Authors: Kenneth C. Johnson
Comments: 7 Pages. 4/22/2016 update: added 8-th order approximant (Eq 22)
This paper reports work-in-progress on the solution of first-order, linear, homogeneous differential equation systems, with non-constant coefficients, by generalization of the Padé-approximant method for exponential matrices.
Category: Functions and Analysis
Authors: Alex Patterson
Comments: 39 Pages. Special thanks for Michael J. Burns, of Hacking Physics
Abstract: in ideal circumstances, we know exactly what to do. But there are no ideal circumstances. That is why we have Critique. The object of critique matters not.
However, this paper is also very concerned not only with critique as such but with a possible intersection, that has arisen out of such critique, of a heretofore un-combined areas of mathematical induction, Gödelian Relativity, and their Algebras within Bayesian Networks. It is very rough attempt, but uses all the right tools, should such an Intersection be theoretically viable in the short term, at least.
Further steps are made into Ethics, which the author believes to be the basis of any elegance for that matter, of any excellent piece of intellectual effort.
This paper uses its own peculiar lettering system for each paragraph. I don’t like it: But the way I write it is the only way I can figure to impose some kind of order for the content. Seemingly arcane references will be made to philosophers such as Vico and Kant, to Heine and Goethe, to Wittgenstein and B.F. Skinner, J.L. Austin, Turing, Thomas Paine, G.H. von Wright, Marx, the “Availability Heuristic,” Quantum Logic, More Classical Systems of Axiomatic Problems, Epistemology, etc., et. al. Towards the end a Narrative will be given that attempts to address some concerns of the present world in its ethical, moral, and political makeup. There will be no cut-off at that point, but the change will be clearly visible, it is hoped that there will be a “fade to gray" effect. The Reader’s forbearance and endurance to “strange thoughts”(but which are informed by the author’s education) is solicited as the paper proceeds: Even a crank might not be a crank, as a liar may not be a liar. Such are our weak paradoxes.
1.New terms and tools are introduced for quantification that creates a more synthetic (logical, reasonable, coherent) intervention and inter-weaving into these (those) now classical problems of the assumptions and the successes in the Gödel material and literature.
2.Asymptotes are used within vertical and horizontal graphs to justify a future that need not be seen as a future in the sense of grammatical future-tense (it is considered by the best philosophical grammarians to be a tense that doesn’t exist), but as a potential part in such systems themselves that we deal with respect to incompleteness.
3.The thesis is that we can approach incompleteness by using theoretical reasoning and available tools that are allowed in theoretical reasoning to critique the very theory of incompleteness itself. That is the essential Abstract Thesis.
4.It will be seen that a real attempt is attempted. It is quite a ride. I’ve looked at everything I can think of so far. In doing Gödel you can’t tell a hypothesis from a position. So it is necessary to be very analytical, use Occam’s razor wherever you can but still brave the undesired feat of blunting the blade. This is not Quine, and there is no Neurath’s Figure to resort to as Quine does, and in his area, must do, much to his discredit, as great as he may be.
This critique (work, paper) works from Gödel’s incompleteness to Gödel relativity. It does so in with the help of formal logic and inductive thinking, and a lot of hard analysis and questioning of various facts, the interrogation of assumptions, so that the critique can end up where it belongs: in the ethical domain of inquiry, not an easy category of thought to express, but which will be further versioned in subsequent editions, or entirely new works.
Category: Functions and Analysis