Mathematics characteristics are universe characteristics by John C Hodge

Stephen Ternyik

Many thanks for introducing me to your approach of survivalist morality, John.At the IA ,I will further study your proposals, e.g. for the US, EU. In the the Goal of Life Essay, you write about the key paradox='as life advances it must become a more efficient user of resources'; this is the ethical imperative that human societies on this globe must learn about the natural construction principles of reality. With reference to this quote, you will receive a little book gift to your blueridge.edu. Best: stephen

Stephen Ternyik

gift went to citcom, blueridge did not work.

John Hodge

I've retired. New email Jchodge@frontier.com.

thanks

John Hodge

Whether we are abstract of not, whether our universe is abstract or not isn't even a speculation much less a hypothesis. At very best it is metaphysics. Therefore, it shows no promise of providing some testable hypothesis much less a prediction of some observation or something useful to humanity. Although there are many things outside our ken, we progress by taking the problems we can sense and making the nest new prediction.

Joe Fisher

You are a real person, you are not an abstract we.

Regards,

Joe Fisher

John Hodge

L. B. Crowell's paper in this contest has an interesting question: ``Does this mean that older forms of mathematics will disappear?'' It suggests math has an evolution or selection--of--the--fittest history in human discovery.

Science has precipitated out of philosophy to be that part of human knowledge that predicts observations. Does science extend as far as metaphysics? Likewise math as we know it today has become the usefulness of counting and geometry. That is, math is the result of a selection of the useful methods (evolution). You noted logic has not been as useful as counting math. Math and logic have not yet reconciled (yes, I know about Russell and Whitehead's book but I like others think he had inadvertently assumed the counting process in his set development.)

One of the characteristics of today's usage of math is the concept that a (counting) number that represents a physical object can be negative. The number system I used as a hunter was one, couple, few, many. We had more need to characterize snow conditions than numbers. Farmers such as in the Bible tend to use 40 to mean many but uncounted. The later development of merchants resulted in the concept of assets as positive number and liabilities a positive number. By forming an equation whose right hand side (rhs) is real/measured quantities with an operation (assets minus liabilities or clock and rulers converted to a geometry) and whose left hand side (lhs) is an abstract (transformation) quantity (net worth, space, time). The interpretation of the rhs is easy. The interpretation of the lhs has great difficulty that admits a negative physical object.

We are much too careless in the interpretation of the lhs, negative objects, division, zero, and infinity (unbounded). Perhaps the hunters were right - when we reach the limit of our concepts we should say ``many'' and leave it at that.

However, set and, in particular, group theory seems to have some usefulness in identifying patterns in the stable points of energy/mass assembly (particles). Like with the periodic table, identifying holes in the group predicted particles and the particle characteristics. This math suggests a still finer structure.

Again, I like the idea that the math we use is a result of the selection from among nature's characteristics.

Richard Lewis

Hello John,

I really appreciated your comment in the conclusion that 'the goal should be to make the universe more conceptually understandable'. This should apply to the physics of the very large and the very small.

I was not clear about your meaning when you said in your abstract that 'several conceptual mysteries may be better modeled by using mathematics as an observation.'

Regards

Richard Lewis

John Hodge

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 mishra

Dear Sir,

According to Ayurveda - the ancient system of medicine, the capability to perceive through sense organs is the definition of life. Reality is whatever exists (has a confined structure that evolves in time and is perceptible), is intelligible (perceptible/knowable) and communicable (describable using a language as defined in our essay). Number is a perceivable property of all substances by which we differentiate between similars. If there are no similars, it is one. If there are similars, it is many. Many can be 2,3,..n depending upon the sequence of perception of one's. Mathematics is the quantitative description of Nature. Thus, it explains only one part. Another part is described by physics, which has meaning only when observed (perceived). Thus, you have correctly held that fundamental principles of life and physics are same.

You description of division is correct. But there are extensions as described in our essay. Geometry is the measurement of closed lines (depicting area or volume) in suitable units. Since these are closed, these are analog internally and digital externally. Space, Time and coordinates arise from our concept of interval and sequence. When the interval is related to objects, we call it space. When the interval is related to events, we call it time. When we describe inter-relationship of objects or events, we describe the sequence by coordinates. Directions are arrangements of the sequences of intervals of objects in space. Dimension is the perception of differentiation between the internal structural space and external relational space of objects. Since we perceive through electromagnetic interaction, where the electric and magnetic fields are perpendicular to each other and both move perpendicularly, we have three mutually perpendicular dimensions. These are invariant under mutual transformation (if we treat length as breadth or height, the object is not affected) and can be resolved into 10 different combinations. Regarding measurement, we have extended your thought in our essay.

Regards,

basudeba

John Hodge

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.

basudeba mishra

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

Sujatha Jagannathan

Your view of the hypothesis statements are much related to the scenic abstractions of life and great numbering in perceivable theories.

Hands-On!

John Hodge

Thanks. I liked your essay, also.

John Hodge

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''.

Akinbo Ojo

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

John Hodge

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.

Akinbo Ojo

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

John Hodge

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.

Akinbo Ojo

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 Ojo

As an addendum: 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).

Vladimir Rogozhin

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 Hodge

Thanks for your comment and kind words.

I have read and commented on your essay.

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