Dear Steve,

The part of quaternionic differential calculus that applies the quaternionic nabla is very compact and comprehensible. This is due to the fact that the quaternionic nabla behaves as a quaternionic multiplying differential operator. The quaternionic product rule separates the product in five terms. This means that also the first order partial differential equation is separated into five terms. The terms define the separation of change into 'directions' along which change takes place. This divides the differential of a field into subfields. That is what Maxwell did in his Maxwell equations. But Maxwell did not do this correctly. He ignored a set of the terms. With other words, quaternionic differential calculus that is based on the quaternionic nabla is more complete than Maxwell equations. This becomes obvious when the second order partial differentials are considered.

Like the three-dimensional spatial nabla operator, the quaternionic nabla has a specification in other coordinate systems, such as in a spherical coordinate system

Dear Hans,

One real visible Universe must only be occurring in one infinite dimension.

Joe Fisher, Realist

Dear Mr Van Leunen,

Thanks for these explainations.It is relevant in all case,that permits to complete the détails of maxwell équations apparently.I didin't know these nablas,they are relevant when we utilise these operators(nabla operators).So if I understand well ,that permits to irmpove the differential calculs with different operators like for the laplacians?.Have you already thought to insert the spherical volumes and the 3 motions of 3D sphères, orbital,linear,spina?

Regards

Steve,

My interest goes to the 'structure' of elementary particles and how these particles implement the deformation of their embedding field.

See: A simple model by Hans van Leunen https://doc.co/yvg1Bv

22 days later

Eigenvalues and eigenvectors are used here ... this modular concepts are really complex, we are not designing the universe, trying understand it

How they lead to intelligence ?

Mathematical concepts using imaginary numbers give rise to solutions which are non comprehensible and are not real.....

    Satyavarapu,

    The fact that numbers are called imaginary does not make them unrealistic. It only means that in such number systems the square root of -1 exists as a member of the number system.

    In Hilbert spaces, operators map Hilbert vectors onto Hilbert vectors. If the map of a normed vector lands on the same vector, then the inner product of the source vector and the map results in a value that is called the eigenvalue, which belongs to the source vector and that source vector will be called eigenvector. The eigenvectors of a normal operator are mutually orthogonal. They form an orthonormal basis of the Hilbert space. The set of rays that are spanned by individual base vectors represents a set of atoms of an orthomodular lattice. This lattice is thought to be the foundation of physical reality.

    Dear Hans,

    I read with great interest your essay deep with important conclusions:

    My high score. I invite you to see and appreciate my version of the simplest dialecticо- ontological model of the Universum as the eternal hierarchical process of the structures generation.

    Yours faithfully,

    Vladimir Rogozhin

    Dear Hans,

    I read with great interest your essay deep with important conclusions:

    "The nice thing about this situation is that the deepest foundation of reality must be rather simple and therefore it can be described in a simple way and without any formulas. For example, if the observed signature characterizes physical reality, then the most fundamental and most influential law of physical reality can be formulated in the form of a commandment: "THOU SHALT CONSTRUCT IN A MODULAR WAY" This law is the direct or nearly direct consequence of the structure of the deepest foundation. That foundation restricts the types of relations that may play a role in physical reality. That structure does not yet contain numbers. Therefore, it does not yet contain notions such as location and time.

    This law is intentionally expressed in the form of a commandment. It is not possible to express this law in the form of a formula... The impact of the commandment is far more influential, than the impact of these famous formulas."

    My high score. I invite you to see and appreciate my version of the simplest dialecticо- ontological model of the Universum as the eternal hierarchical process of the structures generation.

    Yours faithfully,

    Vladimir Rogozhin

    7 days later

    Didn't Hilbert's program prove untenable?

    Incidentally, do you share Pauli's opinion concerning avoidability of i? I gave the reference in my essay.

    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