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)?

          4 days later

          John,

          You wrote: "How nature chooses the laws of physics may be unknowable". In my article I provided metaphysical arguments for the necessity of many paradoxical features of quantum physics. So I think there are knowable reasons for the choice, as I found such reasons (not for all details of course but for some main features), as opposed to other classes of universes such as deterministic ones like those described by classical mechanics, which I consider excluded from the possibility of physical existence able to carry conscious life.

          "Quantum field theory suggests there are infinite combinations". From a mathematical point of view it is indeed naturally analyzed as involving potential infinities of underlying full descriptions (shapes of fields or trajectories), however the global result of these combinations is that they only leave a locally finite number of possible effective states (in a quantum sense) for each given limited amount of available energy, as I also explained in my essay. (See also my web page of introduction to quantum theory, starting from principles coherent with quantum field theory even if the mathematical correspondence between the formal infinity of combinations of quantum fields and this effective local finiteness of available states is a rather subtle one).

          To roughly explain this articulation : these mathematical details of the continuous description (the shape of a field or trajectory) are not physically real but can only become real when created by an act of physical measurement of these details at a given scale of resolution (and the thinner details we want to measure, the more energy we need to measure them).

          "the statistics of QM is really a measure of measurement error as the Bohm Interpretation suggests. The Bohm Interpretation argues against ideas of infinitely many paths of particles until a collapse happens".

          How amazing to see you simply claim how things would "really" be, as if it was obvious or simply acceptable without problem, this kind of view that of course very many physicists were very persistently trying to imagine, but which scientific evidence also persistently dismissed for any try to keep things reasonable. See my page on the Bohm interpretation, where I show it has so many troubles that I cannot consider it seriously plausible. Even in this interpretation that is the closest we can find to the idea of "measurement error", randomness is still not any effect of a measurement error but the result of the absolute impossibility to measure something even in principle. Ironically as opposed to your remark, one of the main troubles I see with the Bohm interpretation is that it reintroduces an actual infinity in physics which the fundamental features of quantum theory remarkably avoided (standard quantum theory considers randomness as a pure fact created by observation that does not hide any real detail, while the Bohm interpretation claims that observation only reveals some data from a hidden actual infinity of real details, those of continuous variables that would really exist with infinite accuracy ; my essay explains how quantum physics makes the continuity of variables only behave as a potential infinity, not an actual one).

          "Mathematics characteristics may eliminate many of the possible interpretations of QM as being unphysical." What do you mean ? Well, we can say that mathematics practically eliminates the Bohm interpretation as being too mathematically inelegant as explained in my web page. But I cannot see what else you may mean here, as you did not even define what means "unphysical" as if there was such a thing as physicality that had to be satisfied (the paradoxes of quantum theory rather argue against the idea of physical reality, as not having a natural fit with what we observe).

          "Newtonian mechanics has a calculation problem as r в†' 0" : only if we assume the presence of point masses, which is not a claim of Newtonian mechanics.

          "GR suggest the universe is homogenous to avoid the r в†' 0 issue." Well no, what GR does instead near r=0 is that a high concentration of mass gives a black hole with a smooth horizon (that is a locally non-special region of space-time) from which no information can go out.

          The difference you assumed that is a difference between point masses and smooth densities, is not an effective difference at all, but only a difference of the mathematical tools which are used for formulating theories or their consequences, but are not really associated to the theory. For example, Newtonian gravitation can be equivalently expressed between formulations using singular masses and formulations using smooth densities, in this way : a smooth density can be understood as a dense regular accumulation of point masses ; a point mass can be understood as the limit of a high density in a small region. According to distribution theory, each concept can be understood as the limit of the other in the dual space of the space of continuous fields g on the physical space:

          A distribution of point masses (mi at point Pi) defines the linear map (from the set of continuous fields g into в„ќ)

          g ↦ sumi (mi g(Pi))

          that is the finite linear combination of Dirac masses at each Pi (that is, g ↦ g(Pi) ), with coefficients mi.

          A smooth distribution with density П† defines the linear map

          g ↦ integralx φ(x) g(x) dx

          These 2 spaces (the space of distributions of point masses, and the space of smooth densities) both duals of the same vector space of continuous fields, are parts of the more general dual of this space where they are the limits of each other and where the law of gravitation is naturally extended as long as we are not considering physical cases where it leads to divergences in its consequences.

          "Mathematics shows only two mutually exclusive characteristics in reality - discrete (counting) and continuous (geometry)"

          No : in the dual space mentioned above, the discrete and continuous distributions are not the only possibilities which are the limits of each other. Another kind of possible distribution, intermediate between the discrete and the continuous distributions, and also corresponding with them as being the limits of each other, is the case of a Cantor set distribution, with any choice of fractal dimension between 0 and the dimension of the containing space.

          However this does not say which kind of distribution is actually involved in physics. When analyzing whether some equations initially written in differential form finally lead to convergent or divergent results, different things can happen.

          What really happens at sub-atomic scales has to be given by quantum field theory, however what this gives is not any definite distribution of anything, since it is a quantum reality, not a classical one: we do not have any definite distribution of anything but states of regions that can be analyzed as differently made of superpositions of possibilities depending on how you analyze it (with which scale of resolution of the analysis).

          Quantum field theory is full of mathematical expressions written in a formalism which seems to require some class of regularity of fields, until it turns out that the fields actually involved are not in this regularity class, so then we need to develop techniques to make these ill-defined equations provide results despite their lack of definiteness. In quantum field theory, this is the question of whether a field (or interaction) is renormalizable or not. Sometimes we exclude some interactions as they are not renormalizable (they diverge), other times we still accept them, admitting that we do not know what happens at very small scales (high energies).

          General relativity admits distributions of mass down to space dimension 1 where the resulting geometry becomes singular (may it be a line or a Cantor set distribution with fractal dimension 1), below which we get black holes.

          You mention "scale relativity". This "theory" by French "physicist" Laurent Nottale is not even a theory but pure senseless bullshit, as I explained in details many years ago. I wrote the detailed explanations in French but you can see here my short report in English on this issue (see also my related notes on science and pseudo-science).

          "Perhaps the "space" of GR, the wave medium of QM, and the plenum are the same physical constituent. If the frequency of the wave is related to the particle, resonance produces quantum entanglement."

          Perhaps, perhaps... of course, as long as you do not make the work of seriously learning the mathematical structures of the world that were discovered and so well verified in modern physics, any fantasy will seem equally plausible to your eyes.

          "The fractal principle suggests that observed geometric relationships apply in all levels of systems. Because pi = circumference / diameter in two dimensions, pi must be the same number in three dimensions."

          Well, pi is the same number no matter anything such as the dimension of anything, because it is absolutely well-defined as a fixed real number independently of anything. However if you ask about generalizations in other dimensions, of the ratio circumference / diameter, then I'm sorry but it takes different values. These values can be expressed using pi, but these are different expressions. By the way, what is the circumference of a sphere ? A sphere has a surface, that you can compare to... the square of the diameter. Then the ratio still happens to be pi in the 3-dimension space but this is a coincidence that no more works in higher dimensions. And it does not have anything to do with the fractal principle (which is not a physical principle but a property of abstract geometrical objects which only happens to approximately fit some natural objects inside some limited range of scales), where things are similar at different scales but with the same fractal dimension (please, please, don't play with the ambiguity of the word "dimension" in the English vocabulary, which may mean 2 completely different mathematical concepts ! this is so ridiculous).

          "The relatively easy developments of Euclidean geometry compared to curved space geometries suggest the universe is flat."

          The universe is not flat. Only the global geography of the universe, that is the map that can be abstractly rebuilt in terms of the relative positions of all galaxies considered at a common age of the universe, has been observed to be quite close to flatness from, for example, the data of the cosmological background radiation. This should not be confused with any cancellation of space-time curvature. For more details, see my text of cosmology.

          "Life on Earth can increase although entropy increases because Earth is an open system with energy supplied by the Sun. That fractal mathematics works suggests the universe must also be an open system. This suggests the universe is not adiabatic."

          Ridiculous. The universe is adiabatic. Its cooling down results from its expansion, giving a wider and wider intergalactic space able to absorb (accumulate) all the entropy created by so many material processes, mainly in the form of visible and infrared radiations.

          I skip parts of your article as I am getting bored, I stumble on "The temperature of the universe appears to be a fine tuned parameter and it is very close to the natural logarithm base e K". Sorry, it is not fine tuned. The universe cools down during expansion. Thus its temperature depends on its age, but anyway it is now cool enough for this heat to be insignificant for the issue of habitability. You are making ridiculous numerology here, because the Kelvin is not a natural unit, but the 1/100 fraction (according to our human decimal conventions) of the interval between the temperature of ice fusion (which is almost independent of pressure) and water boiling which is highly dependent of pressure : we take here as reference the average atmosphere pressure at sea level on Earth, which has no reason to be the same on other habitable planets. Other habitable planets may have different sea level atmospheric pressures, such as half or twice ours, leading to very different values of water boiling temperature, and thus other conventions of temperature units, still assuming by chance these aliens to have the same numerical conventions.

          "Mathematics is deterministic. Given an equation and the initial data, a definite result is calculated. This implies that the universe is deterministic. If there is free-will, then the mathematics humans have developed needs a new function like fractal development or a model of the mechanism of apparent free-will."

          Your sentence seems to express a confident belief in determinism, though it is not clear as you seem to beg for an articulation with a possibility of free will. Why expect something new ? As I explained in my essay, we already have the needed "math of free will" under hand : determinism was spectacularly dismissed by quantum physics, and all the so popular tries to reinterpret it in deterministic manners remain so desperate (mainly with the Bohm interpretation, even though I do not see it genuinely deterministic, while other interpretations are even less deterministic). Determinism is only sociologically normal in the sense that it is a very popular sport to keep bumping one's head on the wall of the physical evidence of indeterminism, baselessly dismissing (by metaphysical prejudice) this evidence from quantum physics as a mere irrelevant temporary accident hiding a deterministic reality that we must work to discover...

          "There may be no standard capable of fulfilling the physics definition of a standard that reflects the mathematics characteristic of different mutually exclusive discrete and continuous".

          In this article and also the other article you wrote ("Photon diffraction and interference") you express your general assumption that there would be a problem in physics about the compatibility between the discrete and the continuous, between the concepts of waves and particles. The real fact is that there is no such problem : the coherent mathematical formulation of quantum fields and how it articulates the aspects of fields and particles, is now well-understood by professional physicists since a long time. Of course this idea looks very unintuitive for people not familiar with these mathematical concepts, which cannot be simply explained without high mathematics, so that many people keep the illusion that a problem subsists. You seem to have this illusion. If that is the case, it would be a pity, meaning that you did not study physics at a high level enough to understand the known solution of this paradox yet.

          Now from your comments:

          "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. "

          This seems to show that you are not familiar with General Relativity either. General relativity explains gravitation by concepts that do not include such a thing as "a gravitational field that exerts a force" in this naive (Newtonian) way you are describing.

          "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." I consider that the fundamental character of consciousness is that it escapes mathematical description. However as I explained in my essay, some special mathematical features of physical laws are needed and provided by quantum physics to allow for the interaction between mind and matter. There cannot be a math to describe consciousness. There is a clear concept of what is math and what is not math. A "new form of math" is nonsense : if it is still math then it is math as we know it in its generality (see the foundations of mathematics describing this generality); if it is radically different then it is not math anymore.

            Poirier

            Today's physics models have many observable inconsistencies (data). The problem is to first explain the mysteries, predict results not yet observed, and, if possible, correspond with current models with restricted parameter definitions. Your approach seems to be to `explain' the current models as if they are God's truth. The truth is these models are in need of improvement. That is, they are wrong as one or two other papers explain. I suggest there exists a Theory of Everything that unites (uses the same postulates) the big and the small and, hopefully, explain a few of the mysteries in the same set of postulates.

            (note: I include in `mystery' the suggestions of ad hoc bandaids to models such as dark matter, dark energy, inflation and the double-slit experiment. Each of these represents a set of data poorly or unexplained in current models. These data only show how limited the current models are. )

            At the outskirts of physics is metaphysics - you know, the postulates that have no reduction to hypothesis, and therefore have very limited, if any, use. Engaging in metaphysics has its conceptual uses. It may suggest a speculation that may lead to a hypothesis that may lead to a model. But if we are progress we should go with a hypothesis with explaining value of some mystery over metaphysics.

            I am taking some of the ideas in the very large set of ideas being published today and forming a model that has corresponded to both cosmology and the small

            (through the double-slit experiment) and explained several mysteries of current models. It has also made a prediction in 2006 which was found a few years later.

            So, what is your ToE? All you seem to have is metaphysics, a poor understanding, and a set of one of among many interpretations of current models.

            5 days later

            I am not working on any theory of quantum gravity as I know it is a very hard problem, that many clever physicists are already working on, while I found other, more useful fields of mathematical research for the progress of the world (namely, cleaning up the basics of maths and physics and redesigning the economic system), and that I do not see any great thinker working on. In particular, what I bring in the present contest is a solution to the interpretation problem of quantum physics, which I see quite simpler and independent of the problem of quantum gravity.

            My essay focuses on the metaphysical aspects of quantum physics, and is indeed expressed in words and metaphysical concepts with no explicit use of physics formulas, however it does not mean that I have a poor understanding. Sorry to disappoint you if you want to believe that my understanding of physics is poor, but it is not. On the contrary, you can check how I provide in my site a clearer understanding of quantum theory as well as other important topics in the foundations of mathematics and physics, such as a clean introduction to tensors and introduction to Special Relativity theory. And I have enough deep and correct understanding of quantum physics to be able to debunk the relatively naive errors committed by someone who seems to have arguments but based on an incomplete understanding of quantum theory and the measurement problem. And I was also some time ago the only one to successfully make the huge work of rigorously debunking a much bigger and very famous (in France) piece of nonsense by a famous crank (Laurent Nottale) that all French popular science magazines mistook as the genius of the century having discovered the theory everything (more precisely, a grand unified theory of everything and anything, including patterns of biological evolution and planetary orbits).

            There is perfect coherence between the concepts I presented in my essay and the mathematical structures of quantum theory. However, of course I could not develop the full proof in details in so few pages. I must assume the reader to understand the established body of knowledge in quantum theory, which is necessary for the understanding of how my metaphysical concepts perfectly matches them. Unfortunately, this assumption turns out to most often not fit the case of most readers here, and this is also not the case for you. But I do not feel responsible for this gap, as I do not consider this to be the place for filling this gap, repeating the teaching that is the normal requirement for any sensible debate on the interpretations of quantum theory.

            Now what appears to me, and as I had a look to your Scalar Theory of Everything, is that your own understanding of quantum theory is very poor, or maybe even non-existent, so that your claim to find a theory of everything uniting it with general relativity is just ridiculous. Just like Laurent Nottale, you also make a sort of grand unified theory of everything and anything while not having started to understand the theories you claim to unify, mixing considerations and claiming things (such as "Investigation into the characteristics of and differences between spiral and elliptical galaxies yielded the conclusion that the Sources of the plenum and hods are in the center of spiral galaxies") that have absolutely no chance to be involved in any serious work of unification between quantum theory and gravitation.

            8 days later

            I have read your essay and I really liked it. The conclusion is spot-on There may be no standard capable of fulfilling the physics definition of a standard that reflects the mathematics characteristic of different mutually exclusive discrete and continuous. Yes discrete vs continuous and what standard you use to breach the two are vital for the current impasse in physics. Very thought provoking essay. I gave your essay a good mark!

            I note that some of the other posts on this thread are very harsh so just ignore them. I appreciate the nice comment you left on my essay. Yes I did read Ojo essay very interesting and pertinent for my work on Sorites Paradox. Yours Harri

              I forgot to mention that I replied to your post about my essay with a long attachment.

              Could space be a continuous empty plenum and time be discrete? Can we always find a middle point between two endpoints for a length (if space is a Real number manifold) I wonder? Just couple of question I thought of. Yours Harri

              13 days later

              Dear Mr. Hodge,

              I thought that your engrossing essay was exceptionally well written and I do hope that it fares well in the competition.

              I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

              All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

              Joe Fisher

              19 days later

              John,

              Good essay, undervalued I think. Also too many score on whether they 'agree' or not, (which isn't the point here) so your scalar approach to a TOE may not help your score. I happen to agree with that approach, (as we've found before) so to compensate I'll let that influence me!

              Times' now short so comments are too;. Fractals and multiple dimensions great! well done. Also 'new physics' needed for the key core problems (but suspect you did well not proposing it here).

              I hope you may manage to read/score mine. (It keeps being knocked back with no comments posted, a little rude I feel!) I agree nature CAN be modeled naturally by maths but identify that the maths is not always model the mechanism, so can confuse (as in the core matters above).

              Well done anyway. When we get the chance we must see if our hypotheses/models are still close and convergent. best of luck.

              Peter