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An Alternate — My Proposed Explanation

14 Sep

In the last post, I took a look at Hawking’s explanation for the current physical universe – analyzing the theoretical development using the standards of Place. Now, I’m going to take a turn and suggest an alternate theoretical development. I’ll put forth a theory to explain phenomena related to physical space, objects and the relative motion of objects. The context defined here is meant to represent a mental model of the physical universe.

——–Begin Massfluid-Time-Space Theory

Start with a blank context. Open a new empty mental space and call it the Context of Physics [CoP]. Now, conceive of an ideal fluid that is homogeneous and without structure. Call this ideal fluid massfluid. Determine that massfluid is present in the Context of Physics so that it completely fills the context.

Introduce time into the Context of Physics such that time fills part, not all, of the context. Time enables sequence, it also defines from -> to in a single direction.

Now conceive of physical space. Introduce physical space into the Context of Physics, displacing massfluid like a big bubble in the middle, such that space is present in time, but whereever space is present, massfluid is not present.

These set-up tasks result in the following axiom being true in the Context of Physics.

Physical Stuff Axiom
Massfluid, time, and physical space are present such that the presence of space determines: a) the absence of massfluid and b) the presence of time.

Introduce the meaning to cut. Now determine that massfluid has the ability to cut space such that massfluid effects separation but not destruction [in keeping with my theory of geometry called Space-Cut Theory]. Create point-like sources for mass to flow into space. Also create a point-like sinks for massfluid to exit space.

These set-up tasks lead to the following axiom.

Ability to Cut Axiom
Massfluid enters space at point-shaped sources and exits through point-shaped sinks and massfluid has the ability to make geometric cuts in space as it flows from source to sink.

Observe that the very successful equations that describe the behavior of electricity and magnetism, Maxwell’s equations, completely support the notion of sources and sinks (divergence and curl). The sources and sinks are perceived as “particles.”

Now, determine that the meanings of to push and to pull are present in the Context of Physics.

As massfluid enters space or moves through space (cutting it), it pushes on space and space pushes back – equal and opposite reactions. I assert that this interaction, space pushing on massfluid and massfluid pushing back, is the fundamental phenomenon involved in what we call gravity. [Proving this goes beyond the scope of this development.]

Ability to Push Axiom
At any boundary between space and massfluid, space pushes on massfluid and massfluid pushes on space such that the magnitude of the pushing force is equal in magnitude and opposite in direction.

The Ability to Push Axiom draws on insight from Sir Isaac Newton that for every action, there is an equal and opposite action. Experience with this law in classical mechanics gives insight about how essential this interaction is.

As massfluid enters space or moves through space (cutting it), it exhibits a kind of internal tension. Massfluid pulls on massfluid. The network of massfluid lines in space provide the means for perturbations, or waves, to propagate. Observation about the propogation of waves in “the vacuum” reveal a uniform tension (associated with the constant speed of light).

Ability to Pull Axiom
Massfluid pulls on massfluid creating a tension that pulls sources and sinks together; the direction is orthogonal to the pushing force and the magnitude of the pulling force is inversely proportional to the magnitude of the pushing force against space.

Consider that in the nucleus of an atom, there is very limited space, so that the tension in lines and planes of massfluid is very strong while the pushing force of space is relatively weak. In the distances between planets and stars, there is a lot of space, so the pushing force is stronger and the tension or pulling force is relatively weaker.

Following are some rules that govern the Context of Physics. Whether they can be deduced from axioms or need to be axioms themselves is a matter that is open for investigation.

The first rule is due to consistent observations regarding the conservation of energy. Note that the units of energy are made up of mass, distance and time. These are measurements respectively of massfluid, space, and time.

P-Rule 1: The total quantity of massfluid, time, and space remains fixed.

This rule implies that the means to destroy massfluid, space, and time is not present in the Context of Physics. It also implies that the rate of massfluid flowing into space is equal to the rate of massfluid flowing out of space.

P-Rule 2: A source-point is an origin for massfluid to flow in multiple directions, different characteristic distances:
•short-range
•medium-range
•long-range

This rule is established due to beta-decay, observations/knowledge regarding neutrinos, and the base of knowledge regarding electro-magnetic waves. The short-range massfluid lines are in the neutron. And perhaps these lines relate to observations of something akin to string vibrations that led to superstring theory. Medium-range flow goes to sinks associated with electrons in the same atom. Long-range flow goes to sinks associated with black holes at the center of stars and galaxies. The long-range massfluid lines provide a network of lines that E-M waves propagate on.

This network of long-range massfluid lines accounts for the constant speed of light. It is known through conventional physics that: “the speed of a wave along a stretched ideal string depends only on the tension and linear density of the string and not on the frequency of the wave.” The network of massfluid lines provide a 3-dimensional network of these ideal lines. The pushing force provides the mass-density of the lines and the pulling force provides the tension. These are constant over distances at the macro level. Thus, so is the speed of light constant.

P-Rule 3: Massfluid lines only intersect at sources or sinks

This rule is established due to the success of Michael Faraday’s research. In his visualization of field lines, this was one of his rules. Also, we know from geometry that unique lines require space between them.

——–End Massfluid-Time-Space Theory

There’s more to do, and more to explain, but this outlines start of a possibly helpful theory.

Now it’s your turn to poke holes and tell me the problems with this theory.

Working Together on Knowledge

28 Jul

Given that language is the means to accomplish many different ends, such as artistic expression, historical accounts, marketing tools, and propaganda, how is written language used to understand ourselves and the world around us?

Language is used to pursue and acquire knowledge through the development of theories.

A theory is essentially an explanation about how the world works with respect to some subject area. For example, we have theories to explain: why the sun, moon and planets move the way they do; why the human eye perceives colors; what is the nature of light, etc. Theories are the substance of society’s knowlege base.

Knowledge can be seen as a large system that many different groups are working on. Not surprisingly, everyone has his or her own idea of the best way to proceed. People who work on knowledge acquisition have experienced regular controversy over assumptions and language standards.

Consider that working together as a group requires some attention to process. In order for a group to be productive, everyone in the group must accept certain standards. For example, consider whether the people working on the US space shuttle would have accomplished anything without agreement on: the language to communicate in, standard work schedules, project planning according to professional standards, rules for inspection, and a standard measurement system (metric or English) among other things.

Typically, theories that advance explanations for society’s knowledge have been advanced in an ad hoc manner. Subjective aspects of the scholar and his academic institution play a large role in how the work is regarded, rather than objective analytical criteria.

What are the standards for theoretical work in the service of science?

There are established standards for logic and methods of proof; however efforts to establish a standard system for formal theories have not been especially successful.

I propose some standards with respect to  definition, construction, communication, and theories to support the objective that a scientific explanation – any scientific explanation – be created so that it is clear and consistent. This body of work called Place of Understanding [or just Place] is a kind of constitution to establish order and regulate controversy with respect to theoretical science. It also offers a protocol for establishing a formal theory.

Please review it. It is published in chapters here (although the Results and Conclusion are still in process):
Working Together on Knowledge
Introduction to “Working Together on Knowledge”
Overview Presentation of Place of Understanding

See if you think it is successful. Consider ways that it could be improved. If we can achieve consensus for a final version of these standards, we will secure an opportunity for significant gains in productivity.

Some Personal Experience

31 Jan

As an independent scholar, I am not the kind of scholar who can get her work peer reviewed. 

From my previous post: “People that work for the journal or the book publisher provide an initial filter to see if a work should be  accepted for peer review. They evaluate if the person is a reasonable candidate to be regarded well by others in the field and they consider the abstract to see if it seems reasonable and offers something new or interesting.” I don’t fit the criteria since I do not have a doctorate from an esteemed school with an esteemed advisor.

 That’s just the way it is.

Maybe it is relevant to share some examples of attempts to get my work reviewed by people in the academic community; although, without knowing the quality of my work, it’s hard to know how justified my brush-offs were.

I developed a paper that captured some defects I have observed in Set Theory — 2 problems with formal set theory and 2 problems with informal set theory. There’s at least one well-known problem with Set Theory associated with a certain type of paradox — so it’s not like Set Theory has an unblemished reputation. However in the absence of another theory in the first half of the 20th century to fill its role as the theoretical foundation of Mathematics, scholars have moved forward with the idea that everything is okay with Set Theory as long as practitioners abandon formalism and avoid the special cases leading to the paradoxes. (1)

If you are up for the challenge, you can judge for yourself if I support my claim in this paper: “Why Set Theory is Not an Acceptable Theoretical Foundation for Mathematics.”
[http://www.placeofunderstanding.us/pdf_files/WhySetTheory.pdf]
I am interested to know if my arguments can be refuted.

I submitted this paper to “The Journal of the American Mathematical Society” (under 2000 Mathematics Subject Classifications 03A05 and 03E99) in September 2002. I was prepared that it would not be published, but I was hoping for some review and comments on my work. I only received a short email saying “I am sorry to say that we will not be able to publish your paper.” No comments, no feedback.

In another case, I found a post-doc in Mathematics at MIT who was willing to read my paper on Set Theory and look at my paper proposing a new foundation for Mathematics. He obtained copies of my references. He seemed to give it a serious go. But he did not deliver any observations on problems with my reasoning.

He consulted with the professor that he took his one course on set theory with.

The professor indicated that formal Set Theory and the Predicate Calculus of formal Mathematical Logic are 2 distinct theoretical systems. This pertains to the first problem with formal set theory.

Per the textbooks I read, formal Set Theory is a formal theory defined within the theory of formal theories, the Predicate Calculus (of Mathematical Logic). Formal Set Theory is formally used to define numbers. So there is a problem with circular definition. Numbers are used to define the Predicate Calculus (supposedly because counting numbers are part of natural language), and Predicate Calculus is the theoretical setting in which formal Set Theory is defined, and formal Set Theory is the theory used to formally define numbers (via successive sets). Natural numbers define the Predicate Calculus, the Predicate Calculus defines Set Theory, and Set Theory defines natural numbers.

Doesn’t it seem on the face of it that the attempt to understand the theoretical foundations of mathematics should not start with using numbers as primitive concepts?

I don’t agree with the position put forward by the professor that formal Set Theory and the Predicate Calculus are independent. Consider this. If Set Theory is defined outside of the Predicate Calculus, is it a formal theory? What makes a theory a formal theory according to the tenets of academic mathematics? I’m interested to know what other scholars think.

The post-doc in a sense agreed with one of the problems of informal set theory, because it is involved with the known paradoxes. He seems to think that the axioms of Zermelo-Frankel Set Theory correct the problem, but ZF Set Theory is a case of formal set theory, not informal set theory. He felt I was wasting people’s time to include this known problem in my paper. I include this issue because it is not some weirdness that can be fixed by avoidance; it is a serious flaw in which “the whole” and “a part, not all, of the whole” are NOT distincly different; they can be the same. 

In the end, the post-doc confessed that he believed the ideas and work of the respected giants of the field must be more correct than the ideas of a lone independent female scholar. I asked, “What about the new numbers defined in my paper on the new foundation for mathematics.” He said, “What are they useful for?”

I have to tell you that I was shocked to get this reaction from a mathematician. Yes, the “imaginary” number also got this reaction; I just thought that a modern mathematician would understand from the example of i (the square root of -1) that numbers are objects worthy of analysis and most likely a practical purpose will show up over time. We agreed to disagree and went our separate ways.

So one of the changes that I would love to see in academic science — working together on knowledge — is a way for independent scholars and scholars from lesser schools to get their work reviewed. Consider that if the current system of academic review existed in 1905, that Albert Einstein would NOT have had his 3 seminal articles published — he was an independent scholar working as a patent clerk.

I think it is relevant to this ongoing monologue to share some of my experience so that you have more understanding about personal context related to the subject. Also, it allows you to get to know me a little bit.

Footnote

1. The Mathematical Experience. Philip J Davis & Ruben Hersh. Houghton-Mifflin, Boston; copyright 1981 by Birkh
Page 331-337
“The theory of sets was developed by Cantor as a new and fundamental branch of mathematics in its own right. …
“Set theory at first seemed to be almost the same as logic. The set-theory relation of inclusion, A is a subset of B, can always be rewritten as the logical relation of implication, ‘If A, then B.’ So it seemed possible that set-theory-logic could serve as the foundation for all of mathematics. ‘Logic,’ as understood in this context, refers to the fundamental laws of reason, the bedrock of the universe. …
“Since all mathematics can be reduced to set theory, all one need consider is the foundation of set theory. However, it was Russell himself who discovered that the seemingly transparent notion of set contained unexpected traps.
“…
“The Russell paradox and the other antinomies showed that intuitive logic, far from being more secure than classical mathematics, was actually much riskier, for it could lead to contradictions in a way that never happens in arithmetic or geometry.
“This was the ‘crisis in foundations,’ the central issue in the famous controversies of the first quarter of this century. Three principal remedies were proposed.
“…
“… In 1930, Gödel’s incompleteness theorems showed that the Hilbert program was unattainable — that any consistent formal system strong enough to contain elementary arithmetic would be unable to prove its own consistency. The search for secure foundations has never recovered from this defeat.”
Page 344
“In recent years, a reaction against formalism has been growing. In recent mathematical research, there is a turn toward the concrete and the applicable.”
Page 347-348
“Thus, Lakatos applied his epistemological analysis, not to formalized mathematics, but to informal mathematics, mathematics in process of growth and discovery, which is of course mathematics as it is known to mathematicians and students of mathematics. Formalized mathematics, to which most philosophizing has been devoted in recent years, is in fact hardly to be found anywhere on earth or in heaven outside the texts and journals of symbolic logic.”