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Showing posts with label Riemann Hypothesis. Show all posts
Showing posts with label Riemann Hypothesis. Show all posts

Monday, July 16, 2012

Where is Our Starting Point?



"The end he (the artist) strives for is something else than a perfectly executed print. His aim is to depict dreams, ideas, or problems in such a way that other people can observe and consider them." - M.C. Escher


Can you trace the patterns in nature toward matter manifestations?


To them, I said,
the truth would be literally nothing
but the shadows of the images.
-Plato, The Republic (Book VII)

The idea here is about how one's observation and model perceptions arises from some ordered perspective. Some use a starting point as an assumption of position. Do recognize "the starting point" in the previous examples?

 Cycle of Birth, Life, and Death-Origin, Indentity, and Destiny by Gabriele Veneziano


In one form or another, the issue of the ultimate beginning has engaged philosophers and theologians in nearly every culture. It is entwined with a grand set of concerns, one famously encapsulated in an 1897 painting by Paul Gauguin: D'ou venons-nous? Que sommes-nous? Ou allons-nous? "Where do we come from? What are we? Where are we going?"


The effective realization that particle constructs are somehow smaller windows of a much larger perspective fails to take in account this idea that I am expressing as a foundational approach to that starting point.




If you do not go all the way toward defining of that "point of equilibrium" how are you to understand how information is easily transferred to the individual from a much larger reality of existence? One would assume information is all around us? That there are multitudes of pathways that allow us to arrive at some some probability density configuration as some measure of an Pascalian ideal.

Of course there are problems with this in terms of our defining a heat death in individuals?

That's not possible so one is missing the understanding here about equilibrium. I might have said we are positional in terms of the past and the future with regard to memory and the anticipated future? How is that heat death correlated? It can't.

So you have to look for examples in relation to how one may arrive at that beginning point. Your theory may not be sufficiently dealing with the information as it is expressed in terms of your approach to the small window?

There are mathematical inspections here that have yet to be associated with more then discrete functions of reality as expressive building blocks of interpretation. The basic assumption of discrete function still exists in contrast to continuity of expression. This is the defining realization in assuming the model that MBT provides. I have meet the same logic in the differences of scientific approach toward the definition of what is becoming?

On the one hand, a configuration space as demonstrated by Tom that is vastly used in science. On the other, a recognition of how thick in measure viscosity is realized and what the physics is in this association. Not just the physical manifestation of, but of what happens when equilibrium is reached. Hot or very cold. Temperature, is not a problem then?

See my problem is that I can show you levitation of objects using superconductors but I cannot produce this in real life without that science. Yet, in face of that science I know that something can happen irregardless of what all the science said, so I am looking as well to combining the meta with the physical to realize that such a conditions may arise in how we as a total culture have accepted the parameters of our thinking.

So by dealing with those parameters I too hoped to see a cultural shift(paradigm and Kuhn) by adoption of the realization as we are with regard to the way in which we function in this reality. So if your thinking abut gravity how is this possible within the "frame work" to have it encroach upon our very own psychological makeup too?

Thursday, September 24, 2009

DNA Computing

DNA computing is a form of computing which uses DNA, biochemistry and molecular biology, instead of the traditional silicon-based computer technologies. DNA computing, or, more generally, molecular computing, is a fast developing interdisciplinary area. Research and development in this area concerns theory, experiments and applications of DNA computing See:DNA computing

***


Clifford of Asymptotia is hosting a guest post by Len Adleman: Quantum Mechanics and Mathematical Logic.


Today I’m pleased to announce that we have a guest post from a very distinguished colleague of mine, Len Adleman. Len is best known as the “A” in RSA and the inventor of DNA-computing. He is a Turing Award laureate. However, he considers himself “a rank amateur” (his words!) as a physicist.

Len Adleman-For a long time, physicists have struggled with perplexing “meta-questions” (my phrase): Does God play dice with the universe? Does a theory of everything exist? Do parallel universes exist? As the physics community is acutely aware, these are extremely difficult questions and one may despair of ever finding meaningful answers. The mathematical community has had its own meta-questions that are no less daunting: What is “truth”? Do infinitesimals exist? Is there a single set of axioms from which all of mathematics can be derived? In what many consider to be on the short list of great intellectual achievements, Frege, Russell, Tarski, Turing, Godel, and other logicians were able to clear away the fog and sort these questions out. The framework they created, mathematical logic, has put a foundation under mathematics, provided great insights and profound results. After many years of consideration, I have come to believe that mathematical logic, suitably extended and modified (perhaps to include complexity theoretic ideas), has the potential to provide the same benefits to physics. In the following remarks, I will explore this possibility.

*** 
 


See Also:
  • Riemann Hypothesis: A Pure Love of Math

  • Ideas on Quantum Interrogation

  • Mersenne Prime: One < the Power of two

  • Lingua Cosmica
  • Thursday, April 16, 2009

    Sacks Spiral

    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. Mathematics Problem That Remains Elusive —And Beautiful By Raymond Petersen


    Sacks Spiral of prime numbers


    Robert Sacks devised the Sacks spiral, a variant of the Ulam spiral, in 1994. It differs from Ulam's in three ways: it places points on an Archimedean spiral rather than the square spiral used by Ulam, it places zero in the center of the spiral, and it makes a full rotation for each perfect square while the Ulam spiral places two squares per rotation. Certain curves originating from the origin appear to be unusually dense in prime numbers; one such curve, for instance, contains the numbers of the form n2 + n + 41, a famous prime-rich polynomial discovered by Leonhard Euler in 1774. The extent to which the number spiral's curves are predictive of large primes and composites remains unknown.

    A closely related spiral, described by Hahn (2008), places each integer at a distance from the origin equal to its square root, at a unit distance from the previous integer. It also approximates an Archimedean spiral, but it makes less than one rotation for every three squares.



    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.). See more info on Mersenne Prime.

    ***


    See:
  • Quantum Mechanics: Determinism at Planck Scale
  • The Whole World is a Stage
  • Nature's Experiment on the Meaning of Weight
  • Friday, January 02, 2009

    The Whole World is a Stage

    Euler product formula


    Now you must know what sets my mind to think in such abstract spaces. "Probability of seeing a stage in a concert."

    All The World's A Stageby William Shakespeare
    From: As you Like It, Act II Scene VII

    Jaques:All the world's a stage,
    And all the men and women merely players:
    They have their exits and their entrances;
    And one man in his time plays many parts,
    His acts being seven ages. At first the infant,
    Mewling and puking in the nurse's arms.
    And then the whining school-boy, with his satchel
    And shining morning face, creeping like snail
    Unwillingly to school. And then the lover,
    Sighing like furnace, with a woeful ballad
    Made to his mistress' eyebrow. Then a soldier,
    Full of strange oaths and bearded like the pard,
    Jealous in honour, sudden and quick in quarrel,
    Seeking the bubble reputation
    Even in the cannon's mouth. And then the justice,
    In fair round belly with good capon lined,
    With eyes severe and beard of formal cut,
    Full of wise saws and modern instances;
    And so he plays his part. The sixth age shifts
    Into the lean and slipper'd pantaloon,
    With spectacles on nose and pouch on side,
    His youthful hose, well saved, a world too wide
    For his shrunk shank; and his big manly voice,
    Turning again toward childish treble, pipes
    And whistles in his sound. Last scene of all,
    That ends this strange eventful history,
    Is second childishness and mere oblivion,
    Sans teeth, sans eyes, sans taste, sans everything.


    So of course I am in this space of a kind looking and trying to orientate to watch the performance. My position to the stage, from the stage to myself. Whose to think such formulas would provide a solid description of the effort? So now I am embroiled in information of all kinds here. Shakespeare plays on.

    "Liesez Euler, Liesez Euler, c'est notre maître à tous"
    ("Read Euler, read Euler, he is our master in everything")
    - Laplace


    The world can be a interesting place once you see it's multi-dimensional ability to have more information then what is apparent around us. We have to open our eyes and listen more carefully. Are you listening Glaucon?:)

    "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." Mathematics Problem That Remains Elusive—And Beautiful By Raymond Petersen


    So in general such a space when held to the "thinking of points" what is it that shall gauge the thinking mind to think it is possible to explain itself "as gaps within the apparent world" of the everyday? Shall every person care when they are embroiled within the business of the media reported? Do you think the person next to you does not care about the world? Do you not think they experience? The voice is cast from the stage and all is heard in it's reverberations. No head involved, just the bouncing and measure of distance, in an echo of reason. Does an elemental thought have no substance?

    Prime Numbers Get Hitched by Marcus du Sautoy • Posted March 27, 2006 12:40 AM

    It would also prove to be significant in confirming the connection between primes and quantum physics. Using the connection, Keating and Snaith not only explained why the answer to life, the universe and the third moment of the Riemann zeta function should be 42, but also provided a formula to predict all the numbers in the sequence. Prior to this breakthrough, the evidence for a connection between quantum physics and the primes was based solely on interesting statistical comparisons. But mathematicians are very suspicious of statistics. We like things to be exact. Keating and Snaith had used physics to make a very precise prediction that left no room for the power of statistics to see patterns where there are none.

    Mathematicians are now convinced. That chance meeting in the common room in Princeton resulted in one of the most exciting recent advances in the theory of prime numbers. Many of the great problems in mathematics, like Fermat's Last Theorem, have only been cracked once connections were made to other parts of the mathematical world. For 150 years many have been too frightened to tackle the Riemann Hypothesis. The prospect that we might finally have the tools to understand the primes has persuaded many more mathematicians and physicists to take up the challenge. The feeling is in the air that we might be one step closer to a solution. Dyson might be right that the opportunity was missed to discover relativity 40 years earlier, but who knows how long we might still have had to wait for the discovery of connections between primes and quantum physics had mathematicians not enjoyed a good chat over tea.




    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.). See more info on Mersenne Prime.




    So of course, how many ways can one travel to get too?

    The river Pregel divides the town of Konigsberg into four separate land masses, A, B, C, and D. Seven bridges connect the various parts of town, and some of the town's curious citizens wondered if it were possible to take a journey across all seven bridges without having to cross any bridge more than once. All who tried ended up in failure, including the Swiss mathematician, Leonhard Euler (1707-1783)(pronounced "oiler"), a notable genius of the eighteenth-century.

    As a lay person being introduced to the strange world of mathematics it is always interesting to me in the way one can see in abstract processes.

    The Bridges of KonigsbergThe Beginnings of Topology...The Generalization to Graph Theory
    Euler generalized this mode of thinking by making the following definitions and proving a theorem:

    Definition: A network is a figure made up of points (vertices) connected by non-intersecting curves (arcs).

    Definition: A vertex is called odd if it has an odd number of arcs leading to it, other wise it is called even.

    Definition: An Euler path is a continuous path that passes through every arc once and only once.

    Theorem: If a network has more than two odd vertices, it does not have an Euler path.

    Euler also proved the converse:

    Theorem: If a network has two or less odd vertices, it has at least one Euler path.

    Thursday, September 11, 2008

    Nature's Experiment on the Meaning of Weight

    "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." Mathematics Problem That Remains Elusive—And Beautiful By Raymond Petersen


    This picture resides at the bottom of my Blogger for a reason. It is to remind me of what was given esoterically for fermentation on what it's meaning may have in my own life. in another culture it might have been referred to as a "Kōan." Persistence, is the key to unlocking these "time capsules." Accessibility, is the rule of thumb about "infinite regressions" under a logical format of reasoned inductive/deductive application. The modelled approach here recognized under the picture of Raphael and the school's of Athens early descendants. What place does this have for any student who has a teacher that resides in them? What will be your accomplishment in life?

    If the heart was free from the impurities of sin, and therefore lighter than the feather, then the dead person could enter the eternal afterlife

    You had to know what pain and suffering is, in relation to sin. Your conscience rules you and in it there is a "voice of reason." Sets the trials and tribulations before you. And somehow our youth have detached themself from any causations as to their destinies?

    If you have never considered what "truth(feather) had for meaning in historical times" how would you know what is being imparted to the youth of today? That what is now seen/felt in the world, is not recognized. Choosing "the heart" in that sense, and a scale to boot, I push forward this relation here under the auspice of "weight and measure as a paradox for examination. That such a measure in scale of those ancient times, might spark one to think about the experiment I am showing under this blog post heading.

    This post has been brewing for some time, and only recently the comment made was included to help ignited some of the thoughts I have had about the "weight of something" tied to some method of sound and a gravitational inclination to the pursuances I have of inclusion to colour and sound respectively.


    I think this is a nice historical consideration toward a "new culture."

    I was looking for something even more natural.

    No "sky hooks" but some place to which this process is tied.

    A gourd of water perhaps, tied to a string and the weight of this gourd adjusted by volume, to embed in the string different tension properties and sound characterizations.


    I do not mean to discredit the young scientist here by connection of this comment, but to attached to what seems relevant to me the natural appearance of a counting system, to a method of "fingerprinting" accord to a natural explanation of curvatures in space.


    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.)
    See:Mersenne Prime: One < the Power of two

    Pacal's Triangle See:Blaise Pascal

    Why only this one time( a numbered base not less then one ensuing from Pascal's triangle on Fibonacci) and I think to differ, that Riemann(Riemann Hypothesis) saw a unique opportunity here. To allow nature to express itself in "non-euclidean terms," that makes for the naturalness of sound to exemplify this unique quality, and an attachment to "colour of gravity" which is exhibited toward my understandings.

    That I may have gone "one step further" on the basis of my "emotive, mental and spiritual search correlations. A search, with respect toward the qualities of gravity. Here it could have been made from the insight of Einsteins example of a "pretty girl and a hot stove?" That "pain" and "excitement" have different values when assigned to a relational quality close to "body home," versus, it's gravitational freedoms, and fleeting examples, that beauty, and mental states can have in "time relational values."

    See:Dialogos of Eide: A New Culture?

    Monday, February 04, 2008

    Mind Maps: Mathematical Structures?


    Plato's doctrine of recollection, however, addresses such criticism by saying that souls are born with the concepts of the forms, and just have to be reminded of those concepts from back before birth, when the souls were in close contact with the forms in the Platonic heaven. Plato is thus known as one of the very first rationalists, believing as he did that humans are born with a fund of a priori knowledge, to which they have access through a process of reason or intellection — a process that critics find to be rather mysterious


    What are Mind Maps?


    A mind map is a diagram used to represent words, ideas, tasks or other items linked to and arranged radially around a central key word or idea. It is used to generate, visualize, structure and classify ideas, and as an aid in study, organization, problem solving, decision making, and writing.

    It is an image-centered diagram that represents semantic or other connections between portions of information. By presenting these connections in a radial, non-linear graphical manner, it encourages a brainstorming approach to any given organizational task, eliminating the hurdle of initially establishing an intrinsically appropriate or relevant conceptual framework to work within.

    A mind map is similar to a semantic network or cognitive map but there are no formal restrictions on the kinds of links used.

    The elements are arranged intuitively according to the importance of the concepts and they are organized into groupings, branches, or areas. The uniform graphic formulation of the semantic structure of information on the method of gathering knowledge, may aid recall of existing memories.


    Well straight to the point then I guess.

    Bee:
    The important thing about the basis of our societies is not actually its fixed structure but the way to readjust it. A bit of scientific method would be good there.


    As I mentioned previously on Backreaction site and in giving subsequent information about this process. It has been a journey of my own discovery, that I would say that at the basis of reality is such a mathematical structure.

    I know when this process started for me and it would not serve any purpose at this point to speak to it directly. People have their reasons for and against such a proposal as their being such a mathematical structure, so what currently leads me to say that their are these two opposing views?


    Wigner’s Gift Horse By JULIE REHMEYER • Feb 1, 2008 See here for article.

    Stephen Wolfram argues that the way to unlock the rest of science is to give up on mathematics and look for explanations analogous to computer code. Very simple computer programs can produce remarkably complex behavior that mimics phenomena science has had difficulty modeling, like the motion of fluids, for example. So studying the behavior of these programs may provide scientists with new insights about these phenomena. Indeed, Wolfram thinks the universe itself may be generated by a computer program simple enough to be expressed in a few lines of code. “If the laws are simple enough, if we look in the right way we’ll find them,” he says. “If they’re not, it will be tougher. The history of physics makes one pessimistic that we could ever end physics. I don’t share that pessimism.”


    Tegmark believes in an extreme form of Platonism, the idea that mathematical objects exist in a sort of universe of their own. Imagine that, Tegmark says, “there’s this museum in this Platonic math space that has these mathematical objects that exists outside of space and time,” Tegmark says. “What I’m saying is that their existence is exactly the same as a physical existence, and our universe is one of these guys in the museum.”


    Also worth reading is the sum of any position that would infer the stance of Plato versus anti-Plato, to help distinguish whether or not one might have something of value in terms of the question of whether Mathematics is invented or discovered.

    Mathematical Platonism and its Opposites by Barry Mazur January 11, 2008. See here.

    For the Platonists. One crucial consequence of the Platonic position is that it views mathematics as a project akin to physics, Platonic mathematicians being—as physicists certainly are—describers or possibly predictors—not, of course, of the physical world, but of some other more noetic entity. Mathematics—from the Platonic perspective—aims, among other things, to come up with the most faithful description of that entity.


    For the Anti-Platonists. Here there are many pitfalls. A common claim, which is meant to undermine Platonic leanings, is to introduce into the discussion the theme of mathematics as a human, and culturally dependent pursuit and to think that one is actually conversing about the topic at hand.


    Mapping the interaction from a scientific point of view?

    As I read through the article I had previous insights while reading through Sir Roger Penrose's lecture on the Extended Physical WorldView. While I myself had picked the title, it would have been nicer to show the very image on the start of that lecture.



    This is a important statement I am making below because it distinguishes between where we think we might be going in terms of computer technologies versus what will always remain within the human domain.


    So on the one hand one might think about technologies in the 21st Century and wonder if computer technology can ever reach the status of Consciousness with which the "synaptic event" could include images, all the while it would include all the history to that point?


    While it is never clear to me about the origins of the universe, it had some relation in my mind to what first allowed any soul's expression. While I had shown the relation to the synaptic event, there had to be a place created for such an expression, to be fortunate and validated.

    Do I know what plan for every individual is, of course not, but that you choose such an expression is self evident. There is much to the word, "self evident" that remains to be explored within context of this site, and of value, in the iconic image of Raphael's expression with Plato and Aristotle at it's centre.

    Now, neuronic networking is supposedly the platform computer technologies can take in their designs, but what true aspect of the emergent process could ever define the human being and one's potential? The information that could enter such an synaptic event within your own thinking mind?

    So the process is one of self discovery. About processes within your own self that allow one to possibly develop the new mathematics that speak directly to the very unfolding of the universe?

    The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Eugene Wigner

    The great mathematician fully, almost ruthlessly, exploits the domain of permissible reasoning and skirts the impermissible. That his recklessness does not lead him into a morass of contradictions is a miracle in itself: certainly it is hard to believe that our reasoning power was brought, by Darwin's process of natural selection, to the perfection which it seems to possess. However, this is not our present subject. The principal point which will have to be recalled later is that the mathematician could formulate only a handful of interesting theorems without defining concepts beyond those contained in the axioms and that the concepts outside those contained in the axioms are defined with a view of permitting ingenious logical operations which appeal to our aesthetic sense both as operations and also in their results of great generality and simplicity.

    [3 M. Polanyi, in his Personal Knowledge (Chicago: University of Chicago Press, 1958), says: "All these difficulties are but consequences of our refusal to see that mathematics cannot be defined without acknowledging its most obvious feature: namely, that it is interesting" (p 188).]


    What can arise from any person, to have defined that it reaches back into the forms. That it chooses to manifest "as the person" you have become? What lies dormant, that you awake to it in such a way that it will manifest in all that you do, and become part of the "history of recollection" that you unfold in this life, and have learnt these things before? You dream?

    I, Robot:

    ....signs of new life emerge as images photonically flicker in the new logic forming apparatus....

    I had a dream....


    We might like to think that computers are capable, while the very idea of the "image" holds such vasts amount of information. This is not a new idea from an historical perspective if one ever thought to consider the alchemists of our early science.

    How would you contain all the probability and outcomes, with ever looking beyond space and time, to realize that the "heavens" in some way, meet the earth. Manifest within you? Can find re-birthing through you? Inner/outer become one.

    Thursday, October 11, 2007

    Comparing Amplitutdes of the String

    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.


    So one tends to get in this mode of thinking, that the way in which one measures "aspects of reality" is somehow couched in the mathematics of a kind, and unbeknownst to us, a hoped a pattern is revealed?

    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


    To have gone to such extremes of thinking of the reality as one would of the elemental design, one hopes to see the "new perspective" will encourage new pathways to develping new phenomenological directions.

    As absurd as this sounds, the current framework did not support the existing structure any longer in regards to sciences development, so theoretical insight needed to be pushed. New ways in which we could look at reality could provide for new experimental considerations?

    It would not be unlike Bohm to introduce his system, and then ask us to think i the possible new way in which language has somehow been transformed. Does it not seem by our very nature, language accustoms perspective to have it's natural physical gestures as expression? Not just physical, but mental as well?

    Friday, October 05, 2007

    Euler's Konigsberg's Bridges Problem

    "Liesez Euler, Liesez Euler, c'est notre maître à tous"
    ("Read Euler, read Euler, he is our master in everything") -
    Laplace


    I should say here that the post by Guest post: Marni D. Sheppeard, “Is Category Theory Useful ?” over at A Quantum Diaries Survivor, continues to invoke my minds journey into the abstract spaces of mathematics.

    The river Pregel divides the town of Konigsberg into four separate land masses, A, B, C, and D. Seven bridges connect the various parts of town, and some of the town's curious citizens wondered if it were possible to take a journey across all seven bridges without having to cross any bridge more than once. All who tried ended up in failure, including the Swiss mathematician, Leonhard Euler (1707-1783)(pronounced "oiler"), a notable genius of the eighteenth-century.

    As a lay person being introduced to the strange world of mathematics it is always interesting to me in the way one can see in abstract processes.

    The Beginnings of Topology...The Generalization to Graph Theory
    Euler generalized this mode of thinking by making the following definitions and proving a theorem:

    Definition: A network is a figure made up of points (vertices) connected by non-intersecting curves (arcs).

    Definition: A vertex is called odd if it has an odd number of arcs leading to it, other wise it is called even.

    Definition: An Euler path is a continuous path that passes through every arc once and only once.

    Theorem: If a network has more than two odd vertices, it does not have an Euler path.

    Euler also proved the converse:

    Theorem: If a network has two or less odd vertices, it has at least one Euler path.


    Leonhard Paul Euler (pronounced Oiler; IPA [ˈɔʏlɐ]) (April 15, 1707 – September 18 [O.S. September 7] 1783) was a pioneering Swiss mathematician and physicist, who spent most of his life in Russia and Germany. He published more papers than any other mathematician of his time.[2]

    Euler made important discoveries in fields as diverse as calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function.[3] He is also renowned for his work in mechanics, optics, and astronomy.


    Portrait by Johann Georg Brucker- Born April 15, 1707(1707-04-15)Basel, Switzerland and Died September 18 [O.S. September 7] 1783
    St Petersburg, Russia


    You have to understand that as a lay person, my education is obtained through the internet. This is not without years of study(many books) in a lot of areas, that I could be said I am in a profession of anything, other then the student, who likes to learn a lot.

    To find connections between the "real world" and what a lot think of as "to abstract to be real."

    Any such expansionary mode of thinking, if not understood, as in the Case of Riemann's hypothesis seen in relation to Ulam's Spiral, one might have never understood the use of "Pascal's triangle" as well.

    These are "base systems of mathematics" that are describing processes in nature?

    See:Euler - 300th anniversay lecture

    Friday, September 28, 2007

    The History of Magnetic Vision

    Grossmann is getting his doctorate on a topic that is connected with non-Euclidean geometry. I don’t know what it is.
    Einstein to Mileva Maric,1902


    Animal Navigation

    The long-distance navigational abilities of animals have fascinated humans for centuries and challenged scientists for decades. How is a butterfly with a brain weighing less than 0.02 grams able to find its way to a very specific wintering site thousands of kilometers away, even though it has never been there before? And, how does a migratory bird circumnavigate the globe with a precision unobtainable by human navigators before the emergence of GPS satellites? To answer these questions, multi-disciplinary approaches are needed. A very good example of such an approach on shorter distance navigation is the classical ongoing studies on foraging trips of Cataglyphis desert ants. My Nachwuchsgruppe intends to use mathematical modelling, physics, quantum chemistry, molecular biology, neurobiology, computer simulations and newly developed laboratory equipment in combination with behavioral experiments and analyses of field data to achieve a better understanding of the behavioral and physiological mechanisms of long distance navigation in insects and birds.


    Tony Smith has some interesting information in response to a post by Clifford of Asymptotia.

    Clifford writes:
    This is simply fascinating. I heard about it on NPR. While it is well known that birds are sensitive to the earth’s magnetic field, and use it to navigate, apparently it’s only been recently shown that this sensitivity is connected directly to the visual system (at least in some birds). The idea seems to be that the bird has evolved a mechanism for essentially seeing the magnetic field, presumably in the sense that magnetic information is encoded in the visual field and mapped to the brain along with the usual visual data


    While my post has been insulted by cutting it short(and stamping it and proclaiming irrelevance,) I'd like to think otherwise, even in face of his streamlining that Clifford likes to do. His blog, he can do what he wants of course.

    In any case, it seems reasonable to agree with Buhler, who concludes in his biography of Gauss that "the oft-told story according to which Gauss wanted to decide the question [of whether space is perfectly Euclidean] by measuring a particularly large triangle is, as far as we know, a myth."



    So I'll repeat the post of mine here and the part, that he has deleted. You had to know how to see the relevance of the proposition of birds in relation to the magnetic field of the earth, to know why the bird relation is so important.

    On Magnetic vision
    Rupert Sheldrake has had similar thoughts on this topic.

    "Numerous experiments on homing have already been carried out with pigeons. Nevertheless, after nearly a century of dedicated but frustrating research, no one knows how pigeons home, and all attempts to explain their navigational ability in terms of known senses and physical forces have so far proved unsuccessful. Researchers in this field readily admit the problem. 'The amazing flexibility of homing and migrating birds has been a puzzle for years. Remove cue after cue, and yet animals still retain some backup strategy for establishing flight direction.' 'The problem of navigation remains essentially unsolved.'


    Many of academics might have steered clear because of the the thoughts and subject he has about this? It seems to me that if this information is credible, then some of Rupert's work has some substance to it and hence, brings some credibility to the academic outlook?

    Update: Here I am adding some thoughts in regards to Rupert Sheldrake that I was having while reading his work. He had basically himself denounced the process of birds having an physiological connection to magnetic fields because of not having any information to support the magnetic vision Clifford is talking about. So Rupert moves beyond this speculation, to create an idea about what he calls Morphic resonance with regards to animals.

    So Rupert presents future data and theoretics in face of what we now know in terms of the neurological basis is experimentally being talked about in the article in question Clifford is writing about.

    On How to see in the Non Euclidean Geometrical World

    8.6 On Gauss's Mountains


    One of the most famous stories about Gauss depicts him measuring the angles of the great triangle formed by the mountain peaks of Hohenhagen, Inselberg, and Brocken for evidence that the geometry of space is non-Euclidean. It's certainly true that Gauss acquired geodetic survey data during his ten-year involvement in mapping the Kingdom of Hanover during the years from 1818 to 1832, and this data included some large "test triangles", notably the one connecting the those three mountain peaks, which could be used to check for accumulated errors in the smaller triangles. It's also true that Gauss understood how the intrinsic curvature of the Earth's surface would theoretically result in slight discrepancies when fitting the smaller triangles inside the larger triangles, although in practice this effect is negligible, because the Earth's curvature is so slight relative to even the largest triangles that can be visually measured on the surface. Still, Gauss computed the magnitude of this effect for the large test triangles because, as he wrote to Olbers, "the honor of science demands that one understand the nature of this inequality clearly". (The government officials who commissioned Gauss to perform the survey might have recalled Napoleon's remark that Laplace as head of the Department of the Interior had "brought the theory of the infinitely small to administration".) It is sometimes said that the "inequality" which Gauss had in mind was the possible curvature of space itself, but taken in context it seems he was referring to the curvature of the Earth's surface.
    See:Reflections on Relativity

    As a layperson, Riemann and Gauss were instrumental for helping me see beyond what we were accustom to in Euclidean, so I find Clifford's blog post extremely interesting as well. Maybe even a biological/physiological impute into our senses as well? Who knows?:)

    Einstein's youth and the compass, becomes the motivation that drives the vision of what exists beyond what was acceptable in that youth. The mystery. Creates a new method on how we view the world beyond the magnetic, to help us include the view in the gravitational one as well.

    From a early age, young Albert showed great interest in the world around him. When he was five years old, his father gave him a compass, and the child was enchanted by the device and intrigued by the fact the needle followed a invisible field to point always in the direction of the north pole.Reminiscing in old age, Einstein mentioned this incident as one of the factors that perhaps motivated him years later to study the gravitational field. God's Equation, by Amir D. Aczel, Pg 14


    While something could exist that is abstract, like for instance the Gaussian arc, this inclusion in the value of general relativity is well known. Mileva's response in quote above was the key for Einstein's views on developing General Relativity, and without it "electromagnetism would not, and could not" have been included geometrically in the theory of GR.

    It was a succession to "Gravitational wave production" that was understood in regards to Taylor and Hulse.


    The theory of relativity predicts that, as it orbits the Sun, Mercury does not exactly retrace the same path each time, but rather swings around over time. We say therefore that the perihelion -- the point on its orbit when Mercury is closest to the Sun -- advances.



    I would think this penduum exercise would make a deeper impression if held in concert with the way one might have look at Mercuries orbit.

    Or, binary pulsar PSR 1913+16 of Taylor and Hulse. These are macroscopic valutions in what the pendulum means. Would this not be true? See:Harmonic Oscillation

    I guess not every string theorist would know this? Maybe even Bee would understand that "German" is replace by another form of seeing using abstract language, for how everything can be seen in relation to the ground state? Where there are no gravitational waves, spacetime is flat.

    You had to know how such views on the navigation of the birds could have a direct link to the evolutionary output of the biology and physiology of the species. What Toposense?

    Yes it's a process where the mathematical minds look at knitting and such, in such modularc forms, to have said, "hey there is a space of thinking" that we can do really fancy twists and such.

    One thing us humans can certainly do is construct the monumental world reality with straight lines and such in the Euclidean view. But nature was there before we thought to change all it's curves.

    But the truth is, the Earth's topography is highly variable with mountains, valleys, plains, and deep ocean trenches. As a consequence of this variable topography, the density of Earth's surface varies. These fluctuations in density cause slight variations in the gravity field, which, remarkably, GRACE can detect from space. See: The Mind Field

    See here for more info on Grace.

    Look out into the wild world that nature itself presents and tell me what the ancient mind did not see. Native Americans lived closer to nature. Hopefully you'll understand why it is we must engage ourselves to experiencing the views of nature?:)

    Mandalic Construction

    See: The Last Mimzy

    The "Ancient Medicine wheels" might have been place accordingly? Do you imagine seeing in the abstract world, the magnetic view we see of earth in it's different disguise?

    So that last line about the "medicine wheels" probably caused Clifford to do what he did in regards to the post I wrote.

    Yes I am creating a direct link between the Medicine Wheels and the Medicine Wheel as a Mandala constructed by early Native Americans. Where they were shamanically placed on the earth.



    What is a Medicine Wheel?



    The term "medicine wheel" was first applied to the Big Horn Medicine Wheel in Wyoming, the most southern one known. That site consists of a central cairn or rock pile surrounded by a circle of stone; lines of cobbles link the central cairn and the surrounding circle. The whole structure looks rather like a wagon wheel lain-out on the ground with the central cairn forming the hub, the radiating cobble lines the spokes, and the surrounding circle the rim. The "medicine" part of the name implies that it was of religious significance to Native peoples.



    Figure 4 - Distribution of medicine wheel sites east of the Rockies


    What was of importance is the underlying psychological patterns that exist in the forms of Mandalas. That such a thing like the Medicine wheel, would retain a impact from one's life, to another life.

    There are various forms of mandalas with distinct concepts and different purposes. The individual representations range from the so-called Cosmic Mandalas, which transmit the ancient knowledge of the development of the universe and the world-systems which represents a high point among Mandalas dedicated to meditation; to the Mandalas of the Medicine Buddha which demonstrates how the Buddha-power radiates in all directions, portraying the healing power of the Buddha.

    It would not be easy to understand this "seed mandala" as it makes it way into conscious recognition. It arises to awareness through the subconscious pathway during our susceptibility in dream time. This open accessibility is the understanding that there is a closer connection to the universality of being, and the realization that the degrees beyond the "emotive body" is developing the understanding of the "mental one" as well as, leading to "the spiritual one."

    This comparative view is analogousness to development beyond the abstract view we see of earth in it's gravitational form.

    However, the signals that scientists hope to measure with LISA and other gravitational wave detectors are best described as "sounds." If we could hear them, here are some of the possible sounds of a gravitational wave generated by the movement of a small body inspiralling into a black hole.


    It would be much like a "energy packet" that would contain all that is demonstrated in "extravagant patterns." Look like a "flower in real life," or a "intricate pattern," while encouraging the person to explore these doorways and move on from.

    That seed contains all of the history we have supplanted to it by how we built previously and embedded all the philosophy we had learnt from it.

    The Emotional Body of the Earth

    Would to me seem very emotive in terms of it's weather. How such weather patterns spread across the earth. Also, it would not seem so strange then that while we would have seen polarization aspects in the cosmos, in terms of magnetic field variances in relation to north and south, we would see "this of value" in the earth as well?

    So would the earth have it's positive and negative developments in relation to aspect of it's weather? Most certainly psychological when the snows have lasted so long, one could indeed wish for warmer weather, but that's not what I mean. I mean on a physiological level, such ionic generations would indeed cause the state of the human body to react.

    Sunday, April 22, 2007

    Prime Numbers and the Landscape

    It would also prove to be significant in confirming the connection between primes and quantum physics. Using the connection, Keating and Snaith not only explained why the answer to life, the universe and the third moment of the Riemann zeta function should be 42, but also provided a formula to predict all the numbers in the sequence. Prior to this breakthrough, the evidence for a connection between quantum physics and the primes was based solely on interesting statistical comparisons. But mathematicians are very suspicious of statistics. We like things to be exact. Keating and Snaith had used physics to make a very precise prediction that left no room for the power of statistics to see patterns where there are none.

    Mathematicians are now convinced. That chance meeting in the common room in Princeton resulted in one of the most exciting recent advances in the theory of prime numbers. Many of the great problems in mathematics, like Fermat's Last Theorem, have only been cracked once connections were made to other parts of the mathematical world. For 150 years many have been too frightened to tackle the Riemann Hypothesis. The prospect that we might finally have the tools to understand the primes has persuaded many more mathematicians and physicists to take up the challenge. The feeling is in the air that we might be one step closer to a solution. Dyson might be right that the opportunity was missed to discover relativity 40 years earlier, but who knows how long we might still have had to wait for the discovery of connections between primes and quantum physics had mathematicians not enjoyed a good chat over tea.


    Seed magazine has become a extremely interesting resource material for the latest in who's doing what in terms of science. As most know Riemann's thought process has become part of the revolution in my own thought processes. It has taken me on a journey in terms of the abstract. What was used in Einstein's revolutionary break through in terms of curvatures in spacetime. Rivals Gaussian coordinates. It is nice to know, that Riemann's teacher had the same ability of thinking in the mathematical abstract

    Friday, March 23, 2007

    Lingua Cosmica

    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.). See more info on Mersenne Prime.

    I always find it interesting that the ability of the mind to do it's gymnastics, had to have some "background information" with which we could assign "the acrobatics of thinking" to special sequences. Thus create some commonality of exchange.

    Might we think the computerized world will give us an "human emotive side of being."

    See here for Against Symmetry explanation.

    So born from it's "original position" what asymmetry was produced to have the universe have it's special way with which it will deal with it's inhabitants? Any "point source" has a greater potential and from a "perfect symmetry" you had to know where this existed?

    Lee Smolin will then lead you away from perfect symmetry and explain why?

    G -> H -> ... -> SU(3) x SU(2) x U(1) -> SU(3) x U(1)

    Here, each arrow represents a symmetry breaking phase transition where matter changes form and the groups - G, H, SU(3), etc. - represent the different types of matter, specifically the symmetries that the matter exhibits and they are associated with the different fundamental forces of nature


    So why not think for a minute that if you had "crossed wires" how might you see the world and think, how strange a Synesthesist to have such "emotive reactions instantaneously" bring forth perceived coloured responses. Colours perhaps, as diverse as the Colour of Gravity?

    How much of a joke shall I play with peoples minds to think the choice of the observer has consequences? That those consequences are indeed coloured. If this is to much for you, and you say, "oh what a flowery pot I am with such a proposal," then think about "the concept" being used.

    The struggle for the emotive language to be explained to the everyday person, as if, the Synesthesist was being simple in their explanation? A "one inch" equation perhaps? They should be so lucky that they could explain themself while they toy with the world and try and make sense of it. That is how different it can be in finding some result of clarification.

    That is how foreign I would lead you to believe, that if I wish to communicate, that any language developed, was speaking directly to the source of all expressions, as if they had a geometrical explanation to it. Use of Riemann is understood i this way. It did not divorce him from his teacher, but added vitality tthe way in which we seen Gaussian Arcs and all.

    The Magic Square

    Hans_Freudenthal

    Hans Freudenthal (September 17, 1905 – October 13, 1990) was a Dutch mathematician born in Luckenwalde in Germany into a Jewish family. He made substantial contributions to algebraic topology and also took an interest in literature, philosophy, history and mathematics education.


    I had to think sometimes that what was common knowledge can sometimes be wrapped in up the language we use. So imagine for a time that you will go out and change the way we see the world and add this particular model of String theory just to confuse the heck out of us all.

    Lincos

    Lincos (an abbreviation of the Latin phrase lingua cosmica) is an artificial language first described in 1960 by Dr. Hans Freudenthal and described in his book Lincos: Design of a Language for Cosmic Intercourse, Part 1. It is a language designed to be understandable by any possible intelligent extraterrestrial life form, for use in interstellar radio transmissions.


    Do you want to take the time and consult with the aliens we have on this earth? :) Now surely you know I jest, because of the way in which this model asks a us to look at the world. What use you say?

    Please don't confuse this language adaptation to the "ignorance and arrogance" of the "Lincos," a being something other then the human beings who are trying to get a GRIP ON OUR PERSPECTIVES. ASKING US TO SEE IN WAY THAT WE ARE NOT TO ACCUSTOM Too.

    Were it Perfect, Would it Work Better?-Bruno Bassi

    5.1. Communication vs Formalization

    The idea of applying achievements from symbolic logic to the design of a complete language is deeply linked to a strong criticism towards the dominant 20th century trend of considering formal languages as a subject matter in themselves and of using them almost exclusively for inquiries about the foundations of mathematics. "In spite of Peano's original idea, logistical language has never been used as a means of communication ... The bounds with reality were cut. It was held that language should be treated and handled as if its expressions were meaningless. Thanks to a reinterpretation, 'meaning' became an intrinsic linguistic relation, not an extrinsic one that could link language to reality" (p. 12).

    In order to rescue the original intent of formal languages, Lincos is bound to be a language whose purpose is to work as a medium of communication between people, rather than serve as a formal instrument for computing. It should allow anything to be said, nonsense included. In Lincos, "we cannot decide in a mechanical way or on purely syntactic grounds whether certain expressions are meaningful or not. But this is no disadvantage. Lincos has been designed for the purpose of being used by people who know what they say, and who endeavor to utter meaningful speech" (p. 71).

    As a consequence, Lincos as a language is intentionally far from being fully formalized, and it has to be that way in order to work as a communication tool. It looks as though the two issues of communication and formalization radically tend to exclude each other. What Lincos seems to tell us is that formalization in the structure of a language can hardly generate straightforward understanding.

    Our Dr. Freudenthal saw very well this point. "there are different levels of formalization and ... in every single case you have to adopt the one that is most adaptable to the particular communication problem; if there is no communication problem, if nothing has to be communicated in the language, you can choose full formalization" (Freudenthal 1974:1039).

    But then, how can the solution of a specific communication problem ever bring us closer to the universal resolution of them all? Even in case the Lincos language should effectively work with ETs, how could it be considered as a step towards the design of a characteristica universalis? Maybe Dr. Freudenthal felt that his project needed some philosophical justification. But why bother Leibniz?

    Lincos is there. In spite of its somewhat ephimeral 'cosmic intercourse' purpose it remains a fascinating linguistic and educational construction, deserving existence as another Toy of Man's Designing.

    Friday, February 23, 2007

    Where are my keys?

    "Yet I exist in the hope that these memoirs, in some manner, I know not how, may find their way to the minds of humanity in Some Dimensionality, and may stir up a race of rebels who shall refuse to be confined to limited Dimensionality." from Flatland, by E. A. Abbott




    The Extra-Dimensions?


    So you intuitively believe higher dimensions really exist?

    Lisa Randall:I don't see why they shouldn't. In the history of physics, every time we've looked beyond the scales and energies we were familiar with, we've found things that we wouldn't have thought were there. You look inside the atom and eventually you discover quarks. Who would have thought that? It's hubris to think that the way we see things is everything there is.


    And what is it that we don't see? I thought of a comment somewhere that spoke about what first started to make it's appearance in how we communicate?

    Time is the Unseen fourth Dimension

    They were able to create what we recognize today as the "elliptical" and "hyperbolic" non-Euclidean geometries. Most of Saccheri's first 32 theorems can be found in today's non-Euclidean textbooks. Saccheri's theorems are prefaced by "Sac."

    One of my greatest "aha moments" came when I realized Non-euclidean geometries. I had to travel the history first with Giovanni Girolamo Saccheri, Bolya and Lobachevsky, for this to make an impression, and I can safely say, that learning of Gauss and Riemann, I was truly impressed.

    Einstein had to include that "extra dimension of time." Greater then, or less then, 180 degrees and we know "this triangle" can take on some funny shapes when you apply them "to surfaces" that are doing funny things.?:)



    Second, we must be wary of the "God of the Gaps" phenomena, where miracles are attributed to whatever we don't understand. Contrary to the famous drunk looking for his keys under the lamppost, here we are tempted to conclude that the keys must lie in whatever dark corners we have not searched, rather than face the unpleasant conclusion that the keys may be forever lost.


    Let me just say that "it is not the fact that any drinking could have held the mind" of the person, but when they absentmindedly threw their car keys. The "point is" that if the light shines only so far, what conclusion should we live with?

    Moving to the Fifth

    So of course whatever real estate you are buying, make sure the light is shining on what your willing to purchase? Is this not a good lesson to learn?

    Moving any idea to a fifth dimension I thought was important in relation to seeing what Einstein had done. See further: Concepts of the Fifth Dimension. I illustrate more ways in which we may see that has not been seen for most could have helped the mind see how this is accomplished in current day geometric methods.

    Why was this thought "wrong" when one may of thought to include "gravity and light" together, after the conclusion of spacetime's 3+1? Gravity. What Had Maxwell done? What Had Riemann done?

    You knew "the perfect symmetry" had to be reduced to General Relativity?

    Greg Landsberg:
    Two types of the extra-dimensional effects observable at collides.



    A graviton leaves our world for a short moment of time, just to come back and decay into a pair of photons (the DØ physicists looked for that particular effect).

    A graviton escapes from our 3-dimensional world in extra dimensions (Megaverse), resulting in an apparent energy non-conservation in our three-dimensional world.
    So why would it matter to us if the universe has more than 3 spatial dimensions, if we can not feel them? Well, in fact we could “feel” these extra dimensions through their effect on gravity. While the forces that hold our world together (electromagnetic, weak, and strong interactions) are constrained to the 3+1-“flat” dimensions, the gravitational interaction always occupies the entire universe, thus allowing it to feel the effects of extra dimensions. Unfortunately, since gravity is a very weak force and since the radius of extra dimensions is tiny, it could be very hard to see any effects, unless there is some kind of mechanism that amplifies the gravitational interaction. Such a mechanism was recently proposed by Arkani-Hamed, Dimopoulos, and Dvali, who realized that the extra dimensions can be as large as one millimeter, and still we could have missed them in our quest for the understanding of how the universe works!


    Of course these ideas are experimentally being challenged, like any good scientist would want of his theory. See EOT-WASH GROUP(4)

    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.

    Friday, January 05, 2007

    Images or Numbers By Themself

    “Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the mind will never penetrate” (cited by Ivars Peterson in Science News, 5/4/2002).


    I have an idea in mind here that will be slow to show because I am not sure how it is supposed to be laid out. So maybe by showing these numbers by them self? What use, if one did not, or was not able to see in another way?


    Figure 22.10: Double slit diffraction


    I looked at the "straight lines" of Thomas Young's trajectories of photon emission and while quite understandably shown to be of consequence in this post "Interference." I was more interested in how something could start off in one place and do this rotation of sorts, and then come back for examination again in the real world. The Spectrum

    Plato:
    What a novel idea to have the methods used by the predecessors like Maxwell, to have been united from Faraday's principals? To have Maxwell's equation Gaussian in interpretation of Riemann geometry, somehow, united by the geometries of Einstein and defined as gravity?


    But it is also in mind "that the image" has to be put here also before the numbers can show them self. What use these numbers if I do not transcend them to what they can imply in images, to know that the thinking here has to be orientated in such a way that what was simple and straight forward, could have non-euclidean orientations about it?


    Michael Faraday (September 22, 1791 – August 25, 1867) was a British scientist (a physicist and chemist) who contributed significantly to the fields of electromagnetism and electrochemistry.


    So one reads history in a lot of ways to learn of what has manifested into todays thinking. What lead from "Gaussian coordinates in an "non-euclidean way" to know that it had it's relation in today's physics. To have it included in how we see the consequences of GR in the world. It had been brought together for our eyes in what the photon can do in the gravitational field.

    Our Evolution to Images


    The Albrecht Durer's Magic Square



    Ulam's Spiral



    Pascal's Triangle


    Evolve to What?

    Who was to know what Leonard Susskind was thinking when his mathematical mind was engaged in seeing this "rubber band" had some other comparative abstraction, as something of consequence in our world. Yet, people focus on what they like to focus on, other then what "lead the mind" to think the way they do?


    Poincaré Conjecture
    If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface. On the other hand, if we imagine that the same rubber band has somehow been stretched in the appropriate direction around a doughnut......


    I have to rest now.