Essay Abstract

Look around and you become easily convinced from the fact that all discrete objects are either modules or modular systems. With other words, the creator of this universe must be a modular designer. His motto is "Construct in a modular way". However, also non-discrete items exist. Universe contains continuums and these continuums appear to relate to the discrete objects. 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.

Author Bio

Hans van Leunen. Born in 1941 in Helmond in the Netherlands. Applied physics at TUE (Eindhoven), Chemistry, Software expert. Career in high-tech industry. Now retired. Started a personal research project "The Hilbert Book Model" in 2009 that investigates the foundation and the lower levels of the structure of physical reality. docs.com/hans-van-leunen

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Hans,

I agree completely that the universe is composed of modular pieces and that these pieces can be combined into larger structures of increasing complexity.

I also agree that quaternions provide a method of analyzing these structures. The difficulty that I have at this point is that to my knowledge, there does not yet exist an operator such as a LaGrangian for quaternion functionss that can be used to determine an optimal path. It seems to me that the needed Mathematics has not been fully developed.

You might be interested in my essay submission for this contest and for the previous contest.

Best Regards,

Gary Simpson

    Elementary modules are point-like objects and would not have many properties if the location of that point-like object would be quite stationary. Instead, at every progression instant, the elementary module gets a new location that is provided by a private stochastic mechanism. Consequently, the elementary module hops around in a stochastic hopping path and the hop landings form a location swarm. The swarm is characterized by a location density distribution. The Fourier transform of this distribution equals the characteristic function of the stochastic process that is applied by the mechanism that generates the hop locations. Therefore, the swarm owns a displacement generator and consequently at first approximation the swarm moves as one unit. The location density distribution of the swarm equals the squared modulus of the wavefunction of the elementary module.

    The swarm contains a huge number of elements. Compared to the vigorous hopping of the elementary module, its representing location swarm moves quite steadily.

    The Hilbert Book Model contains a section about a multi-mix algorithm that starts from the hopping path and the fact that the location swarm owns a Fourier transform. The algorithm results in an equivalent of the Lagrangian and the Hamiltonian. In fact, the multi-mix algorithm takes the reverse of Feynman's path integral, which starts from the Lagrangian. The HBM does not take all possible paths. Instead, it takes the stochastic hopping path.

    Look at Report of the Hilbert Book Model Project

    Sorry, I appear not to understand the FQXi link system well. The above link is contained in docs.com/hans-van-leunen or you can search docs.com for "the Hilbert Book Model"

    Dear Hans,

    As I have thoughtfully pointed out in my brilliant essay, SCORE ONE FOR SIMPLICITY, the real Universe consists only of one unified visible infinite surface occurring in one infinite dimension, that am always illuminated by infinite non-surface light. All visible modules have surfaces Hans.

    Joe Fisher, Realist

    Hans,

    Of course, you have the right to your own unrealistic "pet theory." Naturally provided reality am not theoretical, and that is why I have thoughtfully pointed out in my brilliant essay, SCORE ONE FOR SIMPLICITY, the real Universe consists only of one unified visible infinite surface occurring in one infinite dimension, that am always illuminated by infinite non-surface light. Reality am not a complicated.

    Hello Mr Van Leunen,Gary,Joe,

    Mr Van leunen, I liked your papper and your generality about quaternions and hilbert works.Congratulations.

    Have you thought about the insertions of operators de Dirac ? and the works of Noether about groups,laws of conservation...Emmy Nother and her theorem was so relevant like mathematician.I discussed also in private with Mr Duplij about padics numbers and groups.It could be also relevant to see the convergences.I like so much her works ,Noether was an incredible thinker.Einstein and Hilbert liked a lot her works.Congratulations for your work about the evolution and quantization of matter and increasing complexification.Best Regards

    Dear Steve,

    The mathematical model that tries to describe physical reality is subject of the Hilbert Book Model project. The paper https://doc.co/WmxXCB describes this project. It contains sections that treat all differential operators including equivalents of the Dirac equation for the electron and the positron. The model applies the fact that quaternionic number systems exist in many versions that differ in the way that they are ordered to define symmetry related charges that are in agreement with the electric and color charges of the standard model. Noether's findings also hold in the mathematical model. The electric charges and color charges represent extreme cases. The fact that multiple versions of quaternionic number systems is not well known and as far as I know it is not applied to explain the origin of symmetry related charges. At docs.com/hans-van-leunen you can find many papers that introduce new and unexpected facts that the HBM reveals.

    The discovery of the modular construction of all discrete object in the universe was never highlighted before. The contest is a nice opportunity to take that chance.

    Thanks for these détails Mr Van Leunen,

    I didn't know well the works of Hilbert,I study a little his works and the works of Banach also.In all case Hilbert was a very incredible mathelmatician.The geometrical algebras also are relevant ,I try to invent the spherical geometrical algebras with the good operators, vectors, tensors, spinors,the associativity, the commutativity or not.....we could find the correct universal logic.It is a big puzzle in fact, we search after all answers to this universe and its laws.Your work is relevant Mr Van Leunen.Congratulations, I have learnt in the same time new things,thanks.Regards

    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.