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It was Feynmann who misunderstood electromagnetic theory in his Lectures. It was an inability to properly visualize and diagram the E and B fields which caused the difficulty. His incorrect use of vectors caused him to think (visually) of the E and B fields as ephemeral under observation from observers with different motion. Now, the vector representation is indeed ephemeral because it is not correct.

But, by comparison, the correct 2-form representation of the Faraday tensor is as steady as a rock under transform, not ephemeral. The 2-sided egg-crate structure of a 2-form is as easy to imagine as a vector, and it is also much more accurate. See GRAVITATION, Chapter 4 for pretty pictures of electromagnetism.

So, when Feynmann is humble about the possible understanding of the universe, I can only think of the problems in understanding that can be easily fixed and improved.

It turns out that correct visualization and diagramming of physical objects, fields, and waves and such, is possible. This is even a foundational principle in itself. The conventional name for this is the principle of general covariance. But, the new name should be geometric reality; things are "geometric objects".

The beginning-level example for general covariance is the proper diagramming of a cross product. It is a bivector that is diagrammed with a pair of vectors, not one vector. See GRAVITATION again. I think it is vital to acquire the bivector concept as a necessary prerequisite for acquiring the concepts of the other geometric forms that are exhibited in field theory.

Neglect of the principle of general covariance has led to a malaise in the study of field theory, I think. But, diligence leads to the adoption of the Einstein-Davis and Kaluza-Klein ideas, and to the rejection of the cosmological constant and of many features of string theory.

And again, vectors are just so inadequate for the task that they are assigned to. In most cases of a given number of dimensions, the total number of components of a vector representation fail to match the total number of components of a cross product. In three dimensions, the number of independent components match, but this is only a coincidence. This is true in three dimensions only, and the nonlinearity of the scaling is an unacceptable difficulty in every number of dimensions.

So, to correctly diagram a tensor, each factor of the diagram must be linear in the scaling of that particular dimension and direction; this is the principle of general covariance. And, a vector can only represent correctly first rank contravariant tensors with a dimensionality of L, namely spacetime intervals, but also 4-momentum in the special case of classical mechanics. Nothing else is ever correctly thought of as a vector.

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Michael J. Burns

A friend of mine advocated Wittgenstein's criticism of Godel's proof. They hold that there is something nongrammatical about Godel's proposition that makes for nonsense and therefore falsehood. And, a professor of physics allowed that mathematics was a failure. I was trying to restudy the matter anyway, so let me formulate my present understanding.

I need a statement of Godel's proposition. I think it can be put like this. A proof, when encoded in its Godel number, does not exist for this very statement, also as encoded in its Godel number.

If I want to make this statement false, the weakness would be in the encoding. If I want to make this statement true, then it is only necessary to uphold a standard understanding of integer arithmetic and computer science.

A proof for this proposition can not be encoded in a Godel number, apparently because the Godel number is a language not made to accommodate the needed metamathematical notation. So, if the Godel language were adjusted to be more of a Spinozist language (and nothing prevents this adjustment), then Godel's proposition would then be provable in the extended language, but would remain not provable in the original language as required by the proposition itself. If the proposition is adjusted to refer to the expanded language, then it would be false.

The nature of integer arithmetic can be adjusted to falsify Godel's statement. The adjustment requires that consistent symbolism by integer numbers be no longer possible, at least in this case. When I consider that recursive infinities interfere with the encoding of both the proposition and a would-be proof, then this adjustment does not seem so extreme.

Or, one could ask what this has to do with integer arithmetic, since it is only used as typesetting. I suppose that the answer to this is that the logic language that Godel encoded in numbers is itself capable of generating integer arithmetic.

But, nothing compels me to denounce the standard model of arithmetic or Godel's code, nor has the case been made that the Godel encoding is wrong or unreliable. So, rejecting Godel's proof seems to be simply a restrictive redefinition of things. There is definitely not a failure of mathematics here. Instead, there is a multiplicity of extensions of integer arithmetic to invoke when they are needed.

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Michael J. Burns

The three axis model of political belief that has been published recently contributes to insight so much that I want to elaborate on it.

The first and primary axis of politics is tribalism, tradition, and religion versus the various modern oppositions, secular city workers, intellectuals and artists, and travelers. (This axis was also discussed in another publication as two components of modernism.) The pole that I name here was dominant in aboriginal bands, and it provided stability of behavior across generations. But, the crisis is that this traditional pole is irrationally motivated, and must be neutralized in order to gain a stable and advanced civilization.

The second and lesser axis is collectivism, voluntary or coerced, versus the various kinds of private power, kings, pirates, and ward heelers as well as ordinary land owners. Collectivism was overwhelmingly strong in the aboriginal hunting band, and for sound reason. The problem of civilization is to concede private power where necessary, while suppressing the destructive and unsound sort.

The third and yet lesser axis of politics is government by law versus individualists and competing organizations. The aboriginal band had enormous weight of precedence to balance against individual decisions and competing organizations. But, civilization requires scope for individual divergence and specialized organizations.

Prof. Lakoff posits just one axis, namely patriarchy versus modern organization. And, where does the psychology of fascism or Maoism fit?

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Michael J. Burns

Matter is where time stops. The different sorts of charge are where different higher dimensions become timelike and likewise stop.

Einstein's equation of gravity is a metaphysical translation wherein spacetime becomes mechanics and mechanics becomes spacetime. It is not the sort of equation where transactions balanced between the sides are allowed; there are too many constraints. Einstein-Davis and Kaluza-Klein theory should have been universally acknowledged long since.

The cosmological constant would be conclusive evidence against the real nature of spacetime. It is actually inconsistent with the Einstein equation, breaking the Bianchi identity - the conservation theorem - which necessarily follows. A cosmological constant would mandate the erasure and recreation at every instant of the whole of spacetime with different curvature than what follows from the conservation theorem. It would mandate the creation or erasure of past history at every point in time.

Even the change in curvature over time, for universes that are not flat overall, is troubling. Simultaneous cohistory could be conjoined or cut off at certain times then. A flat universe would have negatively curved space to balance against the positive curvature that is centered in matter, momentum and energy.

White holes are loopholes, not long tunnels. They would have negatively curved space - negative momentum density that is conserved - to stabilize the edge. This is the opposite of black holes. And, what meaning would a curved and closed or divergent spacetime have if there are many white holes usable for egress?

Negatively curved space, contrary to popular descriptions of exotic matter, is not repelled by gravitation. It would be attracted to the center of the sun, for instance. But, it would be repelled by other regions of negative curvature, even at a distance. Negative curvature would repel normal matter as well, while being attracted by the normal matter at the same time.

Twenty of the ideas presented in this collection are just remedial level. But, it is too much to expect that most professional physicists can work through all of them. An error of logic is likely where the rest of the issues are dismissed after the first instance of misunderstanding.

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Michael J. Burns

It was Spinoza who put forward the notion of a-priori certainty of the great principles. And, he also realized that these a-priori principles are expansive to the full range of possibility. Academic physicists simply do not recognize the productivity of work along the lines of Spinoza.

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Michael J. Burns