Mathematics characteristics are universe characteristics by John C Hodge

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

thanks

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.

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.

Thanks. I liked your essay, also.

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.

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

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:

``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.