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**Hans van Leunen**: *on* 4/8/17 at 22:17pm UTC, wrote Vladimir, Hilbert spaces can only cope with number systems that are...

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**Vladimir Fedorov**: *on* 3/29/17 at 5:30am UTC, wrote Dear Hans, With great interest I read your essay, which of course is...

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**Hans van Leunen**: *on* 3/14/17 at 11:56am UTC, wrote Willy, The elementary modules are pointlike objects. The only properties a...

**Willy K**: *on* 3/14/17 at 6:40am UTC, wrote Dear van Leunen I was really enthused to read your account of modular...

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FQXi FORUM

September 20, 2021

CATEGORY:
Wandering Towards a Goal Essay Contest (2016-2017)
[back]

TOPIC: Intelligent species from first principles by Hans van Leunen [refresh]

TOPIC: Intelligent species from first principles by Hans van Leunen [refresh]

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.

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

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

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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

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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

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

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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

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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…..

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How they lead to intelligence ?

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

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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.

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.

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.

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

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

Best Regards

=snp.gupta

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Best Regards

=snp.gupta

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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

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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

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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

report post as inappropriate

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

report post as inappropriate

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

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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

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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.

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.

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

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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

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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

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

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...

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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...

view entire post

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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.

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.

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

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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

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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...

view entire post

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...

view entire post

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

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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

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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

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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

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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

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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

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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.

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

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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

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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

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

I am glad that you are

Your assumptions are very close to me

«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

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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

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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

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Vladimir,

Hilbert spaces can only cope with number systems that are division rings. Only three suitable division rings exist. They are the real numbers, the complex numbers, and the quaternions. These numbers are used to specify inner products and eigenvalues of operators. Octonions and bi-quaternions are not division rings. Quantum physicists apply Hilbert spaces to model their theories.

Elementary particles are elementary modules and pointlike objects. At every instant, they take a precise spatial location. Thus they hop around in a stochastic hopping path. The hop landing locations form a coherent swarm. That swarm owns a location density distribution. The hop landing locations are generated by a stochastic process that owns a characteristic function, which is the Fourier transform of the location density distribution and acts like a displacement generator. The characteristic function and the location density distribution lead to Heisenberg's uncertainty relation. Elementary modules configure higher level modules. There, similar relations between swarms and characteristic functions exist.

Hilbert spaces can only cope with number systems that are division rings. Only three suitable division rings exist. They are the real numbers, the complex numbers, and the quaternions. These numbers are used to specify inner products and eigenvalues of operators. Octonions and bi-quaternions are not division rings. Quantum physicists apply Hilbert spaces to model their theories.

Elementary particles are elementary modules and pointlike objects. At every instant, they take a precise spatial location. Thus they hop around in a stochastic hopping path. The hop landing locations form a coherent swarm. That swarm owns a location density distribution. The hop landing locations are generated by a stochastic process that owns a characteristic function, which is the Fourier transform of the location density distribution and acts like a displacement generator. The characteristic function and the location density distribution lead to Heisenberg's uncertainty relation. Elementary modules configure higher level modules. There, similar relations between swarms and characteristic functions exist.

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