hold on the atomic scale and it is likely we find
additional hyperstates there in addition or subtraction to those
shown here. It is also likely that periodic and non-periodic
(event-driven) hyperstates can be realized on the atomic scale. On
the atomic scale the hyperstate realization hops around because the
plurality of electrons can instantly transition into another
computable assembly on the real plane where tractability holds (the
real and temporary states are at times called eigenstates). Much
promise is in understanding the tractability of the core, for
completely new elements could be created. A [easy] case can be made
that the core eigenstate is periodic and that its period is constant.
On
the cosmic (macro) scale, the manifestation of a particular
hyperstate is the solution – that is, a particular hyperstate
realization is the last step in itself. Hyperstates do not change or
evolve because they are solutions (final condensate) resulting from
unbounded and concurrent computations of the whole. One can argue
that a gradual change from a dual-sun system to a sun-planet system
can be called evolution but in fact it is a two-body system that is
the one and the same hyperstate. New hyperstates, though, are created
every day through hyperspace and that is the norm (Pythagorean
spring, source) of universe creation and expansion. When a sun parts
into a dual sun system a new hyperstate is formed. When a new sun
forms from ether [Atum's mound, scarab], another new hyperstate is formed.
Because
the hyperstate is the final solution, there are no migrations or
evolutions. There may be logical similarities such as discus, ring,
or one-body orbit (moon or planet) topology states but there are no
in-betweens and this is because the solutions coagulate around
integers. We will not find two or more planets in an identical orbit
where there would be a gradual migration to a ring of planets.
Similarly, we will not find a planetary ring that would gradually
become a moon because, again, the ring is a particular hyperstate
that is a final solution yielding ring topology. Finally, we will not
find a discus that would reduce into a body. When the hyperstate is
not composed of (near) integers, as is the blue dot, we see greater
topological similarity as in the bar and spiral galaxies.
A good
way of looking at hyperstates is that it is a framework for real
solutions. A particular hyperstate is a tractable topology and
such topology (such solution) is independent of scale. We can find a
particular hyperstate manifestation in a planetary system, not in
solar system(s), but then it forms again in a galactic system. Scale
independence results from nonlocal computational aspect of quantum
mechanical gravitation.
|
|
QUANTUM
PYTHAGOREANS
Of all things Pythagorean
Applying the
Tetractys, Quantum Pythagoreans book describes and explains
all observable cosmic topologies. For example, the hyperstate 1,1,1
is the bar galaxy. The spiral and bar galaxies differ in but one
parameter. All topologies are particular stable solutions and they do
not "evolve" from one to another. Because all topologies
are covered in the book, Newton's two body and Kepler's orbit laws
are included as well. More.. |
|
Tetractys is not a
component of the cabala. Any method could be
used in an attempt to explain Tetractys, yet the original oath of the
Pythagoreans that speaks of the Tetractys has the most authentic root
of its meaning.
The interpretation
of Tetractys with cabalists' tetragrammation
methods, for example, does not advance the symbolism and does not
give Tetractys a measure of application. Some cabalists attempt to
modify or corrupt Tetractys by claiming that the corner states are
not real. The corner states (3,0,0; 0,3,0; and 0,0,3) are very real.
At times cabalists substitute Tetractys dots with Hebrew letters
without rhyme or reason -- and end up with graffiti. At times
cabalists add Hebrew letters to Tarot -- and end up with graffiti.
Cabala contains no geometry,
which may have been the intent. (Geometry issues from numbers and is
the first step toward creation.) Cabala partially addresses modulo
math through summation and recycling of numerical values. |
|
Quantum Pythagoreans book
explains the purpose and the need for the transformative agency,
which is altogether missing from the stick-to-orthodoxy Old Testament. |
|
Mystical Pythagoras
Mystic or mythical label stems
from two aspects of the Pythagorean knowledge
(1) Keep the knowledge
foundation broad for the widest possible applicability.
Tetractys is but the triangular
number ten. Take it from here.. [What? This is worse than
one-hand-clapping koan!]
Even though the hyperstates issue
from Tetractys, there is no attempt to replace Tetractys with the
HyperStates symbol. Tetractys serves as the platform for geometry in
general (0, 1, 2, and 3D) and, also, the ratios of the triangular
progressions 4:3, 3:2, and 2:1 form the basic harmonious cords of the
Western musical scale. Forced substitution of Tetractys in effect
cuts off other applications and can be seen as corruptive. Yet, in
its naked (virgin) form the ten dots of Tetractys seem impenetrable
and, to some, mystical.
(2) The richness of the
universe springs from the Pythagorean Tetractys and each individual
can grow and use Tetractys in different ways toward some new solution.
The mystical part is that
Tetractys works for some but does not work for others. It happens
that the student encounters a wall and will need to take a break. You
will penetrate "the veil of secrecy" with patience and
possibly with some background studies. If you apply Tetractys toward
some useful solution, (you can publish if you so desire, but) you
want to return Tetractys to its original form.
In addition, the student needs to
overcome the possibly genuine frustration, obfuscation, reduction, or
the corruption of Tetractys by others.
|
|
|
Pythagoreans
do not dwell on and do not fancy descriptions of reality because the
Pythagorean way is about the creation of reality. The making of
reality is not about pretensions but it is about the understanding of
pretensions. Pythagoreans do not claim that some parts of the
universe are delusions, either. The creation of real and stable and
objective systems, then, requires a thorough understanding of the
virtual domain that deals with the infinite superposition and
relation of virtual energies, each of which brings in a measure of
relevance. Conflicts resolution such as those stemming from a war,
global warming, or financial markets instability call for stable
solutions that -- short of outright destruction (usually possible) --
are not obvious or straightforward. From among the myriads of
plausible answers Pythagoreans find the ones that are executable and,
in the end, tractable. |
|
* If
you are familiar with incommensurable/irrational numbers and how
their discovery created consternation among some non-Pythagoreans,
consider that it is the sum that yields the hyperstate solution. The
individual components (addends) are integers, near-integers, rational
numbers, and reduced (truncated, rounded, fractioned) irrational
numbers -- that is, the individual components of the hyperstates are
real numbers. (Quantum mechanical aspects in the Quantum Pythagoreans
book deal with yet another mechanism besides truncation and rounding
-- that of the ancient Egyptian fractions.)
Perhaps the best
way of starting on irrational numbers is by taking a look at the golden
ratio with one original application, or It
cannot be exact
from March, 2005, DSSP topic [advanced]. |
|
What
is behind The Numbers |
|
Hyperstates
framework is difficult, though not impossible, to figure out. The
thing about hyperstates is that in the process of figuring it out you
will find the answer to something that is important to you. Your
solution may be personal or it may have wide applications. While it
is possible to teach "everything" about hyperstates, the
idea is that your solution is the most important solution. |
|
If you look at the
missing axial parameters as a mystery, you may be able to figure out
the parameters and thus the maxim. The secret behind the secret is
not the lock that would be in front of the secret, for once you
figure it out you will know there is no better lock than the
engagement of the mystery. In fact, there is no lock but an interlock
that creates order out of the competition of the triad.
The Hyperstates
interlock is so robust it cannot be stolen or given away, so
extensive it cannot be memorized, so unique you will know right away,
so practical it can be applied every day, and so logical that even a
wrong answer bespeaks of a correct concept.
Should you come
upon a person who claims the earth is flat and square while showing
you a triangle, you can laugh and enjoy the conversation while,
maybe, you will be able to appreciate there is more than one way to
the center of the maze. For there are benefits in a discourse on
square portholes when it comes to building ships and transforming new
energy sources.
Overall,
Pythagoreans may find HyperStates a significant yet natural extension
to Tetractys. |
|
|
Living
with Numbers |
|
Pythagoras
and the Pythagorean tradition puts numbers first. This may seem
difficult to some and indeed Aristotle had a field day poking fun at
Pythagoreans. The basic aspect to 'All is number' is that each number
can be constructed -- that is, each number can become.
Each number, then, can be actualized. A number is not at the core,
it is the core.
A
number can be written on a piece of paper and then the number is a
representation of something real, irrational, or transcendental.
(Irrationals and transcendentals form virtual variables.) Yet numbers
can be applied to actually come alive and that is the meaning of 'All
is number.'
Pythagoreans
not only use numbers to measure somebody else's creation -- they
create new stable and alive entities with numbers. A good question
is: What is the number or numbers the human is made of? [Actually, it
is a root of a number.] |
|
(1)
Real numbers
represent real
variables that come from real (tangible) things. Real numbers are all
positive numbers that are naturally finite in magnitude and unbounded
in multitude. Some applications need to differentiate between
unbounded [masculine] and infinite [feminine] -- and real numbers are
unbounded but not infinite. (Riemann is an excellent source on this
-- and without the Pythagorean male-female esoterica [yet, you want
to be well grounded before applying Riemann's North and South poles,
as both Cantor and Gödel got sucked in].) For real numbers, zero
is not necessary but is included -- for zero's benefits prevail over
formalism. [You will know you are over-doing it when you talk mostly
about things you don't have.] Real variables result from a
measurement of real entities. In reverse, real numbers create and
constrain real things. The result becomes a real value -- that is,
magnitude. Real numbers relate to other (mostly real) numbers with
operations such as +, -, *, and ÷.
Commutative property holds and is applied through the (real) rules of arithmetic.
Real numbers also
spawn the degrees of independence (some say freedom). Pythagoras'
Tetractys also includes the representation of the degrees of
independence as four levels: Top dot is 0D (a geometric point), two
dots on the next level is 1D (a line), three dots on yet another
level is 2D (a plane), and four dots on the last level is 3D (a
volume). Pythagoras' Tetractys also creates geometry through
geometric constructs of degrees of independence. A most powerful
finding here is that each level of increasing freedom provides different
context within geometry. This aspect is not presently
understood, as all mathematicians try to treat geometry uniformly and
"as a whole" where dimensions are "just trivial extensions."
Pythagorean
geometric concepts provide powerfully simple answers to very complex
problems. For example, a question "What is and where is the
difference between a point and a line?" seems almost impossible
to answer objectively. This is the same question as "what is the
minimum separation between two points so that we can connect them and
call it a line?" Yet there exists a real answer
that also yields insight on the smallest possible separation between atoms. |
|
In the generally
commensurable world of Euclid, the size of one
thing can be used to determine -- that is to measure -- the size of
another thing. The real world of Euclid is, therefore, commensurable.
All measures in this world then also have finite (or repeating)
mantissa. The Pythagorean discovery of incommensurables also points
to "another world," which was aptly, albeit partially (and
negatively), described by Proclus. |
|
|
(2) Incommensurable numbers
form a class of
numbers in addition to real and virtual numbers. Incommensurables are
a tough crowd to understand. First, there is a separation of
incommensurables into irrational
and transcendental,
which is based on their origin; irrationals arising from straight
geometry while transcendentals arise from curving geometry. Among
irrationals there is also a separation based on applications.
Incommensurables have an infinite mantissa and, furthermore, numbers
in their mantissa do not repeat, individually or as a group.
Mainstream math
guys got it mixed up and to them the incommensurables and irrationals
are synonymous. However, transcendentals are incommensurables that
exist on a curve or, by the same token, they exist in 2D or 3D. Pi is
the prime example of a transcendental number. Irrationals are
incommensurables that are straight -- that is, they exist in 1D.
Construction-wise, transcendentals need a pyramid for their
actualization while all irrationals are constructible through the
Pythagorean Theorem.
(3)
Virtual numbers
represent virtual
(intangible) variables. Virtual variables enjoy exclusive existence
in the space of incommensurable numbers (much more on this in the Quantum
Pythagoreans book because it leads to working with geometric
constructs such as the pyramid). The virtual variable comes from (or
creates) a virtual entity just as a real variable is associated with
a real entity. Virtual numbers center about zero and include zero,
positive, negative as well as imaginary (i-based)
numbers. Virtual variables exist in infinite superposition and each
virtual variable is processed as a whole (in one, two, or
three-dimensional representation) by such operations as projection or
reduction, but most operations establish the leadership
(independence) of a variable. Presently, however, the projection,
leadership and to great extent reduction operations are not
understood very well and operations among virtual numbers are limited
to matrix arithmetic (commutative property does not hold).
The group theory
can be applied to establish transition operations between real and
virtual numbers because the operation of transformation deals with
both the variance and invariance of variables. (Pythagorean even-odd
grouping of numbers was a good start.) Virtual numbers' positive and
negative values are generally (but not always) subjective. Virtual
variables "fold in about zero" when these transform
(reduce) into real numbers. This is analogous to folding-in of a hand
held fan while the pivot (zero) becomes excluded.
A scientist has
difficulty understanding the virtual variables because the QM
wavefunction is treated mathematically as but a technical parameter
while its actual (though virtual) existence is denied.
(4) Circumpositional numbers
Here is where
geometry shines. The only way to explain and prove harmonious and
disharmonious tones is through these numbers. Circumpositional
numbers divide a circle exactly and they are treated in introductory
fashion on our pentagon
page. The complete formula on which pairs of tones are harmonious and
why is in the Quantum Pythagoreans book.
Applications-wise,
transcendentals
create closed -- that is atomic -- topologies. Applications of
irrationals are 'good' or 'bad,' and absolutely so. Some irrationals
such as the SQRT(5) form
the golden proportion and are life-supporting. Other irrationals may
not be agreeable to humans. Incommensurables are not well understood
throughout this planet's (written) history, other than that the
incommensurables are important in transformations and extraction of
cosmic energy from ether (Viktor "Cool" Schauberger,
Reiki). Proclus' description of
irrationals is probably the best description so far, although he
focuses on the undesirable aspects of irrationals.
The Western
preoccupation with reality handicaps incommensurables' applications.
The free energy (zero-point energy) effort, however, got a good start
in the US and may yet rebound. In the East, incommensurables are used
mostly for personal empowerment and healing. Incommensurables can be
actualized (come alive) only through its construction. So, the square
root of two is an irrational number that is, however, not actualized
per se. Moreover, some people think 1.41421356 is the same thing as,
or close enough to, the square root of two, but such number is a real
number and cannot be actualized
as an irrational number. Incommensurables are in the virtual domain
but their means of construction can be real, as Pythagoras
discovered. There are other aspects to the actualization and this
introduces yet another subset of irrationals. Overall, a very
intriguing number group.
The squaring
of the circle atempts to resolve the differences between curving
and straight geometries -- that is transcendentals and reals -- think
atomic construction with adaptive orbitals. |
|
Incommensurables
consist of transcendentals and irrationals.
Another way of differentiating transcendentals from irrationals is
that transcendentals do not come out as a solution from an algebraic
equation. For examples and additional discussion see the section on (in)commensurables
inside the article on golden proportion. |
|
Complex numbers is
a compound group composed of real (say, a)
and virtual (say, b)
numbers. Popularized by Gauss,
the general format is a
+ ib,
where i
is the SQRT(-1).
The i
is shorthand for ccw rotation by 90 degrees, which facilitates
transformation from the real to the virtual domain. Numerically, i
signifies that the transformation has taken place but such operation
is a paper operation. Reportedly, to be actually able to facilitate
the transformation between the real and the virtual domains (and do
so reversibly) calls for unusual skills or technologies. Anyway, the
utility of complex numbers and its notation is that real and virtual
numbers (a
and b)
exist side-by-side but do not freely interact -- much like apples +
oranges remain apples + oranges. The summation (superposition in
general) of real and virtual numbers remains as summation and does
not advance. Yet, certain operators such as multiply do mix it up and
a transformation takes place.
Real numbers are
numbers having naturally finite mantissa. Virtual entities are
comprised of incommensurable numbers with infinite mantissa and have
no real -- that is, tangible, existence. Virtual entities exist as
two kinds of energy [advanced].
As a Pythagorean,
you want to understand the meaning of all operators such as
multiplication as they work in nature. |
|
Mathematicians'
understanding of incommensurables via Dedekind is incorrect
because these numbers' mantissa must be infinite if the
incommensurable number is to remain (or become) incommensurable. If
bounded in the magnitude of the mantissa (if the mantissa is cut),
incommensurables irreversibly become real (commensurable, finite) numbers.
Dedekind could
easily earn the label of the dumbest math guy of all time.
Yet, he also serves to show the basic derailment of math today --
intractability. Intractability is well understood as the property
that does not offer solutions in real-time. Intractability, once
encountered, is something that should serve as the dead-end sign.
Intractability means that the solution is available eventually, but
not now and not anytime soon. In an example, a code-breaking that
uses exhaustive methods does not yield a solution anytime soon --
perhaps in a thousand or a million years. In an intractable situation
the exhaustive methods are, by themselves, useless. Dedekind does one
up on that. He uses a procedure in his proof that is intractable and
the proof becomes valid in the infinite time in the future. That
should be sufficient to have Dedekind declared a winner of a prize
such as "The Deep Pocket That Was" [all governments would
make short list on that]. |
|
|
Relating Numbers
While there are
plenty of differences between animate and inanimate entities, the
organizing principles hold for both. People will continue to
emphasize whole numbers as well as their sums, ratios, spatial
(geometric) relations, and logical combinations. You may note that
Pythagoras uses one for a point, two for a line, three for a plane,
and four for a volume (solid or irreducible entity). Actually, point
is zero
dimensional, line is one
dimensional, .. Get your reference straight when someone talks about
four or three or..
Numerology is not
strict and, for example, two
entities produce one
relationship. Numerology can be context-dependent when, for example,
three variables result in tractable matter while three bodies are in
general chaotic -- the number three can stand for both stability and
chaos.* Numbers, then, do not exist only in standalone fashion
because numbers also spawn the operators
(relationships). Perhaps the best example of the operator is in the definition
of Pi.
Once a group of
numbers reaches a stable system, Pythagoras calls it the Monad.
Monad is 'one-sum', a unique summing sequence or
grouping of numbers that relate through the operators. The simplest
monad is a triad -- that is, you need at least three numbers or three
variables to make something lasting out of it. Indeed, three
parameters build the whole real universe. The mystical aspects are
treated in alchemy, which deals with transformations and invariance
-- that is, a transforming or "becoming" monad has some of
its numbers variant and some invariant (see group theory). Monad is
synonymous with 'object,' 'entity,' or 'conglomerate.' A Monad is
always a real entity that is commensurable with any other monad.
(Self-Test:-) If your ears perked up on this paragraph, you are doing
well. Monad is also the first counting real number issuing from the
first real thing.
The numerology
(coming up) has a qualitative division on the interpretation of
numbers as these apply to the real and the virtual domain. You may
note that letters issue from numbers in that the vowels have even
symmetry**. In all Latin vowels the even symmetry survives, although
in the letter 'E' the even symmetry survives via the horizontal axis. |
|
|
* Religion
and mythology deals with this through the multiple talent of the
Personalities, or Aspects, of gods. Shiva can be creator at times and
destroyer at times.
** Odd
symmetry is a symmetry about a point (origin) while even symmetry is
a symmetry about a line (axis). Symmetry contains reflected
duplication about axis or rotated duplication about a point. All
Latin vowels preferentially carry even symmetry. Pythagoreans call
even numbers feminine and "inclusive" while odd numbers are
masculine and "exclusive." The Tibetan alphabet is highly
developed along both symmetries.
We
apply incommensurables/irrationals in an article on free
energy because
geometries have a pivotal role there. We also have an article on ether. |
|
Pythagorean
College Numerology |
|
|
Number or Shape |
Real Domain [
He said ] |
Virtual Domain
[ She intuits ] |
|
0 (zero) |
Naught, Nothing
(not a thing), Empty, Vacant, Symmetry about a point, Point (tip) of
the short sword or spear, Dot (molecule, atom but think smaller).
Indivisible or irreducible point (geometry), 0D. Transitions to
infinity in the virtual domain [advanced]. |
Center, Balance,
Infinity, Neutrality, Locus, Crosspoint, Intersection, Air (loose
atoms, i.e., smoke, perfume), Into zero (banish operation), 0D (point) |
|
1 (one)
|
For Pythagoreans, Unit
1 is the Great Differentiator between cosmic and atomic
Unit 1 in
geometry: the shortest length (or distance) in a particular construction
The Monad, the
first real thing and, therefore, the first counting number
One thing, unity,
single. Edge of the long sword (one-dimensional object), Solid line,
Cut into two using the edge, 1D |
Unity, entity,
conglomeration. Symmetry about a virtual line (an empty
slit is a virtual line). Single joint (or a joining operation such as
force) between two (axle, wavy wand, baton, snake, string), Drawing
down, Lightning across ("fire" operation), 1D |
|
2 (two)
|
Cutting into two
Movement, Growth,
Spin-off, Coin, Cover (blanket), (X-Y) plane, Shield, 2D
Real and Virtual
duality (3 vs. 4)
Squaring circle
duality (1D vs. 2D). Circle on top
Yin-Yang duality
with Yang above. Tao symbol well suited for dantien (hara in
Japanese, couplex in English), a "mystical" point between
heaven and earth (or yin and yang, or virtual and real) |
Doubling by
addition of the same. (This is important. The best way of seeing this
is in the biology application of cell "division." The
doubling operation "divides" the cell about the virtual
axis and two cells arise. Contrast this with the male
division, which is a real operation and the cell is physically
halved.) Tangents here on the golden proportion, left-right brain
separation, energy symmetry..
Amulet,
Relationship. Table (anything flat), Plate. Earth. 2D
Virtual and Real
duality (4 vs. 3)
Squaring circle
duality (1D vs. 2D). Square on top
Yin-Yang duality
with Yin above |
|
3 (three)
|
Monad. Stability.
Volume. Three-sided pyramid (tetrahedron). Cube [cube is not
representative of number four -- the volume is the principal
character here]. Realization, manifestation, actualization.
Projection (into real). 3D
Three is very real
despite the "spiritual" constructions of Trinities. Monad
is the first real thing that, moreover, consists of three entities.
Also, once you
accept there exists duality, the next quastion is, "if duality
forms and does not merge into one, what's keeping it separated?"
The separation is not only about isolation but also about the
transformation from one to the other (and vice versa). The
transformative element becomes the third element resulting in the
trinity (also think diagonal). |
Cauldron. Water
(incompressible but adaptable volume). Containment. 3D |
|
4 (four)
|
Square,
Rectangular, Ratio-metric, Mandala (by definition based on number
four), Cartesian coordinates.
Incommensurable
squares (very special Pythagorean concept, pyramid construct)
Non-causal
(relational). Informal |
Four corners,
Cardinal directions, Four-sided pyramid, Stability, Computability
[very complex, different levels], Two pairs (X vs. Y) of two virtual
variables (with positive and negative values), Quadrature, Infinite
superposition, Projection (virtual, square pyramid).
Inclusive |
|
5 (five)
|
Pentalpha,
Pentacle, Pentagon. Friendship, marriage (dual ring, pentagonal
pyramid). Health. Seal (protection), Root of life creation
(pyramid guts).
Division
of a circle by five is ancient, exact, and originally a secret
[Pythagoreans declassify things, too.] |
Pentacle. Safety,
closure (interlock), bonding. {Marriage and bonding is multi-faceted
topic and the best article on that is Venus-Earth merged
orbit |
|
6 (six)
|
Two
triangles, one pointing up (say, light blue) and one pointing down
(say, navy blue). Front triangle dominates. Triangles cannot merge:
May be confused with dantien,
which we gave the English name couplex and which is located
at navel. (There is much work that would have to be done for the
so-called Star of David to have the functionality of the couplex. As
it is, the Star of David is closer to being earth-earth (earth-bound)
than being about self-organization. The diagonal is there but the
count is incorrect and the point of transference is not explicit.)
Several overlays
and perspectives with hexagonal geometry can result in confused
symmetry (hence hex or hexing), which needs to be understood to be
avoided or neutralized through the understanding of all (and finite) possibilities.
Because a circle
can be divided by six exactly, you can draw a six-pointed star in a
circle. However, a six-pointed star does not harmonize and is not
derived from planetary orbits (see right column). As a single star --
derived from 3-pointed star -- the symmetrical six sided arrangement
in a single circle is (could be) associated with potentially
unbounded energy accumulation within the circle using 2D and possibly
3D Fourier -- important to know what form of energy we are dealing
with -- it can blow, too. (On the back cover of Quantum Pythagoreans
book, the drawing called 'The Heart Of The Sail' hints at this issue.) |
Heart
charka/chakra is not a six pointed star but a quadrant-based mandala
or cross or Cartesian coordinates or locus of the virtual domain. The
exchange (transformations) of earthly and divine energies happens
through dantien, aka couplex.
[Buddhists need to separate numbers three and four, and revisit
charkas' symbols. You do not want to merge three and four. Having
said that, Buddhists figured out the derived ("by
convention") existence of time and maybe they think they do not
need to tinker with numbers.]
While six is
reported to be "a perfect number," the experience does not
support it. One can make number six unlucky because it is "behind
seven, nine, eleven, and thirteen," and none of these numbers
harmonize with 6. (13 passes the octave for 6.) Number 15 and all even
numbers cannot help because the duo reduces to a triangle. A
six-pointed star does not derive from planetary orbits. This means
that the six pointed star cannot be made in the dual circle.
There is no 7/6
ratio on the musical scale but there is 6/5 ratio (G/E) [try it
together to see if it sounds harmonious -- it should be]. Much fun
can be had with planetary orbit
ratios and the tones and the multi-pointed "orbit
stars" they make. |
|
7 (seven)
|
Seven notes
(steps) in between the octave
Circle is not
divisible exactly by seven -- important just for this attribute.
Seven and nine are the only numbers between 2 and 10 that cannot
divide a circle into geometrically-equal segments. Seven-spoke wheel
should be the strongest! |
3 (Real) + 4
(Virtual) = 7 parameters for self-organization: All there is. Whole, holistic
Also, 3 + 4i
can be seen as "seven" even though the real and virtual
remain separate. Alpha and Omega could apply here except that Alpha
and Omega as presently understood is separate (correct) and static
(incorrect). See below |
|
8 (eight)
|
Octave, musical.
Earth-Mars orbits interlock in an octagon, which is musical (harmonious).
Check to see if
the construction of eight is: incremental (octagon), skipping one
point (two squares), skipping three points, or skipping five points
(octacles). [Muslims have a clue but they do not know the root. One
of these is disharmonious.] |
Four pairs of
inner states in the four-sided pyramid
Cardinal and
semi-cardinal directions. [Union Jack's center can be seen as Couplex (Dantien).]
Semi-cardinal
(diagonal) direction is about transformation. [Catholics think
cardinals and semi-cardinals are about the Sun and possibly Venus but
the doctrine cannot let them see transformations -- particularly individual-empowered
salvation.] |
|
9 (nine)
|
Nine is a good
candidate for a so-so number. [Nein? Okay, how about tic-tac-toe.]
Need to
differentiate between the areas of squares and the diagonals of squares
Nine is a
composite number but cannot "decompose" (divide) circle
evenly and thus nine is not musical. Nine can have hexing (confusing)
qualities because it has both "forbidden" and composing
qualities and it is a square number. Metaphysically, number nine is a
"traitor" or "spoiler." Chinese emperors might disagree. |
Grid for cardinal
and semi-cardinal directions |
|
10 (ten)
|
Tetractys,
hyperstates. Projection into 3D (becoming real). Multiple and
tractable realizations. Real plane. Transition between dimensions
(0-3) as well as transformation. Universal frequency multiplier 43210
(personal theory). Tractability
Calling number 10
the perfect number detracts from its powerful properties |
|
|
|
Whole
numbers spawn rational numbers and are at the heart of the real
world. In addition, whole numbers also construct irrational numbers
-- that is, integers actualize irrationals in 1D through the
Pythagorean Theorem. However, transcendental numbers deal with
curvature and with infinite addition (superposition) of numbers. For
transcendentals, then, straight numerology is inadequate and the
following categories are offered for the transcendentals. |
|
Many to One |
Focus. Receive.
Crystal, feather (to stem) -- energy intake.
Omega to Alpha
(with transformation in between), Buddhist Thunderbolt, Zeus
Thunderbolt. Closing a circle -- with transformation |
Wand notched on
receiving end, Talisman. Bushy or hairy wand [yep, this includes
broom]. Infinite superposition followed by instant action. |
|
One to Many |
Transmit. Crystal,
feather (from stem), Wand pointed on sending end [yep, this includes horns]
Alpha to Omega,
Buddhist Bell, Emperor's apple |
Sigil |
|
Irrational |
Does not and
cannot have real representation. No magnitude is associated with
these numbers. [And for 2000 years Greeks were looking for magnitudes.] |
Potentially
dangerous -- see Proclus. Life promoting -- see Pythagoreans.
Potentially energy releasing -- see Schauberger |
|
Rotation |
Geometric
operation. Rotation of an object in space. Point symmetry
(multiplication by -1)
Need to
differentiate between a number (male, this column) and operator
(female, in the right column) |
Transformation (if
90 degrees) to/from virtual. Line symmetry (if 180 degrees)
Many geometric
representations for this operation: Pentacle, right angle (open),
square (close), etc. |
|
Diagonal |
Line with 45 (or
so) degrees. Mathematical conjugation in matrix arithmetic (very
promising with Hermit). Dantien. Energy transformation, Couplex |
See Hanub-Ku
[every person needs to work this one out. Diagonal
form needs to make it to the American flag in some fashion.] Healing |
|
The semicardinal
line is the only geometric construct having even and odd symmetry. It
is the only line where masculine and feminine meet |
|
Spiral |
Rotation with
changing radius |
Virtual energy
release or absorption. Magic (and company) -- see Schauberger or
Reiki or .. |
|
Circle |
Infinity.
Transcendental, transformative (Complex subject: See Circle
and Pi).
Alchemical dragon |
Delimiter of
context. Enticement or invitation to stay, permanence (circle
segment, bowl). Protection |
|
Circum-positional |
Numbers that
divide a circle exactly: 2, 3, 5, 15, and 17; including all of their
doubles. Harmony |
Protection and
healing via tones |
|
|
Universal
Harmony |
|
While many
authors speak of the harmony of the universe or about the universal
balance, the basic idea behind harmony is that it takes two
sounds before these can be called harmonious or disharmonious. Any
two notes of the Pythagorean (Western) octave are for the most part
harmonious. The difficult part is that -- while we can agree on
harmonious or disharmonious sounds -- there is no written procedure
or mathematical logic that would allow us to determine ahead of time
if the tones will be one way or the other. However, in the article on
the five
pointed star orbit, which is made from two other orbits
(Venus and Earth), there is enough disclosure to begin to appreciate
what it takes to be in harmony. To build the universe, the harmony is
a requirement in that it makes lasting planetary orbits or galactic
structures. You do not have to make it harmonic but then the system
will be rudimentary, degenerates, or comes apart.
The book Quantm Pythagoreans explains what makes two numbers
-- or two orbits or two frequencies -- harmonious or disharmonious.
The harmony is then expressed geometrically for the reader as the stars.
Golden
proportion is a unique pair of two numbers -- one incommensurable
(irrational) and one rational. Because the ratio and other
relations of these two numbers also have interesting arithmetic and
geometric properties, they should be included in the Pythagorean
style harmony analysis. We have a page on
golden
proportion with
new application and (of course) a relationship to the Great Pyramid.
The unreduced real number of the golden
proportion is 2, and it is likely the number 2 (or ½) is
representative of the octave, for octave doubles the parameters such
as frequency or spatial distance and deals with (relates to) square numbers. |
|
You, A Pythagorean |
|
If you
think you are a Pythagorean, chances are you are. It is not easy to
arrive at such designation without joining a real organization. But
you know that by truth you know conceit and that is how the truth prevails.
The
Pythagorean way of learning, teaching, and building does not deal
with suffering, for conflicts exist as the imbalance that leads to
the next level of the truth. The building part, moreover,
establishes the truth in the objective realm. Enjoy.
You might
not think yourself a Pythagorean but others may think you are.
Galileo would not think of being a Pythagorean but his discoveries
and his mathematical thinking earned him a Pythagorean label from no
other than the members of the Inquisition. Enjoy. |
|
|
|
Mother Goose of Tetractys |
|
Presently,
the Pythagorean Theorem mnemonic exists as "Pythagoras'
Trousers," which is a tie-in between Pythagoras' attire (unusual
at the time) and his theorem in its geometric form. It is quite
likely the Pythagorean numerology of small numbers (1-10, say) was
designed to introduce Pythagorean concepts to larger audiences -- not
unlike the verses of Mother Goose that combine the poetic and magical
qualities of English: "..and the cow jumped over the moon."
In the next step the numerical compositions are put together to
create stable environment (monad). |
|
It is about the
atom staying together
Organization of
matter going on forever
It is the physical
plane of emerging matter
It explains
galactic clusters being made better
Something nice but
don't know what
Forgot to put the
eye on top
Whimsical
extension of Pythagoras' Tetractys
Perhaps for those
who think of abyss
Reminds me of the
ancient alchemy of sulphur, salt, and mercury
With the winged
shoes there is no hurry
Something
separated and joined at the same time --
gives me the creeps
It has everything
to do with quantum mechanics
One, two, three, four,
Cannot count
dimensions four.
One, two, three,
Thanks for making
house for free |
|
 |
QUANTUM
PYTHAGOREANS
Book by Mike Ivsin
Tetractys of
Pythagoras organizes the universe at all scales. Degrees of
independence play the role that up to now has not been disclosed.
Quantum Pythagoreans
book describes numbers, their properties, and their ability to make
reality through geometric constructs such as the pyramid. The
Pythagorean way is the road to reality, for the creation of reality
in the form of a new atom is the only proof you need. More
.. |
|
|
Go
or select another topic from the gold post 
HyperFlight home Portal
in new window.
At Portal are
other site links to Pythagoreans under Welcome -- Related Topics
Minor revs
3/31/05. Added paragraphs on Irrationals and Becoming July 2005.
©
2002 -- 2008 Backbone Consultants Inc. Copyrights Information
Last update March
25, 2008 |
