Perhaps I should expand on one of the examples about a conceptual mystery such as the double slit experiment that math may show some insight to a better model. That the math of quantum mechanics (QM) works has been shown. However, the mystery is why? Thus, several concepts (interpretations) such as wave--particle--duality and the Bohm Interpretations have been conceived. But both (all) start from concepts and try to derive the Schrodinger equation (the math part of QM that works). But suppose we start with the observation that the math works and try to conceptually model why it works. Ask ``what is the math doing?'' Schrodinger equation defines the total energy as the sum of the potential and kinetic energy. The kinetic energy is the inertial mass energy. The potential energy derives from the potential field (whatever a field is) that imparts (somehow - by contact or action at a distance?) energy onto the (inertial) mass. These energies seem to have some relation to wave dynamics. Our scale observes waves in mediums that have unbounded differentiability (continuous). So I suggest the wave and its medium is real (yes I know there is argument here.) But then general relativity also mathematically suggests gravitational ether. A gravitational ether (called ``space'' today) is influenced by matter and influences matter through a gravitational field that exerts a force by contact through its divergence. Just what is need for the photon inducing potential energy Photon diffraction and interference .

The universe has 2 components - discrete matter and a continuous plenum (gravitational ether, space) and their interaction.

Well, why not?

Basudeba

I had noted your essay. I'm unsure what to comment on it. So, I'll start with your comment here.

Reality to me is whatever influences my survival even if I don't know it is doing so. Humans now measure many things that were unknown a few centuries ago. There may be other things that influence our survival of which we are ignorant. So relationships such as spirits and souls are real to me. Because we cannot yet create a universe, I'm sure there are such other things.

I think concepts that can predict observations are clear. If some concepts are defined differently in separate places (sometimes in the same paper), the concept is vague. For example, what is your ``space''? Is it a backdrop used to measure such as a coordinate system (you mention ``coordinate system'' separately but suggest space measures distance)? How about the general relativity concept of a medium (gravitational ether) that provides a gravitational field that influences matter. How about the void between matter as some ancient Greeks would have it. Or is ``space'' the left hand parameter in the GR field equation - and abstraction of calculating value, only. I'm unsure from your essay about what you consider a line (surface, volume) to be. Is a line a series of points or an extension? I think one of you other commenters was addressing this. Note I differentiate between the measurement and the abstraction such as saying a ``clock''(right hand side) and time (left hand side). Saying a clock implies some form of standard of duration measurement that I view as a set of problems requiring advancement in physics understanding.

Dear Sir,

There is no fundamental difference between your comments here and our essay, though certain things might have been unsaid. Regarding reality, please refer to our condition "intelligible/knowable". Everything is not intelligible to everyone at all times. Our actions for survival are influenced by our knowledge of our surroundings and how can we meet our needs. This knowledge; and its application; changes over time and space. Thus, what you say is covered in our definition. Regarding soul or spirit, we have not discussed. But if you define these terms precisely, we may not differ.

Your statement: "concepts that can predict observations are clear", has to be taken cautiously, as often our concepts are based on our observations and observations can be misleading. It may also be possible that the concepts define specific aspects only leaving out other aspects. For example, in our definition, space is both a backdrop as well as the interval between objects. Coordinates are used to measure spatial interval due to the following reasons:

1. To precise describe their relative order of arrangements with reference to an arbitrarily chosen origin.

2. Spatial interval may not represent true interval (e.g., on curved surface, etc).

3. To represent the macro representation of fundamental forces acting on a body: forces other than gravity act within the particle or from out of it (strong force attracts, weak force limits movement like in n-p chain or throws out like in beta decay, electromagnetic force moves from higher concentration to lower concentration, etc). Unless a conscious agent applies a force, all bodies due to the net effect of all internal forces against the gravitational force acting on any point. If the net is zero, the object is at rest or moving with fixed inertia. Coordinates show that representation.

Regarding GR, we had shown that it is a wrong description of mathematics. If you find anything wrong in our description, kindly elaborate. A line is either an imaginary concept (physically non- existent) or a marking on the surface of any three dimensional object including fields or graphs. The surfaces of these objects have no independent existence. Hence they are not one or two dimensional. Describing them as such is part description of a whole, which misleads. A line is not a series of points - which does not have dimension; hence do not physically exist. You are right about measurement, which is a mechanical process and abstraction of the result of such measurement as perception, which is a conscious process.

Regards,

basudeba

I think Leibniz introduces the relational problem of my ``spirit'' with consciousness (modern term). Would space and time exist, for Leibniz, if there were no minds to perceive the objects and events that around them? Suppose, if we may, that the best of all possible worlds had turned out to be one in which consciousness did not exist (note the Anthropic principle is a Principle not a derived model). God would have actualized that world instead of our world. (What is the Upanishads similar concept?)Would that world be a world in space and time? Therefore, the ``consciousness'' is part of our world and physics and math should be able to study it. But there is no math to describe consciousness, yet. As I said a new form of math is required.

You had noted the relational concept that the whole is greater than its parts and used H, H, and O to form water as an example. But this is not what I mean by ``spirit'' however tempting. The combination of H2O releases energy and therefore entropy. This rearrangement of energy is accounted in physics. The successive combinations increase entropy that requires a continual input of energy into Earth for life and into the universe - my ToE. Entropy was not accounted a few centuries ago in Liebniz's time. We can forgive Liebniz for including entropy concepts into his ``fictitious forces'' (careful, this is not Newton's concept of fictitious forces).

Forces in physics rearrange energy (your concept). Spirit also rearranges energy but without the 4 modern forces or entropy. For example, a student calls home and says send money. Money arrives is due course. The money represents a vast transfer of energy (time, effort, and material) relative to the cause (the call plus postage). Spirit is the ``force'' producing this rearrangement. This is related to ``consciousness''.

Thanks John. You certainly put a lot of intellectual energy into your essay. Well done. I agree that "Division presents a quandary in both discrete mathematics and continuous math", but I disagree that discrete and continuous are mutually exclusive. I have given this some thought and write about this in my essay.

What do you mean by 'discrete'? What is and acts as the 'separator' of the things you call discrete? Next, what separates the 'separator' from that thing so that the separator and that thing are not One thing?

I hope I make myself understood.

The Newtonian problem of r 竊' 0 that you discuss is an interesting one. I believe it has not yet found a satisfactory solution.

Finally, there is a question I have asked a few others and will ask you being a retired but not tired physicist :)

In his book, The Emperor's New Mind, p.113, Roger Penrose has this to say, "The system of real numbers has the property for example, that between any two of them, no matter how close, there lies a third. It is not at all clear that physical distances or times can realistically be said to have this property. If we continue to divide up the physical distance between two points, we should eventually reach scales so small that the very concept of distance, in the ordinary sense, could cease to have meaning. It is anticipated that at the 'quantum gravity' scale (...10-35m), this would indeed be the case".

I therefore ask you whether if the system of real numbers applies to distance, if there is always a third element between two elements and going by geometrical considerations these elements, (which would be points in the case of lines) are uncuttable into parts how can a distance be divided?

Regards,

Akinbo

    Akinbo

    Thanks for your comment/questions. I'll reply also in your entry and in the interest of dialectic discourse.

    I think the interest of physics is the prediction of observations and the usefulness of such knowledge to the survival of us (our gene, our progeny, etc.). If a set of definitions fail to result in the advancement of physics, they have little use in physics. However, humanity has experienced may times some set appearing to have no use at a given time only to have a use found later. So math study and documentation keeps them alive. I reject the Zeno and other such paradoxes as not useful.

    Multiplication is the successive addition of a number. The inverse of this operation is not division - the inverse of multiplication is successive subtraction. Division as currently defined has only a calculation convenience in which great care to avoid many physical pitfalls must be take. Often this requisite care is not taken that results in non-physical results.

    (My web site links) to papers that describe my views. I answered many of the questions you ask, selected the set of definitions, and wrote papers addressing many mysteries of cosmology and, currently, the quantum world in the study of the double-slit experiment.

    I read your essay to discover your definition of ``separator''. I think (you should check) that your ``separator'' in my ``discrete''. Do you agree that your separator is mutually exclusive from your continuous? My continuous is the plenum that is a physical component in our universe. The plenum is ubiquitous, is unbounded differentiable, and extends in 3 dimensions. As suggested in my essay, a universe of only one component cannot be our universe. There must be another component and the relation between the components. Relations among the discrete components is called algebra. The relation between continuous and discrete is called matter. This implies the discrete component cannot occupy a third dimension - I call it a hod. The hod is a 2 dimensional surface. It forms a discontinuity in the plenum. The discontinuity part is the role of your separator. A thing cannot be continuous if it can be cut with a distance between the pieces. So separation is done by a discontinuity in the density.

    Real numbers do not apply to distance. A number is a counting abstraction. Distance is a number of standard lengths between 2 hods or assembly of hods. The minimum distance is the diameter of the hod. This set of definitions makes the question you pose undefined.

    John,

    Redefinition of things that are already defined is one way to resolve paradoxes and absurdities. But then such redefinitions must stand up to scrutiny and should be verifiable or falsified.

    I like your definition of Multiplication and Division. It can resolve paradoxes of motion like Zeno's, if "Real numbers do not apply to distance" as you say.

    My own contention is that the plenum is discrete and also continuous in some sense. Thus displaying a duality. Continuous because there is no distance between its lengths, but discrete because those lengths can perish or be created from Nothing. The fundamental unit of my plenum is the extended (not zero-dimensional) point.

    You will have a task ahead to show that John or Akinbo are 2 dimensional objects and therefore no volume can be ascribed to them. You may have further explanation in your links, which for lack of time I have not viewed. But would do that some time.

    In your cosmology, does the plenum perish or change in size? Or is it infinite in extent and duration?

    Lastly, let me leave you with a food-for-thought that I have left for some, especially as you said, "Real numbers do not apply to distance".

    Roger Penrose in his book, The Emperor's New Mind, p.113 says, "The system of real numbers has the property for example, that between any two of them, no matter how close, there lies a third. It is not at all clear that physical distances or times can realistically be said to have this property. If we continue to divide up the physical distance between two points, we should eventually reach scales so small that the very concept of distance, in the ordinary sense, could cease to have meaning. It is anticipated that at the 'quantum gravity' scale (...10-35m), this would indeed be the case".

    Regards,

    Akinbo

    Akinbo:

    ``You will have a task ahead to show that John or Akimbo are 2 dimensional objects and therefore no volume can be ascribed to them. ''

    The STOE (Scalar Theory of Everything) suggests there are 2 components of the universe - Hods (2 dimensional and forms kinetic energy) and plenum (forms potential energy). Matter has both types of energy and, therefore, both types of components. The photon is suggested to be a column of hods oriented flat to flat with plenum being held between the flats and holding the photons in place. Likewise matter is structures of photons. This allows the release of energy when matter is converted (annihilated?). The direction of photon travel is parallel to the hod surface. Because this presents zero cross section to the direction of travel, the photon travels at the maximum rate - called the speed of light which is the speed of the hods. Lorentz suggests this rather than having a specific speed in a vacuum for indeed the STOE has no vacuum. Newton suggested that the plenum wave speed (not matter and therefore not matter speed) was faster than the photons (see my essay). This has an interesting side issue. I use the heat equation to describe the plenum density (the scalar quantity) at any given position. The heat equation is not amenable to wave solutions unless the wave can travel (much) faster than the inducing force (the hod). The divergence of the plenum density is gravity.

    This shouldn't be too strange. The electromagnetic force binds atoms so tightly that atoms are thought of a being a single entity and not a nearly empty volume. Indeed, John and Akinbo don't fall through the earth because of the binding forces.

    ``In your cosmology, does the plenum perish or change in size? Or is it infinite in extent and duration?''

    Short answer: plenum and hods are ejected (perishes) from our universe and the plenum changes in extent. Let me use a little space here to save you some reading.

    The heat equation concept requires a Source and a Sink of energy. It yields a 1/distance density (temperature, energy) from the Source or Sink. Both components enter our universe through the center of spiral galaxies and sink out of our universe through elliptical galaxies. The components flowing out from the Source cool. The 1/distance divergence of the plenum outward from the Source counters the gravitational force of the hods (1/distance from the hod called gravity) to produce the many spiral galaxy (mysterious) characteristics such as the (usually but not always) flat rotation curves of spiral galaxies. An edge of the spiral galaxy is defined where some of the hods (now hydrogen) coalesce and form stars that fall back to the Source because their cross section on which the plenum acts is smaller and the gravitational force predominates. This explains many ``infall'' mysteries. Some plenum and hods continue out to form a flow to the elliptical galaxy. This is called a cooling flow because the material must loose energy to be allowed to coalesce into the center of the elliptical galaxy to the Sink and out of our galaxy. The material that falls back to the center of the spiral galaxy must also cool. That is its entropy must increase. So it forms larger, denser stars or radiates photons out of the galaxy. The stars form neutron stars, quark stars, and ultimately black holes that fall to near the Source. The very high density near the source compresses the black hole into the photons (X-ray radiation that occasionally -2-3 times per year- erupts/bursts from the center of the galaxy). BTW the infall's need is to increase entropy. Life is very efficient at this as my thought of ``spirit'' suggests. Therefore, life is encouraged because it aids the universe's need (see my essay last year). BTW the galaxy clusters have many spiral galaxies close to each other. The nearby galaxies' plenum outflow influences a galaxy's rotation curve to form the ``asymmetric rotation curve'' found in nearly all spiral galaxies (this observation is usually ignored).

    Now for simplicity consider one source and one sink. The components expand in all directions until the flow is into the Sink. Some material will travel away from the sink but the divergence will intimately be toward the Sink. Therefore, the universe is flat and has a limited extent - is bounded.

      Dear John,

      I read with great interest your essay. I fully agree with your very important conclusion:

      "The goal should be to make the universe more conceptually understandable. This aids understanding and predictability that aids human survival. Considering mathematics methods as a physical observation would open new avenues of physics understanding and, perhaps, physics insight." My high score. I invite you to read my essay .

      Kind regards,

      Vladimir

        John,

        We have areas of convergence at some level and divergence on some specifics. Convergence in that your Plenum is a sort of 'substantivalist' model. My model also falls in this category, as opposed to Relational theorues.

        I woke up this morning thinking about your definition of Division as subtraction and Multiplication as addition. In Zeno's Dichotomy Argument, if this redefinition is brought to bear on the paradox, Atalanta the runner races towards his goal by subtracting distance rather than dividing distance. In doing this he reaches his goal in a finite time, unlike the infinite time using division.

        Now, if you look at this again, you will observe that as Atalanta is subtracting distance from his goal, distance is being added between him and the origin (which is your redefinition of Multiplication).

        Now, something to ponder: When you subtract something from another, where are you keeping it? And when you add distance to another distance, where did what you are adding originate from? This would be one area our models diverge.

        It will be difficult for me to swallow the way you ascribe source and sink to galaxies. Galaxies to me are mere collection of stars and I think I have even read somewhere that an elliptical galaxy can evolve to a spiral type or the reverse, I am not sure.

        Lastly, at least you have surfaces in your model, if not lines. Are they composed of fundamentally indivisible things? If so, how do you cut a surface into two?

        Battery running too low to make my last point clearer...

        Regards,

        Akinbo

        Akinbo

        Thanks for the continued dialog.

        ``In doing this he reaches his goal in a finite time, unlike the infinite time using division.'' Yes. Thus the idea is physically practical whereas the division is not physical.

        When you subtract something from another, where are you keeping it?

        The subtraction is merely a calculation to determine a physical relation. What does it mean to ``keep it''. There is nothing to keep. The distance from the starting point remains the distance from that point to the goal until some force expends energy to move one or the other.

        The idea of evolution of elliptical galaxies to spiral galaxies is an old idea (discredited) called the Hubble sequence. The classification scheme is still used but the idea of evolution has been dropped.

        I mentions the broad differences between elliptical and spiral galaxies in Scalar potential model of redshift and discrete redshift which was published in New Astronomy 11 (2006) 344-358. The data and comments are from Binney,~J., Merrifield,~M., 1998. Galactic Astronomy. Princeton University Press, Princeton NJ

        Below is an excerpt:

        ``The great majority of elliptical galaxies are observed to be much poorer in cool gas and hydrogen than spiral galaxies of comparable luminosity \citep[pages 527-8]{binn}. The bulk of the interstellar matter (ISM) in spiral galaxies is H{\scriptsize{I}} and hydrogen. In elliptical galaxies, the bulk of the ISM consists of hot plasma distributed approximately spherically rather than in a thin disk \citep[pages 525-6]{binn}. A characteristic of elliptical galaxies not found in spiral galaxies is that the X-ray surface brightness is nearly proportional to the optical surface brightness \citep[pages 526]{binn}. The study of dust lanes suggests that gas and dust are falling into elliptical and lenticular galaxies \citep[pages 513-6]{binn} and are formed internally in spiral galaxies \citep[pages 528-9]{binn}. Some evidence has been presented that suggests irregular galaxies will settle down to being a normal elliptical galaxy \citep[page 243]{binn}. In low surface brightness (LSB) spiral galaxies, the outer rotation curve (RC) generally rises \citep[and references therein]{debl}. In contrast, ``ordinary'' elliptical galaxies, with luminosities close to the characteristic $L^*$ (=2.2 $\times 10^{10} \, L_{B,\odot}$ in B band solar units for a Hubble constant $H_\mathrm{o} = 70 $ km~s$^{-1}$~Mpc$^{-1}$) show a nearly Keplerian decline with radius outside $2R_\mathrm{eff}$, where $R_\mathrm{eff}$ is the galaxy's ``effective radius'' enclosing half its projected light \citep{roma}.''

        ``Galaxies in groups and clusters (``clusters'') are much more likely to be elliptical or lenticular than in the field. Spiral galaxies lie farther from the center of clusters than do elliptical galaxies. The fraction $f(E)$ of galaxies that are elliptical galaxies in clusters varies from 15\% to 40\%. Clusters with a large value of $f(E)$ tend to have a regular, symmetric appearance, often with a large cD galaxy at its center. Clusters with a low value of $f(E)$ generally have a ratty appearance. The fraction $f(Sp)$ of spiral galaxies in centrally-concentrated clusters increases with radius $R$ from the center of the cluster. The observations are consistent with the model of their being no spiral galaxies in the cores of regular clusters. The lenticular (S0) galaxies become increasingly dominant at small radii. Nearer the core the fraction $f(S0)$ of S0 galaxies declines sharply as $f(E)$ increases sharply. Also, the $f(E)$ increases and $f(Sp)$ decreases as the projected number $N_\mathrm{d}$ density of galaxies increases. There appears to be a close relation between $N_\mathrm{d}$ and $R$. The morphology of galaxies appears strongly correlated with the current surrounding density. ''

        Most of these observations are mysteries in current cosmology. But you'll notice the STOE fits these observations very well especially the bit about the flow of matter out of spiral galaxies (like from a source) into elliptical galaxies (like into a sink). This is data. Ascribing the nomenclature of Source and Sink is mine.

        ``If so, how do you cut a surface into two?'' I suppose you're talking about the hod. The diameter of the hod is postulated to be the smallest that a single object can be. Part way across the surface can be contemplated. But to physically cut the smallest thin in the universe would violate the postulate and the usefulness of the hod. However, I have thought a future line of thought is to construct the structure of particles larger than the photon. The STOE suggests the structure of particles with the same type of material accounts for the size and differences among the particles.

        My first try was to consider a hod could be perpendicular and through another to form a structure. first try .

        ``Something "distance" that can be subtracted from can in some real sense be labelled a substance since it can be acted upon. And whatever can be acted upon MUST also be capable of reacting (or acting).'' Distance is a measurement. The distance between 2 objects can be reduced by application of a force or change in energy. If you mean something else, please define your term.

        My plenum is like the `space' of GR. Hods act on the space to create the gravity well and the plenum acts on hods to direct their path.

          One of your applications, "If the three rooms are at differing temperatures, the bars will be of different lengths. The coefficient of expansion is a reorganized physics phenomenon. But when we make a bar a standard, the unit of length becomes a function of temperature," indicates how human mathematics is derived from human perception in this case, but the applications I noted relate to the classical world. What about the quantum world? Are you saying that the models we use for quantum modeling also derived from human perception? How do you make math an observation?

          My "connections" essay doesn't question derivative qualities of math, and only mentions the peer reviewing process of concepts like BICEP2. How are mathematical models missing the boat, if the community treats math as a non-derivative of human perception.

          Your essay is thought-provoking and certainly requires close reading.

          Jim

            The larger issue is math in society. Economics, the social studies, and people in general reject math. Consequently, math is `unreasonable' in physics because physics/science accepts math as part of the prediction process. But humanity is reticent to accept math as a description of nature. But why? I suggest, because the goals of those other branches of knowledge are to support a political model that rejects math. I suggest humanity needs to incorporate math and nature into the new world order.

            This topic has been informative on many subtopics. Thanks folks.

            Math works in physics because both disciplines are seeking the way nature works.

            The ages of humanity are labeled according to the predominate set of beliefs that inspires and consoles individuals. Religion provided this in the medieval period, reason in the enlightenment, nationalism with a view of history in the19th and 20th centuries, and science and technology in our age.

            If math describes how nature works, math should apply to the advancement of humanity. Math needs a measure such as in physics. Our knowledge of nature means we can predict nature's response to a given set of conditions. The study of politics and humanity requires a measure and a goal. I suggest Survival is the only moral goal of life]survival is the only moral goal of life. The difficulty is that the actions necessary to obtain survival are rejected by humanity. My 2014 contest paper noted a few such examples.

            The politicians don't like the answers that math predicts. Therefore, the study gets diverted into vague realms that fail to make good predictions. I took economics in college using `Economics' (a Keynesian model) by Samualson. I found it lacking in data comparisons and full of hand--waving. Later I found the Friedman economic model with data comparison and with math. My 2014 contest paper notes the Friedman economic model did make predictions. But the competing Keynesian model is accepted because it produces a politically accepted view although it fails to predict observations. The difficulty caused by complexity is compounded by marginalizing knowledge that has successfully predicted events, but is politically awkward. For example, the Friedman economic model predicted stagflation that Keynesian derived doctrine said could not happen, predicted the collapse of the soviet system that Keynesian derived doctrine praised, and predicted negative results of big government. The Keynesian derived doctrine of big government has repeatedly been falsified. Friedman argued for a small national government, which the politicians vote against.

            Further, the actions and morals needed for survival are contrary to many morals in modern society. The phrase `no good deed goes unpunished' is largely true because the current definition of a `good deed' needs revision. .A `good deed' needs to be according to nature's justice not humanitarian justice. Tainter (in the 2014 paper) noted several observations and characteristics of a collapsing society. It is not that the conditions that cause collapse are unknown. Yet, to behave in a manner that yields survival seems contrary to how people vote and the politicians act. Science has produced a better life for the average person in the scientific societies but has also produced much more destructive weapons. So some want to reduce science, and, presumably, to revert to the moral systems of long ago that produced a nasty, short, and brutish life for most people. But the better solution is to embrace nature and science. Nature will win even if it must kill civilization.

            Are the morals to change and collapse be avoided?

            Jim

            `... but the applications I noted relate to the classical world.' Yes, Note the idea of fractal (self--similarity) is that the perceptions and math of our scale world should relate to all scales including the quantum world.

            Math is made an observation by considering valid math concepts as data for the physical world. `Valid': note the 1/3 example in the essay and the conversation in the comments above. Division is not a valid operation. You may also note the comment was raised in a previous comment where I referenced the Schroedinger indicated waves. When combined with a Newtonian view, the double--slit experiment may be explained

            Hi John,

            I enjoyed reading your essay. The idea "Mathematics shows only two mutually exclusive characteristics in reality - discrete (counting) and continuous (geometry).", caused a pause and some thought on my part, but I think I agree with its importance. The two different approaches leads to some interesting ways to understand things as you point out.

            Thought your closing was appropriate "Making physics more complex and less conceptual reduces the ability to predict and is, therefore, not the goal. The goal should be to make the universe more conceptually understandable."

            Very nice, Thanks

            I follow these contests because there usually are 3-4 papers with something interesting to me. I'm finishing a study about the double--slit experiment and am beginning to search for the next project.

            Dear Richard Lewis:

            You asked about taking a math solution and applying it to physics.

            What do you think about the following?

            Would you classify the group models of particle classification the same as you classify statistical analysis. The periodic table was developed first by noting common characteristics of elements. A few holes were filled (predicted) by where the hole was in the classification scheme. Later, the causal underlying structure of atoms explained the periodic table. Indeed, the position of an element indicated something about the atomic structure. The same type of classification is true for the group models. Holes in the group model have been used to predict particles that were found. Can this be used to imply an underlying structure of particles? How would such a study proceed? Is anyone working on the structure of particles (papers I see seem to stop with the group description with no indication of an underlying structure)?