Probably Original Scientific Discoveries

There exist many people in the modern world who claim that I lack credibility, for the sole reason that citations of my name are just about totally absent from the peer review journals.

Without intending to blow my own didgeridoo,the purpose of this file is to correct that major over cite (sic!). Every paper accessible from this page is on Ferment Magazine. Each contains an idea, an insight, an invention, which the author believes originates with himself.

I am too busy to investigate alien priority claims.However, if readers of these articles come across the same ideas propounded elsewhere, please feel free to cry out to the plagiarist: "Hey! That idea comes from the Ferment Magazine website!"

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1. Weakly Infinite Cardinals

   A set is, by definition, unstructured. It is endowed with no order relations,no metrics, no topology, no algebraic relations.A set is defined only by its elements,and uniquely so.

   To handle the problems associated with "counting", or "enumerating" an unstructured entity, Zermelo and others came up with the Axiom of Choice. This states that it is not necessary to know anything about the structure imposed on a set to be able to select elements from it.

   This works very well at the beginning of the counting process;but what does one do when one has no information about how the process terminates? In particular, let C be an "unstructured" set that represents the first (countable) transfinite. By the Axiom of Choice, one can (without replacement), continue to choose elements from C until it is exhausted. As one makes the selection, one arrange these elements in a simple total linear ordering. However,by doing so,one is liable to end up with any one of the uncountable number of countable transfinite ordinals! There is no guarantee, at the beginning, that one arrives at ϖ, or ϖ +1, or 2ϖ.

   In other words, one needs an Axiom of Choice at the beginning,and yet another Axiom of Choice at the end, one that which states that it is possible to "choose" a countable ordinal α from the set U of countable transfinite ordinals, and a method of selecting the elements of C, so that one will end up with α.

   My paper, "Weakly Infinite Cardinals"proposes several possible solutions to this problem.Go to:

   Weakly Infinite Cardinals(docx)
   (doc)
   (pdf)

   The Clock Paradox

   Here are several papers on a certain anomaly that I appear (and appearances can be deceiving)to be the only person to have pointed out:lets say one has a finite collection K of clocks,a,b,c,d,e.etc.Since the collection is finite,one of them must have the minimum period, ψ.

   Theorem: it is impossible, using just the clocks of K, to put together (either by a finite or an infinite process!) a clock q, whose period = ½ψ.

   Without giving the game away,let me just point out that one cannot apply a Euclidean Algorithm process to temporal lengths. Details may be found in:

   (i)Non-Metrizable Time
   (ii)Topological Paradoxes of Time Measurement
   (iii) Time, Euclidean Geometry and Relativity

   On Spontaneous Changes in the Speed of Light

   Thesis: It is impossible,within the universe described by Special Relativity, to design an experiment that can detect a change in the speed of light.

   Go to: On spontaneous changes in the speed of light (pdf)
   (docx)
   (doc)

   Observations on the Expansion of the Universe

   Subtle yet important alterations in the "standard model of cosmology"are deduced from the observation that space can no more expand than time can move.Go to:

   On the Hubble Expansion(pdf)
   (docx)
   (doc)
   (htm)

   An ordinal index for classifying all functions with domain and range on the real line

   Ordinal Maps (doc)
   Ordinal Maps (pdf)

   Dynamical Systems and Universal Algebra

   This paper generalizes the notion of a one-variable "fixed point"in the language of rational maps, to that of a bivariate "fixed and closed binary algebra".From iterating one variable functions f(x), one moves to iterating 2-variable functions f(x,y).Go to:

   Dynamical Systems and Universal Algebra:

   The proof of the (difficult) General Collision Theorem is based on the (simple) Restricted Collision Theorem. These state:

   Restricted Collision Theorem:

   "Let the number of particles moving on a line be n. Given the masses,velocities and locations of these particles, the total number of collisions is finite."

   Restricted Collision Theorem

   General Collision Theorem:

   "Let the number of particles moving on a line be n. Given their masses and velocities, with a free choice of initial locations, there is a finite maximum bounding the total number of collisions for all systems."
   

   Note that if the number of particles is fixed, but the masses and velocities can vary, there is no such maximum.

   General Collision Theorem

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