So I appreciate the discussion about the "ideas" I have posted on this forum.
Now my original answer to this above quote was music theory and then I
referred to Pregadio pointing out that Daoist alchemy meditation is
based on non-western music theory.
So then the discussion switched over to math. So people think I am
bragging about my correspondence with professors. Yes I am bragging but
only because of the absurdity of it - and by "absurd" - I mean the
"surd" - or going out of the "unutterable" - the "unheard" - the Alogon
of irrational numbers. It is quite clear and well proven by math
professor Luigi Borzacchini that Western math originates from music
theory! This, of course got covered up.
So the claim then being made is that noncommutative "geometry" is too
advanced and I'm just "hiding" behind it without really understanding
it, etc.
OK so let's go back to the very origins of Western math from music theory.
I looked at the links posted - by the person who has given a sympathetic reading to the information I've posted.
I've read the comments about those links.
Consider this comment:
When you get into the nitty gritty you are forced to become really
precise about what counts as a "number." Consider three properties that
both the real numbers and the complex numbers have:
1. For every number x ≠ 0 there is another number y such that x·y = 1 (i.e., every non-zero number has a reciprocal)
2. For all numbers x,y,z we have x·(y·z) = (x·y)·z (this is called the "associative property")
3. For all numbers x,y we have x·y = y·z (this is called the "commutative property")
Now keep in mind again the WEstern math is from music theory. Look at number 1.
Let's say to be reciprocal - we are dealing actually with a Logos (a ratio) of time and frequency.
So let's say we have x = 3/2 and y = 2/3. Therefore we have a reciprocity that equals 1.
Now let's consider the empirical truth of music theory, the secret origin of Western math.
As I have pointed out, if C is 1 (as is common in music theory - the
root tonic is C) then C is also 2 since it's the same pitch that we
visualize as being a "doubling" of frequency. So far so good.
But this is where things get interesting.
For 3 then as 3/2 as X, the 3 is actually G while for 3 as 2/3 as Y, then the 3 is actually F.
So the non-commutative logic is actually BEFORE quaternions - it is
inherent to number have a "hidden dimension" - to quote the above video.
But more so - Western math defines dimension as a geometry, assuming
that irrational magnitudes are logically valid.
But quantum physics changed all that - what was rediscovered is the new foundation of science as "time-frequency uncertainty."
That "uncertainty" is due to the noncommutative "measurement problem" of the linear operator of time to frequency.
So the uncertainty is not "limited" to the quantum realm - it is based on the inherent logic of the math itself.
And so what we are discovering with noncommutative phase logic - is
that, as math professor Alain Connes points out, when there is a zero
point in geometry there is a hidden noncommutative time-frequency to
that zero point of geometry. The frequency-time is primary or what math
professor Louis Kauffman calls "primordial time" that is synchronizing
reality. This was also discovered by de Broglie as the Law of Phase
Harmony.
O.K. so that also changes what "1" means - which brings us back to what
is a square root "really." It is "absurd" - in the sense that time is
literally the future and past overlapping. We can logically infer it but
we can not OBSERVE it. We can "listen" to it but we can not SEE it.
OK so to make my post more "fancy" I'll provide a quote from math prof.
Louis Kauffman (yes with whom I've corresponded). Maybe I didn't post
this yet here - maybe I did?
.
..All of this points out how the complex numbers, as we have
previously examined them, live naturally in the context of the
non-commutative algebras of iterants and matrices.... A natural
non-commutative algebra arises directly from articulation of discrete
process and can be regarded as essential information in a Fermion. It is
natural to compare this algebra structure with algebra of creation and
annihilation operators that occur in quantum field theory. ..."In the
notion of time there is an inherent clock and an inherent shift of phase
that enables a synchrony, a precise dynamic beneath the apparent
dynamic of the observed process....By starting with a discrete time
series of positions, one has immediately a non-commutativity of
observations, since the measurement of velocity involves the tick of the
clock and the measurement of position does not demand the tick of the
clock....In this sense, i [square root of negative one] is identical in
concept to a primordial time."
So now I'll repeat the quote with my emphasis added:
.All of this points out how the complex numbers, as we have
previously examined them, live naturally in the context of the
non-commutative algebras of iterants and matrices.... A natural
non-commutative algebra arises directly from articulation of discrete
process and can be regarded as essential information in a Fermion. It is
natural to compare this algebra structure with algebra of creation and
annihilation operators that occur in quantum field theory. ..."In the
notion of time there is an
inherent clock and an inherent shift of phase that enables a synchrony, a
precise dynamic beneath the apparent dynamic of the observed process....By starting with a discrete time series of positions, one has immediately a non-commutativity of observations,
since the measurement of velocity involves the tick of the clock and
the measurement of position does not demand the tick of the clock....In
this sense, i [square root of negative one] is identical in concept to a primordial time."
OK now let's go back to that original comment I quoted - and we will
continue with the comment - to one of the videos linked above:
If we require that our numbers have properties (1), (2), and (3) then
the complex numbers are as far as you can go. If we require that our
numbers only have properties (1) and (2) then you can create a new set
of "4-dimensional" numbers called the quaternions. With the quaternions,
multiplication isn't commutative, i.e., it's not always the case that
x·y = y·x for two quaternions x,y. The quaternions are as far as you can
go if we insist out numbers respect (1) and (2), but not necessarily
(3).
We can see now that this "normal" definition of math is logically no longer valid.
More youtube comments:
i = mathematics
j = electronics and electricity
i = SQR(-1) potential
i^2 = -1
I^3 = 1 + i
i^4 = 1 (real)
Someone disagrees:
i^3 = -i, not 1 + i
The answer:
r^3 = -i OR 1 + i (given real & antimatter )
as in electronics Z=((Xl- Xc)/R
Z = imaginary / real
or (i,j) polynomial expansion
as Xl Xc are reactive and R is real resistance
OK so a thread on Daoist Meditation?
I document that Daoist meditation IS non-western music theory!
I tell people to read the Daoist Meditation literature.
Yes it is true that non-western music is NOT Western science.
It's also true that Western science originates from non-western music theory.
Also
it's true that Western science is starting to realize this non-western
music origin as also being the "end point" of Western science.
For
example - in terms of meditation we confront the problem of
"consciousness" in the West - it is usually called the Hard Problem
based on what is qualia.
As I blogged recently - the problem
of "qualia" which is really a problem of logical identity - is solved by
non-western music theory. Science calls this the
http://elixirfield.blogspot.com/2018/09/the-phase-between-eigenstates-secrets.html
"Asymmetry Proof."
So
we want to think that science is "objective" and it measures an
"external reality" but actually science is based on left-brain dominance
with right hand dominance.
Non-western music is
right brain /left hand dominance just as ecology relies on left-handed
amino acids and right brain dominance.
So Western science "works" unless you consider the ecological and social justice crisis created by the "entropy" math.
It
might seem childish to turn to music theory as the "answer" to science
and yet Fields Medal math professor Alain Connes has done just that!!
So
he corroborated my music theory "complementary opposites" logic claim
that I discovered on my own while in high school. I have compiled quotes
from Fields Medal math professor Alain Connes regarding music theory
(Keep in mind that no other Western music-math analysis has realized
this noncommutative logic secret of music theory!!). Quite amazing.
“And
it could be formalized by music….I think we might succeed in this way
to educate the human mind to deal with polyphonic situations in which
several voices coexist, in which several states coexist, whereas our
ordinary logical allows room for only one. Finally, we come back to the
problem of adaptation, which has to be resolved in order for us to
understand quantum correlation and interrelation which we discussed
earlier, and which are fundamentally schizoid in nature. It is clear
that logic will evolve in parallel with the development of quantum
computers, just as it evolved with computer science. That will no doubt
enable us to cross new borders and to better integrate the mathematical
formalism of the quantum world into our metaphysical system....
When
Riemann wrote his essay on the foundations of geometry, he was
incredibly careful. He said his ideas might not apply in the very small.
Why? He said that the notion of a solid body of a ray of light doesn't
make sense in the very small. So he was incredibly smart. His idea, I
have never been able to understand his intuition...But however he wrote
down explicitly that the geometry of space, of spacetime, should be
encapsulated, should be given by the forces which hold the space
together. Now it turns out this is exactly what we give here...One day I
understood the following: That we are born in quantum mechanics. We can
not deny that... Quantum mechanics has been verified. The superposition
principle has been verified. The spin system is really a sphere. This
has been verified. This has been checked so many times. That we can not
say that Nature is classical. No. Nature is quantum.
Nature
is very quantum. From this quantum stuff, we have to understand our
vision, our very classical, because of natural selection way of seeing
things can emerge. It's very very difficult of course. ...Why should
Nature require some noncommutativity for the algebra? This is very
strange. For most people noncommutativity is a nuisance. You see because
all of algebraic geometry is done with commutative variables. Let me
try to convince you again, that this is a misgiving. OK?....Our view of
the spacetime is only an approximation, not the finite points, it's not
good for inflation. But the inverse space of spinors is finite
dimensional. Their spectrum is SO DENSE that it appears continuous but
it is not continuous.... It is only because one drops commutativity
that variables with a continuous range can coexist with variables with a
countable range....
What is a parameter? The
parameter is time...If you stay in the classical world, you can not have
a good set up for variables. Because variables with a continuous range
can not coexist with variables of discrete range. When you think more,
you find out there is a perfect answer. And this answer is coming from
quantum mechanics....The real variability in the world is exactly is
where are you in the spectrum [frequency] of this variable or operator.
And what is quite amazing is that in this work that I did at the very
beginning of my mathematical studies, the amazing fact is that exactly
time is emerging from the noncommutivity. You think that these variables
do not commute, first of all it is that they don't commute so you can
have the discrete variable that coexists with the continuous variable.
What you find out after awhile is that the origin of time is probably
quantum mechanical and its coming from the fact that thanks to
noncommutativity ONLY that one can write the time evolution of a system,
in temperature, in heat bath, the time evolution is really coming from
the noncommutativity of the variables....
You really are in a different world,
then the world of geometry, which we all like because we all like to
draw pictures and think in a geometric manner. So what I am going to
explain is a very strange way to think about geometry, from this point
of view, which is quite different from drawing on the blackboard...I
will start by asking an extremely simple question, which of course has a
geometrical origin. I don't think there can be a simpler question.
Where are we?....The mathematical question, what we want, to say where
we are and this has two parts: What is our universe? What is the
geometric space in which we are? And in which point in this universe we
are. We can not answer the 2nd question without answering the first
question, of course....You have to be able to tell the geometric space
in an invariant manner....These invariants are refinements of the idea
of the diameter. The inverse of the diameter of the space is related to
the first Eigenoperator, capturing the vibrations of the space; the way
you can hear the music of shapes...which would be its scale in the
musical sense; this shape will have a certain number of notes, these
notes will be given by the frequency and form the basic scale, at which
the geometric object is vibrating....The scale of a geometric shape is
actually not enough....
However what emerges, if
you know not only the various frequencies but also the chords, and the
point will correspond to the chords. Then you know the complete
thing....It's a rather delicate thing....There is a very strange
mathematical fact...If you take manifolds of the same dimension, which
are extremely different...the inverse space of the spinor doesn't
distinguish between two manifolds. The Dirac Operator itself has a
scale, so it's a spectrum [frequency]. And the only thing you need to
know...is the relative position of the algebra...the Eigenfunctions of
the Dirac Operator....a "universal scaling system," manifests itself in
acoustic systems....There is something even simpler which is what
happens with a single string. If we take the most elementary shape,
which is the interval, what will happen when we make it vibrate, of
course with the end points fixed, it will vibrate in a very extremely
simple manner. Each of these will produce a sound...When you look at the
eigenfunctions of the disk, at first you don't see a shape but when you
look at very higher frequencies you see a parabola. If you want the
dimension of the shape you are looking at, it is by the growth of these
eigenvariables. When talking about a string it's a straight line. When
looking at a two dimensional object you can tell that because the
eigenspectrum is a parabola....
They are
isospectral [frequency with the same area], even though they are
geometrically different....when you take the square root of these
numbers, they are the same [frequency] spectrum but they don't have the
same chords. There are three types of notes which are different....What
do I mean by possible chords? I mean now that you have eigenfunctions,
coming from the drawing of the disk or square [triangle, etc.]. If you
look at a point and you look at the eigenfunction, you can look at the
value of the eigenfunction at this point.... The point [zero in space]
makes a chord between two notes. When the value of the two
eigenfunctions [2, 3, infinity] will be non-zero. ...The corresponding
eigenfunctions only leave you one of the two pieces; so if there is is
one in the piece, it is zero on the other piece and if it is non-zero in
the piece it is zero there...You understand the finite invariant which
is behind the scenes which is allowing you to recover the geometry from
the spectrum....Our notion of point will emerge, a correlation of
different frequencies...The space will be given by the scale. The music
of the space will be done by the various chords. It's not enough to give
the scale. You also have to give which chords are possible....The only
thing that matters when you have these sequences are the ratios, the ear
is only sensitive to the ratio, not to the additivity...multiplication
by 2 of the frequency and transposition, normally the simplest way is
multiplication by 3...2 to the power of 19 is almost 3 to the power of
12....
You see what we are after....it should be a
shape, it's spectrum looks like that...We can draw this spectrum...what
do you get? It doesn't look at all like a parabola! It doesn't look at
all like a parabola! It doesn't look at all like a straight line. It
goes up exponentially fast...What is the dimension of this space?...It's
much much smaller. It's zero...It's smaller than any positive....
Musical shape has geometric dimension zero... You think you are in bad
shape because all the shapes we know ...but this is ignoring the
noncommutative work. This is ignoring quantum groups. There is a
beautiful answer to that, which is the quantum sphere... .There is a
quantum sphere with a geometric dimension of zero...I have made a
keyboard [from the quantum sphere]....This would be a musical instrument
that would never get out of tune....It's purely spectral....The
spectrum of the Dirac Operator...space is not simply a manifold but
multiplied by a noncommutative finite space......It is precisely the
irrationality of log(3)/ log(2) which is responsible for the
noncommutative [complementary opposites as yin/yang] nature of the
quotient corresponding to the three places {2, 3,∞}. The formula is in
sub-space....Geometry would no longer be dependent on coordinates, it
would be spectral...
The thing which is very
unpleasant in this formula is the square root...especially for space
with a meter....So there is a solution to this problem of the square
root, which was found by Paul Dirac....It's not really Paul Dirac, it is
Hamilton who found it first...the quaternions is the Dirac
Operator....Replace the geometric space, by the algebra and the line
element...for physicists this thing has a meaning, a propagator for the
Dirac Operator. So it's the inverse of the Dirac Operator.... You don't
lose anything. You can recover the distance from two points, in a
different manner....but by sending a wave from point A to point B with a
constraint on the vibration of the wave, can not vibrate faster than 1;
because what I ask is the commutator of the Dirac Operator is less than
1...It no longer requires that the space is connected, it works for
discrete space. It no longer requires that the space is commutative,
because it works for noncommutative space....the algebra of coordinates
depends very little on the actual structure and the line element is very
important. What's really important is there interaction [the
noncommutative chord]. When you let them interact in the same space then
everything happens....
You should never think of
this finite space as being a commutative space. You have matrices which
are given by a noncommutative space...To have a geometry you need to
have an inverse space and a Dirac Operator...The inverse space of the
finite space is 5 dimensional....What emerges is finite space...it's
related to mathematics and related to the fact that there is behind the
scene, when I talk about the Dirac Operator, there is a square root, and
this square root, when you take a square root there is an ambiguity.
And the ambiguity that is there is coming from the spin structure.... We
get this formula by counting the number of the variables of the line
element that are bigger than the Planck Length. We just count and get an
integer.... There is a fine structure in spacetime, exactly as there
is a fine structure in spectrals [frequencies]....Geometry is born in
quantum space; it is invariant because it is observer dependent....
Our brain is an incredible ...perceives
things in momentum space of the photons we receive and manufactures a
mental picture. Which is geometric. But what I am telling you is that I
think ...that the fundamental thing is spectral [frequency]....And
somehow in order to think we have to do this enormous Fourier
Transform...not for functions but a Fourier Transform on geometry. By
talking about the "music of shapes" is really a fourier transform of
shape and the fact that we have to do it in reverse. This is a function
that the brain does amazingly well, because we think
geometrically....The quantum observables do no commute; the phase space
of a microscopic system is actually a noncommutative space and that is
what is behind the scenes all the time. They way I understand it is that
some physical laws are so robust, is that if I understand it correctly,
there is a marvelous mathematical structure that is underneath the law,
not a value of a number, but a mathematical structure....A fascinating
aspect of music...is that it allows one to develop further one's
perception of the passing of time. This needs to be understood much
better. Why is time passing? Or better: Why do we have the impression
that time is passes? Because we are immersed in the heat bath of the 3K
radiation from the Big Bang?...time emerges from noncommutativity....
What
about the relation with music? One finds quickly that music is best
based on the scale (spectrum) which consists of all positive integer
powers qn for the real number q=2 to the 12th∼3 to the 19th. Due to the
exponential growth of this spectrum, it cannot correspond to a familiar
shape but to an object of dimension less than any strictly positive
number. As explained in the talk, there is a beautiful space which has
the correct spectrum: the quantum sphere of Poddles, Dabrowski, Sitarz,
Brain, Landi et all. ... We experiment in the talk with this spectrum
and show how well suited it is for playing music. The new geometry
which encodes such new spaces, is then introduced in its spectral form,
it is noncommutative geometry, which is then confronted with physics.
Fields Medal math professor Alain Connes,
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