Showing posts with label Ramanujan. Show all posts
Showing posts with label Ramanujan. Show all posts

Wednesday, October 27, 2010

Ducks Know Game Theory


A Beautiful Math: John Nash, Game Theory, and the Modern Quest for a Code of Nature (2006)

The ducks, naturally, were delighted with this experiment, so they all rapidly paddled into position. But then Harper’s helpers began tossing the bread onto two separated patches of the pond. At one spot, the bread tosser dispensed one piece of bread every five seconds. The second was slower, tossing out the bread balls just once every 10 seconds.

Now, the burning scientific question was, if you’re a duck, what do you do? Do you swim to the spot in front of the fast tosser or the slow tosser? It’s not an easy question. When I ask people what they would do, I inevitably get a mix of answers (and some keep changing their mind as they think about it longer).
Perhaps (if you were a duck) your first thought would be to go for the guy throwing the bread the fastest. But all the other ducks might have the same idea. You’d get more bread for yourself if you switched to the other guy, right? But you’re probably not the only duck who would realize that. So the choice of the optimum strategy isn’t immediately obvious, even for people. To get the answer you have to calculate a Nash equilibrium.

After all, foraging for food is a lot like a game. In this case, the chunks of bread are the payoff. You want to get as much as you can. So do all the other ducks. As these were university ducks, they were no doubt aware that there is a Nash equilibrium point, an arrangement that gets every duck the most food possible when all the other ducks are also pursuing a maximum food-getting strategy.

Knowing (or observing) the rate of tosses, you can calculate the equilibrium point using Nash’s math. In this case the calculation is pretty simple: The ducks all get their best possible deal if one-third of them stand in front of the slow tosser and the other two-thirds stand in front of the fast tosser.

And guess what? It took the ducks about a minute to figure that out. They split into two groups almost precisely the size that game theory predicted. Ducks know how to play game theory!

Saturday, August 09, 2008

First Principals of Quantum Mechanics

Of course the discussions are leading me to gather my thoughts on things, as they are being spoken too, by Bloggingheads.

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.

I am some what disappointed that Sean Carroll deleted my response to Lawrence Crowell and Rebel dreams.

Lawrence referenced GH Hardy, and I expanded on this in relation to Ramanujan. The point is in regards too pure mathematics. Some might have become offended by my saying "one's God" too imply, that one can idolize and put into stone, graven images of God, yet, this is so far from the truth of my statement that I hope the post I wrote was kept and seen in this light that I am to explain.

Some would never recognize the developmental aspect of a "higher self" and what images that we unconsciously induce to allow this communication within to take place.

It is not the forgetfulness with which one would like to make those graven images and form, "but the realization" that what ever we attach to something being meaningful, becomes meaningful, and pray too, can come through with an extraordinary amount of wisdom.

IN this context I would not judge another human being on the position they hold too in life, as this sets the stage for what is to come. In Ramanujan's case, the information of his mathematics came through in such a form.

My point is that while we build the inductive/deductive application to our "principals of infinite regress" that ultimately such an exercise is reduce too, yes, the mathematical framework that lies very close to that light.

While in relation to creation stories, such responsibility is on the adherence that we adopt to scientific endeavour, with which we place observation and experimentation to understanding what reality is about. I do not advocate irresponsibleness in this regard, but push to rigour that science requires.

The Craftsman

BEHOLDING beauty with the eye of the mind, he will be enabled to bring forth, not images of beauty, but realities, for he has hold not of an image but of a reality, and bringing forth and nourishing true virtue to become the friend of God and be immortal, if mortal man may. Would that be an ignoble life? PLATO


Genesis Timaeus 27c-34a

First then, in my judgment, we must make a distinction and ask, What is that which always is and has no becoming; and what is that which is always becoming and never is? That which is apprehended by intelligence and reason is always in the same state; but that which is conceived by opinion with the help of sensation and without reason, is always in a process of becoming and perishing and never really is. Now everything that becomes or is created must of necessity be created by some cause, for without a cause nothing can be created.
See Timaeus:Laying the Ground rules on Genesis

The Demiurge (Creator)

Literally, “craftsman.” The creator of Plato’s physical world is not a divine intelligence or a personal ruler, but (as it were) a manual laborer. Cf. Vlastos, Plato’s Universe (pp. 26-27):

That the supreme god of Plato’s cosmos should wear the mask of a manual worker is a triumph of the philosophical imagination over ingrained social prejudice. ... But this divine mechanic is not a drudge. He is an artist or, more precisely, what an artist would have to be in Plato’s conception of art: not the inventor of new form, but the imposer of pre-existing form on as yet formless material.


The Man Who Knew Infinity

Sunday, May 11, 2008

Pattern recognition

"To understand is to perceive patterns" - Isaiah Berlin

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.

Pattern recognition is a sub-topic of machine learning. It can be defined as

"the act of taking in raw data and taking an action based on the category of the data".

Most research in pattern recognition is about methods for supervised learning and unsupervised learning.

Pattern recognition aims to classify data (patterns) based on either a priori knowledge or on statistical information extracted from the patterns. The patterns to be classified are usually groups of measurements or observations, defining points in an appropriate multidimensional space. This is in contrast to pattern matching, where the pattern is rigidly specified.

Within medical science pattern recognition creates the basis for CAD Systems (Computer Aided Diagnosis). CAD describes a procedure that supports the doctor's interpretations and findings.

A complete pattern recognition system consists of a sensor that gathers the observations to be classified or described; a feature extraction mechanism that computes numeric or symbolic information from the observations; and a classification or description scheme that does the actual job of classifying or describing observations, relying on the extracted features.

That's part of the problem when the pattern has been identified, it sometimes then becomes the rest of the life's work to bring more clarity to what was brought back from the subtle journey the soul had taken into a seemingly chaotic world.

The pattern is worked on, and represents three dimensional model. While a two dimensional picture, it represents life's "attentive intent to build." While this pattern is not specific to me,it is used to explain the process, and exemplifies the soul attempt too, find one's wholeness. While speaking t the cyclical nature of this experience, and it's further meanings as a "time capsule" or, "written record." It can then become the fictional medallion that one might ware to be reminded of the life they have chosen.

(The Fifth Dimension)
Idea of the pipe
/ \
/ \
/ \
Picture of the pipe
/ \
/ \
/ \
The real pipe and form


  • Monday, May 22, 2006-Pattern Recognition
    Betrayal of Images by Rene Magritte
  • Sunday, October 14, 2007

    The Artist In Us All

    ""Deep play means no analysis, no explanation, no promises, no goals, no worries. You are completely open to the drama of life that may unfold.""-Dianne Ackerman

    See more on Deep Play.

    This post entry under the heading of the "Artist in us All," is a culmination of information that I had transmitted on Bee's discussion board, under the heading of Art and Communication.

    The whole jest is a preclude to a much more detailed analysis of Art and Science and the following post to this one, prepares the readers for a understanding that I myself strongly advocate.

    But before I move to far ahead of myself, let me take you to the post entries that will prepare one for future considerations.

    The Format

    A final aspect of beauty that was often cited by readers might be called "deep play". This is the sense that we are actively engaged with something outside ourselves that is responding to us - rather than watching a game of our own construction or watching nature from a detached distance.

    The timing of "preparing the format" asks that any given time be considered as the source from which we will move human experiences further along it's path to growth. We can "remove names" and this exercise will be of value to who ever inserts their name or responds accordingly to the questions posted in that same name.

    This is the valuation of interplay that is part of our own gathering system. This post then is the template for what is happening within your own self. A "perceived constant" is being examined in relation to your contact with reality? What ever that is for you at this time?


    "It is sometimes the scientist who takes "to the edge." Then it is the artist, who takes us much further." Plato( this is my quote Bee :)

    Susskind did exactly this, by envisioning a rubber band? Some may laugh, yet, it is a mathematical insight.

    Penroses Influence on Escher

    During the later half of the 1950’s, Maurits Cornelius Escher received a letter from Lionel and Roger Penrose. This letter consisted of a report by the father and son team that focused on impossible figures. By this time, Escher had begun exploring impossible worlds. He had recently produced the lithograph Belvedere based on the “rib-cube,” an impossible cuboid named by Escher (Teuber 161). However, the letter by the Penroses, which would later appear in the British Journal of Psychology, enlightened Escher to two new impossible objects; the Penrose triangle and the Penrose stairs. With these figures, Escher went on to create further impossible worlds that break the laws of three-dimensional space, mystify one’s mind, and give a window to the artist heart.

    But on the other hand you speak about the longevity of the musician, in place of what artist can do, but I would remind you of Dali's picture "on time" as a masterpiece?

    Not least to mention his geometrical views on the hypercube and the crucification?

    Number theory is the type of math that describes the swirl in the head of a sunflower and the curve of a chambered nautilus. Bhargava says it's also hidden in the rhythms of classical Indian music, which is both mathematical and improvisational. He sees close links between his two loves -- both create beauty and elegance by weaving together seemingly unconnected ideas.

    There is a "inherent beauty in the mathematics" when we think about this music?

    Not to mention the relationship of the "Monte Carlo methods" in relation to the cubists.

    Bee, you were to soft in your opinion of artists when I am showing you otherwise. :)

    Here is another quote you might recognize in relation to a form of mathematics.

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

    It is how Srinivasa Ramanujan received his "inspiration" and the place from which this mathematics emerged, that few people realize is of significance.

    From "a chaotic mind" it resolved itself "to the subconscious" that we realize the pattern that is inherent underneath.

    12:50 PM, October 10, 2007

    Part of the understanding here is our connection to the "universality of the subconscious mind" and it's reservoir of impressions received, as we try to express our perspective of the world. "How deep" is your subconscious mind, that you would not understand the complexity of all "self evident information" makes you who you are? That this interplay that takes place with you and your environment, is an exchange that is taking place not only on a "deductive and inductive Archean constant" that all of us would then be writing the "postulate of experience" here?


    It is not about God, but how we dress up the mathematics in our everyday lives. Then, we have to decipher the context of the mathematics other then the "resolved experience-science" we have in moving mathematics forward?

    To Srinivasa Ramanujan it was about his dream and how he received his messages, yet, how absurd that such a place as the subconscious we could receive such inspiration?

    It is not about "heliocentrism" that we are, "the centre of the universe," but rather, that we are connected to the universe in such a way?

    Liminocentric structures?

    Finally, we also hope that this series furthers the discussion regarding the nature and function of 'the mandala'. In the spiritual traditions from which Jung borrowed the term, it is not the SYMMETRY of mandalas that is all-important, as Jung later led us to believe. It is their capacity to reveal the asymmetry that resides at the very heart of symmetry. By offering a new view about how consciousness itself is structured - in a fundamentally paradoxical fashion - and how these structurings are reflected in principles according to which the mandala is organized, we are able in this series to show how personality itself may be thought of as having an essentially 'liminocentric' design.

    The "source of symmetry" is our perfection with the universal inherent in each of us. Our delving into this large pool is in part the effort of our recordings, that what is gained in experience is mapped on the brain's structure, and beyond that. This interplay has to have consequence? Not just in the development of the brain's structure, but far beyond what we see of the physical body.

    1:40 PM, October 10, 2007

    Bee:I tend to believe we are taking ourselves too seriously. If there is a God how could we be sure we'd be able to understand his (her?) thoughts? Genderless for sure eh?:)

    From a psychological perspective and I am no expert for sure, but our present state of consciousness has to be supported in one way or another. Animus and Anima, depending on that gender?

    An "all wise mother figure" who appears in your dream( your higher self speaking to you), or for those men, who recognize that the higher self is talking to them in a way that they have their "wise white haired person offering insight."

    But before I loose you here, I wanted to show you that on first appearance Jean Shinoda Bolen is telling a story. This is the artist aspect of herself, showing the depth of our natures. She is showing it in a way that is helping people identify aspects of themself. Showing underlying causes for such "fantasy development."

    Richards Wagners's Ring of Nibelung Jean Shinoda Bolen, M.D. Ring of Power was interesting.

    Strange that we could have seen A Jungian Understanding of the Wagner's Ring cycle, portrayed in todays world and how could have this been accomplished. But by re-introducing a fictional story and embuing it with the archetypal structures of what Jean Shinoda Bolen called, "The Abandon Child, The Authoritarian Father, and the Disempowered Feminine."

    Under the search of "Jean Shinoda Bolen on my site." One reason the "nav bar" was of good use. If you have a search feature otherwise?

    It's never clear from all appearances, yet there is a deeper understanding of what is culminating in a person's experiential life.

    I follow your thoughts on Bohm for I read him a long time ago too, and somehow it seems fitting that art and communication, might have incorporated "language as a developmental phase" to seeing reality, in new ways?

    Sort of like being initiated into string theory, to help get past some of the blockages that are stopping science from developing further?

    7:56 AM, October 11, 2007

    These blockages manifest within the self, and become impediments to our experience and progression to further learning. This is not to say learning stops. It is the "greatest effort" that what has become apparent in the state of self evidential experience, is the potential to great transport human experience beyond the self's own limitations. Provides for, the "intuitive leaps" necessary once the basis of this experience is resolved. How deep this blockages goes, that the subconscious mind will allow images to transport the self to a future place for consideration.

    Bee:It might not be an universally applicable source of inspiration?

    To Hardy I don't think that mattered one bit. It is just part of the process to understanding how we humans like to fabricate our realities. Yet, there is a universal connection that we have that is a very consistent. One in relation to the artist in us all.

    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.

    We are the best predictors of ourselves and our experiential conditions that we put forward. A model perhaps in developmental insight as to what we have to do in science?

    So in the psychology......

    If any such resolve is not forthcoming in our "supposed awake reality," then there is a culminating effect that someone(archetypal) is speaking to us to help us resolve these disputes. "Our universality" is there in us all. I see no race religion, or gender.

    So like Jean above we write our own story, and show the affect our experiential life has on the new conditions if not resolved.

    So I apply these things to our current search for understanding the math creation (calculus for Newton)and the derivatives needed to push insight further into "new realms of experience."

    Would you denigrate Calculus as a language to helping you discern the nature of reality? Newton knew he had to do something. Einstein realize it when Grossman was developing a new language, as was Reinmann preparing us from his predecessors, on the issue of "non euclidean geometries?" Gauss was very delighted with his student

    8:18 AM, October 11, 2007

    Understanding that human experience is "cradling the times for breakthroughs to further understanding" is the incubation period necessary for preparing these intuitive leaps and future predictability.

    Here 50% or 100% provides for whether the human side of us really understands and knows what is necessary for us to progress. How would the probability of all human experiences to know to draw for one own postulate, "the self evident" and then understand that the leap to growth in experiences requires this and this?

    While such is th evastness of the human experience it is not without our understanding that each of us has repercussions of actions to every decision we make. I cannot tell which, only that this probability can be played out time and time again and it will result in the growth of each of us at varying times. There is a constancy that is being talked about here that can be debated, but as far as I can tell this is the postulate that has been written.

    To them, I said,
    the truth would be literally nothing
    but the shadows of the images.

    -Plato, The Republic (Book VII)

    I used this quote in "your other thread" for a reason. Images? Think about this for a minute.

    If one can "translate" and transfer the image mathematically for each other, then what has happened? A level of communication not understood before?

    Arthur Miller

    Miller has since moved away from conventional history of science, having become interested in visual imagery through reading the German-language papers of Einstein, Heisenberg and Schrödinger - "people who were concerned with visualization and visualizability". Philosophy was an integral part of the German school system in the early 1900s, Miller explains, and German school pupils were thoroughly trained in the philosophy of Immanuel Kant.

    When I referred to Susskind I did so for a reason as well. This is the culmination of what mathematically is derived. Thus, the image is a culmination, yet, it is only a "shadow of the truth."

    I used Magritte, When is a Pipe a Pipe painting, to illustrate this.

    Hawking shows this in his book as well.

    You have to remember Plato's analogy was even used by Gerardus t'Hooft. See here and Heisenberg so you are in good company.

    P.A.M. Dirac was a gifted mathematical inventor who saw how quantum mechanics rises from classical mechanics, yet transcends it. Dirac did not know of the Bohr atom when he arrived at Cambridge in 1923; yet he quickly began contributing to the mathematical structure demanded by quantum phenomena, discovering the connection between the Poisson bracket and the commutator of Heisenberg”s matrix representation of observables. Then, with careful attention to its classical antecedent, Dirac found the equation governing the evolution of the matrix elements which had eluded Heisenberg in the operator ihdA/dt = [A,H]. He then went on to discover spinors in describing the relativistic electron and antimatter implied by the quantum in relativistic space-time. Dirac conceived the many-time formulation of relativistic quantum mechanics and laid the foundations of the Feynman path integral thereby opening the way to quantum electrodynamics. Newton synthesized the foundations of classical mechanics. In fitting kinship, Dirac, who did the equivalent for quantum mechanics, filled the chair at Cambridge held by Newton.

    Some people are better suited to visualization then others, and this comes out in some mathematicians and in artists as I had shown you of Escher and Dali. I could never judge Dali for his character an his life, but I can say how important he tried to push the envelope. Maybe for all his indulges, he thought if he could think of the cross and his geometrically tendency he might have found some relation?

    Of course, to Plato this story was just meant to symbolize mankind's struggle to reach enlightenment and understanding through reasoning and open-mindedness. We are all initially prisoners and the tangible world is our cave. Just as some prisoners may escape out into the sun, so may some people amass knowledge and ascend into the light of true reality.

    What is equally interesting is the literal interpretation of Plato's tale: The idea that reality could be represented completely as `shadows' on the walls

    12:19 PM, October 12, 2007

    Monday, September 24, 2007

    Are there Patterns to Life?

    Its grandness, goodness, beauty and perfection are unexcelled. Our one universe, indeed, the only one of its kind, has come to be.Timaeus concludes

    I was just thinking about the idea of being a mathematical structure, and having been made aware of Max Tegmark, it drew me back to the idea of the "soccer ball universe."

    "If this holds up to the test of time, it's a real landmark," said Max Tegmark, a cosmologist and cosmic microwave expert at M.I.T. "I really feel like the universe has given up one more clue," he said.
    See: Scientists Get Glimpse of First Moments After Beginning of Time by DENNIS OVERBYE

    Now yes I'd admit the universe is a far cry from the person we are, but we are much more complex, and I'd liken it to the universe. Why not?

    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.
    See:Srinivas Ramanujan(1887-1920):

    Anyway twice I have been reminded of the mathematics "are not" the reality of the situation, and that governing such thought is devoid of the reality we are dealing with. I have an issue with this because, we have discovered number patterns that underly nature just as Coxeter believes that "the process" is just awaiting to be discovered. Then, we have found the thread through things.

    So, people do not like to believe that we are a mathematical structure, yet, we have seen where hidden numbered processes have been detailed for us in the expressions of nature.

    The Valley and our Place in the universe

    Jacques Distiler:
    Rather, it is assumption 2) that is suspect. I argued that it is suspect in much greater generality in the comment thread I linked to above. But, in the specific case of the proton lifetime, we already have seen two mechanisms, discussed in this thread, either of which could constrain the proton lifetime to be far longer than the anthropic bound.

    Jacque Distler:
    Obviously, no one has yet found a convincing candidate for the Standard Model, among the string vacua explored to date (in that sense, no one has made any predictions yet). But that’s not what you’re saying(Peter Woit). You are claiming that the framework itself is inherently unpredictive.

    Italicized is my addition.

    A mathematics man who does not like math?

    So you see we are looking for the constants(a product of the standard model), yet, we do not know what that constant will look like in the valley. While it is based on a "gravitational inclination," the formation has a probability "greatly enhanced" when thinking about the entropy of the blackhole. The "energy valuation" from mass while in gravitational collapse, creates the multitude of possibilities(heat)?

    Saturday, January 06, 2007

    Mersenne Prime: One < the Power of two

    It looks as though primes tend to concentrate in certain curves that swoop away to the northwest and southwest, like the curve marked by the blue arrow. (The numbers on that curve are of the form x(x+1) + 41, the famous prime-generating formula discovered by Euler in 1774.)

    This is part of the education of my learning to understand the implications of the work of Riemann in context of the Riemann Hypothesis. Part of understanding what this application can do in terms helping us to see what has developed "from abstractions of mathematics," to have us now engaged in the "real world" of computation.

    In mathematics, a power of two is any of the nonnegative integer powers of the number two; in other words, two multiplied by itself a certain number of times. Note that one is a power (the zeroth power) of two. Written in binary, a power of two always has the form 10000...0, just like a power of ten in the decimal system.

    Because two is the base of the binary system, powers of two are important to computer science. Specifically, two to the power of n is the number of ways the bits in a binary integer of length n can be arranged, and thus numbers that are one less than a power of two denote the upper bounds of integers in binary computers (one less because 0, not 1, is used as the lower bound). As a consequence, numbers of this form show up frequently in computer software. As an example, a video game running on an 8-bit system, might limit the score or the number of items the player can hold to 255 — the result of a byte, which is 8 bits long, being used to store the number, giving a maximum value of 28−1 = 255.

    I look forward to the help in terms of learning to understand this "ability of the mind" to envision the dynamical nature of the abstract. To help us develop, "the models of physics" in our thinking. To learn, about what is natural in our world, and the "mathematical patterns" that lie underneath them.

    What use the mind's attempt to see mathematics in such models?

    "Brane world thinking" that has a basis in Ramanujan modular forms, as a depiction of those brane surface workings? That such a diversion would "force the mind" into other "abstract realms" to ask, "what curvatures could do" in terms of a "negative expressive" state in that abstract world.

    Are our minds forced to cope with the "quantum dynamical world of cosmology" while we think about what was plain in Einstein's world of GR, while we witness the large scale "curvature parameters" being demonstrated for us, on such gravitational look to the cosmological scale.

    Mersenne Prime

    Marin Mersenne, 1588 - 1648

    In mathematics, a Mersenne number is a number that is one less than a power of two.

    Mn = 2n − 1.
    A Mersenne prime is a Mersenne number that is a prime number. It is necessary for n to be prime for 2n − 1 to be prime, but the converse is not true. Many mathematicians prefer the definition that n has to be a prime number.

    For example, 31 = 25 − 1, and 5 is a prime number, so 31 is a Mersenne number; and 31 is also a Mersenne prime because it is a prime number. But the Mersenne number 2047 = 211 − 1 is not a prime because it is divisible by 89 and 23. And 24 -1 = 15 can be shown to be composite because 4 is not prime.

    Throughout modern times, the largest known prime number has very often been a Mersenne prime. Most sources restrict the term Mersenne number to where n is prime, as all Mersenne primes must be of this form as seen below.

    Mersenne primes have a close connection to perfect numbers, which are numbers equal to the sum of their proper divisors. Historically, the study of Mersenne primes was motivated by this connection; in the 4th century BC Euclid demonstrated that if M is a Mersenne prime then M(M+1)/2 is a perfect number. In the 18th century, Leonhard Euler proved that all even perfect numbers have this form. No odd perfect numbers are known, and it is suspected that none exist (any that do have to belong to a significant number of special forms).

    It is currently unknown whether there is an infinite number of Mersenne primes.

    The binary representation of 2n − 1 is n repetitions of the digit 1, making it a base-2 repunit. For example, 25 − 1 = 11111 in binary

    So while we have learnt from Ulam's Spiral, that the discussion could lead too a greater comprehension. It is by dialogue, that one can move forward, and that lack of direction seems to hold one's world to limits, not seen and known beyond what's it like apart from the safe and security of home.

    Tuesday, October 24, 2006

    Raphael the Painter

    By 'dilating' and 'expanding' the scope of our attention we not only discover that 'form is emptiness' (the donut has a hole), but also that 'emptiness is form' (objects precipitate out of the larger 'space') - to use Buddhist terminology. The emptiness that we arrive at by narrowing our focus on the innermost is identical to the emptiness that we arrive at by expanding our focus to the outermost. The 'infinitely large' is identical to the 'infinitesimally small'.The Structure of Consciousness John Fudjack - September, 1999

    Self-portrait by Raphael

    While I am no great philosopher, the idea of truth was very important one to me. Finding some method by which to proceed was very difficult without the teachers handy. So I learned to trust my intuition as I was lead from one place to another. By it's own design, the correlation I termed in relation to cognition were very important discover about my own potential. I had to symbolically discribe the very actions of what goes in, and what comes out, turns through that channel in much the same way a electromagnetic field governs by analogy the principle of life around the human body, as information passes through the center.

    If conceived as a series of ever-wider experiential contexts, nested one within the other like a set of Chinese boxes, consciousness can be thought of as wrapping back around on itself in such a way that the outermost 'context' is indistinguishable from the innermost 'content' - a structure for which we coined the term 'liminocentric'.

    Will this become part of the greater complexity of the life form, as information becomes part of the larger context of the souls growth? How is that measured? How is t external world brought back in and then turned outward, and the "colors change" as the truth begins to dawn?

    For me the story here starts with a painter and from the very painting itself, one can imagine a larger story unfolding, as one peers into the center of the School of Athens.

    For now, the music is set aside, for the "foundational perspective" that issues forth from this blog.

    I added this biography of the artist himself and "crunched" behind him is a speculation of a kind that becomes the basis of this bloggery. It is about observation and the search for truth as we look at the work of Raphael and the following information that I hold in consideration of this painting.

    Our attempt to justify our beliefs logically by giving reasons results in the "regress of reasons." Since any reason can be further challenged, the regress of reasons threatens to be an infinite regress. However, since this is impossible, there must be reasons for which there do not need to be further reasons: reasons which do not need to be proven. By definition, these are "first principles." The "Problem of First Principles" arises when we ask Why such reasons would not need to be proven. Aristotle's answer was that first principles do not need to be proven because they are self-evident, i.e. they are known to be true simply by understanding them.

    Do we know what Raphael was trying to impart through these images?

    Inductive and Deductive

    While holding the School of Athens by Raphael then picture in mind and consider the following?

    Aristotle from a a posteriori leads perspective in one way, and Plato a prior?

    PLato saids, "Look to the perfection of the heavens for truth," while Aristotle saids "look around you at what is, if you would know the truth"

    So from that basis look at what is portrayed in the opening statement above with regards to Plato finger pointing up and Aristotle's hand sweeping pervasively?

    So while I lead one through a vast maze of links here it is not without doing my own research that I could now point you to wikipedia for examination of the many things that we could learn of Plato. Imagine Plato continues to live through all this information?

    Without Plato a a personification of the some of the ideals I have, I know who I am. The sun as a symbol of enlightenement? Then following, Plato's Cave Analogy?

    As a beginning, you see I started to point out some of the more important features of the leadng perspective of Aristotle, and the link I see to Robert Laughlins building blocks of matter?

    But before I jump so far ahead, maybe it is indeed useful to link wiki here so one gets the jest of what may be implied by an example?

    Epistemology or theory of knowledge is the branch of philosophy that studies the nature and scope of knowledge. The term "epistemology" is based on the Greek words "επιστημη or episteme" (knowledge) and "λόγος or logos" (account/explanation); it is thought to have been coined by the Scottish philosopher James Frederick Ferrier.

    Much of the debate in this field has focused on analyzing the nature of knowledge and how it relates to similar notions such as truth, belief, and justification. It also deals with the means of production of knowledge, as well as skepticism about different knowledge claims. In other words, epistemology primarily addresses the following questions: "What is knowledge?", "How is knowledge acquired?", and "What do people know?". Although approaches to answering any one of these questions frequently involve theories that are connected to others, there is enough particular to each that they may be examined separately.

    There are many different topics, stances, and arguments in the field of epistemology. Recent studies have dramatically challenged centuries-old assumptions, and the discipline therefore continues to be vibrant and dynamic.

    So while some would point to the very functions of perceiving aspects of the higher self, if there is such a thing accept in one conceptual framework, or messages from God, as Ramanujan received the equations in dream time. I think of this as a very dynamical process, that each of us possesses. If without the teacher to guide us, then the teacher most certainly makes it's way into the mind for observation?


    Innatism is a philosophical doctrine introduced by Plato in the socratic dialogue Meno which holds that the mind is born with ideas/knowledge, and that therefore the mind is not a tabula rasa at birth. It asserts therefore that not all knowledge is obtained from experience and the senses. Innatism is the opposite of empiricism.

    Plato claimed that humans are born with ideas/forms in the mind that are in a dormant state. He claimed that we have acquired these ideas prior to our birth when we existed as souls in the world of Forms. To access these, humans need to be reminded of them through proper education and experience.

    While it is referred to the young born into this world, what said that any person could not become that "blank slate" that would allow the wider perspective of what has been lived, is not confined to this life, but is exposed as that channel is opened for the wider perspective about life?

    I say,"
    I mean really, if, each of us is born into this world with such a blank slate, then how is an idea incorporated into such a design of our blank slate. Especially, if there had not been some influence predisposed, to draw ideas into the appropriate environment for consideration?

    While we provide for the nurturing aspect of creativity to express itself, we find that such freedoms are encouraged by observation of the introspective attitude we gain by learning about ourselves.

    The Medicine Wheel as a Mandala

    It is not so much that we learn about the very "drawing here for you" but that it is circular in nature, and by the very discription the mandala is pretty "clear cut" as to what manifested from a deeper level in my own mind.

    Now what you do not understand is that the center is very important feature on what we focus on. While the "purity of thought" is presented here. It is the idea that the closer to the source you get, the purer the thought/idea that manifests into the theoretical world.

    While I attempt to explain the process this does not disavow you from experimenting and testing, so that the advancement of knowledge and understanding reawakens you to the "nature" of one's being? What is this?

    Monday, May 22, 2006

    Pattern Recognition

    That was the problem we had to solve. In order to count microstates, you need a microscopic theory. Boltzmann had one–the theory of molecules. We needed a microscopic theory for black holes that had to have three characteristics: One, it had to include quantum mechanics. Two, it obviously had to include gravity, because black holes are the quintessential gravitational objects. And three, it had to be a theory in which we would be able to do the hard computations of strong interactions. I say strong interactions because the forces inside a black hole are large, and whenever you have a system in which forces are large it becomes hard to do a calculation.

    The old version of string theory, pre-1995, had these first two features. It includes quantum mechanics and gravity, but the kinds of things we could calculate were pretty limited. All of a sudden in 1995, we learned how to calculate things when the interactions are strong. Suddenly we understood a lot about the theory. And so figuring out how to compute the entropy of black holes became a really obvious challenge. I, for one, felt it was incumbent upon the theory to give us a solution to the problem of computing the entropy, or it wasn't the right theory. Of course we were all gratified that it did.

    I mean sure we can say to ourselves, "that one day I was very ignorant" and I had all these speculative ideas about the "Golden Ratio," but then, I learnt the math and the truth of it all?

    But while we were being crazy......?:) Ahem!

    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.

    In "past life bleed throughs," it was very important to realize that while speaking in context of "overlapping," the underlying archetecture allowed for expression of those different interpretive assignments I had given. These were significant for me, because it help me to realize the "mapping" that we can unconsciously have revealled in such "experience dream/real patterns," that had one not be aware it, would have escape one's notice as a mundane realization.

    You had to understand how "geometrical seeing" is held in context of Dirac's wording, to know that this tendency to draw lines at the basis of consciousness, was also evident in Feynman's toy model construction. It is something that we do, do.

    So what did I learn?

  • 1. That it revealled a model for consciousness, from the reality of the day, to the transcendant.

  • 2. That it housed an experience in the way it can overlapped using "1" as a central pattern of emergence.

  • 3. That present day models now use this schematic are psychologically endowed in speculation(liminocentrically structured), but has a basis in fact, as I am showing it here.

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

    What sense would any of this "cognitive idealization" make, if one did not have some model in which to present, and know, that it was the underlay of all experience, and that the time of our day, might see us use it in topologically in different ways?

    I used Sklar for this example.

    But more then this what use is "Pascal Triangle" if we did not understand the emergence of "patterned numbers" from some initial beginning and cognitive realization, had we not recognized Pascal's model intepretation?

    With no know emergent principals, or geometry arising from inside the blackhole, it was important that the basis of expression be realized as a pattern forming recognitive valuation? Is it right? I am not sure, but part of the developing model application had me wonder about how we could have encapsulated the cyclical nature of, what was collapsing into the singularity, was now actually, the motivational force for the developing new universe?

    When it was discovered that black holes can decay by quantum processes, it was also discovered that black holes seem to have the thermodynamic properties of temperature and entropy. The temperature of the black hole is inversely proportional to its mass, so the black hole gets hotter and hotter as it decays.

    So it was important to know the basis of D brane recognitive values, in how the blackhole is interpreted?

    Sunday, May 21, 2006

    Past Life Bleed Throughs?

    In studying over the many years, certain concepts and ideas brought from other cultures stayed with me of course, while I explored the dream world enviroment on my own.

    The idea here is that similar patterns used in construction of mandalic interpetations, serve to illustrate model applications, that when bleeding, overlap experiences, whether they be drean information gathered, or, historical correlations, these struck me as significant.

    This is not to say that all people who dream will be good mathematicians, just that the road to cogitive realization held in context of Ramanujan should be seen as the developing subsconscious as a very important tool in moving the cogitive revelations that the creative mind can utilize, in developing math models for the future?

    THatpattern had to be understood a dLimincentric structures as well. If you didn't you would not have seen the importance of the schematics that Liminocentric structures reveal of themself as mandalic models of intepretation.


  • A Pure Love of Math

  • A Tribute to Hinduism

    The inexhaustible Ramanujan was an observant Hindu, adept at dream interpretation and astrology. His work was marked by bold leaps and gut feelings. Growing up he had learned to worship 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.

    Ramanujan could never explain to G H Hardy how he arrived at his deep insights in mathematical terms; but he did say many of his discoveries came to him in dreams, from the goddess Namakkal, and that he had a morning ritual of awakening and writing them down.

    Having heard of Ramanujan method of information gathering, it was interesting from the standpoint of how the consciousness could organzed itself and bring forth abstract notions(jumbling experiences in that dream world), to have the method of mathematical explanation bear tangible proof in our reality now.

    This is of course are some of the ideas I have around cognitive recognitions of getting to the source of creation and bringing back tangible equative solutions.

    Perhaps it is of some use for a example to better understand this?

    While journalling for many years and recording my dreams, I came up with what I called "dream poetry," because I wanted to try and catch the rhythmn and story behind it as best I could without subjecting it to the scrutinization of my mind and analysis.

    Of course having a pen and paper beside the bed was always good advice. There was always a definite difference in the lucidness of those dreams, that seemed to indicate this past life referencing, then the normal dream periods.

    Also by doing this "awareness of the dream time" it became very pronouced in terms of the recall before getting busy with the day.

    Since ancient times, Mandalas have been used for meditation and healing. In old Tibet, Mandalas were used in the process of training the mind to be quiet, so that That Still Place Within was more easily accessible.

    It was said that the Divine lives at the center of the Mandala. With that in mind, the Mandala was used as a focus point for meditation.

    As the mind quiets and becomes still, the meditator finds the Divine at the center of his own being.

    I read about this use of Mandalas years ago. When this series of designs came through me, I realized that that was the intent within them: that the Divine would reside at each design's center.

    Research I've done indicates that Mandalas are the visual forms of the resonance traces of specific frequencies of sound/light. Some pretty amazing research done by Hans Jenny shows that if sound is transmitted through a thin layer of sand on a metal plate, the sand vibrates in such a manner as to create designs in the sand, the patterns shifting with the sounds transmitted.

    If one wanted to pursue it further then it makes sense that the Chaldni plate becomes a interesting piece of equipment in analyzing the nature of such vibrations. A balloon dipped in a dye solution and subjected to different sounds, has an interestig perspective to it.

    Nodes and anti-nodes

    On beautiful mandalic designs see:

  • Flower Mandalas Project
  • Wednesday, May 10, 2006

    Intuitively Compelling

    While it does appear that Einstein has indeed given us a paradigm which was indeed world-changing and affected everyone, how well might he have known himself?

    He was "driven," as to the" focus and outcome" of GR's growth? Yet, being Jewish, and the meaning he might have had for God(Old ONe) had a perspective about nature, that was embued with a certain terminology?

    So having engaged the wording of scientist as of late, I wanted to stay as close as I could to the thinking being developed as they engaged society through their blogging site perspectives.

    It was most troubling that any discussing of the timeline and any other constructs place in accordance with that timeline, would/could have been insulting to some, even though it fit into a perspective in terms of microseconds, lesss then somany eseconds of expression.

    Again for sure, "thought constructs," most appropriate measures as yard sticks of reality conforming to model approaches? Be open.

    Thomas Torrance
    In 1978, he won the Templeton Prize for Progress in Religion for his contributions to theology and the relationship between it and science

    You must understand there is a current struggle in today's world with those who support the Templeton Foundation, it's scientists, and those who believe science should remain free of such influences, so they propagate any information forthcoming as tainted?

    Einstein and God By Thomas Torrance"Do you believe in the God of Spinoza?" was asked of Einstein.

    I can't answer with a simple yes or no. I'm not an atheist and I don't think I can call myself a pantheist. We are in the position of a little child entering a huge library filled with books in many different languages. The child knows someone must have written those books. It does not know how. The child dimly suspects a mysterious order in the arrangement of the books but doesn't know what it is. That, it seems to me, is the attitude of even the most intelligent human being toward God. We see a universe marvellously arranged and obeying certain laws, but only dimly understand these laws. Our limited minds cannot grasp the mysterious force that moves the constellations. I am fascinated by Spinoza's pantheism, but admire even more his contributions to modern thought because he is the first philosopher to deal with the soul and the body as one, not two separate things.

    The Nature of Reality
    Having read all of Jane Roberts books( some might not have taken a shine to such information, but part of the developing perspective included information that was written "intuitively compelled"), so she might have answered a little different, but in essence, thought, to the nature of the universe.

    I'll try and find her definition of the building blocks.

    So you are give this question as to what the nature of the unverse is? What is it, and people are lead through theoretcial constructs to develope perspective on what that question might be?

    Robert Laughlin, does not care if they are Lego bricks or Drunk Sargeant majors:)

    Self Organization of Matter, by Robert Laughlin

    What Lies Beneath, by Eugene Samuel
    Likewise, if the very fabric of the Universe is in a quantum-critical state, then the "stuff" that underlies reality is totally irrelevant-it could be anything, says Laughlin. Even if the string theorists show that strings can give rise to the matter and natural laws we know, they won't have proved that strings are the answer-merely one of the infinite number of possible answers. It could as well be pool balls or Lego bricks or drunk sergeant majors.

    One had to indeed understand that the maps drawn, were drawn from thOught constructS engaged from wanting to understanding where first principles may have emerged from?

    How would you do that without undertanding where this map began?

    So what use to Engage Strangelets, New Physics

    So from a resulting comprehension of such first principles, there came this resulting course of events, that went through all the phase transitions, to become what it is, in context of the strangelet, a perspective about a measure in the IceCap?

    I have been following this research for sometime now. I will be updating this information here].

    One has to know where to begin with all this information, and that such "mental constructs" had to know where this beginning was. While there are few here mathematically endowed, I wanted to come here and share perspectve in context of the neurological idea behind the mental constructs that we develope in science.

    This is not without foundation that, "globally," when we now see, we had indeed step back to access the greater potential in "thought generation," and that "mass psychosis," (could we call it that as such a verification by the masses?)" endowed to measure, experimentally verified.

    I'll wait to see if you want some time to digest and rethink, if you think, it worth doing that? :)

    True creativity often starts where language ends-Arthur Koestler

    Intuitively Compelling=Intuitive Grasp of Self Evident First Principles

    No matter the ideology spread, is there something today that is quite useful in our approaches to cognizing relevance, from "thought constructs" to actual processes, currently asking us our about the beginning of the universe?

    While such solidification ensues from taking a stand, as a concluson drawn, is it compelling as to the nature of what first principles might mean? You had to understand the current environment, to conclude an opinion about the measures and constructs, as to those measures asking if there was another way?

    You couldn't know that, unless you might have read the links of Robert Lauglhin and understood reductionistic tendencies(science), as to the nature of our universe? It's like joining quantum perspective with General Relativity? You would have to known how this was acomplished? It's result, and hence it's application within society?

    If one had not understood, shall we call it a "probabilistic discourse," to have now understood, that a new course may be set today, was different from the past, by "one additional grasp of self evident first principle?" That a new page may be written( what thinking had done so) which may change the course of our lives?

    Of course, some will not have confidence yet. :)
    That the potential exists within each of us to understand we are partaking of a quest to percieve where this point in existance might be revealled. If not at the basis of reality, then what use the math? While I generalize becuase of my inefficieny of these interpretations, the vastness of the world of math, there was some undertanding geometrically inclined, that is revealled as we followed the logic leading to GR.

    Did it mean we should be devoid of our belief in a God, if we held to science principles, while, we engaged in the subjectivity of our opinions?

    It All Began in a Dream?

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

    So to me, it is still all out there for us to look? How we might entertain that awe and beauty in nature?

    "God does not play dice" by Thomas Torrance
    Einstein was not a determinist but a realist, with the conviction that, in line with Clerk Maxwellian field theory and general relativity theory, nature is governed by profound levels of intelligible connection that cannot be expressed in the crude terms of classical causality and traditional mathematics. He was convinced that the deeper forms of intelligibility being brought to light in relativity and quantum theory cannot be understood in terms of the classical notions of causality–they required what he called Übercausalität–supercausality. And this called for "an entirely new kind of mathematical thinking", not least in unified field theory–that was a kind of mathematics he did not even know, but which someone must find.

    Once Comsuming any Model

    It is difficult to explain how one might have "the feeling" for curvature on cosmological plateau while such tendencies for quantum perception would be rule by uncertainty?

    I wonder if such states held in context to what consciousness might be able to percieve at that level of high energy areas, would give indications to particle natures and the curvatures assigned to each particle nature. What gave these meomntum ad emotive feelings to such travel from the initial contact?

    How are we able to pierce this veil and environment, while talking about the nature of such curvatures? We wouldn't survive realistically, yet, we are able to perform "thought constructs" to such models?

    So looking at time dilation, the photon within environments, what indications for such curvatures, and one gets this sense of momentum, and in another way, something that I have called toposense.

    Variable "constants" would also open the door to theories that used to be off limits, such as those which break the laws of conservation of energy. And it would be a boost to versions of string theory in which extra dimensions change the constants of nature at some places in space-time.

    Constants with and without dimensions

    Nature presents us with various constants. Some of these constants, such as the fine-structure constant, are dimensionless and are not expressed in terms of units. However, other constants, such as the velocity of light or the mass of the proton, are dimensional and their numerical values depend entirely on the units in which they are expressed. The laws of nature do not, of course, depend on a man-made system of units.

    To put this another way, if we want to measure a dimensional constant, we need a "yardstick" to make the measurement. But if we obtained one value when we measured the speed of light on a Monday, say, and a different value when we measured it on a Friday, how would we know that our yardstick had not shrunk or expanded? We would not. Moreover, if we were to interpret our observations as a change in the length of the yardstick, how could we verify it without reference to a second yardstick? Again, we could not. And so on.

    However, dimensionless constants are fundamental absolute numbers, measured without reference to anything else. Therefore, if we want to investigate if the laws of nature are changing we must measure dimensionless quantities such as the fine-structure constant or the ratio of the electron and proton masses

    Wednesday, March 15, 2006

    Increase in Output of Inverse Square Law Calculatons ?

    Oh my poor layman brain. It hurts.

    String theory and the crisis in particle physics by Bert Schroer
    The third point of the list is perhaps the most serious one. A theory which has in more than 30 years been unable to get its relation to physics straightened out is presented to physics students as a theory of everything which supersedes QFT before their critical faculties have been strengthened by learning about the concepts and open problems of the most successful theory of particle physics.

    When is enough, enough? I think all the warnngs have been heard and the continued barage of statements and genralizations enough to make one sick.

    Don't worry Lubo about the context of statements ancestroy or otherwise. As to what you might have wrritten on the blackboard about strings, and what Einstein might have written instead.

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

    For me, Ramanujan's statement was really clear. Although, it(math) manifested in the dream, the langauge spoken was the recognition of the source through which mathematics would make itself known to the world. First Principle. If one was listening what was emerging then? Ramanujan might have been so engrossed in math, that such an insight was the key to the open doorway with which quantun grvaity would now not become destitute.

    So focused are the many in math that taking the time from all it's calculations, by a quiet strean, or sitting in nature's presence, it all comes together in a "flash of insight."

    You have to find the conditions that will speak to theorectical valuation. If such a wide sweeping generalization is levelled at the "mathematical field in question," then, how shall you ever know what this model could have lead one too, in comprehension?

    Will we have lacked sufficient knowledge that one might have never had seen it excell beyond the confines of bias and opinion?

    Geometrical insight is greater then the axiomization indicated, was from other thoughts of Dirac, and not just the mathematical statements assigned? Such inclination to a quantum perspective and dynamical valuation, of what GR is assigned in curvature, was taken down to the ideas of what signaled the curvature indicators with regards to high energy considerations?

    Inverse Fourth Power Law

    Quantitative studies of future experiments to be carried out by LHC show that any signatures of missing energy can be used to probe the nature of gravity at small distances. The predicted effects could be accessible to the Tevatron Collider at Fermilab, but the higher energy LHC has the better chance.
    These colliders are still under construction, but results also have consequences for "table-top" experiments, being carried out here at Stanford, as well as the University of Washington and the University of Colorado. Here’s the basic idea: imagine there are two extra dimensions on a scale of a millimeter. Next, take two massive particles separated by a meter, at which distance they obviously behave according to the well-known rules of 3-D space. But if you bring them very close, say closer than one millimeter, they become sensitive to the amount of extra space around. At close encounter the particles can exchange gravitons via the two extra dimensions, which changes the force law at very short distances. Instead of the Newtonian inverse square law you’ll have an inverse fourth power law. This signature is being looked for in the ongoing experiments.

    In context of a "complete geometrical process(including microperspectve processes)" how is this possible? It's "motivation" from the gravitatinal collapse, cosmologically is well understood? Analogies in the Laval nozzle, would have been capable of seeing superfuid anomalies occuring that are "counter intuitive" at such extreme temperatures? Yet a channel is provide for the increase in energy values as the output is increased?

    Again supefluid states would have to be considered here, and the output generated? What else could it be?

    Haines’ explanation theorizes that Z’s magnetic energies create microturbulences that increase the kinetic energies of ions caught in the field’s grip. Already hot, the extra jolt of kinetic energy then produces increased heat, as ions and their accompanying electrons release energy through friction-like viscous mixing even after they should have been exhausted.

    Mind you this is from 2001

    Stanford's Savas Dimopoulos:
    New Dimensions in Theoretical Physics

    Our new picture is that the 3-D world is embedded in extra dimensions," says Savas Dimopoulos of Stanford University. "This gives us a totally new perspective for addressing theoretical and experimental problems.

    And from the same article. Persepctive has now been changed. We do not discard what has already been built up.

    Instead of the Newtonian inverse square law you’ll have an inverse fourth power law. "This signature" is being looked for in the ongoing experiments.

    So. What value when looking at the Z Machine with such theoretical speculation?

    Awareness of counter intuitive anomalies present in such development of the supefluids? Forces us to consider how "bulk manifestion values" are increased? Where did this "extra energy" come from?


  • The Z Machine

  • Visualization: Changing Perspective
  • Friday, January 13, 2006

    Riemann Hypothesis: A Pure Love of Math

    Mathematics Problem That Remains Elusive — And BeautifulBy Raymond Petersen
    Dyson, one of the most highly-regarded scientists of his time, poignantly informed the young man that his findings into the distribution of prime numbers corresponded with the spacing and distribution of energy levels of a higher-ordered quantum state

    Prime numbers are more than any assigned multitude of prime numbers.
    Euclid Book IX Proposition 20

    Mathematical ProblemsLecture delivered before the International Congress of Mathematicians at Paris in 1900 By Professor David Hilbert

    8. Problems of prime numbers

    Essential progress in the theory of the distribution of prime numbers has lately been made by Hadamard, de la Vallée-Poussin, Von Mangoldt and others. For the complete solution, however, of the problems set us by Riemann's paper "Ueber die Anzahl der Primzahlen unter einer gegebenen Grösse," it still remains to prove the correctness of an exceedingly important statement of Riemann, viz., that the zero points of the function (s) defined by the series

    Clay Mathematics Institute

    The Riemann hypothesis asserts that all interesting solutions of the equation

    ζ(s) = 0

    lie on a certain vertical straight line. This has been checked for the first 1,500,000,000 solutions. A proof that it is true for every interesting solution would shed light on many of the mysteries surrounding the distribution of prime numbers.

    Over at Cosmic Variance, Clifford posted something in regards to this Hypothesis that I had been piece mealing over time trying to understand the implication of what is being offered here.

    Prime Finding: Mathematicians mind the gapErica Klarreich

    Goldston and Yildirim's novel idea was to examine the distribution not just of pairs of primes, but also of triples, quadruples, and larger groupings. Studying this wider question simplified the formulas estimating the spacing of primes, and to the team's surprise, the new result about smaller-than-average prime gaps fell out.

    I learnt a lot by looking at the relationship of Gauss as the teacher of Riemann, and in this, itself is telling to a degree about the nature of how we move our thinking and our perception in a different way that we are not accustomed.

    Primed to go

    The algorithm at the centre of his method first checks whether the number in question is a perfect square, cube, or other power of a smaller number. If so, it is clearly not prime. If not, a sequence of tests using a type of mathematics called modular arithmetic is carried out. If certain conditions are satisfied, the number is definitely not prime. If they are not, then it is. Crucially, the time it takes to run the algorithm increases only slowly as the size of the number rises.

    These tendencies are recognized in our consideration that were progressive, and Grossman's helping Einstein to think about the geometry taking place as you move to the consideration and the nature of GR and the curvatures that gravity implies.

    On the Number of Prime Numbers less than a Given Quantity.Monatsberichte der Berliner Akademie, November 1859. by Bernhard Riemann

    I believe that I can best convey my thanks for the honour which the Academy has to some degree conferred on me, through my admission as one of its correspondents, if I speedily make use of the permission thereby received
    to communicate an investigation into the accumulation of the prime numbers; a topic which perhaps seems not wholly unworthy of such a communication, given the interest which Gauss and Dirichlet have themselves shown in it over a lengthy period.

    Ulam's Spiral

    Gauss saw this bright thinking, as a student gave his talk while he sat as a pround parent. What was he so proud of? I believe it is in the way that our vision had been changed from the confines of the natural world. Taking what we saw in all that it is.

    Gaussian Primes

    IMagine Einsteins youth and the meme's of compass instigated, that became modified in the request of science, as it progress's and propels the student along with the anomalies that one's perceptions had encountered.

    Dynkin diagrams that if alloted to the way in which Baez talks about this, then how would such curvatures UV Gaussian coordinates or topologies, ever have been mapped from the 2d diagram to be viewed from these points drawn to a torus. Distances that would look so much different in how Gaussian coordinates are observed in relation to how these primes are aligned?

    The Riemann Hypothesis in Song

    Prime Obsession has an appendix containing the lyrics of Tom Apostol's song about the Riemann Hypothesis, with a full explanation of the lyrics. (Tom is Professor Emeritus of Mathematics at Caltech.)

    Now the piece mealing makes it hard for someone to see anything of significance if one only seen the minute part of the process, and in context of what math would mean to the underlying basis of reality. Pure thought, and pure math, which would not refute the way in which we dress up reality and hide this pure thought under the forms that we do.

    Andrey Kravstov

    If you held the view of supersymmetry at the beginning of Andrey's image, then how would you discern the lengths of lines held under these gravitational perspectives? While we are often treated to time clocks and such, Gaussian coordinates change the way we can see these lines. That's part of the change in perception.

    If one would have seen the gravitational collapse in context of the temperature values increased as this collapse, degrees in the boundaries of the blackhole then what have we been taken back too, instead of the singularities that are talked about in the production of the Princess's Pea, now, we see the superfluids?

    I would have to explain myself as I do that in terms of what has happened with how I see what Conformal theory and temperature valuation(Bekenstein Bound and the 5d recognition of what goes on the horizon) might have meant when looking at the blackhole horizon. How such quantum mechanical interpretations, would increase the "probabilities of things" happening in regards to those temperatures (entropic increase to expansive considerations), that we had contained the whole system, within these views, as it cooled.

    So if we thought of each collision process and all the scattering that went on in how we look at this in the Calorimeters, how well the concepts are considered along side of the energy valuation and primes?

    Boltzman, Pascal, and the basis of the ordering of the selection of these numbered systems and how they make themself known? While issuing from a such a pure state of 5d considerations what transpired to see pascal's triangle would/should include primes?

    IN binomial series such expressions are raised and probabilty characteristics, that would define position and momentum, as we see correlations to particle ejection formed from such collisions?

    One would have to know why this particular numbering system? What pattern is there?

                 1   2   3   4   5   6   7   8   9  10
    11 12 13 14 15 16 17 18 19 20
    21 22 23 24 25 26 27 28 29 30
    31 32 33 34 35 36 37 38 39 40
    41 42 43 44 45 46 47 48 49 50
    51 52 53 54 55 56 57 58 59 60
    61 62 63 64 65 66 67 68 69 70
    71 72 73 74 75 76 77 78 79 80
    81 82 83 84 85 86 87 88 89 90
    91 92 93 94 95 96 97 98 99 100

    .....and so on.

    Primes to 500

    2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47,
    53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127,
    131, 137, 139,149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197,
    199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277,
    281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367,
    373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449,
    457, 461, 463, 467, 479, 487, 491, 499, ...

    Eratosthenes (275-194 B.C., Greece) devised a 'sieve' to discover prime numbers. A sieve is like a strainer that you drain spaghetti through when it is done cooking. The water drains out, leaving your spaghetti behind. Eratosthenes's sieve drains out composite numbers and leaves prime numbers behind.

    How do such things make there way into reality and these prime numbers as signatures of the atoms and ways in which they would relate themself to this elemental table for viewing, and something then shifts in my perception. I don't know why?

    If you turn probabilities above all the things held to entropic design, held in context of this universe, then such probabilities would have had to been recognized?

    Does this bring us any closer to understanding of what issued from the mind of all probabilties, and in this, the idea of Bell's curve, or a bose condensate, or as a soliton form. In this situation, what said "this prime" to be associated to the probable outcome?

    Ramanujan Modular Forms

    Modular functions are used in the mathematical analysis of Riemann surfaces. Riemann surface theory is relevant to describing the behavior of strings as they move through space-time. When strings move they maintain a kind of symmetry called "conformal invariance"

    Conformal invariance (also called "scale invariance") is related to the fact that points on the surface of a string's world sheet need not be evaluated in a particular order. As long as all points on the surface are taken into account in any consistent way, the physics should not change. Equations of how strings must behave when moving involve the Ramanujan function.

    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 assigned 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.

    Riemann's Hypothesis was always held in my opinion in context of a 5D consideration as sounds analogy) of billiards balls making that clicking sound as they collide, or, as how Wayne Hu might look at the universe in it's hill and valleys.

    So looking at Heaven's ephemeral qualities, I could 't but help think of Ramanujan here, and the exercise of Hardy and the Taxi Cab.

    What was the pattern incited here that would be transfered to how we see probabilistic outcome reduced, from 5D considerations and higher. It had to be reduced, but how?

    Tuesday, December 13, 2005

    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:

    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.:)


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