Essay Abstract

Fundamental and foundational are subjective terms denoting an essential core; or central or primary rule or principle of a subject matter. In the context of physics (as the subject matter), because all physical phenomena are measured and determined empirically. It is natural, indeed imperative, to consider experiments, themselves, as statements within the paradigm. Further, since even at the simplest level, primary rules and principles have mathematical descriptions. If physics is not a mathematical construct, where does the inability to quantify (measure) end and a magical core begin? Thus, a physics paradigm, as a mathematical construct is fundamental and foundational if and only if the essential core is consistent with all statements (experiments) within the paradigm. A process examining a fundamental and foundational core of a physics paradigm, as a mathematical construct is implemented.

Author Bio

Authored several mathematics and Mathematical Physics books and numerous mathematics and mathematical physics videos. Taught mathematics courses at U.C.,Riverside, Crafton Hills College, & University of Redlands from 2005 through 2008 Academic Honors: 2004 SJSU Math Department Hoggatt Award Scholarship 2003 SJSU Math Department Fuller Award Scholarship Earned M. A. Mathematics, SJSU 05/2004 Earned B.A.Mathematics, at CSU, Chico 06/1973

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Cassano,

The language of maths is not accessible to everyone.... Some prosaic conclusion would have been appreciated. On the other hand, I got the following:

Only one force. May I take this as only "one cause"?

Marcel,

Physics is a quantitative science, ergo a mathematical discipline.

From begining courses subject matter: Newton's Laws prescribe mathematical

methods of analyzing projectile motion, the incline plane, friction, etc.;

Lagrangian dynamics, Hamiltonian dynamics, statistical mechanics; and

electromagnetic field theory provide further methods and precision for

analysis; and wave mechanics provides more even into the quantum realm.

Since this essay discusses fundamentals and foundations in the context of

physics (FQXi) if it's discussion is not at a mathematical level it is

easily rebuked, by simply querying how any of the above analytical methods

described above arise from any supposed foundation.

Discussion of fundamentals of language, politics, art or other fields may be

appropriate elsewhere, but are out of the scope of a physics (FQXi)

forum article/essay - except as where physics is a part of fundamentals in

those fields (such as perspective, color, lighting, etc.); but then, again

in those areas fundamental would still undergo analysis as done in the

article/essay.

"So, is this enough for foundational? Some might say yes. Others, that it

only describes two forces." This was an implied quotation.

The previous and later following statements implied:

"... a single vector space algebra manifesting characteristics having an

appearance of distinct forces."

After spending years developing and applying new mathematics, what is

clear and obvious to me requires study of my references to become so to

others. That is why I always include references to my material. Common

mathematics, even at the graduate level, is antiquated mathematics,

insufficient to understand reality. Only through my transcendental mathematics

may the "First Fundamental Design of GOD" be comprehended.

    Dear CLAUDE MICHAEL CASSANO,

    You wrote: "Thus, for a paradigm or system specified by a core, everything within which must be consistent; i.e. the paradigm/system is self-consistent."

    I have concluded from my deep research that Nature must have devised the only permanent real structure of the Universe obtainable for the real Universe existed for millions of years before man and his finite complex informational systems ever appeared on earth. The real physical Universe consists only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

    Joe Fisher, ORCID ID 0000-0003-3988-8687. Unaffiliated

    4 days later

    Claude,

    Physics studies our experience of the universe, but the universe is not made of "experience"; it is made out of stuff! What is fundamental is what the universe IS and DOES before we even look or think about it, and this is the hard part to accept.

    Thanks,

    Marcel,

    How do they make TV's , smart phones , radios , nuclear bombs , etc. ?

    How do they know the flight of baseballs, cannonballs, rockets, drones, etc.?

    Because they have determined what are referred to as "physical laws" that

    the motion of the "stuff" must follow, and even that determines the "stuff".

    That is what the "fundamental" is.

    As noted in a previous reply:

    Physics is a quantitative science, ergo a mathematical discipline.

    From begining courses subject matter: Newton's Laws prescribe mathematical

    methods of analyzing projectile motion, the incline plane, friction, etc.;

    Lagrangian dynamics, Hamiltonian dynamics, statistical mechanics; and

    electromagnetic field theory provide further methods and precision for

    analysis; and wave mechanics provides more even into the quantum realm.

    Since this essay discusses fundamentals and foundations in the context of

    physics (FQXi) if it's discussion is not at a mathematical level it is

    easily rebuked, by simply querying how any of the above analytical methods

    described above arise from any supposed foundation.

    Discussion of fundamentals of language, politics, art or other fields may be

    appropriate elsewhere, but are out of the scope of a physics (FQXi)

    forum article/essay - except as where physics is a part of fundamentals in

    those fields (such as perspective, color, lighting, etc.); but then, again

    in those areas fundamental would still undergo analysis as done in the

    article/essay.

    Murray Gell-Mann received the 1969 Nobel Prize in physics for his

    Eightfold Way organizing the mesons and spin-1/2 baryons into an octet,

    and further work on the theory of elementary particles. Gell-Mann

    introduced, independently of George Zweig, the quark--constituents of all

    hadrons--having first identified the SU(3) flavor symmetry of hadrons.

    This led to the development of the Standard Model (SM), the widely

    accepted theory of elementary particles.

    The "fundamental"-ness of my finite-dimensional constructive algebra realities

    lies in not only fundamentally describing the fields of physics, but he WHY of

    the foundation of the quarks (including the WHY of the SU(3) symmetry),

    Eightfold Way of hadrons, fundamental particle interactions, and even the

    values of the fundamental particle masses and charges.

    As noted, physics is not metaphysics. It's not astrology, not alchemy, not sociology, and not politics. Physics describes physical phenomena with reproducible mathematical precision.

    5 days later

    Hi CLAUDE MICHAEL CASSANO

    Wonderful idea "Thus, a physics paradigm, as a mathematical construct is fundamental and foundational if and only if the essential core is consistent with all statements (experiments) within the paradigm. A process examining a fundamental and foundational core of a physics paradigm, as a mathematical construct is implemented" dear CLAUDE MICHAEL CASSANO...... Dynamic Universe model is totally based on Experimental results or predictions coming true after 8 or 9 years.............. Yours is a very nice idea.... I highly appreciate your essay and request you please spend some of the valuable time on Dynamic Universe Model also and give your some of the valuable & esteemed guidance

    Some of the Main foundational points of Dynamic Universe Model :

    -No Isotropy

    -No Homogeneity

    -No Space-time continuum

    -Non-uniform density of matter, universe is lumpy

    -No singularities

    -No collisions between bodies

    -No blackholes

    -No warm holes

    -No Bigbang

    -No repulsion between distant Galaxies

    -Non-empty Universe

    -No imaginary or negative time axis

    -No imaginary X, Y, Z axes

    -No differential and Integral Equations mathematically

    -No General Relativity and Model does not reduce to GR on any condition

    -No Creation of matter like Bigbang or steady-state models

    -No many mini Bigbangs

    -No Missing Mass / Dark matter

    -No Dark energy

    -No Bigbang generated CMB detected

    -No Multi-verses

    Here:

    -Accelerating Expanding universe with 33% Blue shifted Galaxies

    -Newton's Gravitation law works everywhere in the same way

    -All bodies dynamically moving

    -All bodies move in dynamic Equilibrium

    -Closed universe model no light or bodies will go away from universe

    -Single Universe no baby universes

    -Time is linear as observed on earth, moving forward only

    -Independent x,y,z coordinate axes and Time axis no interdependencies between axes..

    -UGF (Universal Gravitational Force) calculated on every point-mass

    -Tensors (Linear) used for giving UNIQUE solutions for each time step

    -Uses everyday physics as achievable by engineering

    -21000 linear equations are used in an Excel sheet

    -Computerized calculations uses 16 decimal digit accuracy

    -Data mining and data warehousing techniques are used for data extraction from large amounts of data.

    - Many predictions of Dynamic Universe Model came true....Have a look at

    http://vaksdynamicuniversemodel.blogspot.in/p/blog-page_15.html

    I request you to please have a look at my essay also, and give some of your esteemed criticism for your information........

    Dynamic Universe Model says that the energy in the form of electromagnetic radiation passing grazingly near any gravitating mass changes its in frequency and finally will convert into neutrinos (mass). We all know that there is no experiment or quest in this direction. Energy conversion happens from mass to energy with the famous E=mC2, the other side of this conversion was not thought off. This is a new fundamental prediction by Dynamic Universe Model, a foundational quest in the area of Astrophysics and Cosmology.

    In accordance with Dynamic Universe Model frequency shift happens on both the sides of spectrum when any electromagnetic radiation passes grazingly near gravitating mass. With this new verification, we will open a new frontier that will unlock a way for formation of the basis for continual Nucleosynthesis (continuous formation of elements) in our Universe. Amount of frequency shift will depend on relative velocity difference. All the papers of author can be downloaded from "http://vaksdynamicuniversemodel.blogspot.in/ "

    I request you to please post your reply in my essay also, so that I can get an intimation that you replied

    Best

    =snp

    Dear Fellow Essayists

    This will be my final plea for fair treatment.,

    Reliable evidence exists that proves that the surface of the earth was formed millions of years before man and his utterly complex finite informational systems ever appeared on that surface. It logically follows that Nature must have permanently devised the only single physical construct of earth allowable.

    All objects, be they solid, liquid, or vaporous have always had a visible surface. This is because the real Universe must consist only of one single unified VISIBLE infinite surface occurring eternally in one single infinite dimension that am always illuminated mostly by finite non-surface light.

    Only the truth can set you free.

    Joe Fisher, Realist

      (2B) | !(2B) =/= ?

      0 - 0 = 0

      X=/= 0 => 2B

      ... a translation to a human understanding:

      To Be OR NOT To Be That is NOT the Question.

      Nothing form Nothing leaves Nothing

      There's got To Be Something If there's To Be.

      One might ask how the "one single unified VISIBLE infinite surface" theory manifests the Maxwell's equations, SU(3) symmetry), the Eightfold Way of hadrons, the fundamental particle interactions, the values of the fundamental particle masses and charges, etc. , and every other physical phenomena with reproducible mathematical precision?

      Dear Claude,

      Does your math model tell us the basic substance of which matter particles, energy photons, and fields are composed or constructed? If so what is it? Does it tell us how this basic substance is structured in each of them to give them their individual observable properties? If so what are those structures?

      It would seem to me that if time is a dimension and one could go back into the past or forward into the future, then, whenever any motion in the universe moved to a new position it would be necessary for that motion to somehow generate a complete new copy of the entire universe in order to always preserve the place to go back to before that motion position change occurred. Given the great size, large number of existent entities, and the great structural complexity of the universe that we can observe, it would seem to me that such an elaborate almost infinite structure would not be in accordance with such concepts as energy conservation and Occam's razor that nature always chooses the simplest most efficient way of doing things, etc. Of course, in order to be able to go into the future, all of those copies of the universe would need to have existed from the beginning of the creation to allow someone to go into any point in the future from any point in the past. It would seem to me that this would mean that all of the choices that you will make in the future must already have been made by you at the beginning of the universe in order for the copies of the universe that included the changes that were generated by those choices to be able to be copied into those future universe copies in which you made those choices so that you could go into the future to places beyond the places where you made those choices and see the proper results of your having made those decisions. In addition to all of this unnecessary complexity, if you could go into the past and change things, all of those changes and all of the additional changes that might directly or indirectly result from those changes as they moved forward in time from that point, would have to in some way be propagated through all of those copies. That type of thing does not look like a natural structure, but like some computer program that would contain all of the additional logic programming to perform such a task. It would seem to me that a universe that contained motions that continually moved from one position to the next in the absence of interactions with other motions would be much more in line with Occam's razor, etc. In such a system, when motions moved from their present positions to new positions these new positions would be their present. The positions that they were in before moving into these current positions would be part of their past, but would no longer exist because those motions would no longer be in those positions. Positions into which all of the motions would move after they moved out of their current positions would be their future positions, but that future condition of all the motions would not yet exist because the motions would not have moved into them yet. This would mean that only the present ever really exists, and there would only need to be one of each motion that is in existence, which fits well into observed reality. Can you use your math model to not only model existing most accepted theories, but to also determine if they are actually true to reality, by going behind the structure of those theories to determine if all of their complex structure is needed and if their resultant outputs are the best way to model reality?

      Sincerely,

      Paul

        Dear Claude,

        For some unknown reason, every extra line space that was in the above comment to you was replaced by the letter n. Can your math theory explain what caused that to happen? When you see the letter n just sitting there by itself just understand that an extra line should be between the text before the n and the text after the n. Isn't man's modern technology wonderful? I don't know if it will happen to this message also or not. I guess we will see.

        Sincerely,

        Paul

        References:

        [8] Cassano, C.M., "Analysis on Vector Product Spaces", M.A. thesis, San Jose State University, 2004.

        [9] Cassano, C.M., "Reality is a Mathematical Model", 2010.

        ISBN: 1468120921 ; http://www.amazon.com/dp/1468120921

        ASIN: B0049P1P4C ; http://www.amazon.com/Reality-Mathematical-Model-ebook/dp/B0049P1P4C/ref=

        tmm_kin_swatch_0?_encoding=UTF8&sr=&qid=

        [12] Cassano, Claude.Michael ; "A Mathematical Preon Foundation for the Standard Model", 2011.

        ISBN:1468117734 ; http://www.amazon.com/dp/1468117734

        ASIN: B004IZLHI2 ; http://www.amazon.com/Mathematical-Preon-Foundation-Standard-ebook/dp/

        B004IZLHI2/ref=tmm_kin_swatch_0?_encoding=UTF8&sr=&qid=

        [13] Cassano, Claude.Michael ; "The Standard Model Architecture and Interactions 1" ;

        http://www.youtube.com/watch?v=GFlmF6WWGxE

        [14] Cassano, Claude.Michael ; "The Standard Model Architecture and Interactions Part 1" ;

        http://www.dnatube.com/video/6907/The-Standard-Model-Architecture-and-Interactions-Part-1

        [15] Cassano, Claude.Michael ; "The Standard Model Architecture and Interactions Part 2" ;

        http://www.youtube.com/watch?v=Mxa2u7-czmk

        [16] Cassano, Claude.Michael ; "The Standard Model Architecture and Interactions Part 2" ;

        http://www.dnatube.com/video/6908/The-Standard-Model-Architecture-and-Interactions-Part-2

        demonstrate that "suitably smooth" constructable algebras yield both geometry and physical laws

        (including the Klein-Gordon equation - which all fundamental particles obey)

        The law of large numbers shows how quantum field theory yields classical mwchanics for large particle number.)

        Therefore, it is only necessary to produce the Klein-Gordon equation, and how to establish fermion architecture and interactions from them in order to design our reality.

        [10] Cassano, Claude.Michael ; "Expressing the Dirac Equation as a Generalization of Maxwells Equations"; http://vixra.org/abs/1504.0012

        [11] Cassano, Claude.Michael ; "The Dirac Equation is a Special Case of the Maxwell-Cassano Equations"; http://vixra.org/abs/1504.0006

        demonstrate that the Dirac equation is a special case of the linearized Klein-Gordon equation (which reduces to Maxwell's equations for zero rest masses (which the Dirac equations themselves do not do).

        [17] Cassano, Claude.Michael ; "All Fermion Masses and Charges Are Determined By Two Calculated Numbers"; http://vixra.org/abs/1311.0182

        demonstrates that the Higgs field and mechanism are superfluous, since all fermion masses may be relatively simply calculated from the above architecture.

        The architecture of the hadrons is also manifested in further videos on DNAtube.

        The four-space-time (see [9]) geometry yielding the metric tensor invariant (second fundamental form) is generated via the constructable algebra (actually, pseudo-metrics).

        Naturally yielding dot and cross product equivalents.

        These dot products in these types of spaces essentially are a projection onto the time-dimension.

        This is interpreted as speed and passage through time.

        Since my smooth constructable algebras (not a math theory) may yield Maxwell's equations; from which resistors, diodes, transistors, etc. may be developed and Ohm's Law and Ampere's Law and Kirchhoff's laws of circuit analysis follow - why the n appear is simply explained.

        The editing software tries to parse strings of ASCII characters, but not all word processing programs use the same end-of-line delimiters. In the case, here, a "n" or "

        " is a residue of the parsing.

        5 days later

        Claude,

        I absolutely agree with everything you said about science, physics and mathematics. But the "smartphone syndrome" is just there to make us believe that we are smart. Toys they are, and we know more than we actually understand. There is a difference. This is 2018 and we still send people into space sitting on huge amount of explosive, hoping they will make it. We won't get far with rockets. So, if brilliant people like you truly believe rockets are "normal" in 2018, then we are in real trouble.

        Anyone, who believes that it is not important to know what the universe is made of and what cause makes it evolve by itself (necessary logical concepts), has got to stand back and consider the big picture. What are we missing and why?

        A successes that blinds us is called a failures.

        Thanks,

        Marcel,

          I am not and have never designed, produced, nor supported the creation of rockets.

          What I have done, is produce a design of "physics spaces" consistent with the

          fundamentals of our four-dimensional-reality; and produce articles and videos

          demonstrating such consistency with empirically known data.

          As noted in my earlier FQXi article: "Physics is a Branch of Mathematics"

          http://fqxi.org/data/essay-contest-files/CASSANO_Physics_is_a_Branch.pdf

          "If there is a sub-mathematical space - magic - underpinning the mathematical surrounding it; where does it start, and where does the mathematical surrounding it begin?

          If such exists, at some point it should reveal itself by not resting on axiomatic foundation."

          Movements of the planets may be predicted with mathematical precision.

          Mankind has built skyscrapers and submarines; and all kinds of mechanisms engineered.

          Civil engineering, electrical engineering, mechanical engineering, etc.

          are all irrefutable mathematical tools for creation in everyday life.

          So, where's the magic?

          "stuff" may be mathematically defined via quantum field theory as is

          done in "Quantum Mechanics", 3rd Ed., Eugen Merzbacher - Chapter 21 ...

          "... there are two and only two forms of quantum mechanics for identical

          particles ... satisfying two classes of commutation relations,

          respectively, ... Bose-Einstein statistics and Fermi-Dirac statistics;

          respective particles of which referred to as bosons and fermions. ...

          Consequences are, that there are no fermion states in which two or

          more particles share the same quantum number - i.e., all fermions

          satisfy the Pauli exclusion principle (can occupy the same place at

          the same time); ... and that bosons satisfy the theory of the harmonic

          oscillator. ..."

          Claude,

          The essay of Vladimir Rogozhin is a good introduction to the content of my essay. He explains it better than me.

          Thanks,

          Marcel,

          Dear Claude,

          First I will explain the situation about the printing of the letter n instead of a line feed because that should be the easiest part. I have used the same copy of Microsoft word to type out my comments for several years and that was the first time that it had that problem, so it could not be due to the word processor's end of line delimiters, since they have remained the same for a long time with no problems. After I finish typing the comment, I do a spell check and read over it to look for errors that the word processor would not find like the word 'there' being used when the word 'their' was intended, etc. I then save the document. That all worked ok. Next, I go to FQXI and open the page that the comment is to go on and log in. After that I select the comment that I am responding to and select the option to comment to its thread. I then go back to my word processor, highlight all of the comment and select copy. Next I go back to the FQXI page and paste the comment into the comment window on that page. I then read over the comment to be sure that it is still ok and in this case it was still ok with the line spaces in their proper places. After convincing the FQXI page that I am a humon, I select the option to post the document. Then I go back to the page and check it again to be sure that it went in ok and in this case that is where I saw the 'n's' instead of the 'linefeeds'. This tells me that the problem was not at my end, but had to be either in the transmission or reception area. Since I noticed that the comment that I made on your page seems to have been corrected now, I assume that FQXI found and corrected the error, so it was probably a glitch in their software unless you corrected it yourself. In addition to that, when I was looking at other comments today I saw another comment that mentioned having the same problem, so the evidence indicates that the error was FQXI's software problem. I have left out some details, but this is an example of conceptual structuring, which involves looking at the known structure of the entities involved, at their action and interaction outputs, and then analyzing them to determine the compositions of the structures involved and how their structure acts by itself and interacts with other entities to produce the observed output results. Once all of this is understood any error generated in the data can be traced back to its cause.

          Currently, I find conceptual structuring ability sadly lacking in man's scientific community. Where I do see it, I usually find that it is focused on some minor structure deep down in a logical or math tunnel that has already departed so far from reality that those involved usually think that they are making great gains when they are really just propagating the errors deeper and deeper. At the same time, the observational data and even the math models are giving indications that if followed up could lead to the next deeper level of understanding of the true structure of the universe and that information is generally being ignored. Your paper demonstrated that you have analytic skills and that they were not only reproductive of previously developed math structures, but showed that you could possibly possess the ability to develop new math structures, so when I asked about the substance and structure of matter particles, energy photons, and fields, I was testing to see if you also have developed conceptual structuring abilities. I have not yet had the time to read the papers that you provided links to in your response, but their titles indicate that you may not have developed those abilities. This is not unexpected because conceptual structuring training does not appear to be provided in man's current educational systems. What I am looking for are those who either have or at least possess the ability to understand both conceptual and analytic structuring systems and can ideally use the results from each system to develop a deeper overall understanding of the complete structure of the universe.

          Basic physical conceptual structuring contains four primary levels of structuring, all of which must be applied to create a physical device or to completely successfully analyze and understand an already created device. Generally they are applied in the same order, but you start at opposite ends of that order depending on whether you are creating a device or just analyzing an already existing device. When creating a new device, however, it is sometimes necessary to look at aspects that are desired to be exhibited by later levels to be sure that the present structural level will allow or generate those desired output properties in the later structural level, etc. These levels are:

          1. Substance: All physical objects are composed of one or more substances. Each individual substance in the device is usually described according to the hierarchical level in which the device is produced and is expected to function. This means that a device that is made and is expected to be used at the large scale level such as a pen to use to write on paper will be expressed as being composed of substances such as a metal or plastic outer shell containing an inner tube made of plastic that contains a fluid or semifluid that contains pigment, which will leave the marks on the paper. At one end of the tube would be a metal piece with a small metal ball mounted in it, such that it can easily rotate, but not fall out. This metal piece will have a hole in it through which the fluid can flow from the tube to the metal ball, so it can then be spread on the paper. All of these substances can be found in many different forms at the large scale, so many different types of pens can be created. If you were to decide to make a new better type of ink for a pen you might want to work at the next lower level of structure in which case the substances that you would use to make it might be described in the form of the molecules that you use to make it. If you were making a specific molecule, you could describe its substances in terms of the atoms of which it is composed and if you were trying to make a specific atom, you would describe its substances as the subatomic particles of which it is composed and the fields that join them together to form the atom. The question that I asked you is; what substance(s) would be used to make a matter particle?

          2. Internal structuring: In the above section on substance you can see that the substances are joined together structurally in one way or another to form the completed device. At the atomic level, the number of each type of matter particle that you used and the field structure that is used to join them together determines the type of atom produced. My question to you was, at the matter particle level, how is its substance structured or put together to make a specific matter particle.

          3. Internal actions and reactions: Since man in this world still does not fully understand the internal actions and reactions within matter particles, atoms, and molecules, it would be best to get a beginning understanding of them by looking at large scale devices. If you look at a mechanical watch that is powered by a battery that can allow it to run for several years, you can see that it contains several internal motions in its parts that interact with those parts in such a way as to provide that the hour, minute, and second hands all continue through their cyclical motion cycles in coordination with each other without the application of any external interactions. The basic motion supplied by the battery is supplied by internal motion transfer interactions between the parts to generate all of the cyclical motions that are outputted in the form of the motions of the hands.

          4. External actions and interactions: External actions and interactions are those that can be detected by another device through external actions and interactions that transfer information from one device to the other device. In the example of the watch above, the movement of the hands on the watch can be detected by us through interactions between the watch face and its hands and light photons that bounce off of those surfaces and then enter and interact with structures in our eyes that ultimately through a large number of internal actions and interactions gives us an understanding of those motions of the hands on the watch. Through such external actions and interactions you could also learn other things about the watch, such as the colors, sizes, and shapes of its external parts, etc.

          When you are trying to get a complete understanding of an already existent complex hierarchical device such as the universe, you must start by analyzing its external actions and interactions because that is all that you have access to for the most part. At this stage analytical structuring methods which generally are math based can be very important in developing understandings of cyclical motion flow structures and their interrelationships or the rules of operation of the devices that are detectable within the hierarchical level that you live in and then to work your way down to the basic structures of that level. When you begin to get to the level that you break some substance down to the point that it becomes two or more other substances, you can begin to understand that those substances were joined together or structured in some way that created a new composite structure or substance with its own internal actions and interactions and its own external actions and interactions due to the way that its parts are put together. At this stage, when you begin to go out of the hierarchical level that you live in and try to understand how things work at lower levels that you cannot directly observe, conceptual structuring begins to become important to focus observational and analytical structuring in the right direction to achieve the maximum development rate and to avoid following mathematical paths that lead to dead ends. At the same time the new observational and analytical information thus derived can correct conceptual errors. The observational, analytical, and conceptual disciplines can each act as a cross check on the accuracy of the others and are thus of equal importance in the acquisition and understanding of the information that is provided to us by the universe.

          Using conceptual structuring we find that as we progress downward through the hierarchical structural levels of the universe, some things such as linear and angular motions, energy photons, and field structures are present and act about the same way at all levels. The entities that make up the substances of each level, however, are different in some ways and tend to become fewer the farther down we go. At the large scale level there is an almost infinite number of different substances that can be made. At the molecular level there are still more possible different molecules that could be made than there are matter particles in the universe from which they could be made. At the atomic level, however, there is a great decrease in the number of different atoms that can be made, especially if you only consider the ones that are stable, and at the matter particle level only a very few stable matter particles can be made. This leads us to the likely possibility that matter particles may be made of only one most basic substance. This concept is strengthened by the fact that matter particles, energy photons, and simple linear and angular motions can be converted into each other. This means that they must all be composed of the same basic substance. Since they each behave differently in one or more ways from the others, they must contain different ways that the substance is structured within them. The fact that when matter particles interact with each other, they can produce several different output interaction results, each of which has its own probability of occurrence tells us that they must contain internal motion structures that can be positioned differently in relation to one another in each matter particle at the point of interaction, such that the different interaction outcomes are generated. The different probabilities of occurrence of each outcome suggest that there are physical spatial areas that motions could be in at the point of interaction that yield each outcome that vary in size for each of them, etc.

          Just as in the past it has been a great help to the advancement of science to have conceptual models of how molecules are constructed and later models of how atoms are constructed, we are now at the point that conceptual models of how matter particles are constructed are greatly needed to guide scientific development into what may very well be the lowest level of structure of the universe. Then the analytical and observational structuring disciplines can be used to model the detailed motion flows and their resultant interaction results for a full in depth understanding of the universe as it is currently known by man in this world. At this point what is needed is someone who can develop the math that can model the complex motion structures of matter particles, etc. and their interaction flows. New math structural concepts such as path flow structuring may need to be developed to make it easier to accomplish this.

          Sincerely,

          Paul