Lately I ran into this book Into The Cool by Schneider and Sagan. It's on the developing science Non Equilibrium Thermodynamics (NET). It's central theme is the 2nd law of thermodynamics, nicely formulated as "nature abhors gradients". Nature likes to even out differences. Concentrations of heat get dissipated in time. Nature likes disorder. The novelty of the book is that it includes life into the 2nd law. That life is an integral part of the machinery of dissipation of order. The paradox here is that life is a process of building order. While it builds order, it consumes gradients which are larger order.
I am still reading the book, but I could not help commenting on the paradox. It is pretty clear that, while nature abhors gradients, it also loves them. It first builds them, and then rides them. For example, the gradient between the heat of the sun and the cool of the earth is consumed by life. Life builds intermediate structures to even out the temperature gradient. But the sun does not come out of the blue. It rides the gradient of the black hole in the center of the galaxy. And the galaxies are, in turn, processes that ride another invisible gradient, probably a white hole.
Another example is the seperation of the sexes. The male-female gradient is built by gradual evolution, starting from hermaphrodites. And then nature uses this gradient to make offspring.
Wednesday, February 28, 2007
Wednesday, February 14, 2007
An analysis of symmetry in BWV-999
This is my second and more detailed look at BWV-999, which is a lone prelude amongst the lute works by Bach. It seems to be the opening piece of all the lute works, which are 4 suites, prelude-fuge-allegro-998 which is a toughie and also very lovely, and a lone fugue which is also from the violine works. Apparently 999 is specifically marked to be for lute, and it also suits the 6 stringed modern guitar perfectly. It is also regarded to be one of the "kleine" keyboard preludes. It would be easy for the keyboard but not so for the guitar, with it's difficult chord changes and fast arpeggio. I will analyse all of it's 83 bars one by one, by looking at it from harmonic, melodic and fractal aspects, as much as I can with my limited musical knowledge. I hope to learn some more music through this analysis, as the piece is a relatively simple one. The main emphasis will be it's fractal structure. I am currently practising 999, 998 and the first suite.
The most outstanding aspect of a musical piece is it's measure, which is 3/4 here. 3/4 is a very special number with mythical, religious and mathematical significance. 999 is a uniform arpeggio piece with 12 sixteenths for each measure. 12 is also a magical number. Bach opens the keyboard prelude and fuges with an arpeggio prelude as well. A bit like a historical reference to the ancient harp. 999 opens with D-minor and closes with A-major.
Like most good musical pieces, it has {bass,mid-range,treble} symmetry. The mid-range is the spine of the piece, and bass and treble reflect each other and dance around it. I will use letters for notes and numbers for octaves, like D and 2D. Here is the first measure coded;
1. [(D,2D,2F,2A),(2F,2D,2F,2D),(A,2D,F,2D)]
The second measure is the same;
2. [(D,2D,2F,2A),(2F,2D,2F,2D),(A,2D,F,2D)]
The spine of the piece falls in the even numbers, or the alternate beats, if a measure is numbered from 1-12. All alternate beats are the same except the 4th sixteenth. The odd numbered notes make either side of the spine.
The first beat is the bass, and sets the dominant tone of the measure. It also completes the harmony started in the end of the previous measure. This bass linking is typical of most, if not all, musical pieces, and it comes from the linking of the scales. To see this, consider a 2 octave C-major scale;
(C,D,E,F,G,A,B,(2C),2D,2E,2F,2G,2A,2B,3C)
When a 1 octave scale is played, it sounds complete only after adding the octave higher root (2C here). Thus we get 8 notes in a complete sounding octave, although there are only 7 different notes. When 2 octaves are played, it sounds complete with 15 notes. The middle note 2C both ends the previous octave and also starts the next. Therefore 2C has a dual, or linking, role.
The measure is divided into 3 quarters, each with 4 sixteenths. The 1st and 3rd quarters reflect each other around the mediator 2nd quarter. The 1st quarter(D,2D,2F,2A) is a typical 4 note chord with it's bass and 3 trebles (D minor here). The last 3 notes of the 1st q (2D,2F,2A) are reflected by the 1st and 3rd notes of the 3rd q ((A),2D,(F),2D), and the 1st note of the 1st q ((D),2D,2F,2A), in reverse order, half speed and in the previous octave (2D,2F,2A)-(A,X,F,X,D). The 2nd q acts as a mirror. But the symmetry is slightly distorted by the shifted position of the 1st chord. This creates tension and movement. Thus we get two chords reflecting each other and dancing around a spine, in a slightly imbalanced form. When you consider different tones for the chords in the rest of the piece, you get the fireworks.
The genius of Bach here shows itself in the complexity contained in the simplicity.
A measure is the smallest unit that contains all essential properties of a piece. In this sense, it corresponds to atoms of physics and cells of life. This is such a powerful metaphor. Universe and life are essentially musical forms.
To continue...
The most outstanding aspect of a musical piece is it's measure, which is 3/4 here. 3/4 is a very special number with mythical, religious and mathematical significance. 999 is a uniform arpeggio piece with 12 sixteenths for each measure. 12 is also a magical number. Bach opens the keyboard prelude and fuges with an arpeggio prelude as well. A bit like a historical reference to the ancient harp. 999 opens with D-minor and closes with A-major.
Like most good musical pieces, it has {bass,mid-range,treble} symmetry. The mid-range is the spine of the piece, and bass and treble reflect each other and dance around it. I will use letters for notes and numbers for octaves, like D and 2D. Here is the first measure coded;
1. [(D,2D,2F,2A),(2F,2D,2F,2D),(A,2D,F,2D)]
The second measure is the same;
2. [(D,2D,2F,2A),(2F,2D,2F,2D),(A,2D,F,2D)]
The spine of the piece falls in the even numbers, or the alternate beats, if a measure is numbered from 1-12. All alternate beats are the same except the 4th sixteenth. The odd numbered notes make either side of the spine.
The first beat is the bass, and sets the dominant tone of the measure. It also completes the harmony started in the end of the previous measure. This bass linking is typical of most, if not all, musical pieces, and it comes from the linking of the scales. To see this, consider a 2 octave C-major scale;
(C,D,E,F,G,A,B,(2C),2D,2E,2F,2G,2A,2B,3C)
When a 1 octave scale is played, it sounds complete only after adding the octave higher root (2C here). Thus we get 8 notes in a complete sounding octave, although there are only 7 different notes. When 2 octaves are played, it sounds complete with 15 notes. The middle note 2C both ends the previous octave and also starts the next. Therefore 2C has a dual, or linking, role.
The measure is divided into 3 quarters, each with 4 sixteenths. The 1st and 3rd quarters reflect each other around the mediator 2nd quarter. The 1st quarter(D,2D,2F,2A) is a typical 4 note chord with it's bass and 3 trebles (D minor here). The last 3 notes of the 1st q (2D,2F,2A) are reflected by the 1st and 3rd notes of the 3rd q ((A),2D,(F),2D), and the 1st note of the 1st q ((D),2D,2F,2A), in reverse order, half speed and in the previous octave (2D,2F,2A)-(A,X,F,X,D). The 2nd q acts as a mirror. But the symmetry is slightly distorted by the shifted position of the 1st chord. This creates tension and movement. Thus we get two chords reflecting each other and dancing around a spine, in a slightly imbalanced form. When you consider different tones for the chords in the rest of the piece, you get the fireworks.
The genius of Bach here shows itself in the complexity contained in the simplicity.
A measure is the smallest unit that contains all essential properties of a piece. In this sense, it corresponds to atoms of physics and cells of life. This is such a powerful metaphor. Universe and life are essentially musical forms.
To continue...
Saturday, February 10, 2007
The need to touch down
One day I was watching a panaromic rain scene on TV. I observed that some lightnings were followed by sudden bursts of rain. I thought, overly excited localities were dumping the extra energy in the lateral electrical dimension when ionisation potential was reached. This caused a sudden cooling down in the locality, leading to precipitation.
Then I thought, it must had been like this when the universe was first starting out it's evolution. The lightnings were it's 5 fields in some succession, and matter was it's rain. It was it's creative moment. This process is called Spontaneous Symmetry Breaking in physics. Rising on two legs was a creative moment of evolution for humans. Excess symmetry was dumped by freeing the hands. The creative moment works similarly for brains. When we mull over a problem long enough, we get a sudden flash out of the blue and realise a point. We get a touch down. Creative moments can be the sources of most intense pleasures. They are the purest orgasms of our minds.
In our more and more materialised world, we seek quick and definite solutions to our more and more intricate problems. We have come to expect rewarding sex through little tablets. We seek creativity through magic mushrooms and marijuana. We expect happiness in a short and expensive "romantic" getaway. But we soon realise that there is a prize for every quick fix.
When boredom arrives at the door of our inner selves, most ppl take up arms against it. Some drink, some smoke, some inject. Some go for a quick wank. Some abuse themselves. Drown themselves in work, in slavery for some arse hole corporation. Some abuse others and become soldiers and killing machines. We seek external solutions to an essentially inner problem. We try and scare it away. Mask it out. Drown it in alcohol. How can we like boredom? It is not a good feeling. If we can address it with a quick and easy solution, why not do it?
Boredom can also be a prelude to a creative moment. If you allow yourself to be bored for long enough, sometimes a sustainable and pleasurable solution comes out of the blue. After a while you may realize that boredom is a good thing. It heralds inner tension. Like weather before lightning and rain. If you ride it long enough, you finally get a flash inside. You may go for a long walk to nurse it. Take a pencil and paper and write it down. Draw or paint it. Tell a friend. Make it. After a while you seek boredom. You know it is good for you.
Long drowned boredom digs into our soul and covers itself. Makes a knot inside. It creates a tension. The space inside loses a part of it's coherence. Makes us biassed unconsciously. We become the knot that we tied and forgotten. If you keep ignoring your boredom, it finally makes an ensemble of knots inside and finally the person becomes a nut case. An alcoholic. A junkie. A freak. A derelict.
Sometimes you have no choice but ignore yourself. You may be poor. You may not be able to satisfy your most basic needs. You may be forced to bury your innermost desires for survival. You may have unhappy parents. Abusive parents. You may fall for wrong company. You may fall in love with the wrong girl. Sometimes it is just bad luck. You may be born in the wrong country to wrong parents.
Too many of us carry the inner knots to the grave and die unhappy. And maybe spend an eternity trying to find ourselves, life after life. Is the truth within? Is it my own self? Who am I? Just an elaborate concoction of chemicals, or something much deeper?
Then I thought, it must had been like this when the universe was first starting out it's evolution. The lightnings were it's 5 fields in some succession, and matter was it's rain. It was it's creative moment. This process is called Spontaneous Symmetry Breaking in physics. Rising on two legs was a creative moment of evolution for humans. Excess symmetry was dumped by freeing the hands. The creative moment works similarly for brains. When we mull over a problem long enough, we get a sudden flash out of the blue and realise a point. We get a touch down. Creative moments can be the sources of most intense pleasures. They are the purest orgasms of our minds.
In our more and more materialised world, we seek quick and definite solutions to our more and more intricate problems. We have come to expect rewarding sex through little tablets. We seek creativity through magic mushrooms and marijuana. We expect happiness in a short and expensive "romantic" getaway. But we soon realise that there is a prize for every quick fix.
When boredom arrives at the door of our inner selves, most ppl take up arms against it. Some drink, some smoke, some inject. Some go for a quick wank. Some abuse themselves. Drown themselves in work, in slavery for some arse hole corporation. Some abuse others and become soldiers and killing machines. We seek external solutions to an essentially inner problem. We try and scare it away. Mask it out. Drown it in alcohol. How can we like boredom? It is not a good feeling. If we can address it with a quick and easy solution, why not do it?
Boredom can also be a prelude to a creative moment. If you allow yourself to be bored for long enough, sometimes a sustainable and pleasurable solution comes out of the blue. After a while you may realize that boredom is a good thing. It heralds inner tension. Like weather before lightning and rain. If you ride it long enough, you finally get a flash inside. You may go for a long walk to nurse it. Take a pencil and paper and write it down. Draw or paint it. Tell a friend. Make it. After a while you seek boredom. You know it is good for you.
Long drowned boredom digs into our soul and covers itself. Makes a knot inside. It creates a tension. The space inside loses a part of it's coherence. Makes us biassed unconsciously. We become the knot that we tied and forgotten. If you keep ignoring your boredom, it finally makes an ensemble of knots inside and finally the person becomes a nut case. An alcoholic. A junkie. A freak. A derelict.
Sometimes you have no choice but ignore yourself. You may be poor. You may not be able to satisfy your most basic needs. You may be forced to bury your innermost desires for survival. You may have unhappy parents. Abusive parents. You may fall for wrong company. You may fall in love with the wrong girl. Sometimes it is just bad luck. You may be born in the wrong country to wrong parents.
Too many of us carry the inner knots to the grave and die unhappy. And maybe spend an eternity trying to find ourselves, life after life. Is the truth within? Is it my own self? Who am I? Just an elaborate concoction of chemicals, or something much deeper?
Tuesday, January 23, 2007
The uncertainty principle and the quantity trinity
DxDp >= h/4pi
{0,1,Infinity}
I have made few cases of the Quantity Trinity already. Like {cell,being,species} and {star,galaxy,universe}. I will call it QT. It seems to be the strongest symmetry of the universe. How is it related to the Uncertainty Principle?
QT is in fact the duality of {0,I} mediated by {1}. In large populations, the smallest is related to the largest. I think nature achieves this through renormalisation. It also comes up with finite quantities to approximate 0 and I.
UP is a statement of measurement of uncertainty in coupled dualities like position and momentum. Momentum is derived from position. More accuracy for one means less for the other. But upto a limit. Beyond that limit, neither can be measured. As if they balance around the mediator of the coupling; Planck's constant divided by 4pi. Like 1 mediates 0 and I.
{0,1,Infinity}
I have made few cases of the Quantity Trinity already. Like {cell,being,species} and {star,galaxy,universe}. I will call it QT. It seems to be the strongest symmetry of the universe. How is it related to the Uncertainty Principle?
QT is in fact the duality of {0,I} mediated by {1}. In large populations, the smallest is related to the largest. I think nature achieves this through renormalisation. It also comes up with finite quantities to approximate 0 and I.
UP is a statement of measurement of uncertainty in coupled dualities like position and momentum. Momentum is derived from position. More accuracy for one means less for the other. But upto a limit. Beyond that limit, neither can be measured. As if they balance around the mediator of the coupling; Planck's constant divided by 4pi. Like 1 mediates 0 and I.
Is Global Village just around the corner?
Last year was the year of the bloggers. They have penetrated the mainstream media and shattered the corporate stronghold on the global consciousness. YouTube has started a revolution in online video, giving rise to a huge video database, growing bigger everyday and promising infinite potential. Internet is empowering the consumer, reshaping the economy. The doom and gloom of few years before is getting replaced by a wonderful optimism.
It is strange that this should be happening just at a time when the world desperately needed a new direction. Internet has not been around long and it has followed a fairly predictable path until now. It's unifying potential was predicted by many. But how can you predict something like the blogging? YouTube? The intensity of the change is amazing. It has weakened the war-mongers and their sponsors. Many corporations are already shifting alliances. But the threats are still strong. Specially the looming climate disaster.
It seems the global unification was in the cards from the beginning. Like the evolution of the natural brain, computers are getting interconnected at many levels, providing instant communication for humans at many levels and forming a progressively unifying meta-brain to support the forming global consciosness. Like a miracle.
It is strange that this should be happening just at a time when the world desperately needed a new direction. Internet has not been around long and it has followed a fairly predictable path until now. It's unifying potential was predicted by many. But how can you predict something like the blogging? YouTube? The intensity of the change is amazing. It has weakened the war-mongers and their sponsors. Many corporations are already shifting alliances. But the threats are still strong. Specially the looming climate disaster.
It seems the global unification was in the cards from the beginning. Like the evolution of the natural brain, computers are getting interconnected at many levels, providing instant communication for humans at many levels and forming a progressively unifying meta-brain to support the forming global consciosness. Like a miracle.
Friday, January 19, 2007
9 aspects of reality
{0, 1, infinity}
{time, matter, space}
{cell, being, species}
{star, galaxy, universe}
I don't know if the words correspond to the symbols but Budh Yantra is ancient and sacred.
I put time in the first position, since it is local. At the base of everything there is time. This is a surprise for me. I have been assuming space to be more fundamental. But when you think about it, everything is a little clock. Everything is an oscillating bundle of energy. Universe is a clock fractal. Being is right in the middle. Everything balance around being. It sits in the middle of a complexity ladder of 9 steps in our universe. Time is the simplest of all and is the origin of all evolution. Being starts as a little bundle of time and climbs the ladder. When it reached the 9 levels of complexity, after a long evolution, it reaches the level of our universe to create beings like us.
Sri Yantra has nine circuits and three elevations apparently.
Monday, January 15, 2007
Cell, being, species
This symmetry reflects to what degree nature follows the number triplet, {0,1,Infinity}. {star,galaxy,universe} triplet shows the power of this symmetry at the grandest scale we know. It is interesting that galaxy should correspond to being.
{0,1,I} is quantity, {-,0,+} is quality aspect. {-,0,+} corresponds to {female,child,male} symmetry. Galaxies fall into few types like elliptical, spiral, irregular. I would say {+} corresponds to {elliptical} and {male} since it has a simpler symmetry. This needs further thinking.
The reprogrammability of the center, or the mainstream, is clearly seen in each of {cell,being,species}. Cell has DNA to control the rest, being has brain, species has the marginals to reprogram, or easily capture, the mainstream. Species also fall into {herbivores,carnivores} duality reflecting {+,-}. How is reprogrammability reflected in {star,galaxy,universe} triplet? Star transforms matter in it's core. Galaxy transforms matter at a deeper level in it's core, a black hole. What is the center of the universe? Dark matter/energy? Is it easily capturable and reprogrammable?
There is also the lateral aspect; complex numbers, i^2=-1. With complex numbers we get rotating things since it's symmetry is U(1), or the symmetry of circle and square together.
{0,1,I} is quantity, {-,0,+} is quality aspect. {-,0,+} corresponds to {female,child,male} symmetry. Galaxies fall into few types like elliptical, spiral, irregular. I would say {+} corresponds to {elliptical} and {male} since it has a simpler symmetry. This needs further thinking.
The reprogrammability of the center, or the mainstream, is clearly seen in each of {cell,being,species}. Cell has DNA to control the rest, being has brain, species has the marginals to reprogram, or easily capture, the mainstream. Species also fall into {herbivores,carnivores} duality reflecting {+,-}. How is reprogrammability reflected in {star,galaxy,universe} triplet? Star transforms matter in it's core. Galaxy transforms matter at a deeper level in it's core, a black hole. What is the center of the universe? Dark matter/energy? Is it easily capturable and reprogrammable?
There is also the lateral aspect; complex numbers, i^2=-1. With complex numbers we get rotating things since it's symmetry is U(1), or the symmetry of circle and square together.
Sunday, January 07, 2007
Rigpa
The nature of everything is open, empty and naked like the sky,
Luminous emptiness, without center or circumference: the pure, naked Rigpa dawns.
(Tibetan book of the dead)
This self-originated Clear Light, which from the very beginning was never born,
Is the child of Rigpa, which is itself without any parents--how amazing!
This self-originated wisdom has not been created by anyone--how amazing!
It has never experienced birth and has nothing in it that could cause it to die--how amazing!
Although it is evidently visible, yet there is no one there who sees it--how amazing!
Although it has wandered through Samsara, no harm has come to it--how amazing!
Although it has seen Buddhahood itself, no good has come to it--how amazing!
Although it exists in everyone everywhere, it has gone unrecognised--how amazing!
And yet you go on hoping to attain some other fruit than this elsewhere--how amazing!
Even though it is the thing that is most essentially yours, you seek for it elsewhere--how amazing!
(Padmasambhava)
Taken from the book "The Tibetan book of living and dying" by Sogyal Rinpoche. Ran into it yesterday. Seems pretty good. Rigpa, or Ground Luminousity or Clear Light is the place dead go, it says. It is not the known physical light.
I thought it is also like a description of the Higgs field which is supposed to underlie everything, including space-time and light. It is not yet directly observed and predicted to be a "scalar" field. Light is a vector field, as it has two polarised electrical and magnetic fields. A scalar field is like money. It has a value but not a commodity itself. Pure numbers are defined to be scalars. They are just numbers and do not represent any specific thing. Therefore numbers are idealisations. Like numbers are at the base of mathematics and science, Higgs field is at the base of everything we know. Similarly, according to Buddhism, life has Rigpa as the base, where spirits reside. When a spirit takes on life, it is bonded to it until death. Lately I saw a doco on ABC about near death experiences. Apparently there are serious scientists who say that Higgs field may allow impressions on it by life.
With the recent confirmations of dark energy and matter, space-time seems not as empty as it looks. In fact they constitute most of the observable mass, something like 95%.
Luminous emptiness, without center or circumference: the pure, naked Rigpa dawns.
(Tibetan book of the dead)
This self-originated Clear Light, which from the very beginning was never born,
Is the child of Rigpa, which is itself without any parents--how amazing!
This self-originated wisdom has not been created by anyone--how amazing!
It has never experienced birth and has nothing in it that could cause it to die--how amazing!
Although it is evidently visible, yet there is no one there who sees it--how amazing!
Although it has wandered through Samsara, no harm has come to it--how amazing!
Although it has seen Buddhahood itself, no good has come to it--how amazing!
Although it exists in everyone everywhere, it has gone unrecognised--how amazing!
And yet you go on hoping to attain some other fruit than this elsewhere--how amazing!
Even though it is the thing that is most essentially yours, you seek for it elsewhere--how amazing!
(Padmasambhava)
Taken from the book "The Tibetan book of living and dying" by Sogyal Rinpoche. Ran into it yesterday. Seems pretty good. Rigpa, or Ground Luminousity or Clear Light is the place dead go, it says. It is not the known physical light.
I thought it is also like a description of the Higgs field which is supposed to underlie everything, including space-time and light. It is not yet directly observed and predicted to be a "scalar" field. Light is a vector field, as it has two polarised electrical and magnetic fields. A scalar field is like money. It has a value but not a commodity itself. Pure numbers are defined to be scalars. They are just numbers and do not represent any specific thing. Therefore numbers are idealisations. Like numbers are at the base of mathematics and science, Higgs field is at the base of everything we know. Similarly, according to Buddhism, life has Rigpa as the base, where spirits reside. When a spirit takes on life, it is bonded to it until death. Lately I saw a doco on ABC about near death experiences. Apparently there are serious scientists who say that Higgs field may allow impressions on it by life.
With the recent confirmations of dark energy and matter, space-time seems not as empty as it looks. In fact they constitute most of the observable mass, something like 95%.
Thursday, December 28, 2006
Bach's seal
.jpg)
Isn't it gorgeous? It has few aspects that I wanted to share with the cyber space.
Mainly it is a representation of mediated duality. Two sides reflect each other and they also merge in the middle to make the mediator. Like (-1,0,+1) and (black,grey,white). Bach is giving the second most outstanding aspect of existence, mediated duality. Unity is the first aspect.
The crown on the mediator has the numbers 4, 5 and 7 coded in a symmetry like Menorah's, the Jewish candle holder icon. There are 5 dashes and 7 knobs on the crown. The center and side knobs are specially capped, leaving 4 not capped. Is Bach giving a clue here about how to link two different symmetries? 4 is also visible in the mediator's inner square divided into 4. 5 is the number of senses, with 4 of them {taste,smell,hear,see} being mediated by {touch}. Thus Bach also gives the third aspect, mediated dual-duality. The reflected JSB on both sides also reveal mediated dualities each, S being the mediator of J and B. The universe is also built on 5 forces, {strong,weak,higgs,light,gravity}. Complex numbers have the same mediated dual-duality symmetry, (-1,+1,0,-i,+i). And as we know, complex numbers are closed.
The symmetry that Bach mastered is the symmetry of music, life and the universe. All music obey the same symmetry, but Bach knew what he was doing, not only feel. What a man. He united the western music with his 48 preludes and fugues. 48=2*24, 4!=24. When the symmetry of the universe is ever found, it may confirm Bach. Bach united music and I think also showed the way forward for science. He heard the sound of unification in his heart and mind in balance, a testament to power of good music. In doing so, he also showed the way for happiness; balance of mind and heart. It is a miracle that he ever existed.
(The seal is from Wikipedia)
...
EDIT 6/4/2013 Check this out! The expected value of Hamiltonian in Dirac formalism.
Wednesday, December 06, 2006
Sex and time
The family tree of a person is like a cone fractal infinitely expanding into past. A person in the past has both sides of the cone until the present. Special relativity defines a light cone for every locality. Sexual reproduction forms the backbone of life's space-time. Every sexual encounter that result in fertilisation forms a node in life's matrix. From this node a being emerges and goes on to make own nodes in the matrix. The distance travelled from one node to the next has a statistical spread. There would be an average speed of gene transmission into the future in this matrix, like speed of light. When looked overall, it looks like a time-cone.
Sexual dynamics may be a clue to quantum mechanics of space-time. What else for life to imitate, apart from space-time itself? Time, light and gravity are intimately linked. Light is like male, gravity like female. Light brings life to matter. Life make space by feeding and doing the chores of life. The locality defined by a life transmits itself through sex to other nodes.
Living make space, fucking make time.
Sexual dynamics may be a clue to quantum mechanics of space-time. What else for life to imitate, apart from space-time itself? Time, light and gravity are intimately linked. Light is like male, gravity like female. Light brings life to matter. Life make space by feeding and doing the chores of life. The locality defined by a life transmits itself through sex to other nodes.
Living make space, fucking make time.
Sunday, November 26, 2006
Balance
{Balance}
Balance is the middle touch and the core of being. It defines one's location in time and space. Balance in space seems to have more priority over balance in time. Evolution clearly displays the importance of territory. In physics, location (geometry) forms the backbone.
For example, hurricane takes it's vortex shape when a highly excited unstable locality brakes symmetry by collapsing and channeling energy in one angular direction. This direction is determined by the rotation of the earth. Spontaneous symmetry breaking is the mechanism used to make balance and define locality.
{OuterTouch, Balance, InnerTouch}
Balance uses inner and outer touch as its agents, when it evolves and differenciates more. Outer touch is the known touch, the screened interaction. Inner touch happens when allowed energy focus in the center. Brain performs the balancing function between these two touches. It mediates by correlating the inner to the outer.
Like reflection and refraction of light at a boundary. The boundary is closed for a being and the allowed energy makes patterns inside, creating an image of the outside. Energy comes in two modes; acoustic and electromagnetic or light. Acoustic energy gives an instant overview of the mechanics of the locality, if it is processed by an algorithm like FFT. Light energy is directional and provides 2D information. Acoustics is like gravity, globally felt. The inner brain develops ways to detect this dual energy pattern. Inner hearing and inner vision would evolve first. And then organs would evolve as the brain grows and differenciates.
{{Taste, Touch, Smell}, Balance, {Hear, InnerTouch, See}}
Then a similar splitting happens for both touch and inner touch, as the organism gets more complex and finds it's fundamental dual duality shape of the outer look. {Taste, See} and {Smell, Hear} correspondence demonstrates the level of correlation. See and Taste form the inner or local, while Smell and Hear form the outer territory. Dogs use smell and hear as the agents for defining outer territory.
Taste --> {Mouth, Stomach, Anus}
Smell --> {Nose, Lungs ? }
Hear --> {LeftEar, InnerEar, RightEar}
See --> {LeftEye, InnerEye, RightEye}
Balance is the middle touch and the core of being. It defines one's location in time and space. Balance in space seems to have more priority over balance in time. Evolution clearly displays the importance of territory. In physics, location (geometry) forms the backbone.
For example, hurricane takes it's vortex shape when a highly excited unstable locality brakes symmetry by collapsing and channeling energy in one angular direction. This direction is determined by the rotation of the earth. Spontaneous symmetry breaking is the mechanism used to make balance and define locality.
{OuterTouch, Balance, InnerTouch}
Balance uses inner and outer touch as its agents, when it evolves and differenciates more. Outer touch is the known touch, the screened interaction. Inner touch happens when allowed energy focus in the center. Brain performs the balancing function between these two touches. It mediates by correlating the inner to the outer.
Like reflection and refraction of light at a boundary. The boundary is closed for a being and the allowed energy makes patterns inside, creating an image of the outside. Energy comes in two modes; acoustic and electromagnetic or light. Acoustic energy gives an instant overview of the mechanics of the locality, if it is processed by an algorithm like FFT. Light energy is directional and provides 2D information. Acoustics is like gravity, globally felt. The inner brain develops ways to detect this dual energy pattern. Inner hearing and inner vision would evolve first. And then organs would evolve as the brain grows and differenciates.
{{Taste, Touch, Smell}, Balance, {Hear, InnerTouch, See}}
Then a similar splitting happens for both touch and inner touch, as the organism gets more complex and finds it's fundamental dual duality shape of the outer look. {Taste, See} and {Smell, Hear} correspondence demonstrates the level of correlation. See and Taste form the inner or local, while Smell and Hear form the outer territory. Dogs use smell and hear as the agents for defining outer territory.
Taste --> {Mouth, Stomach, Anus}
Smell --> {Nose, Lungs ? }
Hear --> {LeftEar, InnerEar, RightEar}
See --> {LeftEye, InnerEye, RightEye}
Then each sense splits to create it's organs. When organs split, they leave the boson of the relationship in the center as the mediator. InnerEar combines two sides to make a stereo image like model of the sound-scape outside. Duality in hearing gives depth, like also in seeing. I am not so sure about the nose-lung connection, in comparision to mouth-stomach. Maybe nose took dual role of mouth and anus at the same time, since it is only air.
{{Strong, Space, Weak}, Higgs, {Gravity, Time, Light}}
The energy expressed by gravity balances that of light. This is known but not integrated into physics properly yet. Potential/kinetic duality of energy comes from this. I suspect a similar thing is happening with {Strong, Weak}. {Light, Weak} and {Gravity, Strong} correlate strongly. The 3*2 symmetry of space is closely related to 3/2 symmetry of Strong. Higgs forms the background field which supports everything. Space is inner touch, time is outer touch.
Light --> {+ECharge, Light, -ECharge}
Strong --> {3 Color Charges, 3 Color Gluons}
Weak --> {W+, Z0, W-}
Then each field splits similarly to form an expanding tree, forming own charges. Strong seems to be like Taste. It branches deeper. Taste has mouth, stomach, anus, liver?, intestines...
Sunday, November 12, 2006
Being, music and universe
ATON-M6 classification thus meets a serious challenge from a modular group like symmetry, {{a,b},{c,d}}, which is also in line with the new multifactorials and Zeta function formulation.
================================
==================================
Time/Space takes the center stage
as Not-Doing/Not-Being.
=================================
A typical cycle of action;
{Feed,Feel,Think,Judge}
displays the 4/4 measure of being
as also done by musical conductors.
Christians do the same sign.
===================================
Do/Be expanded to reveal
a model of nothingness or slumber.
My kind of model this one.
================================
==================================
Time/Space takes the center stageas Not-Doing/Not-Being.
=================================
A typical cycle of action;{Feed,Feel,Think,Judge}
displays the 4/4 measure of being
as also done by musical conductors.
Christians do the same sign.
===================================
Do/Be expanded to reveal
a model of nothingness or slumber.
My kind of model this one.
Mirror Set, rev-2
After discovering the multifactorials, or Barnes G-functions, a revision is necessary since G-functions are more general. Mirror Set maps pairs of naturals to rationals;
Where m,n are natural, G(m,n)=m!n is multifactorial of m to depth n. Revising and broadening Mirror Set previously defined as M(m)=M(m,2). This form is more general and combines G-functions and Zeta function. It has a ying-yang look and variables do not commute, G(m,n)=/G(n,m). Here are some small values;
M(1,1-4) = (1, 1/2, 1/3, 1/4)
M(2,1-4) = (2, 1/2, 2/9, 1/8)
M(3,1-4) = (6, 3/2, 8/9, 3/4)
M(4,1-4) = (24, 18, 4^4/3, 6^4)
Previously I took M(3,2) as the center. Now M(2,2) =2/4=1/2 takes the center, standing for time/space. {2,2/9}={light,gravity}, why 2/9 for gravity? (3/2,1/2}={strong,weak} is reasonable.
Applying continuity by setting m-->z and summing gives a harmonically weighed G-function. For G=1 it is the Zeta function;
Assuming continuity holds, G may be generalised to a function of 2 complex variables;
Where z!w stands for the multifactorial to depth w, G(z,w). The form of M seems to imply the extension of G but it remains to be seen if it can be made continuous. I think G works like a local correlation function.
Thus naturals take the center stage of ATON, instead of sets. Maybe not surprising. Don't they (mathematicians) consider number theory as the purest?
Where m,n are natural, G(m,n)=m!n is multifactorial of m to depth n. Revising and broadening Mirror Set previously defined as M(m)=M(m,2). This form is more general and combines G-functions and Zeta function. It has a ying-yang look and variables do not commute, G(m,n)=/G(n,m). Here are some small values;
M(1,1-4) = (1, 1/2, 1/3, 1/4)
M(2,1-4) = (2, 1/2, 2/9, 1/8)
M(3,1-4) = (6, 3/2, 8/9, 3/4)
M(4,1-4) = (24, 18, 4^4/3, 6^4)
Previously I took M(3,2) as the center. Now M(2,2) =2/4=1/2 takes the center, standing for time/space. {2,2/9}={light,gravity}, why 2/9 for gravity? (3/2,1/2}={strong,weak} is reasonable.
Applying continuity by setting m-->z and summing gives a harmonically weighed G-function. For G=1 it is the Zeta function;
Assuming continuity holds, G may be generalised to a function of 2 complex variables;
Where z!w stands for the multifactorial to depth w, G(z,w). The form of M seems to imply the extension of G but it remains to be seen if it can be made continuous. I think G works like a local correlation function.
Thus naturals take the center stage of ATON, instead of sets. Maybe not surprising. Don't they (mathematicians) consider number theory as the purest?
Saturday, November 11, 2006
Multifactorials
Lately I found, to my great surprise, that ATON Exponential Set is in fact already defined in the number domain as the second multifactorial, also called Barnes G-function;
G2(z+1)=Gamma(z)*G2(z)
G2(1)=1
Gamma(z+1)=z*Gamma(z)
Higher multifactorials follow. To see how it works, expand 3 to depth 6;
G0(3) = 3 = 3*2^0
G1(3)=3.2.1.1 = 6 = 3*2^1
G2(3)=(3.2.1.1).(2.1.1).(1.1).(1) = 12 = 3*2^2
G3(3)=[(3.2.1.1).(2.1.1).(1.1).(1)].[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)] = 24 = 3*2^3
G4(3)={[(3.2.1.1).(2.1.1).(1.1).(1)].[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.
.{[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.
.{[(1.1).(1)].[(1)]}.
.{[(1)]} = 48 = 3*2^4
G5(3)={{[(3.2.1.1).(2.1.1).(1.1).(1)].[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.
.{[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.
.{[(1.1).(1)].[(1)]}.
.{[(1)]}}.
.{{[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1)]}} = 96 = 3*2^5
G6(3)={{{[(3.2.1.1).(2.1.1).(1.1).(1)].[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.
.{[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.
.{[(1.1).(1)].[(1)]}.
.{[(1)]}}.
.{{[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1)]}}}.
.{{{[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1)]}}}.
.{{{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1)]}}}.
.{{{[(1)]}}} = 192 = 3*2^6
Therefore Gn(3)=3*2^n.
Instead of multiplying, one could add the expanded elements (with no apparent benefits);
GS0(3)=3
GS1(3)=7
GS2(3)=14
GS3(3)=25
GS4(3)=41
GS5(3)=63
GS6(3)=92
G2(z+1)=Gamma(z)*G2(z)
G2(1)=1
Gamma(z+1)=z*Gamma(z)
Higher multifactorials follow. To see how it works, expand 3 to depth 6;
G0(3) = 3 = 3*2^0
G1(3)=3.2.1.1 = 6 = 3*2^1
G2(3)=(3.2.1.1).(2.1.1).(1.1).(1) = 12 = 3*2^2
G3(3)=[(3.2.1.1).(2.1.1).(1.1).(1)].[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)] = 24 = 3*2^3
G4(3)={[(3.2.1.1).(2.1.1).(1.1).(1)].[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.
.{[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.
.{[(1.1).(1)].[(1)]}.
.{[(1)]} = 48 = 3*2^4
G5(3)={{[(3.2.1.1).(2.1.1).(1.1).(1)].[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.
.{[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.
.{[(1.1).(1)].[(1)]}.
.{[(1)]}}.
.{{[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1)]}} = 96 = 3*2^5
G6(3)={{{[(3.2.1.1).(2.1.1).(1.1).(1)].[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.
.{[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.
.{[(1.1).(1)].[(1)]}.
.{[(1)]}}.
.{{[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1)]}}}.
.{{{[(2.1.1).(1.1).(1)].[(1.1).(1)].[(1)]}.{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1)]}}}.
.{{{[(1.1).(1)].[(1)]}.{[(1)]}}.
.{{[(1)]}}}.
.{{{[(1)]}}} = 192 = 3*2^6
Therefore Gn(3)=3*2^n.
Instead of multiplying, one could add the expanded elements (with no apparent benefits);
GS0(3)=3
GS1(3)=7
GS2(3)=14
GS3(3)=25
GS4(3)=41
GS5(3)=63
GS6(3)=92
Thursday, October 26, 2006
Future >= Present/Past
The uncertainty principle (by Heisenberg) is expressed by a dual duality in physics,
D={{P,M},{T,E}} = {{Position,Momentum},{Time,Energy}}
It states that the uncertainty in the measurement of "coupled" entities is always larger than a cetain limit, Planck's constant divided by 4pi. Momentum is also a function of position, and energy is also a function of time.
It is a statement of prediction. It predicts that nothing can be measured beyond a certain limit, with the available means of D. It applies to every measurement process, therefore to everything. For example, measurement of pitch in sound is optimised by balancing accuracy (the length of the buffer (window)) with timeliness. Speech recognition and synthesis is an event that has to happen in real time. Therefore parameters like pitch are measured in flight. Longer windows give more accurate measurement of pitch, but the location is lost. Shorter window locates the pitch better but misses length for accuracy of intensity. Therefore an optimum buffer length is used.
Note the black hole form in the action divided onto a spherical surface. 4pi is the amount of solid angle around a point in 3D space.
Since it is a statement of prediction, it suits quantum mechanical language well. QM's language is probability. It has an involved derivation but I will go through it, since it is so important...
Tuesday, October 24, 2006
Complex Normal Distribution
I called it CND but I haven't seen it defined. I just put complex variables in ND;
z=(1/c1*sqrt(2*pi))*e^((-1/2)*((z-c0)/c1)^2)
Where c1 and c0 are standard variation and mean. In the following c1 is the free parameter. A surprise here is that Mandel and Julia are similar in large scale. Although ND has that property of looking similar after a frequency transformation.
As before, restricting expansion also limits domain. I think I made a mistake with the expansion of CND. Fractal Explorer's Exp(z) does not give Taylor's expansion to a number. The expansion is not so trivial to calculate. Too many terms. I will keep the "expanded to 6" ones until I correct them. Currently I am trying to learn some Java.
Mandel
e^x expanded to 6
Sitting Buddha, hmm
Julia
e^x expanded to 6
c1=(1.01,-1.11)
Doesn't it look like infinity sign?
Unfortunately the above Mandel
is not at the same c1, Mandel is below
Mandel
e^x to 6
Mandel
bailout=49
Mandel
bailout=324
Julia
bailout= 25
Mandel
bailout=25
Julia
bailout= 361
Mandel
bailout=361
Mandel
c0 free
Mandel
c0=(0,-1)
e^x expanded to 6
Mandel as mouth
z=(1/c1*sqrt(2*pi))*e^((-1/2)*((z-c0)/c1)^2)
Where c1 and c0 are standard variation and mean. In the following c1 is the free parameter. A surprise here is that Mandel and Julia are similar in large scale. Although ND has that property of looking similar after a frequency transformation.
As before, restricting expansion also limits domain. I think I made a mistake with the expansion of CND. Fractal Explorer's Exp(z) does not give Taylor's expansion to a number. The expansion is not so trivial to calculate. Too many terms. I will keep the "expanded to 6" ones until I correct them. Currently I am trying to learn some Java.
Mandele^x expanded to 6
Sitting Buddha, hmm
Juliae^x expanded to 6
c1=(1.01,-1.11)
Doesn't it look like infinity sign?
Unfortunately the above Mandel
is not at the same c1, Mandel is below
Mandel
e^x to 6
Mandelbailout=49
Mandel
bailout=324
Juliabailout= 25
Mandelbailout=25
Juliabailout= 361
Mandelbailout=361
Mandelc0 free
Mandelc0=(0,-1)
e^x expanded to 6
Mandel as mouth
Performance and nothingness
Performance of a difficult piece needs higher concentration and relaxation at the same time. Regardless of what piece. Musical piece, sexual piece academic piece. A paradox. How can you relax and concentrate at the same time? How can you create on demand? Even a purely mechanical performance needs a lot of juice. The key it seems is passion with wisdom. Passion knows the destination, wisdom knows the way. The destination is beauty, the way is nothingness. Like drops making an ocean.
Playing guitar needs a lot of concentration and relaxation at the same time. To learn a difficult piece, the fastest way is to play as slow and light as possible. A paradox. As Abel Carlevaro states clearly in his guitar method, you gotta give your full attention to balance from the start. Balance is achieved fastest by building it from little. So to learn you decrease tempo and power as much as possible but keep good balance and control. The {position, amplitude} duality of Delta Function is here as {tempo, power}. After all, learning is locating. Slowing down is as difficult as playing faster. You have to hold notes longer with your left hand, but the real difficulty is to remember. It is easier to remember when you play in a relaxed tempo which happens to be the natural tempo of the piece. The brain likes different speeds for different things. Intensity or power is also difficult to reduce. You have to play your right hand really close to the strings, which is really hard. So it is as hard to play slow and light as fast and powerful. But to learn, or to teach the piece to your brain, you have to slow down. Like learning a language.
Performing for musicality is similar. If you don't relax you can't bring the beauty out. Improvisation must be the real test for any musician. Improvisation, or creating on the go, is the way to go. The way is nothingness.
In the end everything is mediation, or compromise, or balance. It is difficult to play powerful and fast or light and slow at the same time. So you find a middle way that suits you best. But you keep pushing the difficult limits to keep your domain nice and roomy. Build strength around your comfort zone, and extend your comfort zone to meet your difficulties.
Playing guitar needs a lot of concentration and relaxation at the same time. To learn a difficult piece, the fastest way is to play as slow and light as possible. A paradox. As Abel Carlevaro states clearly in his guitar method, you gotta give your full attention to balance from the start. Balance is achieved fastest by building it from little. So to learn you decrease tempo and power as much as possible but keep good balance and control. The {position, amplitude} duality of Delta Function is here as {tempo, power}. After all, learning is locating. Slowing down is as difficult as playing faster. You have to hold notes longer with your left hand, but the real difficulty is to remember. It is easier to remember when you play in a relaxed tempo which happens to be the natural tempo of the piece. The brain likes different speeds for different things. Intensity or power is also difficult to reduce. You have to play your right hand really close to the strings, which is really hard. So it is as hard to play slow and light as fast and powerful. But to learn, or to teach the piece to your brain, you have to slow down. Like learning a language.
Performing for musicality is similar. If you don't relax you can't bring the beauty out. Improvisation must be the real test for any musician. Improvisation, or creating on the go, is the way to go. The way is nothingness.
In the end everything is mediation, or compromise, or balance. It is difficult to play powerful and fast or light and slow at the same time. So you find a middle way that suits you best. But you keep pushing the difficult limits to keep your domain nice and roomy. Build strength around your comfort zone, and extend your comfort zone to meet your difficulties.
e^((z^2+c1)/c2), expanded to 6
Expanded the exponential to power 6, like M6. Bailout does not expand the domain in this case. The set looks similar from either of c1 and c2, which is interesting. Limiting the expansion of e^x to 6 seems to restrict the domain. A bit like the top of the pyramid flying off in the Egyptian mythology. Hunab Ku also seems to imply that ying-yang part is seperate.
Expansion to 6 is faulty. I found that expansion of ND is not easy. It has too many terms and difficult to calculate. I am trying to shift to Java at the moment.
Mandel
c2=(1.36,-0.66)
Julia
(0.5,0.5)
c2=(1.36,-0.66)
What do you reckon?
Mandel
c1=(0.26,-0.35)
Julia
(0.5,0.05)
c1=(0.26,-0.35)
I always wondered what those points were inside.
Expansion to 6 is faulty. I found that expansion of ND is not easy. It has too many terms and difficult to calculate. I am trying to shift to Java at the moment.
Mandelc2=(1.36,-0.66)
Julia(0.5,0.5)
c2=(1.36,-0.66)
What do you reckon?
Mandelc1=(0.26,-0.35)
Julia(0.5,0.05)
c1=(0.26,-0.35)
I always wondered what those points were inside.
Monday, October 23, 2006
e^((z^2+c1)/c2)
c1=(2.05,-2.01), max-iter=194, bailout=25,100,1024,10000
I like this form because it looks like the normal distibution. It also has a similar form to Mirror Set, as exponential for given H-fractal of z^2+c form. Totally unexpected looks though. Look at the smiling Buddha Mandel!
I made this with Fractal Explorer which is free. The diameter increase in both Mandel and Julia (which are contained in circles) corresponds to the bailout. Thus the domain is half the complex plane which is weird.
Check out the amazing similarity to Mayan icons.
Mandel
bailout=25
Julia
bailout=25
Etznab
Hunab Ku
Mandel
bailout=100
Julia
bailout=100
Mandel
bailout=1024
Julia
bailout=1024
Mandel
bailout=10000
Julia
bailout=10000
Another Julia
bailout=25
Julia up close
Bronze age
Gold
I like this form because it looks like the normal distibution. It also has a similar form to Mirror Set, as exponential for given H-fractal of z^2+c form. Totally unexpected looks though. Look at the smiling Buddha Mandel!
I made this with Fractal Explorer which is free. The diameter increase in both Mandel and Julia (which are contained in circles) corresponds to the bailout. Thus the domain is half the complex plane which is weird.
Check out the amazing similarity to Mayan icons.
Mandelbailout=25
Juliabailout=25
Etznab
Hunab Ku
Mandelbailout=100
Juliabailout=100
Mandelbailout=1024
Juliabailout=1024
Mandelbailout=10000
Juliabailout=10000
Another Juliabailout=25
Julia up close
Bronze ageGold
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