Really,
now, what is Pi? Scientists with algebra do
not have a handle on it
"A
circle is a delimiter of context -- and it's not by convention."
"What?
Never heard of it."
"That's
the idea .. "
Circle
and Pi, the definition
You
don't want to and you really cannot use the circular
reference like the scientists;
Easy
to define Pi the Pythagorean way and it
starts by drawing an arch of a semicircle. Yes, integers are in the
definition and the operators show up when integers begin to move;
Pi
is more than was said by all, and it has
to do with the even and odd symmetry. Actually, this is about the atom
Pi
figures in the conservation of energy. Ouroboros
sums it up but not on a silver platter
Intro Everybody
has something nice to say about a
circle, as if a
circle were perfect
Carl Jung
put a circle in the archetype category -- you have to go really deep
to connect with it and a circle is something very basic and innate.
On the other hand, many writers go straight up and call a circle a
solar this or a cosmic that, possibly with the help of a shaman's drum.
Geometers hang on
to the equidistance from a point and use a compass when constructing
a circle. This also results in a symmetry about a point -- a point
being perhaps the most important geometric construct. Arithmetic
works the point equidistance through a mathematical relation of the
Pythagorean Theorem and by applying the horizontal and vertical
distances in the Cartesian coordinates of Rene Descartes.
Each point of the circle's periphery is computed and then displayed,
and if you use random numbers the circle nicely fills in one dot at a
time. The actual circle has an infinite number of points and we (have
to) stop the computer when the circle is nicely visible. Or you can
step through the angles and keep drawing the circle over and over.
Math guys also like the stuff that has some periodicity in it because Fourier
picks on repeating things very fast.
For Pagans, a
circle is the symbol of closure that has repeating periods, and from
there it goes on to yet another harvest of nature's bounty and
certainly a good cup of wine. You do not need to be a magician, here
or in Tibet, to see a circle as the delimiter of context. A judge
will make a circle around the case to make the universe of evidence
admissible or inadmissible.
When all
descriptions of a circle are exhausted, some scientists give a circle
another name such as infinity. Scientists tend to think of infinity
as being stuck round and round in a rotary, and do not know the
difference between unbounded and infinite. With recent Eastern
imports a circle is zero and
infinity, and maybe you should think which part is the good part
before making a corporate logo -- Lucent and Vodafone coming to mind.
All in all, we
understand Pi from school as something to use when going from a
straight line that is a diameter to a curved line of a circle, or
vice versa.
Once you
understand how Pi is correctly and geometrically defined, you will
also encounter the most interesting part about Pi and a circle: Pi
cannot be made into a straight line. This is about the squaring
of a circle and what it also means is that the transcendental
numbers describing the Pi are different from rational or irrational
numbers. Yet the scientists are wikkily (rhymes with happily) showing
a wheel running over a flat surface claiming that one revolution of
the wheel is the straight line on the road having the Pi in its
length measurement. Not so. You are here to learn more than any
scientist ever could. Not only that. You just might have fun with the
scientists as you move on a path of the truth, directly or indirectly.
The scientists'
brain is left-centered, which means it is object-rich and
relationship-poor. In one paragraph the ~wiki~ page named Pi shows
the moving wheel producing the Pi on a flat path -- and right in the
next paragraph the scientist talks at length about the impossibility
of the squaring of a circle and speaks derisively about people
working to square a circle. The scientist simply does not recognize
the clear conflict in the presented information, for the scientist
sees the two paragraphs as two separate objects and two separate
topics. And this is just the beginning.. ..
While the real energy is well
known as kinetic energy, the virtual energy takes some
work. Free energy
is about transforming the virtual energy into real energy.
When squaring
a circle we must reconcile the infinite
transcendental numbers (incommensurables) with naturally finite
numbers (rationals). The golden
numbers make certain proportions that just might help with the
infinite addition (superposition) of the virtual energy.
Leibniz(bio)
first came up with an infinite series that adds up to a half of a
circle's quadrant: Pi/4. Leibniz series issues
from a trigonometric function and is the first real improvement over Archimedes'
methods from 300 BCE that approximated Pi via geometric polygon construction.
Let's say you ask
100 math teachers: "If Pi is irrational,
how could you teach that Pi is a ratio
(of C/D)?" How many of these teachers will answer with something
similar to, " .. perhaps the format of the circumference-Pi
relation for a circle is not clear."? Possibly one out of a
hundred. How many will defer to a committee to fix it? All of them!
Yes, algebra cannot do it but scientists do not mind reducing the
task until they are just plain wrong while the teachers go along.
This topic needs
differentiation because division (or rationing) -- in and of itself
-- does not always result in a rational number.
The golden ratio is a ratio but it is not a rational number. You may
want to take a look at the explanation
of commensurables and incommensurables (both transcendentals and irrationals).
A circle of
diameter D could also be an irrational number
but when you-the-builder pick up the compass and declare the distance
between points to be of some length, D must now have a finite
mantissa. This is crucial to universe (atom) building. One may argue
that even God's tools become limiting to God, but a better way of
looking at it is that reality -- if it is to remain organized -- is finite
and God may wish to make reality that is organized. This logic has
larger implications and even contains a gateway to gravitation. Think
of gravitation as an extension to atomic construction.
Careful on how you
define Pi.It may
seem easy to do that but you want to be alert. Pi is routinely
defined as the circumference C of a circle divided by its
diameter D, and there appears nothing wrong with such
definition in the scientist's mind. It is easy to paste the C/D = Pi
all over the Internet and print it in books (even in books about Pi),
but this kind of arithmetic is of limited use. Scientists say that Pi
stems from an algebraic ratio between two numbers but the Circumference
in the numerator is no ordinary number.
It may not be
obvious, but even if you measure the Diameter exactly and now
you want to put the Circumference in the numerator, the
circumference of a circle will not be exact because the circumference
is a transcendental number. A trancendental number has an infinite
mantissa, which is the sub-unity portion of a number. So, you cannot
take a transcendental number with the infinite mantissa to start your
computation to get Pi because this number does not fit in the
computer to begin with, and there is not enough paper in the universe
to write down one transcendental (or irrational) number. Pythagoreans
also say that irrational numbers are unspeakable -- that is,
nonverbal, as you would need an infinite number of words to express
just one irrational number.
Pi is not possible
to define algebraically because Pi is a transcendental number, which
cannot be obtained from an algebraic relation (that uses a finite
number of terms). The best definition of Pi is through integers and
radial movement (coming up).
You will find you
can obtain the numerical value of Pi -- or the circumference
of a circle -- only by superposition (subtraction and/or addition) of
an infinite quantity of components.
Surprise, but Pi
and the half-circumference of a circle (semicircle) are equivalent.
They are the one and the same. Unlike the scientist, you know you
cannot define a word by using the word itself in the definition (aka
circularity of reasoning). Pi
and C
differ from each other by a constant D but because Pi
and half-C
are equivalent then you cannot use one in the definition of the
other. Whenever you speak of Pi you also speak of a circle. Whenever
you speak of a circle, you also speak of a sphere.
Using a shorthand
notation, the Pi and the circumference C of a circle would look like this:
Pi equ C/D
and also Cequ D•Pi
In math notation Pi C/D
The equivalence
sign (three horizontal lines) means that Pi and C are
qualitatively equivalent and you cannot derive one from the other.
It is not possible
to explain, 'How to catch an elephant?' by saying 'Catch two and let
one go!' If you have the
cicle's
Circumference you have 2•Pi•R (Pi•D)
already. So, when the scientist says that Pi = C/D, he or
she is saying that Pi = (Pi•D)/D and then Pi is defined as Pi.
For a circle of radius 1 the scientist says that Pi is (Pi•2)/2
and then again Pi is defined as Pi. Scientists
are not very smart and when they get together they herd together.
The (infinite)
addition mechanism to get Pi or Pi^{2} is substantively
different from the procedure that generates the SQRT(2),
for example, and this may lead you to suspect that transcendentals
such as Pi and the irrationals -- really the straight-line
incommensurables -- belong to two different classes of numbers. For
starters, SQRT(2) is constructible with the Pythagorean Theorem in a finite
number of steps, but transcendentals are not constructible with real
methods in finite time, with or without the Pythagorean Theorem. This
starts another chapter on Pi that deals with the squaring
of a circle. The basic question is: Can the area or the
circumference of a circle be equated exactly with the area of a
square? You need to know the physical parameter represented by area
to appreciate this issue.
We have two book
reviews on Pi, both books authored by scientists.
It is a sad story on what today's scientists can say about Pi.
Semicircle and the Pythagorean
Theorem leads to the construction of the geometric
mean, which makes a square out of any rectangle
and also solves for a square root of any distance -- even the
irrational distance.
We
have a collection of designs inspired by the five pointed star.
View select
designs
-- or visit our
store at Zazzle (.com/Mike_Geo) and
see how well you could look in a tee, a hoodie, or a long sleeve
shirt. It is about being ahead of the crowd. All
designs come from nature. The design on the right is called The Embrace
but I also like to call it The Red White & Blue At The
Court of The Yellow Emperor.
Water and Salt
design below.
Easy definition of Pi,
the Pythagorean way
Now that we
criticized the scientists' definition of Pi,
we should offer our own, unencumbered, strict, literal, and
unambiguous definition of Pi:
Semicircle is
a curve that has the unit distance of 1 from a point that that
lies on a line. The semicircle has the starting and ending points on
the line. At the starting point it is possible to traverse either a
straight distance 2 or a semicircle distance Pi
to get to the same ending point.
But
of course, because the unit 1
can be of any size, Pi will always be Pi no matter how big the circle
you come up with. Pi is created by a radial movement of the unit 1
and it is no wonder Pi is the same for all circles.
The
Pythagorean definition of Pi makes it easy to see that Pi and the
semicircle are equivalent because the semicircular distance is
Pi. The semicircular distance is the value of Pi. [It is also
a nice definition because it gives you a choice. You can go straight
in 1D to get to the ending point and you know exactly how far it is.
Or you can take a more circuitous route where you'll get to meet the Pi.]
On the
technical side, Pi is classified as a transcendental number. There
are also irrational numbers such as the square root of 2. Both the
transcendentals and irrationals have an infinite sub-unity portion of
a number. Transcendentals always exist in 2D while irrationals do it
in 1D. This is our way of differentiating transcendentals and
irrationals and you can read up about these two families on our page
dealing with incommensurable numbers.
It is said Pythagoras
started his studies with a semicircle. Not surprisingly, we need
integers 1 and 2 to define Pi. Perhaps more accurately,
we need the unit 1 and a doubling operator
to arrive at Pi. You can get metaphysical
here because 1 is odd and masculine while the even (2, doubling) is
feminine. If you start with the length of 2, which is feminine, you
will need the operation of halving to determine the point O at
which to draw the semicircle. Halving is masculine. (Yes, cutting is
masculine and you will find it in the left brain.)
Self-referencing (or circular
reference or circularity of reasoning) can be
fun. Because a scientist produces a ratio of two
distances that are inseparable to begin with -- namely the
Circumference and Diameter -- the scientist profoundly announces that
Pi is a constant. You can do one up on the scientists using
self-reference when you say, for example: "Divide the number of
cats you have by the number of legs they have -- and you will always
come up with the number ¼. Therefore, the cats-to-legs ratio is
a constant for small or large cats."
So, how many cats
do you have? That's easy. Add all of cats' legs
and .. ..
Ok, is Pi an exact distance or
not? Because we can express Pi only with non-repeating
and infinite number of digits (after the decimal point), we can argue
that Pi is not exact; except that this is true in straight 1D
geometry only. In a circular geometry, Pi is exact and only waves
(wavefunctions) can achieve spanning the circumference exactly.
Perhaps you can see in this the fundamental power of geometry from
yet another angle. {June 8, 2013}
You can also see it
as a way of showing the impossibility of the squaring of a circle
because the circumference of a circle cannot be equated with a finite
(or irrational) number. However, it is possible that, going around
the circle, some distance can become a finite (rational) number and
then a particular segment(s) of a circle can be linearized. There is
another 'however' in this. In orbital jumps we are concerned with the
difference in two energies -- that is, the difference between two
circles. Could the difference in two circles be linearized? This is
about atomic sustenance and not about atomic construction.
What then is the actual value
for Pi? There is an infinite series by Leibniz that is quite
simple and it converges toward Pi/4 -- that is, this series converges
to the length of one-half of a circle's quadrant. This formula is
also the first qualitative improvement over Archimedes' method of
"exhaustion," which uses inscribed and outside polygon
construction to determine the ever-improving value for the circle's
circumference of 2•Pi.
This formula happens to converge
to Pi very slowly. With an increasing number of new terms we get more
accurate (closer to Pi) but -- compared to other methods -- the
computer must do a lot of computing to show progress. Self test:-) If
this paragraph does not make much sense to you, you are doing well.
So, as a Pythagorean, you are not
as much into expressing the magnitude of Pi on paper as you are into
the actual construction and actualization of Pi. You start by seeing
that the pluses and minuses can be implemented through superposition
and in QM the superposition
is instantaneous. Nice!
In our
definition of Pi we use 'distance' instead of 'length.' The straight
distance is in 1D while the semicircle exists in 2D. Both exist in
space (and all geometry exists is space). There are no restrictions
on the diameter and the unit distance can be rational or
irrational. That is, the unit distance is not limited to finite
numbers such as rationals and this opens yet another metaphysical
dimension. (Perhaps you understand now that the unit distance cannot
be transcendental because it is always a straight distance.) If the
unit distance were an irrational number the radius (and diameter)
should be dashed because we change the context from unit length to
unit distance but Pi will still be Pi (this is more important than
you might think). Even Euclid
thinks 1
is more than a counting number. On our Pythagorean page we
have the Pythagorean Theorem working with
circles aka loones.
Operators are well
understood by the present day mathematicians
(with a likely exception of i
and minus1).
The treatment of operators is generally adequate and includes the
null operator, which can be applied as having a body at rest
(Aristotle would scratch his head on this one). The doubling operator
is for some reason not included explicitly but there is, of course,
the operation of 'multiplication by 2.' You will note that
'multiplication by 2' and 'addition of the same' arrive at the
identical result but both of these are different operators because
they represent different domains. (There is a tangent here on the
golden proportion.)
When you use words
such as 'traverse' or 'measure distance,' you are describing a movement.
In order to unambiguously define Pi, you need to get from here to
there. It is the movement itself that uncovers the operators.
Metaphysically, men at times need to make a pilgrimage or a quest in
search of something. (In the book Quantum Pythagoreans the
growth of the universe is accomplished through orbits, for the
continuous accumulation of matter in a single body unbecomes
tractable. The book explains why operators are forces.)
Aetius iv. 2; Dox.
386. "Pythagoras holds that number moves itself, and he takes
number as an equivalent for intelligence."
Archimedes
All
topologies of a circle and sphere -- the periphery, area, and volume
-- are equivalent
to Pi through
rational (exact, finite) constants. This
is really a summary of Archimedes work from 300 BCE but [as you might
agree] it has not survived in clean relations because of algebra. Archimedes
also added the cone
to the equivalence of Pi because he found a rational number that
relates the volume of a cone to the volume of the cylinder (1/3). It
is said he was very happy about that.
The
story has it that Archimedes had the cone volume formula inscribed
on his tombstone.
[While
this story could be difficult to verify, a much better story would
be that upon discovery he threw a great party and gave everybody a
hat. The tradition of the cone shaped party hat would then have been
started by Archimedes and it would also have become the longest
surviving tradition in the history of the world. There. Then one guy
built an arch in
the honor of Archimedes
and the world was never the same since. As you may well imagine, the
guy called himself the architect.]
There
is more to equivalence
When
Newton (bio)
speaks of "equal and opposite force" (action-reaction), he
is speaking of equivalence
of forces that arise simultaneously and one (action) cannot exist
without the other (reaction). Because forces are equivalent, one
cannot arise before the other. Another way of getting to the same
result is by understanding that all forces issue from the even
(wave)functions. This is also the foundation of the
action-at-distance because mass bodies separated by a distance act
with the gravitational force that is equivalent. Yes, the earth is
exerting force on the apple that is equivalent to the force apple is
exerting on the earth. (Because the masses of the earth and the apple
are in a huge ratio, the resulting acceleration will also be hugely
lopsided -- but the forces are the same and pointing in the opposite
direction. This is true of any and all forces -- such as when a
photon is absorbed.)
Action-at-distance
is no big deal for quantum mechanics and
this happens when the even wavefunction reduces: one big one
for Newton. The gravitational wavefunction is an even wavefunction.
Reversibility
of a math relation
The
equal sign of algebra signifies reversibility rather than
equivalence, but this can be applied only in situations when there
are but two
and mutually exclusive outcomes happening over a single
bidirectional path such as potential vs. kinetic energy (spring,
weight lifting, pendulum) or pressure vs. volume (piston). It is easy
to construct such bidirectional paths -- and the equations with equal
signs to go with it -- in a closed system. But not all paths
are bidirectional because at times the reversibility can be had only
over a triangular path or a multi-state path having more than two
states. For example, an absorbed photon
can create several forms of energy. Some of the resultant energy
quanta are not readily transformable back into photons and need to be
worked over several stages before a photon could be recreated.
Algebraic
relation needs a bidirectional path for the equation to hold. So,
while a bidirectional path can be created through a specific (closed
system) context, a triangular path is a more general case found in
nature. The kicker is that when dealing with virtual variables the
system cannot be closed -- you cannot use real things and real
methods to confine virtual variables. (You can use virtual methods
but presently there are no guarantees and we usually speak of magic.)
This also gets into intelligence and organization.
The
triad and tetrad of Pythagoras also indicate that the bidirectional
path is not about the creation (of life, new materials, new systems,
new abilities). Ancient Egyptians have several triads and
quarterrnaries corresponding to various stages and methods of creation.
In another example
of algebra inadequacy, the equation E=m•c^{2
}allows you to "calculate mass"
of the photon by placing its energy on the other side of the equal
sign. But a photon has no mass and then the algebra weakness is
"explained" by calling the mass the 'effective mass,' while
some algebra holdouts continue to hang on to a photon's mass and
coming up with their own conclusions such as "tired" or
slowing-down light. This equation simply and nicely shows that
algebra is inadequate in general and incomplete in particulars. The
equal sign works fine in the real domain where the commutative
property holds (ab=ba). As soon as the virtual entities are
encountered -- and light is a virtual entity -- algebra falls apart.
This equation is incorrect in another way but the error discussed now
is that irreversible transformations are paraded as reversible via
the equal sign. Algebra is not representative of reality when
transformations (reversible or irreversible) take place. [Einstein is
a prototype for dumb and dumber.]
Reversibility or
irreversibility of a mathematical relation is
an exceptionally important determinant and algebra needs to be
replaced with another methodology. Presently, scientists muse about
some of their weird or unusual results they get from their inadequate
math while unable or unwilling to question math itself [think the
left and the right brain].
Semicircle
in the Buddhist tradition
There is a
nice dot and a semicircle at the top of the AUM (or OM) symbol found
in Buddhism. There are sparse interpretations of the AUM symbol, most
of them deferring to the infinite, the unconscious, or to taking your
own and individual path to its understanding. Because this site is
about numbers and geometry, and because the numbers are at the heart
of it all, we are not shy about delving into the aspects of the AUM,
no matter how infinite and all-encompassing it may be.
<–
"The best"
The dot is
indeed the nothing (indivisible, has no parts) as well as the
everything (infinity). Because this dot is not real -- it is a
geometric construct -- I prefer to draw it as a small circle. The dot
is then infinitely small inside the small circle. It is through this
dot the real and the virtual components are interconnected. This is
indeed a big leap and so you may need to take it as a given for now.
Intelligence
in general is virtual energy and can be thought of as organized
energy. One property of the virtual energy is that it is always
symmetrical about 1D axis (the axis is not shown on the AUM). The
total intelligence of the entire universe is symbolized by the
component that looks like the number three on the AUM symbol. This is
not the counting number 3 and neither it is a trinity but the two
humps deal with the even, or axial, symmetry that is inherent in the
formation of the virtual knowledge -- that is, intelligence. As you
look through (or move through or think through) the dot you will
extract, or copy, the kind of intelligence that is relevant to your
needs. This, by now subjective, intelligence issues from the total
intelligence of the universe and moves into the circle that could be
you, for the circle is the delimiter of context. In Tibet, you could
make the circle .. .. [yeah, make your own magic].
I'd put a
little curlicue between the total intelligence and the circle to
indicate spin (really a vortex).
I'd also put
horizon(tal) lines on each side of the point. If you are into the
ancient Egyptian texts, think Aker.
Oh yes, the
semicircle. That is about reality, for all real entities have odd
symmetry and that means that all real entities are always symmetrical
about a point. You guessed it, it is the same point. You could
interpret the semicircle in that you want to make something real from
the intelligence you have received.
You are still
left with some unanswered questions such as "why is it a
semicircle and not a circle," and "why is the horizon
important and what qualitatively differentiates horizontal from
vertical," and "where does Pi fit in," but now the
answers are not all that difficult -- consider it your brainwork.
In an
advanced stage you want to develop the ancient Egyptian meaning of
'horizon' (horizon of fire,etc.)
It's a thrill to arrive at some
conclusion and then find a reference to Pythagoras that supports that
-- in our case the idea of the 0D point and infinity being "the
same." Before Aristotle criticizes Pythagoreans he writes (in Metaphysics):
"The Pythagoreans,
however, while they in similar manner assume two first principles,
add this which is peculiar to themselves: that they do not think that
the finite and the infinite and the one are certain other things by
nature, such as fire or earth or any other such thing, but the infinite
itself and unity itself are the essence of the things of which
they are predicated, and so they make number the essence of all
things. .. .."
There
could be a tie-in between one Pythagorean idea and the AUM.
Pythagoras is reported to have said something similar to: "The
eternal world is revealed to the intellect [mind] but not to the
senses." It is conceivable Pythagoras was teaching the freshmen
and freshwomen from behind a curtain just to make that point.
How do you make the sound
of AUM? (Words are mostly about objects.)
You
start with A as a
broad sound and imagine it as opening a book .
This is the energy part. You are a smart person and you realize that
the spine of the book is the vertical axis of symmetry.
You transition to U as,
of course, the semicircle. This tone then changes a bit as you go
sounding ("curving") the semicircle. Pages of the book are
now free to rotate about the axis. This is the charge part. Yes, the
charge is always symmetrical about a point. (The charge and matter
are closely linked. There is no matter without charge.)
You move to
vibrating M, where
the spikes are the points that nail the two of the above components
together in zero-dimensional points.
The Latin letters
fit in nicely considering the geometry and the associated symbolism.
The Emerald Tablet is of an
ancient origin that, while fully verbal, has its meaning purposefully
obscured in alchemical language. Well, an alchemist would not say
that their work is purposely obscured. Rather, an alchemist would say
that the language of alchemy is condensed and symbol-association-based
so much it appears obscured. And so it happens that we have the
Tablet's interpretation on our Alchemy page.
A
circle and a sphere are made from a semicircle
The
starting and the ending points of both the straight and the
semicircular distances are identical.
A circle exists as the doubling of a semicircle and so the
definition of a circle is also about the exact
division of a circle by 2. Are there
other numbers that divide a circle exactly? Or is it that any number
can divide a circle exactly? You will need geometry to answer that.
Metaphysically,
the semicircle is feminine because the entire
curve is symmetrical about the (vertical) axis. When making a full
circle by, again, doubling, the 1st and 3rd quadrants become
symmetrical about a point and, therefore, masculine. Metaphysically,
then, "masculine arises from the feminine via the reflection
about the horizon." If you get huffy about this, consider that
masculine (feminine) is not the same as man (woman). If you still
cannot get over it, don't go on a date with a witch.
Perhaps
the best application of a semicircle is the geometric
mean. Because the geometric mean works for
both the rational and irrational numbers, there are significant
implications here to such (for some people esoteric) topics such as
stopping moving bodies at a distance. Incidentally, since the
geometric mean also constructs the square root, your attempt at
achieving the squaring of the circle now includes Pi^{2}
because you could then readily obtain the square root via the
geometric mean. Pi^{2} has an infinite convergence series by Euler
(if you want to give chase via QM superposition).
There is more
to Pi and a circle
Even and odd symmetry
There are two
basic functions applicable in the virtual domain of the atom: Even
and odd mathematical functions. The property of the even function is
that it is symmetrical about the vertical axis: f(x) = f(-x),
while the odd
function is symmetrical about a point: -f(x) = f(-x)
(the equal sign
means the author or the user of the equation thinks that the
operation is reversible, and it is). The even function has infinitely
inclusive properties such as those of a photon and it is an agreeable
extension to call even functions 'feminine.' If the operation of
translation or rotation have unique symmetries, then these operations
can acquire gender as well. Inclusiveness is at times called
superposition and it is truly infinite, not just unbounded.
Generically, all even functions are forces [and may she be with you].
The odd function, you guessed it, has exclusive properties such as
those of a proton and calling the odd functions 'masculine' then also
makes sense because protons "butt heads" and displace each
other -- at least in the real domain. Generically, all odd functions
are real things, and bumpers with automobiles are just such things.
Every atomic entity has properties that fit either the even or the
odd function.
The circle is the
one and only geometry that has even and
odd symmetry. This does not make a circle the gender neutralizer.
Instead, because the circle is acceptable as both the even and the
odd function in particular quadrants, the circle is the originator
and the go-between among the two. The circle is the vehicle for the
initial gender differentiation and the circle also facilitates the
transformation between the two. There is a bit more here
on the rotational symmetry associated with the five pointed star.
Is
i
a number or an operator?
Is
-1
a number or an operator?
i
is a square root of minus 1.
We
know that -1=1/-1
but does the reciprocal of i
equal i ?
So,
we take the equation i
= 1/ i
If
you square both sides the equation is correct but
if you multiply both sides by i
the equation does not hold.
If you try the
above equation & non-equation on a real or self-proclaimed
mathematician, chances are 99.9% he or she will not know where the
problem is. You can tell him that squaring and/or multiplying both
sides of an equation are both legal algebraic operations -- and
chances are he knows it. Don't push it if you don't want to confuse
the poor guy. (But of course, get him the book.)
QUANTUM
PYTHAGOREANS
The
Book
There
is much more to numbers than counting. With the i
you enter the virtual domain and with it one of the largest chapters
in the book. Continue
..
With the odd
function you could begin to see how you could really explain the
two-body collision mechanism. You will need to
take the moving energy as a wave (easy) but then you will need to do
a transformation.
How can a circle become or stand
for zero? You will need to visit India and learn how
the zero came to be. Since a circle is the delimiter of context, the
circle you draw can be evacuated of every real thing -- and you have
zero. There are some who think this is not just an intellectual
exercise because the circle can be emptied of real and
virtual things.
How can a circle become (or hold)
infinity? This is a bit more complex than a simple
reversal of the above. Think about and sound out the AUM,
and go for it. Yes, you will need geometry.
Transformation, as used by
mathematicians, is not very transformative. The math
guys see transformation as something that translates (moves, shifts)
some function (a graph) along a line either horizontally or
vertically to another spot. This just moves the reference and is not
really transforming anything. Another form of transformation math
guys claim is a transformation is to change the scale and this
amounts to zooming in or out. Again, not very transformative.
Finally, math guys speak of transformation when they flip a function
about the axis and make a mirror image. You can easily see that none
of these operations are transformational. For example, just because
you shift from meters to feet as the new scale the math guy would say
you are transforming but you know that the word 'transformation'
should be reserved for something bigger than that.
In our, that is Pythagorean,
definition of transformation we speak of a change in
the entity -- or the function describing such entity -- from the
even to the odd function or vice versa. So, when a photon (even
function) reduces by being absorbed, the energy is now converted to
momentum that moves a couple of bodies such as molecules away from
each other and the moving molecules now acquired an odd function as
the two are moving away from a point. Similarly, when a real electron
becomes the virtual electron it transforms from an odd function
entity that is a real thing into an even (wave)function entity.
(There is a bit more to this, for an electron has two components.
Esoterically it is the Sphinx.) Dirac,
a physicist and a mathematician, was pretty close and actually spoke
of electron transformations. Incidentally, math guys are quick to
point out that most functions are neither even or odd. What they do
not say is that in the atomic environment there exist only the
even and the odd functions. The reason is that only the even and the
odd functions are transformable into each other, albeit in a
non-trivial fashion.
We have a couple
of Pi stumpers
you can try on your math teacher. Because math teachers subscribe to
lame committee rules they are easy game.
Ouroboros
In a simple and
practical explanation, Ouroboros shows the difference between
straight and curving geometry. If you have a string of some length
then the expression of such length is always finite -- that
is, the number that is the length of the string always has finite
mantissa (it is a rational number). But the circle's circumference
made from such string cannot and will not be of the same length
because the circumference of any circle is not a finite number. The
circle's circumference will always be shorter or longer than
the length of any string. At times, then, Ouroboros is shown
with excess or with a deficiency in the length of its tail.
What this also
means is that a circle cannot be made with a specific (exact)
circumference because a specific number is a finite number and does
not have an infinite mantissa. A more general case can also be made
because a circle's circumference is a transcendental number and even
the irrational number with an infinite mantissa cannot be made into a circle.
Circles, ellipses,
and other curving things are made from many zero-dimensional points.
Because a geometric point is dimensionless, the number of points
making a circle is infinite. Then there is also the question,
"what entity can exist in the circumference of a circle?"
By now you know it is not a real thing because no real thing such as
a string can be made into a circle. If such curving entity is not
real -- can it be virtual? If it is virtual -- does it exist? Can we
see virtual things or entities? Does the electron become the virtual
electron when it forms an orbital? Are dragons made of electrons?
Some comment on
Ouroboros as "eating its own tail." Perhaps you see now
that such is not the case. Some could argue that the material can at
times be transformed into virtual and that is the "eating"
part. While technically true, it says nothing about the creation of
the real world and why the creation of the real world prevails over
its destruction.
Continuing on,
there is one other aspect of Ouroboros that shows up in the Mayan tradition.
You might notice
the Mayan dragon has seven segments. The number seven is the first
number that does not divide a circle exactly and so there is a gap
because seven wavelengths do not fit around the circle exactly. This
has larger implicatons that are best explored via the Hunab-Ku
symbol. If you think the "fiery breath" of the dragon has a
link to a gap in a circle and consequent release of "free
energy," you are doing well. You also want to be careful.
The Christian aspect of control deals with the "slaying of a
dragon" and your free energy work needs to be trully hidden (not
just renamed). But of course, free energy is closely watched by any
and all govt agencies.
There are also
more esoteric interpretations of the Ouroboros. Skip the following if
you don't fancy esoterica.
Pi has an infinite
amount of components calling for an infinite number of decimal
places. You are pretty good if you asked a question:
"What happens
when its tail is chopped off?"
Why, you could
even discover there are different ways of drawing Ouroboros. As you
look at all of them the Ouroboros of the ancient Egyptians looks the
best, for it has a white belly on the inside. And then you might say:
"Pi is a
serpent? With scales or feathers, no less. Come on, get real!"
My point,
precisely. But this may all be too obvious and you do not see the
woman. There must be a woman.
"She is
holding the sword .. vertically. There is a pivot, too."
Yeah, the guy
should be in charge of that pivot. But you can do better.
"Engage the
Couplex on the diagonal."
There is not much
to say.
Pi is also about
nonlocal entities the likes of the electron
Pi must facilitate
energy conservation when entity's motion changes between the curving
and the linear motion. Because Pi is transcendental then Pi's value
is expressed with infinite quantity of components [here she is
again]. The real domain, however, consists of object's values that
have finite length (finite precision) that's just right for the real
world. The curving geometry expressed by Pi is reconciled with the
linear (straight) geometry of Euclid through some form of
transformation. That's the importance of Pi and the basic
differentiator between straight line irrationals and transcendentals.
Talking about the squaring
of a circle, eh? Talking about the nonlocality of an orbital
electron and its 2D/3D energy.
Pythagoras is
likely to agree that classifying Pi as the transcendental number is a
good call.
If you wish to
give a test indicating the level of understanding of physics by
physicists, here is one question where the answer is not very
encouraging. Ask any physicist: "Why would the Planck constant h
be routinely divided by 2•Pi?" and he or she will say:
"Because it is convenient."
Yikes!
We
are almost there. The classification of some numbers as
'transcendental' presents a very old challenge. All non-transcendental
irrational numbers the likes of the square root of two are readily
constructed with the Pythagorean Theorem. The transcendentals,
however, take you for another and altogether different ride.
A
circle can take you places. Possibly the longest unanswered cry is
that of Archimedes: "Give me a point and I will move the
earth!" Is there such a point? Such fulcrum? Is it a fixed point
or is it a geometric 0D point? Ah. Think golden proportion.
Now that we
created the circle, it may be fun to explore the exact division
of a circle. Some numbers do it, some don't.
QUANTUM
PYTHAGOREANS
Book by
Mike Ivsin
If
an atomic component changes from linear to radial geometry, energy
imbalance arises because linear and curving paths cannot be exactly
the same. The atom maintains its stability by radiating or absorbing
energy to or from the environment because the geometric
transformation must be energy-neutral.
Quantum
Pythagoreans describes linear and
curving topologies, and the sustenance role of light for the two
topologies. The pyramid then also provides the geometric constructs
for the creation of new matter and for healing too.
The
duality of the real and virtual energies is not only introduced but
is fully developed as two interacting domains.