String Theory Displays Golden Ratio Tendency?

Srinivas Ramanujan (1887-1920):

Ramanujan was a mathematician so great his name transcends jealousies, the one superlatively great mathematician whom India has produced in the last hundred years. "His leaps of intuition confound mathematicians even today, seven decades after his death. ..the brilliant, self-taught Indian mathematician whose work contains some of the most beautiful ideas in the history of science. His legacy has endured. His twenty-one major mathematical papers are still being plumbed for their secrets, and many of his ideas are used today in cosmology and computer science. His theorems are being applied in areas - polymer chemistry, computers, cancer research - scarcely imaginable during his lifetime. His mathematical insights yet leave mathematicians baffled that anyone could divine them in the first place.'

Namagiri, the consort of the lion god Narasimha. Ramanujan believed that he existed to serve as Namagiri´s champion - Hindu Goddess of creativity. In real life Ramanujan told people that Namagiri visited him in his dreams and wrote equations on his tongue.

Artist's impression of the setup.

The disks represent the bosonic condensate density and the blue balls in the vortex core represent the fermionic density. The black line is a guide to the eye to see the wiggling of the vortex line that corresponds to a so-called Kelvin mode, which provides the bosonic part of the superstring (image and text:

http://arxiv.org/abs/cond-mat/0505055

Plato:

When I was a kid, I liked to take buttons and place a thread through them. Watching Mom, while I prep the button, she got ready to sew. I would take both ends of the thread and pull it tightly. I liked the way the button could spin/thread depending on how hard I pull the thread

I was thinking about this toy model developed for strng theory comprehension and all of a sudden the attempts by Lubos of Solving the Riemann Hypothesis came into view?

Now some of you know that such consistancies built up from the very idea of "Liminocentric structures" are always pleasing to me. Because of the energy valuations I might have associated to the "circles within circles" as ideas manifest( their degrees of manifest).



A KK tower about 1r radius valuation seen in the varing shapes of tubes? At what stage were these and what could I tell about the idea as it merged from that deep source and probabilstic value of where we all draw from.




That soothing watery world( our dream world ) of ideas that could manifest for us into nature, taken as an consequence relayed, from the continued circles of action? We are better predictors then we think? We did not know where this idea could manifest from, and what energy relations could have given such suttle thoughts repercussions in the very world they could have manifested into?

The relation and perplexing problem I had with identify how such a structure intrigued by Sklar would make it difficult to identify which circle is describing which stage of whee we are at with the innner/outer, was raised when it came to the developing the understanding and differences on how rubber bands placed over a apple, might have a different connotation, when moved over a donut?

Continuity of this action as a color vaiation would have made me then think of Mendeleev in his table of constituents, as I looked at the relation in the world of such discrete things.



Imagine the complexity of music that could be most pleasing, could also be very destructive in the "fields of thought"? I had espoused this in Plato's academy? All of this contained in the light sensation in a little music disc?

What stories indeed have we converted to light, in our apprehensions? Philosophically, I could be committed for my heresy, for all the things I might have assigned to "Heavens ephemeral qualities." Verging on the crackpotism, I know.:)

See:

Fool's Gold

Big Horn Medicne Wheel

Parallel lines to spherical and hyperbolic functions

Like different musical instruments, different types of stars produce different types of sound waves. Small stars produce a sound with a higher pitch than bigger stars, just like the 'piccolo' produces a higher sound than the cello

Did one ever figure out the value of the pitch? So you see, the universe is a concert as well:) You remember Pascal's triangle? The probabilistic valuation asined to the marble drop? Well I created another triangle, but it is a little different model, and does not use numbers for mathematic discretion as a emergent property of first principal. Although mine is distinctive of these characteristics the universe is being applied in sound relation.

An equation means nothing to me unless it expresses a thought of God.

Srinivasa Ramanujan

The most rarified of the matter is a "energy relation in sound", while at the base of this pyramid, all the myriad forms of matter in expression.

Artists such as M. C. Escher have become fascinated with the Poincaré model of hyperbolic geometry and he composed a series of "Circle Limit" illustrations of a hyperbolic universe. In Figure 17.a he uses the backbones of the flying fish as "straight lines", being segments of circles orthogonal to his fundamental circle. In Figure 17.b he does the same with angels and devils. Besides artists and astronomers, many scholars have been shaken by non-Euclidean geometry. Euclidean geometry had been so universally accepted as an eternal and absolute truth that scholars believed they could also find absolute standards in human behavior, in law, ethics, government and economics. The discovery of non-Euclidean geometry shocked them into understanding their error in expecting to determine the "perfect state" by reasoning alone.

Sometimes it is good take this idea of sound as a analogy like fluid dynamics so that you can see how far one can be lead to non-eucildean views, and ideas of resonant points that are localized, yet, recognizing the quantum view here, would be a dynamcial one and as fluid? Putting reverberations aside, and discrete measures, think how such blurring could take on new meaning here in uncertainty?



By studing the early inclinations of people who have this affinity to "sound" how can one not be intrigued by what is to follow after, in the generalizations of mathematcial minds and physicists who are struggling to measure those same gravity waves?

In the late 1950s, Weber became intrigued by the relationship between gravitational theory and laboratory experiments. His book, General Relativity and Gravitational Radiation, was published in 1961, and his paper describing how to build a gravitational wave detector first appeared in 1969. Weber's first detector consisted of a freely suspended aluminium cylinder weighing a few tonnes. In the late 1960s and early 1970s, Weber announced that he had recorded simultaneous oscillations in detectors 1000 km apart, waves he believed originated from an astrophysical event. Many physicists were sceptical about the results, but these early experiments initiated research into gravitational waves that is still ongoing. Current gravitational wave experiments, such as the Laser Interferometer Gravitational Wave Observatory (LIGO) and Laser Interferometer Space Antenna (LISA), are descendants of Weber's original work.

Athena:

The angle of the strikes in relation to the sides of the triangle would be the same as well, delivering similar tones. With other triangle types, depending on the lengths of the sides and the angles, you may have to adjust for the differences while you were playing if you didn’t want those effects.

While one might think of the triangle of consideration, it would not be to hard to figure that architectural features would have also harnessed? Similar respective examples of solutions from angled to parallel lines, leads to hyperspherical "inner" solutions of the dome, as a consequence of dimensional shape exploitation?:)


Bernhard Riemann once claimed:

"The value of non-Euclidean geometry lies in its ability to liberate us from preconceived ideas in preparation for the time when exploration of physical laws might demand some geometry other than the Euclidean."

So how would they overcome this commanding voice and spread out what is focused? A saucer?

An Acoustical Nightmare

"According to one parishioner, the echoes were so bad under the egg-shaped done of Oklahoma City's First Christian Church of Tomorrow that when the minister spoke it sounded 'as though God were repeating every word he said, only much louder." In the hope of deflecting the echoes, a 20-ft saucer was hung from the apex, but it had no effect. An acoustician finally solved the ploblem by overpowering the echoes with an amplifying system. Carefully filtered sound now come from the round speakers on the walls and spreads evenly-and without echoes-over the congregation." Time-Life, Sound and Hearing, p189.

While seeking to provide good journalism and link to hyperphysics I wanted to extend this to a image. It is unfortunate this could not be done. So, you are left with the source for consideration and perspective. I thought it fitting to the struggles of "sound production" and your "tone variation" on the triangle's length and angle being hit.



So let's say Michelango sought to send God's "word" to some mortal human like Adam for consideration in the garden? Would he have done it in the way a artist might see such features of sounds reduced to the "chorus of shape" foculizing this power in mortal man? It had to be a thunderous approach? NOn! Oui

Michelangelo's Creation of Adam in the Sistine Chapel in Rome

Make sure you hit "next" three times

Strings: The First Three Seconds

I didn't want to invoke God here, but in any "flash" is there not some pattern that mathematically needed to describe the way everything began? A word, or sound?

An equation means nothing to me unless it expresses a thought of God.Srinivasa Ramanujan

Before the Beginning
Interview with Sir Martin Rees, Part 2

Helen Matsos (HM):

Last year the big "science event" was measuring the cosmic microwave background and dating the big bang to 13.8 billion years ago, within an 8 to 10 percent margin of error. Can you give us some idea of the boundaries of the big bang -- what was it like in the first seconds, and how far will the universe expand in the future?

So indeed the universe become entrophically considered, as the evidence starts to make itself known in all it's forms, yet there is a space. Now by itself, such expression of the universe would have one event, but imagine down on earth our moments, can cause such repercussions ahead in time?

AM:

You played yourself--twice--in the movie, "Frequency". The movie is about a father communicating from 1969 with his son in the present on a ham radio, due to an unusual atmospheric aurora that bounces radio signals across time, not just space. You played Brian Greene being interviewed by Dick Cavett as both a younger and older man. Any reflections on either the interesting premise of the movie, or the adventures of being on the big screen?

So how we categorize such encounters with the child in our hopes of encouraging it's future, or our very presence and example lead. As a sign post, of what any society could become in the eye of good moral men and women? So one can move quietly no doubt and remain unseen, while the work can be a gentle reminder, of how we can affect "each" in time. Words like "etc" that could take on greater meaning, to have the hand slight a deletion. Remember how sensitive we can be to music? In Plato's academy I had made this point clear. I make clear what dissonance can do:)It can definitiely ruffle the field. Straight up and straight forward, a comment should do for those that would like to learn.

Brian Greene

Time is far more subtle than our everyday experience would lead us to believe. In many ways, time may simply be a psychological construct for organizing the world. It is a device we scientists have found useful, but it may in fact be a dim approximation of something far more complex."

WEll here is a better view on the relation to the The Powers of Ten

I talked briefly on the "chance encounter" of a child with a scientist, and the alluring role of powers of ten takes on. As if, it can "reverberate" in the probabilities of a future time.

Who is responsible for this creative surge?:)Creative endeavors, are always fueled by another?

IN such a cultural context, how is it that we could not see underlying reality is a musical inclination taken form in what any future could become. So, by the very value of the resonance contained, a feature of any moment?

What Pattern Emerges?

Problem solvers have a way of getting to the heart of the issues, and unfortunately when ones engages competent minds like Peter Woit in the world? Whose sign post is,"anti-string with no explanation"? This is simple in the minds of the general public? It then becomes a rant, without a substantial basis? Why? Because he had no platform with which to refute?

So this attempt was fruitless, in wondering why strings should not be.

What I did find viable in looking for myself, is finding out where strings applicable features pervaded and what they were describing. Both bottum up and top down have to find approaches that emerge from a place that asks us to map this progress, and there is only one place that allows me to understand this operation.

The spectrum.

When you look at Glast operations this idealization of using the spectrum in cosmological discernation, helped to clarify why the move of strings to a cosmological operation platform was necessary from a experimental and scientific undertanding. Why was this move important?

It had to do with the amounts of energy needed to explore the principles of reductionism? How could we extend reductionism to a cosmological question about the origins of our beginning? There were no limitations as to the question of the energy that could be displayed for us all to wonder on that cosmological pallete, and here Relativity Ruled.

While complexity, asks us about the means of what is established in the forms, stands for us in our observations, as existing? Many people feel safe in what they can see?

I looked for comparative features. Like how ideas could emerge and as a good example of what math could issue from the minds of those whose good observation could speak about natures manfestations.

How good are the observatory minds of mathematicians? That would systematically describe for us this idealization of quantum reality and Relativity to join in a way that makes sense?

Macroscopic and microcosmo perceptions joined?

You say Time? Julian Barbour wants to do away with Time? Yet his goal is the same? He calls Time a human construct? What isn'taside from everythng else that we don't see? Science reveals a deeper truth?

Killing Time

Barbour posits that time is, in fact, an illusion - a measure imposed on the world by humanity. He explains this with the concept of a 'now', which he describes as a snapshot in time - a completely frozen, self-contained instant (much like a Polaroid photograph). Time is simply the measure of the space between two separate and unrelated 'nows.'

BarryTo offer that I am an engineer and a sculpture with a carear of problem solving. To offer that making me understand the final solution is to achieve making it clear to anyone.

I am somewhat like a philosopsher as you are, minus, the engineering, yet I am quite capable of peering past the veil that good minds construct.

In the end, what is taken with you might be the realization that of all the thought forms we have estanblished and created. The illusion that we move through, hides a deeper truth, and we were emersed within it the whole time. Science, verified the anomalies that we saw?

How much power then could we grant the mind who escapes this realization, to find that all the thoughts that have ever existed, were weighted with the gravity that held us to earth? That the forms, revealled a deeper realization of their beginnings?

As the temperature cooled, the solification was final and so was the idealization that manifested from the idea.

When is a pipe a pipe? Is a question about what supergravity reveals in the forms manifestation. Crystalization. What pattern emerges?


Betrayal of Images" by Rene Magritte. 1929 painting on which is written "This is not a Pipe"

Yet probablistic in nature, how could such things arrange themselves as they have?

There is a deeper question here about the reality. If the idea is born in mind how would it not burn up, comparative to the beginning of our universe? Yet nature has supplied a good analogy of bubbles that form, rise to the surface, and this could have been information that arose from the fifth dimension? It all arose form the mind of the subconsious? It was always closer to the source. Why Ramanujan and Einsteins note taking in the subtle realms help to spur the incubation of reality to a deepr level of questions.

People might say indeed, that this departure point from the sane world of forms, is the moving further into the illusions? But if we cannot find a way to free ourselves, then surely, one will accept the consequences of there reality, as they take it with them?:)

Left or Right Brain Doesn't Matter, When your In The Dimenisons?

Einstein in response tyo Minkowski's Space World: Since there exist in this four dimensional structure [space-time] no longer any sections which represent "now" objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four dimensional existence, instead of, as hitherto, the evolution of a three dimensional existence

If we recognize the valuation of what exists regardless of the things that would hold the photon for consideration, the realization is, that the inetrplay would have revealled the Halo in definition of that gravitational radiation?

THE NOTION OF DIMENSION IN GEOMETRY AND ALGEBRAYuri I. Manin

“A natural or acquired predilection towards geometric or algebraic thinking and respective mental objects is often expressed in strong pronouncements, like Hermann Weyl’s exorcising “the devil of abstract algebra” who allegedly struggles with “the angel of geometry” for the soul of each mathematical theory. (One is reminded of an even more sweeping truth:

This goes back to the origins of the math, as to whether it is manufactured or is natural? Some of these distinctions are self evident as we look at Pascal's triangle for a selection of what may arize out of what might be called quantum geometry. We had to understand it's origins and the distant functions that would have been revealled? We also understood where such a view would have become realizaed in the detrminations of the nergy that was produced and the curvatures that would be inherent in this scalable feature relegated to dimension.



If the brain resonates, then it may become aware of the undercurrents that would subjectively be realized in the subconscious, to have understood that it too was capable of determining the outcome to a pressupposed course of action taken in life? Chaldni plates, but much subtler in the brain's organization?

The subconcious was able to predict the outcome of the actions that have been set, by the actualization of consensus. Ramanujan moduli forms may have, from what I understood found such expressions and spoken to the predictabiltiy of outcome, in relations to what I have just said above.

Einstein's usage:
We can distinguish various kinds of theories
in physics. Most of them are constructive.
They attempt to build up a picture of the more
complex phenomena out of the materials of a
relatively simple formal scheme from which
they start out. Thus the kinetic theory of gases
seeks to reduce mechanical, thermal, and
diffusional processes to movements of molecules
-- i.e., to build them up out of the hypothesis of
molecular motion. When we say that we have
succeeded in understanding a group of natural
processes we invariably mean that a constructive
theory has been found which covers the
processes in question.
Along with this most important class of
theories there exists a second, which I will
call 'principle-theories'; These employ the
analytic, not the synthetic, method. The elements
which form their bases and starting-point are not
hypothetically constructed but empirically
discovered ones, general characteristics of
natural processes, principles that give rise to
mathematically formulated criteria which these
separate processes or the theoretical
representations of them have to satisfy. Thus
the science of thermodynamics seeks by
analytical means to deduce necessary conditions,
which separate events have to satisfy, from the
universally experienced fact that perpetual
motion is impossible.
The advantages of the constructive theory
are completeness, adaptability, and clearness,
those of the principle theory are logical
perfection and security of the foundations.
The theory of relativity belongs to the latter
class. In order to grasp its nature, one needs
first of all to become acquainted with the
principles on which it is based. Before I go
into these, however, I must observe that the
theory of relativity resembles a building
consisting of two separate stories, the special
theory and the general theory. The special
theory, on which the general theory rests,
applies to all physical phenomena with the
exception of gravitation; the general theory
provides the law of gravitation and its relations
to the other forces of nature.
Found in: "What is the Theory of Relativity?",
Einstein, Ideas and Opinions, Three Rivers
Press, p. 228-9.

Part of the difficulty in understanding the analogies to scientific pursuite is the relationship what might be drawn to the "idea"? Like sound, consolidation in nodal points lines of the Chaldni plate. Such predictive features of the marble drop of course ask us to question what outcome waould be a viable model to what might be demonstrated in the Bell curve?

Quantum gravity models in the membranes show nodal point flips as in the monte carlo model for comprehesnion. Demonstrates the triangular function of this energy, and becomes quite pronouced, the greater the energy?


We do not know for sure how particles get their mass. The current best idea is that they acquire it by interacting with a field (like a gravitational field), known as the Higgs field. The more strongly a particle interacts with this field, the greater its
mass. The field is expected to produce a new particle called the Higgs particle.

INherent in the quest for the appropriate visaulization of course depends greatly on where these abstractions exist? Without this ocean in which we are immersed, it would make no sense to speak about maths which do not arise into fractorialized states of existance. Not arisng from states of nothinness, but from states of possibile outcomes?

The Man Who Knew Infinity:

A Life of the Genius Ramanujan
by Robert Kanigel



Srinivas Ramanujan (1887-1920)In the past few decades, we have witnessed how Ramanujan's contributions have made such a profound impact on various branches of mathematics. The book, "The man who knew infinity", by Robert Kanigel reached out to the general public the world over by describing the fascinating life story of Ramanujan. And now, in the form of a play, the public is made aware, once again, of this wonderful story. This is a very impressive play and I had the pleasure of seeing it with Prof. George Andrews, the world's greatest authority on Ramanujan's work and on partitions.


The more I read about Ramanujan I was attracted to the idea of him being able to predict outcomes devised in some general mathematical way that seemed easy to him, but in the case of the Taxi Cab and Hardy's question, what was the nature of the taxi cab's number?

When looking through this infomration I come across interesting perspectives about such a man whose culture was far away from the society of currents math and physics. Who developed logically, through his own study. This is a intersting case to me of what could be brought to a world steep in mathematical structures. CRanks or not, whohave found joy in peering into a world that few would cosider in their day to day lives.

No account of Ramanujan is complete without the Taxi Cab episode. There is a charming scene of Hardy meeting Ramanujan in a hospital, and when Hardy mentions that he arrived by the taxi numbered 1729, Ramanujan immediately points out that 1729=10^3+9^3=12^3+1^3, the smallest positive integer that can be expressed as a sum of two cubes in two different ways. Of course, the Ramanujan taxicab equation x^3+y^3=z^3+w^3 yields Fermat's equation for cubes by setting w=0, but it is to be noted that the taxicab equation has positive integer solutions, whereas Fermat's does not.

There is something deeper here that has caught my attention. The Harmonical nature permeates my thoughts, about the extra dimensions and how we could look at the bulk?

If such thinking went beyond the two points and our focus was drawn to the space in between, what would such a nature exemplified by such harmonical attributes? Would it not have made one wonder how the world would seem in ways that our current perceptions are not accustomed too? How would Ramanujan fit here, as a emergent property of strings?

When strings vibrate in space-time, they are described by a mathematical function called the Ramanujan modular function.26 This term appears in the equation:27

[1-(D - 2)/24]
where D is the dimensionality of the space in which the strings vibrate. In order to obey special relativity and manifest co-variance), this term must equal 0, which forces D to be 26. This is the origin of the 26 dimensions in the original string theory.

In the more general Ramanujan modular function, which is used in current superstring theories, the twenty-four is replaced by the number eight, making D equal to 10.28

In other words, the mathematics require space-time to have 10 dimensions in order for the string theory to be self-consistent, but physicists still don’t know why these particular numbers have been selected.

I was interested in how this man came to think and I place this here for consideration from another poster.

Dick Well, in Ramanujans case we have some clues.

He spent his teenage years studying and mastering one book, on analytical function theory and analytical number theory (which are joined at birth). The format of the book was step by step: it started with (x-y)(x+y)=x2 - y2. You proved that and then came a slightly harder theorem of the same kind, in which the proof uses the first theorem, and so on one result building on another up to the state of the art as it was when the book was published (1880s). The book was intended to prepare or "cram" Cambridge students for the math exam known as the Tripos.

Ramanujan became not just familiar with the math in this book, it became his environment.

A recent author has suggested that math ability derives from the brain abilities used in social understanding. Think of living in a tribe or small town where "everybody knows everybody". By growing up in such an environment you know not only everyone else's name, but their preferences and personal characteristics. You are freely able to think what so-and-so and such-and-such would talk about if they had a conversation. And it is proposed that mathematicians have this same ability, only with the abstract things they think about and discuss, rather than people.

And so Ramanujan's "town" was the complex number system and the various peculiar things that could happen there. This was the focus of his imagination throughout his growing up and it is scarcely surprising that he was able to see relationships that more lazily prepared mathematicians (including great ones like Hardy) could not.

You don't have to postulate extra dimension, the depth of the human capabilities is sufficient.

As you can see Dick rejected the idea that such information could have settle in any mind, from a fifth dimensional consideration, and the extra dimensions, as he has stated. It just made sense to me, that solid things, had other information that it concealed. The harmonical nature was not only limited to the numbers and oscillations?

The Planck Epoch to now, contained interesting information. Should we find some structure to contain it all, and yet, find that this structured world is not limited to such structures alone? It was just a pattern, and one of many?