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.

Wednesday, October 10, 2007

A classification of life and universe

The universe starts from a fuzzy state;

0. {universe}

and it remains essentially fuzzy while building structures. Then it polarizes into a mediated duality;

1. {sense,{field}}

The transition {} --> {,{}} has two implied directions of evolution;

{,{}} = [,[]] + [,[]]*[[],] + [[],]

Where the format is loosely stated, but it is somewhat like the Clifford algebra. It is undecidable whether 'sense' leads to 'field' or vice-versa. Like the chicken-egg dilemma. The fuzzy parent state transforms to [,[]]*[[],], and becomes the mediator of the duality. Like a tossed coin settling on it's rim, or having sexually fuzzy offspring.

The mediated duality form is observable in many areas;

. {mathematics} --> {operator,{number}}
. {quantum mechanics} --> {observer,{observed}}
. {music} --> {listener,{performer}}

Then, iterate again to get offspring functionality;

1. {sense,{field}}

2. {exclusive,{inclusive}, {space-time-gravity*-light, {weak-strong}} }

Where 'exclusive' stands for 'observe-move' or soft interaction, and 'inclusive' for 'reproduce-feed' or hard interaction. '*' stands for the field-antifield pair.

The combination 'space-time-gravity*-light' is non-intrusive or soft interaction, while 'weak-strong' is hard.

In mathematics;

1. {operator,{number}}
2. {additive,{multiplicative}, {0,{1}} }

'additive' is not intrusive like 'observe-move', yet 'multiplicative' is intrusive like 'feed-reproduce'. '0' and '1' are are the identity elements of the operators.

Therefore, 'field' seems to correspond to 'higgs'. The scalar field and it's associated operators are at the foundation of all systems. Like numbers for mathematics, money for economy.

Then, iterate until 6;

2-0. {exclusive,{inclusive}}
3-0. {observe,{move}, {reproduce,{feed}} }

2-1. {space-time-gravity*-light, {weak-strong}}
3-1. {space-time,{gravity*-light}, {weak,{strong}} }

;;;

3-0-0. {observe,{move}}
4-0. {analyze-hear,{imagine-see}, {sustain-propel,{navigate-manipulate}} }

3-0-1. {reproduce,{feed}}
4-1. {non-sexual,{sexual}, {taste*,{smell*}} }

,,,

3-1-0. {space-time,{gravity*-light}}
4-2. {space,{time}, {gravity*,{light}} }

3-1-1. {weak,{strong}}
4-3. {neutral-weak,{charged-weak}, {strong,{residual-strong}} }

The symmetry of 'weak' seems to be the symmetry of reproduction. Taste-strong correspondence is reasonable. Residual-strong refers to the force between nucleons.

;;;

4-0-0. {analyze-hear,{imagine-see}}
5-0. {analyze,{hear}, {imagine,{see}} }

4-0-1. {maintain-propel,{navigate-manipulate}}
5-1. {maintain,{propel}, {navigate,{manipulate}} }

,,,

4-1-0. {non-sexual,{sexual}}
5-2. {self-repr,{shared-repr}, {female,{male}} }

4-1-1. {taste*,{smell*}}
5-3. {taste,{untaste}, {smell,{unsmell}} }

...

4-2-0. {space,{time}}
5-4. {along-space,{lateral-space}, {along-time,{lateral-time}} }

4-2-1. {gravity*,{light}}
5-5. {gravity,{antigravity}, {electric,{magnetic}} }

,,,

4-3-0. {neutral-weak,{charged-weak}}
5-6. {organism-cell,{dna-molecule}, {star-planet,{moon-comet}} }

===> There seems to be a problem here with 'neutral-weak' to life mapping. Star-weak mapping seems to be OK. Still thinking about this.

4-3-1. {strong,{residual-strong}}
5-7. {black-hole/galaxy,{neutron-star/white-dwarf}, {hadron-lepton,{neutron-proton}} }

Male/female and star-planet/moon-comet correspondence rings a mythological bell.

;;;

5-0-0. {analyze,{hear}}
6-0. {specialize,{generalize}, {left-hear,{right-hear}} }

Analyzing is dual and performed by the two halves of the brain. While one side concentrates on detail, the other side concentrates on the context. This gives a clue to how we hear as well. The {bass,{treble}} duality of music corresponds to this.

5-0-1. {imagine,{see}}
6-1. {plan,{aim}, {left-see,{right-see}} }

Imagining is also dual, but lateral to analyzing and in the forward-backward direction. The frontal cortex does the long term planning ('aim' above). This gives a clue to how we see as well.

,,,

5-1-0. {maintain,{propel}}
6-2. {sustain,{break}, {propel-forward,{propel-backward}} }

Breaking is a part of maintaining, like sustaining.

5-1-1. {navigate,{manipulate}}
6-3. {left-turn,{right-turn},{make,{unmake}}

Navigation seems to be more than just left and right turn, but in general this is the case. Cars have just a steering wheel for navigation.

Manipulation is essentially an upmarket type of navigation involving choices along the way.

,,,

5-2-0. {self-repr,{shared-repr}}
6-4. {undifferentiated,{hermaphrodite}, {host,{guest}} }

5-2-1. {female,{male}}
6-5. {feminine-female,{masculine-female}, {masculine-male,{feminine-male}} }

,,,

5-3-0. {taste,{untaste}}
6-6. {eat,{drink}, {defecate,{urinate}} }

At the 6th step, sense becomes organ related.

5-3-1. {smell,{unsmell}}
6-7. {breathe-in,{breathe-out},{impregnated,{impregnate}}

Nose and sexual organs are closely related.

---

5-4-0. {along-space,{lateral-space}}
6-8. {forward,{backward}, {left,{right}} }

Space is essentially one complex dimension. Complex numbers are closed, and they have one along and one lateral dimension; {1,i}. There is only one space dimension between two objects. The surface of the earth can be viewed as a complex plane. There seems to be 3 perfect dimensions of space, but this is never the case, since there is always gravity distortion. Space can not exist without gravity. I think the apparent threeness of space is related to it's content; matter.

5-4-1. {along-time,{lateral-time}}
6-9. {forward,{backward}, {left,{right}} }

This point is also surprising for me, like the previous one on space, although it is well known that time is complex. Time travel is predicted here.

,,,

5-5-0. {gravity,{antigravity}}
6-10. {+gravity,{-gravity}, {+antigravity,{-antigravity}} }

Gravity is a polarized field like electric field. Anti-gravity is predicted here and it maps to magnetic field below, to give a clue about it's character. It seems anti-gravity can be produced by electric currents.

5-5-1. {electric,{magnetic}}
6-11. {+electric,{-electric}, {+magnetic,{-magnetic}} }

The poles of magnetic field do not exist separately, but electric field's do.

,,,

5-6-0. {organism-cell,{dna-molecule}}
6-12. {organism,{cell}, {dna,{molecule}} }

===> There seems to be a problem here with 'neutral-weak' to life mapping. Star-weak mapping seems to be OK. Still thinking about this.

5-6-1. {star-planet,{moon-comet}}
6-13. {star,{planet}, {moon,{comet}} }

5-7-0. {hadron-lepton,{neutron-proton}}
6-14. {hadron,{lepton}, {neutron,{proton}} }

5-7-1. {black-hole/galaxy,{neutron-star/white-dwarf}}
6-15. {black-hole,{galaxy}, {neutron-star,{white-dwarf}} }

***

Senses and fields expand into two parallel binary trees complementing each other. The numbers involved correlate strongly with mythology.

(6,5,4,3,2,1,0,1,2,3,4,5,6)

They add up to 2*(1+2+3+4+5+6) = 42 (The answer maybe 42 after all!). The tree expands into 64 distinct categories at the outer edge. Reminding I-Ching and the Jewish mythology about creation. Many more interesting numbers can be extracted from the tree, depending on how it is looked at.

Complex numbers, modular group and Mobius transformation are closely related.

A link to computers is also made. Electronic computing is based on binary trees. The universe seems to be a boolean computer at the overall category calculation level.

Friday, October 05, 2007

13 senses

I have proposed that measure and balance are complementary senses mediated by their corresponding touch sense. The balance sense is out of the way and and it's two organs are hidden in the middle ear. For this reason it is usually not regarded as a sense. I have not been able to figure out the organ for the measure sense. I proposed that it is somehow related to the central clock in the brain. But what is this clock and where is it?

I concluded that the organ of the measure sense is in fact the body itself. We touch the universe with our bodies while measuring and balancing. Without measure and touch one can not balance. In fact both measure and balance senses are types of touch evolved from their root touch sense. Like {see,touch,hear} and {smell,touch,taste}. Touch is a generic sense, the scalar field of the senses.

A good connection to quantum mechanics is made as well. Quantum mechanics studies scattering of quanta. Basically it studies touch. I have already attempted a mapping of senses and organs to fields and charges. Thus this study of the senses is an attempt to figure out the universe by comparing it to life. A top-down look at or a short cut to unification. The string theory has already proposed ten dimensions, corresponding to my ten senses.

When a dynamical system goes through the process of quantization, it has to keep it's balance. An organism is made of cells and higher quanta (organs) while it balances itself. Without balance, it can not execute it's other senses and survive. Strangely enough, the balance sense couples to hearing, like space couples to gravity. I think {measure,balance} coupling corresponds to {space,time} coupling, suggesting that space and time are fields. The organs of the balance sense are three liquid filled hairy (inside) and coupled rings for each ear. Thus balance maps to space, and measure maps to time.

The heart is the organ of the measure sense, and the whole body is the organ of the mediating touch sense. It provides the essential rhythm for the brain and the body. The brain's (and the body's) clock is the heart. The definition of 'second' comes from the heart's rhythm.

Senses and organs are not stand-alone things; they interact. I find the {balance,hearing} coupling most interesting, like {space,gravity} coupling. There is a duct between the nose and the eyes, mapping to the {weak,light} coupling.

The following format exposes the importance of {measure,balance} coupling;

{measure,{see,{taste,{touch},smell},hear},balance}

They are foundation of existence, like space-time. Both are hidden. Of course the real foundation is the touch sense, like the Higgs field. Previously I proposed that {taste,smell} were the foundation. I am still somewhat undecided on this point, but I prefer the {measure,balance} coupling as the base.

Another interesting point is the {mouth,stomach,anus} coupling. I think there is connection to the black holes here. Black holes couple to space-time strongly, like {mouth,stomach,anus} making a hole right through the body. Life is essentially a filtering process from the feeding angle. Nose couples to mouth, and genitals couple to anus. There seems to be a strong link between the nose and the genitals. It seems that while the nose was differentiating from the mouth, genitals differentiated from the anus. Reproduction and feeding come from the same base. Is that why many humans (and animals!) like anal and oral sex I wonder?

Are there senses corresponding to the genitals? Which fields do they map to? Maybe there are 12 senses. What are the two complementary senses of sex? Penetrating and being penetrated? I will call them 'pen' and 'vag' for the moment. The organs are obvious; penis and vagina and their attached organs. If they are all listed together in a suitable format exposing their hierarchy;

{measure,{see,{taste,{pen,{touch},vag},smell},hear},balance}

or all 12 of them with their corresponding mediating touch senses;

{{measure,touch,balance},
{see,touch,hear},
{taste,touch,smell},
{pen,touch,vag}}

With the all inclusive nothingness {}, they are 13. That strange prime number with lots of ancient historical reference. 13 and 20 make the foundation of the Mayan calendar. I wonder where 20 comes from?

Wednesday, June 20, 2007

Senses and organs, fields and charges

The parallels between life and the universe has been suspected for a long time. After all, we are a subset of the universe and also situated in the middle of it, as also proposed by my recent 'Ten Aspects of Reality (TAR)' posting. Cliff Pickover's Reality Carnival occasionally prints the following;

'If we wish to understand the nature of reality, we have an inner hidden advantage: we are ourselves a little portion of the universe and so carry the answer within us.' - Jacques Boivin

I have come across to this concept for a while now, but not seen any explicit comparison. Since my recent TAR, I have been thinking about this a bit more. Previously I posted '7 Senses' but the fields were not right.

TAR suggests that there are ten senses;

{{measure,touch,balance},
{taste,touch,smell},
{see,touch,hear}}

Together with the all inclusive nothingness {}, they are ten. Each triplet is mediated by it's own type of touch sense. In a sense, they differentiate or evolve from this root sense. They touch each other by this sense in the brain. The three touch senses are mediated by the touch sense mediating the {taste,smell} duality. The feeding related touch sense is the origin of all senses.

There are 5 known fields;

{{strong,weak},{higgs},{light,gravity}}

Higgs is not observed yet and theorized to be a scalar field. Each field has it's own charges. Light has (+,-) charges, Gravity has mass, Strong has the color charges, and Weak has the (W+,W-) charges.

Similarly senses have their own organs. Vision has eyes, hearing has ears, taste has mouth, and smell has nose. They are all mediated by the root senses in the brain. Clearly the brain mediates all senses. I propose that there is a root sense doing all this mediation. Consider the following mapping;

{see,hear} ---> {light,gravity} ---> {star,universe}
{taste,smell} ---> {strong,weak} ---> {cell,species}
{measure,balance} ---> {?,?} ---> {time,space}

The last column is from TAR.

The first line groups {see,light,star} and {hear,gravity,universe}. The fist triplet is reasonable. In the second, {gravity,universe} correspondence is also fine since gravity is the force shaping the outer aspect of the universe. Interesting that hearing gets mapped to gravity. Gravity makes the geometry for light to operate in, and hearing sets the context for vision to operate in. Bats use the this context setting property of sound to navigate. In movies, audio sets the mood, while video coveys information.

The second line groups {taste,strong,cell} and {smell,weak,species}. {taste,strong} relationship is reasonable, since both are short range. It is interesting that {cell} falls in this triplet. It seems cell is all about taste. They have to touch each other to do things. {smell,weak} correspondence also seems reasonable. Weak has a longer range than Strong, like Smell and Taste. Why does Species fall into this triplet?

The third line groups {measure,?,time} and {balance,?,space}. {measure,time} and {balance,space} correspondences are reasonable. The organs of the balance sense are the three liquid filled hairy rings for each inner ear. What is the organ of the measure sense? It is known that the brain is run by clocks. Maybe there is a central clock. What are the fields standing for the question marks? There must be two unknown fields. Thus ATON predicts two new fields and their corresponding charges. Maybe space-time are the charges of these fields. Maybe space-time is a field of the black holes. This seems quite credible since they are the boundaries. Also rings a bell with Hawking's holographic principle.

Moreover, there must be ten fields to reflect the ten senses proposed by TAR. Higgs is like touch; it is a scalar or generic field. Maybe Higgs divides into three.

Saturday, June 02, 2007

Nucleon, brain, and black hole

This is a another look at the Ten Aspects of Reality (TAR), which are;

{{time,matter,space},
{cell,organism,species},
{star,galaxy,universe}}

With the all inclusive bracket {} nothingness, they are ten.

Recently it occurred to me that the new cosmological models predict ten dimensions. Anyway, this is not the main point here, I just wanted to mention it.

Hawking's entropy formula for a black hole is proportional to the area of the event horizon. This means that nothing gets lost in a black hole and there is a maximum entropy density, which happens to be on a surface. I suppose the area of a black hole is calculated according to the flat space-time much further away from the horizon, since space-time does not exist at the surface itself.

Encouraged by the TAR, I wanted to compare the brain to the black hole. Neurons are distributed on the surface of the brain and all the inner bits are wiring. Whatever happens in the brain, actually happens on the surface. Like a black hole. The difference is that black holes are connected to it's body from the outside, and brains from the inside. Black hole is like the brain of a galaxy. It's body consists of stars, nebula, gas, dust and other stuff. Latest research suggest that the earliest galaxies also had black holes. Brains also form very early in organisms.

Galaxies seem to form a huge collective meta brain, like humans and other organisms form a huge meta brain. Now we are building the internet to take this meta brain to a new level. I think the internet is the first step of humanity in the merging of our minds to the hardware of the universe. This has been suggested before. I think there are types of black holes, as there are types of galaxies. There are two main types; elliptical and spiral. Like organisms; male and female. Galactic society seems to be a reflection of the organic society, but maybe inside out.

Nucleons are made of 3 quarks and 3 gluons. There are two types; proton and neutron. Proton is stable by itself; neutron decays to proton, electron, and neutrino. Proton seems to have infinite life-time. Maybe it has the life-time of the universe. There are also 3 primary and 3 secondary senses of an organism; {{measure,see,taste},{balance,hear,smell}}. Touch is a generic sense and mediates all senses. All senses are types of touch. Brain is made around the senses. Proton seems to be the smallest possible black hole. Well, maybe not a black hole but something closely related. It's constituents are confined. As if it reflects the outer world; space-time. It is also connected to it's body (electrons, photons, and other stuff} from the outside.

It seems the organic brain mediates two types of 'material' brains; {nucleon,brain,black hole}. It exists by sandwiching itself between two reverse brains. And it's form obeys the quantity triplet; {0,1,infinity}. The question is; what is the nothingness that includes the lot?

The following Escher work (from http://www.mcescher.com/) reflects the symmetry of the brain triplet quite well I thought. There are two boundaries, inner and outer, and everything happens in between;

Tuesday, May 29, 2007

Ten aspects of reality

The seven senses are;

{measure,{see,{taste,{touch},smell},hear},balance}

Measure and balance are not normally regarded in the senses. Balance is achieved in the inner ear's hardware in the form of three liquid filled hairy rings for each ear. Balance seems to qualify to be a sense. Measure is more difficult to judge as a sense. If sciences are also listed in the same manner, measure becomes clearer when it is mapped to mathematics;

{mathematics,{physics,{chemistry,{biology},psychology},intelligence},aesthetics}

Psychology is usually regarded to be a pseudo science. Intelligence is gaining more acceptance amongst cognitive sciences as computing advances. I think psychology will also acquire a respectable place amongst cognitive sciences in due time. Aesthetics includes things like philosophy, art, music, poetry, and not regarded as science. It studies beauty and sometimes uses mathematics as a tool.

This particular ordering of sciences has two aspects that relates to senses. All sciences are based on mathematics and they form a complexity ladder. Biology seems to mediate all sciences in dualities. Psychology couples to -or based on- chemistry, in that it operates in a field of chemicals like hormones. Intelligence couples to physics, in that it uses electricity -or light- in the neuronal circuitry provided by brain. As suggested before, aesthetics somewhat couples to mathematics.

Aesthetics is used by most animals, if not by all animals and maybe all life. Aren't the flowers' smell and looks selected by insects? Similarly most plants are selected and shaped by animals. Animals also select and shape themselves. Isn't the sexual selection largely responsible for humanity's success? I think the universe shapes itself through a common sense of aesthetics. Don't many animals have a similar sense of music? My cat likes Bach. I was amazed with a camel's love of music when I saw the film Weeping Camel.

Similarly touch mediates all senses in three mediated dualities, as it is essential for sensing;

{{measure,touch,balance},
{taste,touch,smell},
{see,touch,hear}}

Smell evolves (or diverges) from taste as breathing separates from eating. {see,hear} coupling is not that obvious, but the symmetry involved is the same. It is like the {audio,video} duality in signal processing. The mathematics involved in video is a more complex version of audio. In both cases, dual sensing gives depth of field. {measure,balance} coupling is the hairiest. I think the core of a brain evolves around these two and their mediating touch sense. Measure is the root of all evolution. In quantum mechanics it corresponds to quantization of a field.

It seems the touch sense involved in each case is different, as there are many different types of touch. Touch is a generic sense. It senses temperature, pressure, hardness and so on. Thus we end up with nine senses, to match the nine aspects of reality;

{{time,matter,space},
{cell,organism,species},
{star,galaxy,universe}}

As life {cell,organism,species} mediates the universe, eating {taste,touch,smell} mediates life. We also get a clue to the nature of the three kinds of touches mediating senses. Consuming or fusing kind of touch mediates the other two; one soft, the other hard. The quantity triplet {0,1,infinity} determines all four mediated dualities. Three dualities themselves form a mediated duality through their mediators.

With the predicted 'zero' to include the lot, we have the ten aspects of reality. The tenth aspect is the aspectlessness, or rather nothingness. If the Higgs field corresponds to 'zero', what is the corresponding sense?

Friday, April 27, 2007

Quantity Triplet and Stern-Brocot Tree

How far can the correspondence between numbers and fundamental categories be pushed? The quantity triplet {0,1,infinity} seems to map to the triplets,

{{time,matter,space},
{cell,organism,species},
{star,galaxy,universe}}

as proposed recently in the Nine Aspects of Reality blog.

{time,matter,space} mapping is not that obvious. Locality of time, as established by the relativity theory, points to separateness of it. Quantum gravity theory proposes quantum space-time and thus also points to the locality of time. Space seems to be made of time quanta.

{cell,organism,species} triplet can be used to get some clues about the nature of {time,matter,space}. Cell is the object that determines organism's life-time. Species is the space in which the genetic information move from node to node. Each node is an organism. For sexual reproduction, two nodes get together to spawn another, thus enlarging the gene space. Hermaphrodite nodes spawn two nodes by themselves. Maybe time is more like hermaphrodites, since it is fundamental. The topology of the genetic space-time of a species must reflect that of space-time.

The life triplet also points to other invisible universes, since there are many species of life.

Stern-Brocot Tree is based on {0,1,infinity};












(From http://www.cut-the-knot.org/blue/Stern.shtml)

Cut-the-knot says 'A remarkable thing about Stern-Brocot tree is that it contains all possible non-negative fractions expressed in lowest terms and each exactly once.' The space between {0,1,infinity} is filled by a simple method of mediants.

Can SBT be mapped to fundamental categories?

0. {0/1,1/0} ... Higgs (U(0)?)
1. {1/1} ... Light (U(1))
2. {1/2,2/1} ... Weak (SU(2))
3. {1/3,2/3,3/2,3/1} ... Strong (SU(3))
4. {1/4,2/5,3/5,3/4...} ... Gravity (SU(4)?)

0. Higgs seems to have locality and universality combined. It seems when you reach the zero, you also reach the infinite.

1. 1/1 ... electric / magnetic. For life, this may be the stem cell.

2. 1/2 ... Z0 / {W+,W-}. For life, blood/{muscle,nerve}.

3. 1/3 and 2/3 make sense since they are used in the make-up of nucleons by quarks, and there are 3 color charges.

4. Gravity comes out of a 3+1 dimensional space-time and mass. The 5th item must refer to 'mass'. 1/4 seems to map to mass/space-time. 3/4 seems to map to space/space-time. I don't know much gravity so I can not interpret the rationals 2/5,3/5.

Note the 5ness of the classification list, {0,1,2,3,4}. 5 is related to 9 in a funny way that relates to the 3 triplets;

1+2+3+4+5+6+7+8+9 = 45
45/9=5

If the numbers are grouped into 3 triplets;

{{1,2,3},{4,5,6},{7,8,9}}
{{time,matter,space},{cell,organism,species},{star,galaxy,universe}}

Giving 5 at the position of 'organism', which has 5 senses. Also time gets 1, and space gets 3. Star gets 7; 7 layers of the periodic table? Matter gets 2; electric/magnetic?

Tuesday, March 27, 2007

Time and pressure

Time displays thermodynamic aspects. Consider the triplets;

{Time, Matter, Space}
{Pressure, Temperature, Volume}

The P-T-V triplet are related to each other by the famous equation of ideal gas; PV = NkT, where N is the number of particles, k is the Boltzmann constant.

Time stops at the event horizon of a black hole. The entropy of a black hole is proportional to it's area; S = k(c^3)A / 4G(hb), where c is speed of light, hb is Planck's constant. This equation contains all the goodies. Black holes are the boundaries of space-matter-time, so they must contain it. It also includes the Boltzmann's constant k, and makes the link to thermodynamics pretty explicit. The great surprise of this equation was that the entropy is proportional to the area A. Time slows down in gravity, and eventually stops at the most intense gravity gradient; the even horizon of a black hole.

Gravity works as if space-time is squishing out it's contents towards less pressure, since space-time dilate in gravity. A gravity field is like a 3D hill's surface of a 4D volume (a normal hill's surface is 2D). We feel the squeeze down of gravity by the counter pressure of the earth. Thus space-time is has strong thermodynamic aspects. {Matter, Temperature} correspondence makes sense since matter is equivalent to energy. {Space, Volume} correspondence is obvious. Thus we get {Time, Pressure} correspondence implied. As we well know, pressure cookers shorten the time of cooking. Sounds funny I know, but I think this fact reflects the correspondence quite well, since pressure increases the event density in time.

Friday, March 09, 2007

What exactly is nothingness?

When I started this blog on nothingness (Nn), I had a vague idea of what Nn is, and I still am not totally clear on it, although clearer. I have come to believe that it is a trancendental and relative concept.

I have already given few examples of what it might be; water for taste, air for smell, space-time for matter and so on. I still think these examples are pretty close, but there is still a problem. Water by itself is not taste, although taste evolves out of water. The smallest amount of taste, as compared to water, corresponds to Nn. Therefore Nn is a relative concept like probability;

Nn0 = ,/,

At the limiting case Nn0, both numerator and denominator are equal in quantity. I use numerical concepts since ATON aspires to be based on numbers. It also relates to the word nothingness since it compares almost nothing to almost nothing. Through comparision to itself, "nothing" (N) gets lifted and becomes "nothingness" (Nn). Thus we seem to get a connection to the concept of equivalence class as well. I like to iterate on this later.

A connection to my Mirror Set is also made;

M(m,n) = m!n / n^m

Where m!n is the multifactorial of m to depth n. M(0,0) is undefined, or fuzzy and multivalued, as I imagined Nn to be.

Let me try another example from my cat Rupty. I adopted her when she was very little, maybe a week or two old. After I brought her to my place, the first thing she did was to inspect the room, starting from a wander around the outer perimeter of the room. She did not get out of the room until she was sure where she was, I gathered. After many hours, she started little trips out of the room to inspect the corridor. Every time she would come back running and excited. In this fashion she finished inspecting the house in a day or two. Then she did the backyard, the frontyard and the street in many days to come.

The way she was doing these inspections was seemingly random. She would pick a direction and time out of the blue and inspect it many times until she was confident. The randomness is also displayed in her switching of the sleeping place. One day, out of the blue, she would swithch the place and start sleeping somewhere else she inspected before. This also applied to her other favorite places where she did one of her numbers like having a nap or sitting and watching.

I concluded that her behavior pattern is a fuzzy and random ball, like nothingness. It changed and took shape over time, but the essential fuzziness remained. We humans are also like cats when we are not regulated too much. We like to slumber along in a fuzzy pattern.

Wednesday, February 28, 2007

Nature abhors gradients?

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 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...

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?

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.

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.

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.

Capturability of the mainstream

Why is it that the human mainstream is so easy to capture?

In Cronulla race riots in Australia recently, a large number of youth were captured by a few well organised extreme racists. Since the Iraq invasion and the subsequent bombing in Bali, racial harmony suffered greatly. Racist Anglos were ready to be captured it seemed (most Anglos are decent good people I must add). Many of them were drunken and wrapped in Australian flags. They displayed a disgraceful scene, chasing and beating any dark skinned person who happened to be there, including women. The police chief later explained it as crowds being "captured". The oragnisers of the event would have been happy with the results, but I am sure they were not too happy with being seen as a mob of drunken losers.

Didn't Hitler capture an entire nation? He took so many of them to the grave. It seemed capturing humans was as easy as capturing sheep, maybe easier. Hitler was not alone of course. The Europian aristoctarcy and corporations were desperate to counter the Soviet revolution. They supported despots all over Europe to suppress local revolutions. Franco did not reach the efficiency of Hitler, but he also killed a lot of people. Mussolini was of the same kind. They keep showing docos on how bad were the dictators, but they never mention the fact that they were the ones behind the curtain. Later Hitler went rogue, as they do, and became an embarrasment. But Franco stayed a darling until the end.

Neo-cons also tried to capture the American mainstream and succeeded to a great degree. If they were successful in the invasion and holding of Iraq, we would have quite a different world order now. It was amazing to watch how easily they did it to the Americans. Few low life religious preachers were enough to mesmerise a large section of the society. As happened before in Europe, we all know who was behind the curtain. Greedy and ignorant corporate bully. The story of US is still unfolding. Democrats are putting a show but not too effective. Most democrats are also sponsored puppets.

Humans are easy to capture in all scales, from one person to large crowds. You just use slightly different methods. Controlling the media helps greatly. Internet must be quite a nuisance to these bastards. Falling in love is a consensual capture, supported by chemistry. Finding friends also falls into capturing. In the end it comes to reprogrammability. The mainstream provides a programmable power base for the marginal elements. It is a good representation of the concept of nothingness. It slumbers in the center to provide stability with it's size and power. We should study and understand this fact about ourselves and bring it to attention, if we want a peaceful future.

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%.

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