ATON is a hopefully evolving classification theory. It aspires to unify knowledge around numbers and prefers naive methods. Some of the older posts are wrong but I'll keep them for the sake of continuity.

Friday, October 19, 2012

24 ASPECTS OF THE UNIVERSE

A basic classification of the universe can be derived from the Ideal Gas equation;

P*V = k*N*T

where k is the Boltzmann constant. It is one of the most fundamental constants of physics. The 4 thermodynamic variables can be mapped to the most universal categories of physics;

P: (Energy,Moomentum)
V: (Time, Spaace)
N: (Mass,Charge)
T: (Gravity,Boson)

Where;

Moomentum = (Momentum,Angular-Momentum,Spin)
Spaace = (Distance,Area,Volume)
Charge = (Electric,Weak,Strong)
Boson = (Light,Weak,Gluon)

The overall 4ness is reflected within each subcategory giving 4*4 = 16 subcategories. It is a mixture of (1,3) and (2,2) symmetries, inside and outside.

Where are the Higgs Boson, Dark Matter and Dark Energy? I think they are in k. They are the fields that the rest float on. They may even make a quartet, predicting another field;

(Higgs,?,DE,DM)

to make 5 categories and 20 subcategories in all.

Where are the Black Hole and the rest? I think they make another quartet;

(Atom,Planet,Star,Black-Hole)

Thus making 6 categories and 24 subcategories. I had a yarn before about the specialness of the number 6. 24 is also a very special number. It is one of John Baez's favorite numbers.

http://en.wikipedia.org/wiki/6_(number)
http://en.wikipedia.org/wiki/24_(number)
math.ucr.edu/home/baez/numbers/24.pdf

If all listed together in a certain order, the symmetry simplifies somehow;

(Higgs,?,DE,DM)
(Time, Distance,Area,Volume)
(Energy,Momentum,Angular-Momentum,Spin)
(Gravity,Light,Weak,Gluon)
(Mass,Electric,Weak,Strong)
(Atom,Planet,Star,Black-Hole)

There is deep symmetry to it with many aspects, each reflecting a mathematical property of 24, starting with the simple arithmetic ones like;

4*6 = 2*2*2*3 = 2*12 = 3*8

Friday, October 12, 2012

BWV-999 analysis continued (3)


There are 43 bars of 3/4 time signature. The last bar is the conclusion and stands apart. The remaining 42 are divided into 7 parts, each with 6 bars. Bach's music, and most music anyway, obey numbers in their organisation. Bach takes it to more extremes.

The harmonic signature (the tonality) is C-minor (Cm) in the original lute version. It has been transcribed to Dm when played on the classical guitar. Dm suits the guitar very well, in that it uses the open strings maximally.

In a way, the prelude is a warm up for the player and the audience and an introduction to the tonality of the instrument and the suites that follow. It is an arpeggio anyway. Its local rhythmic structure is frozen to the arpeggio chosen.

It is divided into melody (temporal) and harmony (spatial). Each supporting the other. The melody is the spine of the piece, and it is made of the even notes, if the 12*16th notes of the bars are numbered 1 to 12. They do not change as quickly, and make a melodic tremolo that cuts through the vertically arranged chords. The arpeggio piece is in fact a melody embellished by the chords that also make up a rhythm with the changes.

The (arpeggio) chords divide into two; treble and bass. They reflect each other. For example the notes (2,3,4) of the 1st bar, are reflected by (9,11,13). 13th note is the 1st of the next bar. This is musical linking, or chaining, that I described before in the link below. The bass chord next to the treble is sometimes an octave above when things resolve and settle down.

Bach used two main chord types here; triads and diminished triads. They are linked by intermediate forms made of inversions (rotations). The treble and bass chords meet at the start of the bars to make the dominant chords made of 4 notes. Eg Dm of the 1st bar; (D,2D,2F,2B). The (1,3) symmetry like that of the Quaternions.

The diminished triads sometimes meet and make a large chord with all notes spaced by a minor 3rd interval. This is the most unstable chord, since it want to be a minor and a major at the same time. Bach uses them as the changing points between the stable triads, which also meet occasionally to make a large chord.

The piece is also divided into two (2*21) with the peak happening in between the 21st and 22nd bars with the EM chord.

Bach builds the harmony around the open strings that are related by being the 4ths (the reverse 5ths) of each other. The guitar has an amazingly harmonic structure in the arrangement of the open strings. More amazingly, the number of the fingers suit this arrangement. 


The previous;
http://a-theory-of-nothingness.blogspot.com.au/2007/02/analysis-of-symmetry-in-bwv-999.html

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