Complex numbers

[Marblehead]

As long as I have no complex numbers in my bank statement I'll be okay.

 

[wandelaar]

Don't think 1,000,000 + 0i would be a problem?

[voidisyinyang]

15 hours ago, wandelaar said:

I wouldn't take the posts of ViYY too serious.  The complex numbers as arrows with the addition and multiplication as defined in this topic form a commutative system.

I would take math professor Louis Kauffman seriously:

Quote

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 it e r-
ants and matrices.

https://www.worldscientific.com/doi/pdf/10.1142/9789813232044_0001

Ooops - you just got busted!

Don't believe the hype folks.

 

[wandelaar]

Anyone taking the trouble to actually examine the construction of the complex numbers as arrows as it was done in this topic will see that no advanced stuff as presented in the article of Louis Kauffman is needed. That doesn't mean that the complex numbers cannot be introduced in other ways than I did, in fact there are lots of other ways. And I said so earlier. The interesting approach of Kauffman is just one more. Here I took the most simple approach to the complex numbers I could think of, and that's why we got as far as we did in this topic. To take the approach of Kauffman I would first have had to study it myself as I am not familiar with it, but that approach would doubtlessly have been incomprehensible to those not being mathematicians or physicists themselves. One can see that for oneself by taking a look at the article linked by ViYY. So it would have served no useful purpose to use Kauffman's approach here.

 

I have ViYY on  my ignore list, and each time I take a look to see whether his posts have improved in the meantime it's clear that they haven't. But I don't have the time and energy to correct all the rubbish ViYY is writing on this forum, so I can only hope that the other Bums are able to recognise it for what it is.

[Marblehead]

Well, I knew when it was time to stop.

 

[wandelaar]

5 hours ago, Marblehead said:

Well, I knew when it was time to stop.

 

It takes time to understand new mathematical concepts, and it often happens that when you reread a mathematical text after some time things suddenly start to make sense. If such a thing would happen to you, I will be happy to take up this topic again to help you understand the full road map as we have covered it in this topic.

Edited September 8, 2018 by wandelaar

[voidisyinyang]

Quote

So it would have served no useful purpose to use Kauffman's approach here.

Unless you want to understand the connection of complex numbers to Daoism. This is a "Dao" website.

Symmetric logic is Western logic NOT Daoist logic. yeah noncommutative phase is not difficult to understand unless you've been brainwashed by WEstern symmetric logic since learning the square root of two. haha.

So a good overview of WEstern math is

Quote

Why Beauty Is Truth: The History of Symmetry Kindle Edition. At the heart of relativity theory, quantum mechanics, string theory, and much of modern cosmology lies one concept: symmetry. ... In Why Beauty Is Truth, world-famous mathematician Ian Stewart narrates the history of the emergence of this remarkable area of study ...

I have corresponded with math professor Ian Stewart. He does NOT believe in natural telepathy whereas the SLAC noncommutative phase scientists DO believe in natural telepathy, as is the case with Daoism.

So to promote complex numbers as commutative logic is to do against Daoist philosophy.

To combine relativity with quantum physics requires noncommutative logic and so noncommutative logic is the foundation of reality - this is the point of math professor Louis Kauffman.

My quantum physics professor made the same point - people learn classical physics in high school whereas quantum physics is the foundation of reality now - and quantum physics is based on noncommutative phase logic. Paul Dirac realized this was the truth from studying the Heisenberg matrices.

Qigong study in China has realized there has to be a revolution in science that combines relativity with quantum physics. Qigong master Yan Xin calls it the "virtual information field" when he does his healing. This is why Westerners do not understand Daoism because all people learn is symmetric logic and so fail to consider the foundation of reality.

 

I am simply conveying what the SLAC scientists teach - Eddie Oshins directly realized that DAoist neigong training is due to noncommutative logic of complex numbers. I realized this on my own by studying music theory. Fields medal math professor Alain Connes has corroborated my research - that music theory is noncommutative and so explains relativistic quantum physics as the ether. Also quantum physics professor Basil J. Hiley argues that noncommutative phase logic is the foundation of reality as well - as a new causative self-force. Professor Shajn Majid is another example, as are Sir Roger Penrose and Dr. Stuart Hameroff.

 

So there is a whole discipline of science connecting consciousness, paranormal spiritual training and noncommutative phase logic of complex numbers. The OP wants to pretend this does not exist. haha. Daoism confirms the noncommutative phase logic.

 

Symmetric Western logic goes against Daoism.

 

Edited September 8, 2018 by voidisyinyang

[OldDog]

5 minutes ago, voidisyinyang said:

Unless you want to understand the connection of complex numbers to Daoism.

 

Soooo ... how does one that is not well versed in advanced math gain a working perspective on noncommutative logic and its general implications? 

 

I have always looked to likes of Hofstadter (GED) or Hawking (Brief Hx of Time) ... talented mathematicians and physicists with a knack for being able to reduce complex subjects to layman's terms. Is there someone working the realm of the noncommutative that has the knack?

 

 

 

[Marblehead]

4 hours ago, wandelaar said:

 

It takes time to understand new mathematical concepts, and it often happens that when you reread a mathematical text after some time things suddenly start to make sense. If such a thing would happen to you, I will be happy to take up this topic again to help you understand the full road map as we have covered it in this topic.

Well, consider that when I started with Algebra I had to drop it twice and the third try I lucked out and got an instructor who knew how to teach in a way I could understand.  Once started I aced all three levels.  So please don't feel my dropping out had anything to do with you.  It's all about how I learn.

 

[voidisyinyang]

39 minutes ago, OldDog said:

 

Soooo ... how does one that is not well versed in advanced math gain a working perspective on noncommutative logic and its general implications? 

 

I have always looked to likes of Hofstadter (GED) or Hawking (Brief Hx of Time) ... talented mathematicians and physicists with a knack for being able to reduce complex subjects to layman's terms. Is there someone working the realm of the noncommutative that has the knack?

 

 

 

https://www.researchgate.net/publication/263763914_Non-Commutative_Operations_in_Consciousness_Studies

You can try this.

Just study the book Taoist YOga: Alchemy and Immortality - it's all based on noncommutative phase logic.

Alain Connes sums up the music theory explanation of noncommutative phase logic as 2, 3, infinity.

This is also the secret of undivided yin-yang as the Yuan Qi.

Eddie Oshins explains how Wing Chun and Baugua moves are based on noncommutative phase logic.

I realized this noncommutative phase logic on my own from music theory.

So the reason that "Moving of yin and yang" exercise works - is that for males the right hand is yin and upper body is yang and lower body is yin and left hand is yang.

This is the same secret of why Santi Shi works also - you visualize the Dragon and Tiger energy connecting the right hand to the left foot and left hand to the right foot.

Ever since the wrong symmetric math promoted by Plato - WEsterners are taught of twoness as a symmetric unit. So two eyes - symmetric. Two hands: symmetric. Two feet: symmetric. This goes against the asymmetric infinite time-frequency energy of Daoism.

So rotating the eyes with the eyes closed connects the yin and yang qi of the two eyes to activate the yuan qi of the pineal gland.

The examples are infinite - going back to the San Bushmen original human culture - the females sleep on the left hand of the fire and the males sleep on the right hand of the fire. This spread around the world - the "three gunas" of India is the same. It's from music theory. Western music theory is wrong - zero does not exist in reality.

 

 

[Lost in Translation]

5 minutes ago, voidisyinyang said:

noncommutative phase logic

 

Can you briefly explain, preferably with a simple example, what the difference between "commutative" logic and "noncommutative" logic is?

[voidisyinyang]

5 hours ago, Lost in Translation said:

 

Can you briefly explain, preferably with a simple example, what the difference between "commutative" logic and "noncommutative" logic is?

This is a Daoist website so let's turn to Eddie Oshins who was paid to research and teach the connection of noncommutative logic to Daoist Neigong training:

 

Quote

 

This representation only works for the (more fundamental) 1/2-integral representations (i.e. spinors/turns/quaternions) but also lets one build the vector and tensor representations. The converse does not hold....this property of "noncommutivity" in itself might be valuable in some way.

My claim, and original idea, has been that this is circumnavigating a T'ai Chi (Yin/Yang) symbol! More recently (Oshins, 1993b) I have suggested that this proximate technique can be used to realize Wing Chun kung-fu's "bong sau/tan sau" movement out of the Kauffman/Oshins "quaternionic arm" discussed and referenced below in end note 5.

I believe that this may be a way to get mind to code the relative relationship of part of oneself with respect to the rest of oneself (self-referential motion) and can explain the concepts of being "centered"/"one"/"integrated"/"extended"/"whole" etc. which one strives for in meditation.

 

 

Oshins, E. (1993). Oshins, E. (1993). A test for classical psychospinors. http://www.quantumpsychology.com/pdf/Test-ClassicalPsychospinors.pdf In Abdullah, F. (Ed.) Conservation and Invariance. Cambridge, UK: Alternative Natural Philosophy Association, London England.

 

So you can read the pdf for more details.

I have referenced Eddie Oshins who was paid grants at SLAC to research noncommutative logic as quantum psychology and he realized it's the secret of Daoist Neigong. He worked with Louis Kauffman - I have referenced his pdf that you can also read. Math professor Kauffman is paid to teach people why noncommutative logic is crucial to the foundation of reality based on complex numbers. He developed the "Hypercomplex Handshake" with Eddie Oshins - as I linked previously in the thread.

Then the director of SLAC was H.P. Noyes - he worked with Oshins and Kauffman - to develop this noncommutative foundation of reality. So I can quote him also on paranormal reality and relativistic quantum noncommutative logic. I can also quote Alain Connes on noncommutative logic and also Professor Basil J. Hiley with whom I've corresponded. Also Dr. Harold Atmanspacher - whom I referenced on noncommutative logic and consciousness studies. There is also Professor Shahn Majid on noncommutative logic and quantum relativistic foundation of reality.

 

There are more sources to draw on if you need to. Just let me know but I recommend reading the people paid to teach on this subject. I figured this stuff out on my own - after my master's degree - doing "free research." haha.

 

Essentially if you do use a commutative version of quantum physics it is inherently "relativistic." Whereas the foundation of reality is quantum and inherently noncommutative. So when statistics are added to quantum physics that is based on assuming or converting to the symmetric math - via the Poisson Bracket, as Paul Dirac developed. But as Kauffman and Hiley emphasize, and Connes emphasize - at the so-called "zero point" in spacetime there is already a non-local noncommutative phase.

 

This is easily explained by music theory and the wrong music theory is also the foundation of the symmetric math. That is my own specialization. I trained in music. This is what got me into Daoism - since I realized that Western music had the wrong logic. Then I realized that Daoism had the same mathematical logic as Pythagorean music theory. Then I discovered Alain Connes and he gives a lecture on music and noncommutative phase logic. I have quoted this lecture at length. The OP claims I am misrepresenting Connes since I only quote part of his lecture. Actually I quote Connes from several sources - since I first discovered his music research in his book "Triangle of Thoughts."

 

OK so going back to that Oshins pdf - he actually references my quantum mechanics professor, Hebert J. Bernstein! I took that class as my first physics class (since I knew that the symmetric logic was wrong but I kept the secret to myself). Again this is how I learned this "Dirac Dance" first hand. You can read that source directly also.  https://www.researchgate.net/profile/Anthony_Phillips2/publication/250802309_Fiber_Bundles_and_Quantum_Theory/links/588e01deaca272fa50e096c3/Fiber-Bundles-and-Quantum-Theory.pdf?origin=publication_detail

 

So Oshins states that hand movement is also found in "Double Covering of the Palms" in Pa Kua (Ba Gua) Chang and Pencak Silat.

 

So then Oshins states that these complex number spinors that are noncommutative have "dichotomic" or 2-valued realizations as up/down and left/right.

 

So this is what I referred to in regards to the book Taoist Yoga: Alchemy and Immortality - meaning for males the right hand is yin and the upper body is yang. So that is one value and then the left hand is yang and the lower body is yin. So when you put those together - it creates  "Yang embracing yin" and "yin embracing yang" as the 720 degree spin of the first movement - the "Dirac Dance" of 1/2 spin.

 

So continued to read Oshins - he refers to the Yellow Emperor stating that the inside/front are yin meridian channels and outside/back are yang meridian channels.

 

 

 

Edited September 9, 2018 by voidisyinyang

[Lost in Translation]

35 minutes ago, voidisyinyang said:

This representation only works for the (more fundamental) 1/2-integral representations (i.e. spinors/turns/quaternions) but also lets one build the vector and tensor representations. The converse does not hold....this property of "noncommutivity" in itself might be valuable in some way.

My claim, and original idea, has been that this is circumnavigating a T'ai Chi (Yin/Yang) symbol!

 

Let's back up even further. Please define "commutative" and "noncommutative" within a logical context.

[OldDog]

6 hours ago, voidisyinyang said:

You can try this.

 

Thank you!  The pdf on noncommutative operations in consciousness studies explains a lot. In particular the introduction sets the stage for distinguishing the two points of view; I.e. commutative vs noncommutative. There are sufficient examples that allow a lay understanding to emerge. One of my take aways is that those immersed in the operational mechanics of the math often are unable to grasp the implications ... a case of not being able to see the forest for the trees.

[ralis]

13 minutes ago, Lost in Translation said:

 

Let's back up even further. Please define "commutative" and "noncommutative" within a logical context.

 

Why not Google it? Start with commutativity which is a really simple concept. 

[voidisyinyang]

52 minutes ago, Lost in Translation said:

 

Let's back up even further. Please define "commutative" and "noncommutative" within a logical context.

O.K. so in terms of music theory being non-commutative as it relates to Daoism - we have to "unlearn" standard Western math logic based on symmetric. First of all we have to unlearn that music has to rely on a physical medium rather instead we should define music as based on logical inference as listening:

 

Quote

 

“harmonious sound is formless” (hesheng wu xiang) and “sound lacks constancy” (yinsheng wu chang), both of which point to two types of phenomena and both of which reveal JI Kang's reverence for Daoist naturalism....

Thus, we see yet again in JI Kang’s thought an adherence to Daoist principles of universal harmony through quiet non-deliberation (wuwei) as seen in Laozi's notion that “the highest note cannot be heard” and Zhuangzi’s preference for “patterning oneself after heaven.”....

one could even argue that music is not comprised of sound at all, for if we are to follow the logic of Zhuangzi, all sounds are a form of natural music (breath) whose notation and composition lies beyond the comprehensive capacity of the human mind....JI Kang believes that the five tones (wu yin) [from the Perfect Fifth/Fourth as yang/yin] came into being through the natural realm of heaven and earth and that there is one unchanging essence.

 

Musical Naturalism in the Thought of Ji Kang David Chai 2009

So the five tones of the nonwestern pentatonic scale are from yang as 3/2 and yin as 4/3.

     

Quote

“Before the idea of frequency existed, however, the same relation was expressed simply in terms of length, the length of a resonating agent multiplied by 2/3 being equivalent to the frequency multiplied by 3/2. The length of a zither string, then, multiplied by 2/3 gives a note which when struck is a perfect fifth higher than its fundamental. This is the first step (or lü) in a process which evolves an unending spiral of notes. The length of the resonating agent which sounds the perfect fifth is then multiplied by 4/3, the resulting note being a fourth below the perfect fifth …”

  Joseph Needham, Science and Civilization in China, Volume 4, Part I, pp. 172–173.    

Quote

    Between heaven and earth, they say, there is perfect harmony. Now, 3 is the emblem of heaven, 2 is the symbol of earth. If two sounds are in the proportion of 3 to 2 [the perfect fifth interval], they will harmonise perfectly as heaven and earth. All the tubes were cut on the same principle, … The lüs [notes] were divided into two classes, the yang lüs and the yin lüs… Everything in Nature belongs to one of these two grand categories, from whose combinations and reciprocal action results all that exists or takes place in the universe.” 

J.A. Van Aalst, Chinese Music (Shanghai: Chinese Imperial Customs Service, 1933), p. 8.

 

In the West these ratios were defined using symmetric math by assuming a physical geometric "continuum" as a cognitive bias. Math professor Luigi Borzacchini has researched this in detail. I first corresponded with him in 2000.

As math professor Luigi Borzacchini states:

Quote

We can suppose that the Quadrivium in its earlier Pythagorean version did not know any discrete/continuous opposition.

I will reference Connes' pdf on this - how noncommutative solves this "opposition" - as the ancients knew.

http://www.alainconnes.org/docs/J-Kouneiher.pdf

So he states that discrete is an internal reality while the continuous must be imposed externally. Then from the discrete the noncommutative logic is revealed. So then Connes states the "defect" of the classic symmetric logic is that real numbers assume an uncountable variable with a continuous range but then any other variable in that range has to have multiplicities that are infinite such that the continuous and discrete can not coexist.

Fields Medal Math professor Alain Connes:

Quote

It is only because one drops commutativity that variables with a continuous range can coexist with variables with a countable range.

O.K. so as I stated, Math professor Alain Connes sums up noncommutative logic from music as 2, 3, infinity. This is the same as Daoist logic.

 

So consider music "pitch" as the phase. So we hear the Perfect Fifth as yang which is 2/3 but the Perfect Fifth is also 3/2. This is noncommutative in terms of geometry. So 2/3 is C to F as a subharmonic and 3/2 is C to G as the overtone harmonic. This basic noncommutative truth was covered up by the West in order to try to "contain" the infinity of time-frequency into a geometric continuum.

So in the nonwestern music scheme - you only use the yang and yin to construct the scale.

In the Western science scheme - these natural noncommutative harmonics are "averaged and divided back" into the geometric continuum to try to maintain the same value of 0 and 1.

In other words "zero" is a negative infinity that assumes this materialistic geometric continuum based on symmetric logic.

But in the nonwestern noncommutative logic - rather the yang and yin just continue infinitely as 2/3 and 4/3.  In other words there is not statistical averaging as a geometric mean equation.

So as Math professor Alain Connes summarizes:

Quote

a “universal scaling system”, ... this discrete scaling manifests itself in acoustic systems, as is well known in western classical music, where the two scalings correspond, respectively, to passing to the octave (frequency ratio of 2) and transposition (the perfect fifth is the frequency ratio 3/2), with the approximate value log(3)/ log(2) ∼ 19/12 responsible for the difference between the “circulating temperament” of the Well Tempered
Clavier and the “equal temperament” of XIX century music. 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,∞}.

-Alain Connes

What he states elsewhere is that the 3 is to the 19th or 3 to the 12th while the 2 is to the 19th or 2 to the 12th but they can be reversed like yin and yang. That is why they are noncommutative.

Quote

This musical property is the counterpart of the principle mathematical characteristic of the Pythagorean diatonic, very Pythagorean indeed, constituted by the fact that each interval of the scale is expressed by the ratios of type 2 to the m divided by 3 to the n OR 3 to the m divided by 2 to the n.  Epimoric Ratios and Greek Musical Theory 

by Fabio Bellissima, in Language, Quantum, Music  Editors: Dalla Chiara, Maria Luisa, Giuntini, Roberto, Laudisa, Federico (Eds.)

So with the standard WEstern symmetric logic the wrong music theory created logarithmic math and its inverse exponential function.

3/2 x 4/3 = 2 (geometric mean squared).

log(3:2×4:3)=log(2:1)

log(3:2)+log(4:3)=log(2:1)

 

Now notice for this math to work - then 2/3 as C to F subharmonic can not be used! It had to be covered up and lied about.

Quote

However, he [Archytas] noted that the product of the arithmetic mean and the harmonic mean is equal to the square of the geometric mean, so this gave a way of dividing the fifth of 3:2 into the product of 5:4 and 6:5.

 

A Truman State University review on Scriba, Christoph J. “Mathematics and music.” (Danish)

Normat

38 (1990), no. 1, 3–17, 52.

 

Quote

“Any who doubt that the musical ratios are all of greater inequality, i.e., that the antecedent or first term in each is greater than the consequent or second term, should consult Archytas DK 47 B 2. This Fragment requires that the ratios be of this form if the assertions about the three means [arithmetic, harmonic and geometric] are to be true. Accordingly, the ratios assigned to the octave, fifth, fourth and minor sixth, must be 2:1, 3:2, 4:3 and 8:5, and not 1:2, 2:3, 3:4 and 5:8, respectively, as Mosshammer and others would have them.”

Alan C. Bowen, "The Minor Sixth (8:5) in Early Greek Harmonic Science," The American Journal of Philology, 1978.

 

Even though 2/3 is also the Perfect Fifth it would not fit into the symmetric commutative math structure to "contain" infinity as a closed geometry.

 

But what quantum physics rediscovered is that there is time-frequency uncertainty that is noncommutative due to relativity. Meaning that as a particle goes towards the speed of light then its energy goes up in frequency based on quantum physics but based on relativity it's time also goes "up" meaning it slows down as an amplitude or wavelength extension. Louis de Broglie realized this violates the basic logic since Pythagoras that frequency is inverse to time.

So de Broglie realized there HAS to be a noncommutative phase from the future - in the opposite direction - at the same time, as a 5th dimensional "guiding wave" to reality.

Qigong Master Shen Wu:

Quote

With his theories of “Music before Medicine” and “Music is also Medicine”, he has revealed the lost remedies of ancient Chinese music therapy and became the first person to introduce Five Tones Therapeutic Music to the modern world.  Over the last decade, Professor Wu spent a great deal of time studying ancient medical texts such as the “I-Ching—Five Tones and Eight Sounds”, “The Yellow Emperor’s Classic of Internal Medicine – Five Tones and Five Major Organs” and “Twelve Scales and Twelve Meridians”. He has combined music melody with physiology to create a systematic and organized subject with a series of musical therapeutic methods. It contains a strong root in ancient philosophy and is differentiated from the Western method of seven scales. The Chinese "lǜ" tuning is closest to the ancient Greek tuning of Pythagoras.

And so now I'll give the extended quote from Connes on music theory and noncommutative logic:

 

Quote

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,

Edited September 9, 2018 by voidisyinyang

[Lost in Translation]

3 hours ago, ralis said:

 

Why not Google it? Start with commutativity which is a really simple concept. 

 

I've already done that. Commutativity itself is not the problem. If we were discussing just math then there would be no issue. But commutativity has been mentioned regarding logic so I want to make sure I understand what is meant in that that context.

 

Is it as simple as something like "All Americans are human but not all humans are American?" If that is the case then I would like it explicitly defined. And if it is not as simple as this then all the more reason why we need to define it.

[Lost in Translation]

3 hours ago, voidisyinyang said:

O.K. so in terms of music theory being non-commutative as it relates to Daoism - we have to "unlearn" standard Western math logic based on symmetric. First of all we have to unlearn that music has to rely on a physical medium rather instead we should define music as based on logical inference as listening:

 

Musical Naturalism in the Thought of Ji Kang David Chai 2009

So the five tones of the nonwestern pentatonic scale are from yang as 3/2 and yin as 4/3.

     

  Joseph Needham, Science and Civilization in China, Volume 4, Part I, pp. 172–173.    

J.A. Van Aalst, Chinese Music (Shanghai: Chinese Imperial Customs Service, 1933), p. 8.

 

In the West these ratios were defined using symmetric math by assuming a physical geometric "continuum" as a cognitive bias. Math professor Luigi Borzacchini has researched this in detail. I first corresponded with him in 2000.

As math professor Luigi Borzacchini states:

I will reference Connes' pdf on this - how noncommutative solves this "opposition" - as the ancients knew.

http://www.alainconnes.org/docs/J-Kouneiher.pdf

So he states that discrete is an internal reality while the continuous must be imposed externally. Then from the discrete the noncommutative logic is revealed. So then Connes states the "defect" of the classic symmetric logic is that real numbers assume an uncountable variable with a continuous range but then any other variable in that range has to have multiplicities that are infinite such that the continuous and discrete can not coexist.

Fields Medal Math professor Alain Connes:

O.K. so as I stated, Math professor Alain Connes sums up noncommutative logic from music as 2, 3, infinity. This is the same as Daoist logic.

 

So consider music "pitch" as the phase. So we hear the Perfect Fifth as yang which is 2/3 but the Perfect Fifth is also 3/2. This is noncommutative in terms of geometry. So 2/3 is C to F as a subharmonic and 3/2 is C to G as the overtone harmonic. This basic noncommutative truth was covered up by the West in order to try to "contain" the infinity of time-frequency into a geometric continuum.

So in the nonwestern music scheme - you only use the yang and yin to construct the scale.

In the Western science scheme - these natural noncommutative harmonics are "averaged and divided back" into the geometric continuum to try to maintain the same value of 0 and 1.

In other words "zero" is a negative infinity that assumes this materialistic geometric continuum based on symmetric logic.

But in the nonwestern noncommutative logic - rather the yang and yin just continue infinitely as 2/3 and 4/3.  In other words there is not statistical averaging as a geometric mean equation.

So as Math professor Alain Connes summarizes:

-Alain Connes

What he states elsewhere is that the 3 is to the 19th or 3 to the 12th while the 2 is to the 19th or 2 to the 12th but they can be reversed like yin and yang. That is why they are noncommutative.

by Fabio Bellissima, in Language, Quantum, Music  Editors: Dalla Chiara, Maria Luisa, Giuntini, Roberto, Laudisa, Federico (Eds.)

So with the standard WEstern symmetric logic the wrong music theory created logarithmic math and its inverse exponential function.

3/2 x 4/3 = 2 (geometric mean squared).

log(3:2×4:3)=log(2:1)

log(3:2)+log(4:3)=log(2:1)

 

Now notice for this math to work - then 2/3 as C to F subharmonic can not be used! It had to be covered up and lied about.

 

A Truman State University review on Scriba, Christoph J. “Mathematics and music.” (Danish)

Normat

38 (1990), no. 1, 3–17, 52.

 

Alan C. Bowen, "The Minor Sixth (8:5) in Early Greek Harmonic Science," The American Journal of Philology, 1978.

 

Even though 2/3 is also the Perfect Fifth it would not fit into the symmetric commutative math structure to "contain" infinity as a closed geometry.

 

But what quantum physics rediscovered is that there is time-frequency uncertainty that is noncommutative due to relativity. Meaning that as a particle goes towards the speed of light then its energy goes up in frequency based on quantum physics but based on relativity it's time also goes "up" meaning it slows down as an amplitude or wavelength extension. Louis de Broglie realized this violates the basic logic since Pythagoras that frequency is inverse to time.

So de Broglie realized there HAS to be a noncommutative phase from the future - in the opposite direction - at the same time, as a 5th dimensional "guiding wave" to reality.

Qigong Master Shen Wu:

And so now I'll give the extended quote from Connes on music theory and noncommutative logic:

 

Fields Medal math professor Alain Connes,

 

No offense, but I'm not going to read a thousand words of quoted text on music theory. If the subject can't be distilled into simple layman's terms then I understand. I don't need to know the answer. Thank you for attempting to help me understand.

[voidisyinyang]

1 hour ago, Lost in Translation said:

 

No offense, but I'm not going to read a thousand words of quoted text on music theory. If the subject can't be distilled into simple layman's terms then I understand. I don't need to know the answer. Thank you for attempting to help me understand.

There's "learning" and then there's "learning how to learn." If you "learn how to learn" that's a whole different story.

This thread as things called "links" by people call "professors" - you can click on those links. The professors are paid to teach people about this subject. Some people reading this thread have actually taken such a bold step - something about the internet using hypertext or something.

Willful ignorance though is an age-old approach to what I call "Mall Science." If it's not "off the shelf" repeatable technology as a commodity than the boy crying to his mom is not going to be happy is he? haha.

So let's stick to "images" - as they speak "1000 words."

 

So this is noncommutative phase logic. Same frequency - different geometry as same pitch.

To go back to the Daoist example. If the frequency is "3" and the root frequency is 1 - and the octave is 2 then G=3=F as nonlocal noncommutative phase. It's in 2 different places at the same time: Same pitch, same frequency as 3 but different geometry.

It's "isospectral but not isomorphic."

Or to put this back into Daoist training terms.

Let's say I'm standing outside with my knees bent and my left hand palm facing my stomach and my right hand up by my head. The typical WEstern person walking by will think I'm doing some:

"Isometric exercise."

Nope - I'm doing noncommutative phase! The right hand energy flows to the left foot and the left hand to the right foot - as non-local noncommutative phase: Undivided yin-yang as yuan qi energy.

 

Isospectral but NOT isomorphic.

So the fascinating truth of human hearing is that it is "faster" than time-frequency uncertainty.

 

So visually this is a phase shift that is noncommutative - it changes the amplitude and frequency. But listening hears a Perfect Fifth still. It's just that one is C to F as subharmonic and the other is C to G as overtone harmonic. One is 2/3 and one is 3/2.

 

OK so enlarge this image.

This is BEFORE symmetric commutative Western logic. So it's actually DAoist noncommutative phase logic.

So to switch this to symmetric commutative logic Philolaus had to do a "bait and switch" by changing the value of 0 to 1.

0 to 8 is the 3/2 frequency of 0 to 12 now converted to 6/8 as 3/4 wavelength of 0 to 8 root tonic!)

To quote professor Richard McKirahan:

Quote

So instead of taking 12:9, which is 3/4 of 12, we take 8:6, which is 3/4 of 8. And so by adding the length 12 to 8 [as geometric magnitude not wavelength!!] with the length 8 to 6, [as geometric magnitude, not wavelength!!] we get the length 12 to 6, which corresponds to the ratio 2:1.

So he states:
 

Quote

beginning at the bottom note...and descending via another (a fifth above the bottom note).

 

So he says "bottom note" twice to emphasize they are symmetric and then says "via another" to HIDE that the "other" is the OCTAVE!!

That is the bait and switch - and then he (professor McKiraha) says -
 

(1, 4) = (7, 5)

What is (1, 4)? It is a Perfect Fourth which is the PITCH of C to F (overtone). Anyone who actually knows how to play music would not fall for this bait and switch! What is (7, 5)? It is a Perfect Fourth which is the PITCH of C to G.!

Edited September 9, 2018 by voidisyinyang

[Lost in Translation]

12 minutes ago, voidisyinyang said:

There's "learning" and then there's "learning how to learn." If you "learn how to learn" that's a whole different story

 

There is also "teaching" and "learning how to teach." I sincerely appreciate your posts but too often it seems you throw words at people and expect them to figure it out. I don't enjoy saying this any more than I am sure you don't enjoy reading this.

[voidisyinyang]

Just now, Lost in Translation said:

 

There is also "teaching" and "learning how to teach." I sincerely appreciate your posts but too often it seems you throw words at people and expect them to figure it out. I don't enjoy saying this any more than I am sure you don't enjoy reading this.

The I is noncommutative.

I will now post math professor Louis Kauffman's talk at Perimeter Institute on the I-thought and noncommutative logic.

https://www.perimeterinstitute.ca/videos/physics-logic-and-mathematics-time

So as Kauffman points out - the imaginary number is actually "plus one" and then "minus one" but since time is inherently noncommutative that means the I-thought is part of the mathematical operation - so that it "takes time" to "do" the math - so that the "one" is plus and minus at the same time but when multiplied in iteration then you get negative one since they alternative from plus or minus, etc.

Quote

A first mathematical
direction is to see how i, the square root of negative unity, is related
to the simplest time series: ..., -1,+1,-1,+1,... and making the
above analysis of time series more algebraic leads to the following

So Ramana Maharshi teaches to repeat the I-thought NOT as a mantra but as logical inference.

I call this the I-One-Eye.

So in other words Ramana Maharshi calls it the "3 in 1 unity" as the source of the I-thought and he states to visualize light on the right side of the heart as the secret pinhole to formless awareness.

Daoist Yoga also teaches that Yuan Qi originates on the right side of the heart.

So there is an impersonal formless eternal time as the source of the I-thought. Ramana Maharshi says this sense of I then emanates out of the heart.

So that is the secret of the I as the one that is noncommutative.

Or as Alain Connes states:

One plus one does NOT equal 2 - since it's noncommutative.

 

[wandelaar]

Now what have we learned about the connection between the complex numbers as defined in the approach of Louis Kauffman and Taoism by reading the posts of ViYY?

 

Did he give any examples that prove the supposed connection?

 

Did he give any proof that Western mathematics is a lie and that it is fundamentally wrong?

 

[vonkrankenhaus]

13 hours ago, Lost in Translation said:

define "commutative" and "noncommutative" within a logical context.

 

Many people assume YinYang is commutative, symmetrical, and "reversible".

 

But it cannot be. 

 

YinYang is not about equation, and is asymmetrical.

 

The upper and lower parts of your body are a YinYang polarity, but are not mirror images or even "equal".

 

Neither are the right and left sides of the body.

 

These even have different organs in them.

 

Day and Night are not a symmetrical polarity either, and Day is not a mirror image reversal of Night.

 

You have to get into western abstraction to find truly symmetrical divisions of anything, and these are actually imaginary anyway.

 

There is no perfect circle in nature to split exactly in half, for example, not even the rotation of a planet is that.

 

So even if Matter and Anti-Matter were created exactly equally at the beginning of the universe, the first Movement was asymmetrical and prevents this polarity from "canceling out" as "equal".

 

 

 

 

-VonKrankenhaus

[wandelaar]

Still don't see what all this talk about asymmetry and non-commutativity has to do with the complex numbers. Besides: even the division of things in Yin and Yang is an idealisation. As soon as you use words or symbols you simplify.

Edited September 9, 2018 by wandelaar

[ralis]

One problem I see with discussions of this nature is that language in general is binary and English is no exception. Binary is limited and conditions the mind in seeking simplictic answers in the form of “is” or “to be”. 

 

Voidisyinyang is presenting a difficult subject in that if one is unwilling to transform personal conditioning which requires critical thinking and curiosity then why bother.