Wednesday, March 17, 2010

Does harmonic complexity reduce to 3-adicity?

I have been updating the chapter Self and Binding of TGD inspired theory of consciousness. The goal is to base the theory from the beginning on ideas like zero energy ontology, hierarchy of Planck constants aand its connection with dark matter, p-adic physics as physics of cognition and intentionality -and in in particular, life as something residing in the interection real and p-adic worlds. The notion of number theoretic entropy makes it possible to assign to rational or even algebraic entanglement probabilities a positive negentropy and this has meant a breakthrough in the understanding of TGD inspired theory of consciousness and life. These updatings are extremely fruitful -not only because they force to throw away the ancient and obsolete stuff- but because the interaction of new ideas with old ones produces something completely unexpected new ideas.

The understanding of music experience is especially fascinating challenge for a consciousness theorists. In TGD framework quite nice vision about the basic aspects of music experience emerges. Octave phenomenon can be reduced to p-adic length scale hypothesis implied if the causal diamonds defined as intersections of future and past directed lightcones and playing key role in quantum TGD have discrete size spectrum coming as octaves of CP2 length. Also the preferred role of certain rational frequencies can be understood in the p-adic context from the fact that sine waves in p-adic context can be defined only by introducing an algebraic extension of p-adic numbers allowing the needed roots of unity. Plane waves are defined p-adically only in discrete subset of points and for harmonics of the fundamental frequency. This implies automatically the preferred role of a limited set of rational valued multiples of the fundamental.

The following little excerpt from the updated chapter provides a inspired vision about one particular aspect of music experience, namely the harmony and allows to interpret Pythagorean vision about music scale in terms of 3-adicity, to deduce a measure for a harmonic measure of the chord, and to replace the Pythagorean tuning of 12-tone system based on perfect fifths with a unique tuning based on 3-adicity.

An interesting question relates to the conditions guaranteing that a chord is experienced as harmonious in the Pythagorean sense. Pythagorean tuning is based on the notion of perfect fifths identified as a scaling by 3/2 producing the sequence C,G,D,A,E,.. In this tuning major-C scale corresponds to ratios C= 1/1, D=9/8, E=81/64, F=4/3, G= 3/2, A=27/16, B= 243/128, C=2/1. Eb and F# correspond to ratios 25/33 and 36/29. All notes are expressible as powers of two and three. Since the multiplication of any note by a power of two does not affect the harmony it should be to drop the powers of two from the integers characterizing the notes in the ratio of three notes. For instance, C-E-G reduces 3:34:1, C-Eb-G to 34:1:33, and tritonus C-Eb-F# to 39:1:33.

The problem of Pythagorean tuning is that one cannot represent 2 as an exact integer power of 3/2 and the scalings give infinite number of tones. If the construction starts from Gb then F# and Gb correspond to frequencies, which are not quite identical in Pythagorean tuning. One could make compromize by introducing the geometric mean of F# and Gb but this would bring in 31/2 and would force to leave the world of pure rationals. For string instruments and electronic instruments the Pythagorean tuning is practical but for instruments like piano the transposition of the scale is impossible.

One should be able to characterize a given chord harmonically by a function F(a,b,c), which is symmetric under the permutations of the reduced pitches a, b and c obtained by dropping powers of two and is invariant under over all scaling of the reduce frequencies. The elementary symmetric functions F(a,b,c)=[a2(b+c)+b2(a+c)+c2(a+b)]/abc and G(a,b,c)=[a3+b3+c3]/abc are the simplest functions of this kind. Either of these functions or their product or ratio could be considered as a measure for the harmonic complexity. The value of the denominator abc equals to 3n, n=3,7,12 in the cases considered. The numerator has in all cases 3-adic norm equal to one for both F and G. This suggests that the 3-based logarithm of the 3-adic norm 1/|abc|3=|F|3=|G|3 having the values 3,7, and 12 for C-major, C-minor, and tritonus could serve as the measure for the complexity. It is indeed smallest for major and largest for tritonus. 3-adic norm for the product 1/ of n tones of the chord defines a measure of complexity in more general case. A good guess is that the 3-adic norms of the elementary symmetric functions give rise to the same measure.

For the chords C-E-G, F-A-C, and G-H-D appearing as basic chords in C- major scale the values of the harmonic measure are 3, 2, and 8. This means that the basic chords are not harmonically equivalent in Pythagorean system whereas in equally tempered system they would be. One might think that this explains why the tonic is remembered. The anomalously low value for F-A-C relates to the fact that it is only tone for which the power of 3 is negative. Situation changes of F is identified as a minimal power of 3 giving F equivalent with Pythagorean F within the resolution of ear to pitch which is about |Δ f/f|= 4.3 per cent . F=35/28 gives |Δ f/f|= 4.8 per cent. This F would give for F-A-C the harmonic measure 8 which equals to that for G. This looks more reasonable than the purely Pythagorean value. This definition would also allow to find a unique choice of powers of three for 12-chord system. For instance, F# is favored over Gb since it corresponds to a positive power of 3.

To sum up, music seems to provide a possible manifestations of 3-adicity, and the proposed measure of harmonic complexity might provide a manner to construct also a theory of aesthetically pleasing harmonic progressions.


Ulla said...

Perfect fifths in music.

gives a link to the golden mean. Perhaps the E8 symmetry also find a place within this concept, and those Platonic solids?

How would a world look like without that self? Would it even be possible?

Ulla said...

One more that I think is highly interesting for you.

As instance:
1) Frequencies of 109 to 1012 Hz are similar to the frequencies of oscillation of protein molecules, DNA and RNA; of membranes and other parts of cells; and of conformational transitions in enzymes, which creates the possibility of resonant absorption of HF EMR.

Matti Pitkänen said...

Thank you. The summary is interesting although it is impossible to say anything interesting by just looking at it.

I made some progress in understanding the role of various frequencies in the higher level sensory representations at magnetic bodies by bringing in zero energy ontology and causal diamonds, hierarchy of Planck constants, and negentropic entanglement. See the updated version of Quantum Model of Sensory Representations.

There are several kinds of frequencies: for instance:

*Cyclotron frequencies: control of biological body by magnetic body.
*Josephson frequencies assigned with Josephson junctions assignable to either cell membrane or identifiedas the flux tubes connecting lipids to DNA nucleotides: communication of sensory data to cell membrane from magnetic body.
* The harmonics of the fundamental frequencies assignable to causal diamonds and coming as octaves and assignable to elementary particles in zero energy ontology. Signal is received by sub-CD when the frequency corresponds to this kind of frequency so that it acts like radio receiver.

The problem is to understand how the geometric data (posititions of the objects of perceptive field and also their velocities plus other geometric data such has shapes) could be coded to frequencies. What is the spectroscpy of consciousness?

*Sub-CDs are imbedding space correlates for mental images. The frequencies f=c/T and their harmonics assignable to CD with time scale T a Lorentz transformation correspond to biologically important time scales. .1 Hz for electron and millisecond for u and d quarks. They act as resonance frequencies.

*The Lorentz transformation of sub-CD representing mental image induces a scaling of these frequencies. This transformation of sub-CD changing itse shape could represent the velocity of object of perceptive field by frequency coding.

*The moduli space of CDs leads to a very precise proposal about the representation of geometric qualia. Also the earlier model for honeybee dance inspired by the observation of topologist Barbara Shipman that honeybee dance and quarks relate to each other in some mysterious manner fits with this general picture nicely.

A new very natural idea was that DNA double strands act as relay stations such that sensory data is mediated from cell membrane via the passive strand to the magnetic flux sheets going through it to "sensory areas" of the magnetic counterpart of brain) and the control by the magnetic "motor areas" is mediated via similar flux sheets going through the active DNA strand. This would lead to precise view about the structure of magnetic body as image of biological body as far as structure (not shape!) is considered.

Also additional evidence for magnetic body besides strange time lapses of sensory experience (Libet) emerges.
For instance, blind sight in which person claims that he is blind but obviously sees although not perfectly, could be understood if the negentropic entanglement between magnetic body and cortical areas is not present. Person would see only with his brains.

All of this of course sounds totally out-landish from the perspective of standard biology but I can only deduce the most probable implications and try to get rid of my own prejudices. The power of good mathematics is immense but it can lead also to astray!

The undesirable effects of ELF fields could be due to the interference of ELF radiation with biocontrol by magnetic body. Cyclotron radiation would naturally relate to the control and Josephson radiation to the communication of sensory data to magnetic body.

Matti Pitkänen said...

Comment to the first posting by Ulla. Music metaphor is one of the earliest ideas about brain. Axons as kind of music instruments.

This idea has generalized considerably and the idea of musical Universe first very nicely with the role of sub-CDs in sensory representations. The frequency defined by the time scale of CD plus its harmonics would make subself a music instrument in mathematical sense and waking up subselves would be based on negentropic music with resonant frequencies;-). What makes this so fascinating that elementary particles would correspond to these basic instruments and the basic scales with fundamental equal to 1280 Hz (quarks) and 10 Hz (electron) are directly visible in biology.

Also massless extremals are mathematically ideal music instruments. In both cases Lorentz boost changes the fundamental frequency continuously so that one is not doomed to play in just few basic scales;-). Also the hierarchy of Planck constants bring in additional fundamental scales.

Ulla said...

This everything sounds very exotic and interesting. My stomach will have much to do :)

I guess my meridians are comparable to subCDs, and the harmonic frequencies ought then to be a octave. What would the frequencies be? Or are they repeated for different classes of frequencies, so that ELF has 8, GHz 8 and THz 8 harmonies? Maybe the cellmembrane has the smallest biol. wavelength, somewhere I read the frequency to be 10^11 Hz (suits well with your numbers). Or is this freq. already the Josephson area? And the biggest wavelength 5 Hz (about, or less). Infrasound interact with the body though, although the wavelength is so big, over 17 m at min. How this is done is open to me yet. Maybe these infrasound wavelengths can also interact in octave fractals?

But the same harmonies ought to be also in the elemental particles - as mass?

I just sort my thoughts on this.

Maybe another way to look at these octaves would be as E8 or Platonics. I know you have something on this E8, but maybe in this new light the answer will be another? I don't understand this Lisi-approach, how a rotating would be possible in reality (but it looks very nice) and give the elementary composites (as helices?). The mechanism is perhaps another too. This would follow the tale 'there are many ways to Rome'.

"sensory data is mediated from cell membrane via the passive strand to the magnetic flux sheets going through it to "sensory areas" of the magnetic counterpart of brain) and the control by the magnetic "motor areas" is mediated via similar flux sheets going through the active DNA strand."

What is passive and active strand in this?
The flux tubes would be very assymmetric. If they go along a nerve they will fuse in the nucleus or before? And there must at the same time be other short ones perpendicular to these long tubes. How can the be held alive? The force must be very different for each tube?

The magnetic field itself is perhaps a part of the solution. It has many 'barriers' along the body, dividing the body into (fractal and topological?) zones/spheres.

I must try to find time to read your writing. This is very interesting. So many questions :D :D

Ulla said...

Bah, I just got an ache in my stomach after looking on your text.:)

I must tell you, I just got my first reflexological baby :) She called me a moment ago, the test was positive :) She has tried to get pregnant for years. A lots of tensions in her stomach-region.

It feels wonderful.

Ulla said...

BTW the biologically important scanning areas are 10 - 100 Hz, used in hospitals. So I guess the first 8 harmonies lies within this. Schuman resonances are 4, the last about 30 Hz.

Ulla said...

Again,an old singing Universe by Walter Russell.

He has an interesting way to do the periodic table. Noble gases are central and makes the octaves.
I think noble gases are interesting interactive media (iniert) for the dark matter. At least they are contaminations.

Ulla said...

I found something (again), although you are not interested maybe someone else.

In your work Quantum Model of Sensory Representations, you have a notice about Mark Germine. That collective self was also evident for Jazz musicians etc. There are much evidence.It means that our brains can be manipulated from outside. I found also a notion of supergenomes from Liboff.

What comes in my mind from this is that Fe++ cyclotron frequencies direct attention, seen as a disturbance from the harmony directed by Ca++ cyclotron frequencies. Guess Li would slow it down much. Betafrequencies are 16 Hz, about. Overlapping of course. Iron is in the blood (paramagnetic) and in the brain (diamagnetic) and regulate partly free radical prod. Is it the free radicals that are our quantum antenna? The magnetoreceptors?

In this way the brain functions can be scaled down to metal ion cyclotronic frequencies. Ca is the most important signal we have in the body and the brain.

One more. Li and Zhang (arXiv:0806.0109v1 [‐ph] 31 May 2008, "The holographic principle and language of genes".
Citation:"We show that the holographic principle in quantum gravity imposes a strong constraint on life. The degrees of freedom of an organism can be estimated according to the theory of Boolean networks, which is constrained by the entropy bound.

Hence we can explain the languages in protein sequences or in DNA sequences. The overall evolution of biological complexity can be illustrated. And some general properties of protein length distributions can be explained by a linguistic mechanism."

There would be certain words then that determined the length? Or is the pattern seen in the tissue enough? That is the negentropic entanglements?

Germine say: "By applying a language, which is universal, the excess number of degrees of freedom in living systems as compared to the holographic boundary can be rectified. The authors say, for example "human language can be viewed as a transformation of cell language." This would imply a universality of cell language, such that "different subjects have a common ultimate theory of all the information in the universe." The universe of information must be used over and over again, in reiterative or sequential fashion. For this to occur, the language of information and mathematics must be universal, and, as a language implies a mind, there must be a Universal Mind.", Mark Germine.

Matti Pitkänen said...

The idea about universal language makes sense to me. I have earlier discussed the realization of genetic code in terms of dark nucleon states. DNA as topological quantum computer would provide second new realization relying on quark-antiquark pairs at ends of magnetic flux tubes connecting DNA nucleotide and lipid and would use the intronic portion of DNA.

Temporal field patterns would provide further mode of gene expression. Nerve pulse patterns generating codons of memetic code with code word consisting of 126 bits. The realization that electron corresponds to .1 second time scale and that quarks could naturally correspond to millisecond time scale in zero energy ontology (causal diamonds, etc...) lead to the idea that temporal sequences of quark causal-diamonds inside electron's causal diamond provide a fundamental realization of memetic code in living matter and that sequence of nerve pulses during .1 second time interval generates memetic codon as bit sequence. Millisecond time scale makes itself visible also in the kHz neural synchrony.

The ontological news would be that a continual creation of universes existing for millisecond/.1 seconds (eternity in the Compton time scale of quarks/leptons) would be taking place in living matter at least and perhaps quite generally. Quantum fluctuations would be the term in standard quantum field theory.

By looking at Wikipedia pages about biology you encounter again and again .1 second and 1 ms time scales and 10 nm length scales. This cannot be an accident.

The first step in understanding of an unknown system is to understand the origin of the characteristic time and length scales: in biology and neuroscience even this understanding -and even the realization how important this understanding is- has been lacking.

Theoretical physics colleagues are to be blamed for this since they have the theoretical tools but are not willing to use them since they refuse to believe that their reductionistic program has failed. The fatal conclusion is that biological systems are just 'dirty' and that there is no hope of understanding these scales from first principles. Same about genetic code, DNA, etc... Everything related to life is for them just accidents. Not a very fruitful attitude for a theoretician.

Ulla said...
This comment has been removed by the author.
Ulla said...

It was me that took away my comment. I must choose my words better :)

My first attempt to catch the magnetic body

It is relevant here :) I thought to continue with the magnetoreceptors.

I must say that this correspondence with you have given me very much, and I know I will get much also in future. You have transformed my thinking :) I know principally now how I can continue with my work. It will be something like 'an unified theory of biology' :D

But I want to defend myself. You should know I'm not the one plattering around the coffee table. Usually I sit silent, because I don't like the sound of my own voice. A memory from school time when I was VERY, VERY shy. I'm not so different from you. I don't like small talk either a bit more than you. I don't like gossiping, in fact I don't bother at all what other do.

But this is so interesting, and I have so much to say, but I shall try to do my melting alone. It only went so much easier when we could discuss. It was perhaps because of your arguments, but I had many objections against them, what made you furious sometimes :) I saw that I also could change your thinking a bit.

I can do so that I write on my blog my objections and gratitudes and you comment there, or here, or not at all if it feels too uncomfortable. If the thought of a book really feels that disgusting I can skip it so far, but I also thought it would give you money. It is such a wonderful story :) If it is something else I'm sorry. Why do you take it? You have done nothing wrong.

You know I think very high of you, but also sometimes not so high. It seems that both ways bother you :)

Ulla said...

A new story:

There are no place to link to your post other than here?