Thank you for explaining eigen values and vector nicely....Can you give some physical examples for these....

Best Regards

=snp.gupta

Eckard,

Hilbert's program did not concern Hilbert spaces. He designed an axiomatic form of physics that treated geometry in a similar way as Einstein did with his general relativity. https://en.wikipedia.org/wiki/David_Hilbert#Axiomatization_of_geometry Further, he indicated a list of problems that were not yet solved.

https://en.wikipedia.org/wiki/David_Hilbert#The_23_problems

Hilbert spaces were the result of his work of functional analysis, which was very successful.

In quaternionic algebra, the square root of -1 has many solutions that are all normalized three-dimensional (imaginary) vectors. Quaternions can be split into two complex numbers. The bi-quaternions are four-dimensional objects that have complex coefficients. The corresponding number system is not a division ring. In a division ring, all non-zero members own a unique inverse. Real numbers, complex numbers, and quaternions form division rings.

Satyavarapu,

The timestamp and the location of an elementary particle are combined in a quaternion and then stored as an eigenvalue of a private operator. The corresponding eigenvalue spans a ray (a one-dimensional subspace). At every progression instant, a private mechanism provides this operator with a new location. The mechanism applies a stochastic process. Therefore, the elementary particle hops around in a stochastic hopping path. The hop landing locations form a coherent location swarm. The hopping path and the location swarm characterize the elementary particle. The swarm owns a location density distribution and that distribution equals the squared modulus of the wavefunction of the elementary particle.

Hans,

I was pleased for the chance to penetrate your Hilbert Book model again and did so. Being more familiar with your language and terminologies now makes it easier. I rather warm to your 'swarm' characterization.

It seems your scores have fallen foul of the direction in the guidelines to 'not use the essay as an opportunity to write about your pet theory' but clearly most here must and do write from their own worldview. We agree we also need to progress understanding from the smallest scale upwards to tackle the topic effectively, which I think we're both doing well, so I don't think your scores so far value your essay highly enough. I think mine will do so.

We also agree the solution should be far simpler than the present theoretical confusion suggests. On that vein I hope you'll read mine which I think takes some small quantum leaps in that direction. I'm interested in to what extend you can understand, connect and agree its parts.

Very best wishes for the contest.

Peter

    Dear Sir,

    We wish you could have defined physical reality (many different definitions are going round, but none satisfactory) and the scope of mathematics as a language. Language is the transposition of some information/command on the mind/CPU of another person/operating system. Mathematics tells us how much a system changes in the right hand side, when the parameters of the left hand side change. This information is universal and invariant in cognition. To that extent, mathematics is a language of physics. But it does not describe what, why, when, where, or how about the parameters or the system. It gives partial information. Generalizing such partial information misleads. Thus, it cannot be the only language of Nature.

    Mathematics, explains the accumulation and reduction of numbers linearly or non-linearly of confined or discrete objects. Even analog fields are quantized. Accumulation or reduction is possible only in specific quantized ways and not in an arbitrary manner (even fractions or decimals are quantized). Proof is the concept, whose effect remain invariant under laboratory conditions. Logic is the special proof necessary for knowing the unknown aspects of something generally known. Thus, the validity of a mathematical statement rests with its logical consistency.

    The validity of a physical statement rests with its correspondence to reality. What is the precise and scientific definition of space? Does the Hilbert and other spaces or sub-spaces have any physical significance and conform to the precise definition of space as a class?

    Synchronization is the operation or activity of two or more things at the same time or rate. There is nothing strange about it. A vane is a broad blade attached to a rotating axis or wheel which pushes or is pushed by wind or water and forms part of a machine or device such as a windmill, propeller, or turbine. Your description: "In the vane, the normalized vector that represents the elementary module is eigenvector of a private operator that attaches a spatial location as the imaginary part of the eigenvalue to the elementary module" is presenting the same fact in a rather incomprehensible language for laymen. How can "Modules act as observers and all observers travel with the vane". Modules can be inert. Can there be inert observers?

    You begin with: "Construct in a modular way". However, also non-discrete items exist. Universe contains continuums and these continuums appear to relate to the discrete objects. Modular design is a design approach that subdivides a system into smaller parts called modules or skids that can be independently created and then used in different systems. Continuum is a continuous sequence in which adjacent elements are not perceptibly different from each other, but the extremes are quite distinct. You cannot deny at least quarks and leptons that constitute every object in the universe. They are perceptible different from each other. What you appear to say by: continuum which "relate to the discrete objects", is, all objects are modular in the space-time continuum. But how do you justify your statement: "‎Further, we as intelligent observers of these facts, want to place everything into an appropriate model, such that we can comprehend our environment. This model appears to be capable to generate intelligent species"? Do we regulate creation? Or is the creation like this because we comprehend it like this? Kindly educate us on these issues.

    Regards,

    basudeba

    Peter,

    High scores only help to win the contest. Instead, the critics onto the document interest much more.

    The Hilbert Book Model considers all discrete objects in the universe as modules or as modular systems. The model also considers all discrete objects as observers. This consideration means that all modules have some degree of consciousness. Sophisticated modules and modular systems show a higher degree of consciousness. Intelligent species exist that own a very high degree of awareness.

    Observers only get access to information that the continuum, which embeds them transfers to them. This information reaches the observers from the past. Thus, observers perceive only a very tiny part of the information that the creator stored into the model.

    Physical reality is what the creator created and stored in a repository. Observers can perceive the stored information that the continuum which embeds them transfers. This information not only arrives from the past, the information transfer also affects the format of the information.

    All discrete objects in the creation are modules or modular systems and all modules are observers. All modules are embedded in a continuum.

    The role of the Hilbert space is to act as a repository. Operators that map the Hilbert space onto itself can impersonate the action of functions and their eigenspaces can play the role of storage places for discrete data as well as for continuums. In this way, the Hilbert space represents a powerful machinery that implements the play garden for the dynamics of the universe. See docs.com/hans-van-leunen for a complete picture of this environment.

    Hans,

    That now sounds like having far more similarities with discrete field dynamics and classical QM than the very tiny part of the information I've previously perceived. Indeed if a 'module' bounded by free fermions can be a galaxy, train, human or detector then we seem in close agreement!

    Now the last bit of logic; Q; Does the velocity of each hop relate to the rest state (frame) of each point hopped from or to the rest state of some others in relative motion elsewhere?

    I'm interested in your claim that "Intelligent species exist that own a very high degree of awareness." exist. I know the evidence of alien visitations is becoming quite overwhelming but it still seems considered by most as verging on crackpottery to say intelligent species exist out loud (though less so than claiming it's us!).

    I see you also now seem to firmly come down on the side of 'God'. I found nothing wrong with that. Do you suggest he may perhaps be the highly intelligent being you invoke?

    I hope you'll get to read mine and discuss the hops. i.e.Do you included cascades? Best

    Peter

    Peter,

    I consider humans as intelligent species. I do not consider the creator as God. God is supposed to care about his creatures. The creator only created them.

    I was once involved in modular software generation and saw the power of modular design and construction in the competition with monolithic construction. In hardware industry, the modular method works. Software industry still does not apply modular design and construction.

    See http://vixra.org/abs/1101.0061 http://vixra.org/abs/1101.0062

    7 days later

    Greetings Hans,

    I like your premise that nature is modular in its design principles. And I am somewhat familiar with the Hilbert Book Model, from your earlier papers on viXra. But I am rather disappointed that you were not able to make a more compelling case for your essay thesis. It would have been a better essay, if some of the technical details were placed later, and the material on page 3 presented sooner.

    It is better, I think, to present what you are talking about first, and then the details of the context. The way you wrote it; it looks like your argument hinges on the rising and falling of the HBM, but I see this is only partly true. The work of Steven Adler in Quaternionic Quantum Mechanics sets the standard, but substantially validates your premise in this essay.

    As it turns out; Adler validates the premise of my essay as well. I also mention the quaternions prominently, but I try to place them in a larger context - and I would appreciate your feedback. My view is that we need to consider the whole of Math, because nature is already putting it to use. For what it's worth, I think the quaternions have more than a passing appeal, and like the other division algebras they are fundamental.

    All the Best,

    Jonathan

      Jonathan,

      The quaternionic model offered by Adler differs considerably from the Hilbert Book Model and not only the quaternions make that difference. Adlers model is merely a quaternionic copy of current physics. The HBM offers a fundamentally different approach.

      In the HBM the creator stores his results into a separable quaternionic Hilbert space that acts of a repository of dynamic geometric data. He also constructed the possibility to embed this separable Hilbert space into its non-separable companion Hilbert space. The embedding occurs as an ongoing process in a subspace that scans as a function of the timestamps of the quaternionic storage containers over the whole repository. In this subspace, the elementary modules are represented by rays that are spanned by the eigenvector, whose eigenvector consists of the timestamp and the current location of the elementary particle.

      Thank you for explaining!

      I hope other participants will find your work, and will mine some of your comments for explanations where the text was insufficient to permit full understanding. I wish you the best of luck in the contest as well.

      Warm Regards,

      Jonathan

      Mr. van Leunen,

      Thank you for the well written essay that takes us from a Base Model to Modular Construction.

      There were a couple statements that really caught my attention in the Modular Construction section:

      'The ability to configure modular systems relies heavily on the ability to couple modules and on the capability to let these modules operate in concordance.'

      'The modular design method becomes very powerful when modules can be constructed from lower level modules.'

      'Modular systems and modular subsystems are conglomerates of connected modules. The constituting modules are bonded.'

      These statements fit very well with my definition for Precise Formations of Matter (PFMs) given in my essay, 'The Cosmic Odyssey of Matter'. Precision Formations are defined by their components (modules) that are connected in precise configurations. The definition allows us to identify a distinct progression of 'modular' assembly, leading to life and social organizations.

      If you have a few minutes, I would very much appreciate your comments on my essay.

      Regards, Ed Kneller

      6 days later

      Dear van Leunen

      I was really enthused to read your account of modular construction since that seems to describe the basic approach that is present in my modeling of intelligence. Without getting my hopes too high, I think the Constitutional nation state I have modeled could be representative of the modular system archetype you have referred to in the essay.

      Needless to say, I am in total agreement with all three of your commandments. But I can't pretend to have understood the explanation with regard to quaternions that you gave at the start of the essay. This is undoubtedly because I have discovered the complex number system of quaternions only very recently, via the essays of Yanofsky and Dickau published on this forum.

      Given that scanty background, if it is presumptuous of me to comment on the mathematics of the quaternions and octonions, please do forgive me! But I found it really interesting.

      Warm Regards, Willy

        Willy,

        The elementary modules are pointlike objects. The only properties a dynamic pointlike object can have are their spatial location and the corresponding timestamp. This data construct fits nicely in a quaternion. The other advantage of this data container is that it is a member of a number system that for every nonzero member comprises a unique inverse. This feature is an important precondition for the existence of a mathematical repository that can hold huge amounts of these data containers in a structured fashion. The repository in question is an infinite dimensional separable quaternionic Hilbert space. Another important fact is that this repository possesses a unique companion repository in the form of a quaternionic non-separable Hilbert space that can embed the separable Hilbert space. An ongoing stochastic process that embeds the elementary modules as a function of their timestamp and their location in an embedding continuum realizes the embedding. Therefore the elementary module hops around in a stochastic hopping path that results in a coherent hop landing location swarm. Both the hopping path and the location swarm characterize the elementary module. Thus, the dynamic behavior, which the stochastic process controls, characterizes the type of the elementary module. Physical theories ignore this stochastic process.

        Dear Hans van Leunen

        I inform all the participants that use the electronic translator, therefore, my essay is written badly. I participate in the contest to familiarize English-speaking scientists with New Cartesian Physic, the basis of which the principle of identity of space and matter. Combining space and matter into a single essence, the New Cartesian Physic is able to integrate modern physics into a single theory. Let FQXi will be the starting point of this Association.

        Don't let the New Cartesian Physic disappear! Do not ask for himself, but for Descartes.

        New Cartesian Physic has great potential in understanding the world. To show potential in this essay I risked give "The way of The materialist explanation of the paranormal and the supernatural" - Is the name of my essay.

        Visit my essay and you will find something in it about New Cartesian Physic. After you give a post in my topic, I shall do the same.

        Sincerely,

        Dizhechko Boris

        Thank you for the Nice explanation Hans van Leunen,

        Is there any Physical examples for the usage are possible....?

        Best

        =snp

        11 days later

        Dear Hans,

        With great interest I read your essay, which of course is worthy of the highest praise.

        I am glad that you are

        «investigates the foundation and the lower levels of the structure of physical reality.»

        Your assumptions are very close to me

        «niverse contains continuums and these continuums appear to relate to the discrete objects.»

        «The foundation of physical reality must necessarily be very simple and therefore its structure must be easily comprehensible by skilled scientists.»

        You might also like reading my essay , where the fractal principle of the device of matter is substantiate.

        I wish you success in the contest.

        Kind regards,

        Vladimir

        9 days later

        Hans,

        I'd hoped you'd have read my essay and commented by now. Did you intend to? I hope you engage. (scoring ends Friday). With more discussion you get more score and thus more reads.

        The importance of the Classic QM derivation the essay builds to now seems to be being being picked up, and I've just been told I've used quaternionic vector rotations without knowing it! (see Gary Simpsons comments).

        Very best

        Peter

        Dear Hans

        I enjoyed reading your paper, although I approach physics geometrically and mechanistically rather than algebraically. One faqxi member explained to me that octonians represent a perspective transformation in geometrical terms. Is there such a geometrical equivalent for quaternions? So while I did not understand the algebra I could read your intention and view your vision of a neat causal world not too different than my own vision.

        In Fig. 31 of my Beautiful Universe Model I interpret the Miller indices of the 3D crystal-like arrangement of nodes in my model as planar Fourier components explaining Heisenburg uncertainty. Is there an equivalent Hilbert interpretation of such a model?

        With all best wishes,

        Vladimir

        Write a Reply...