Blyth Institute Press
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90 research outputs found
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When is Explanation Transitive? A Methodological Note
No full textThe article considers the following explanatory- transitivity question: assume that A explains B and B explains C: does A also explain C? In the present paper the term explanation signifies causal explanation. The discussion of this question arrives at the answer that a necessary condition for explanatory-transitivity can be proposed. Accordingly, if B explains observation O (bEo) and A explains B (aEb), then A also explains O (aEo), when: if the same E is not preserved in the three expressions (bEo, aEb, aEo) then the transitivity of E will not be preserved. This answer is supported by an analysis of a large number of examples. The article also analyzes the relations among explanation, reduction and transitivity
Comets, Water, and Big Bang Nucleosynthesis
No full textWe argue that the cosmological origin-of-life problem is tightly connected to the origin-of-water problem, because life is not possible without abundant water. Since comets are astronomically dark and composed of water, as well as possessing microfossils, they are an underestimated candidate for the origin of life. If in addition dark matter is composed of comets, then water outweighs the visible stars, possibly solving several cosmological mysteries simultaneously. This motivates us to consider how it is possible to build a cosmological model in which water is formed in the Big Bang and then hidden from modern astronomy. In the process, we discover that magnetic fields play an important role in making water, as well as addressing several well-known deficiencies of the standard lambda-CDM cosmological model of the Big Bang. We do not see this paper as a demonstration but as an outline of how to address the origin of life problem with dark comets
PREPRINT: Riemann's Rearrangement Theorem in the Light of Hyperreal Numbers
No full textRiemann's rearrangement theorem has long been used to demonstrate that conditionally convergent series do not establish a single, coherent value. The theorem states that by simply regrouping the members of a conditionally divergent series, that a person can make that series converge to essentially any real number, or to diverge. Here, we will show that the problems usually associated with the rearrangement theorem disappear when using hyperreal numbers
Tiling Efflorescence of Expanding Kernels in a Fixed Periodic Array
No full textContinually expanding periodically translated kernels on the two dimensional grid can yield interesting, beau- tiful and even familiar patterns. For example, expand- ing circular pillbox shaped kernels on a hexagonal grid, adding when there is overlap, yields patterns includ- ing maximally packed circles and a triquetra-type three petal structure used to represent the trinity in Chris- tianity. Continued expansion yields the flower-of-life used extensively in art and architecture. Additional expansion yields an even more interesting emerging ef- florescence of periodic functions. Example images are given for the case of circular pillbox and circular cone shaped kernels. Using Fourier analysis, fundamental properties of these patterns are analyzed. As a func- tion of expansion, some effloresced functions asymp- totically approach fixed points or limit cycles. Most interesting is the case where the efflorescence never repeats. Video links are provided for viewing efflores- cence in real time
Proving the Derivative of sin(x) Using the Pythagorean Theorem and the Unit Circle
No full textThis provides a more straightforward and student-friendly proof of the derivative of sin(x) which doesn't explicitly utilize the limit (x->0) of sin(x)/
PREPRINT: The Products of Hyperreal Series and the Limitations of Cauchy Products
No full textThis is now officially published here
PREPRINT: Grid Logic Java Program
No full textThis program is a game to try to discover hidden patterns (and flaws in patterns) from data generated by simple logic functions. To run the program, download the Java file attached to this entry (upper right on the page), and save it as "GridLogicPuzzle.jar". Then, in the same folder you downloaded it to, run the following command from your command line:
java -jar GridLogicPuzzle.jar
This requires that you have Java installed. Use the help menu for how to work the puzzle and also for hints on the current puzzle
PREPRINT: Proving the Conjecture (-1)^(infinity) = 0
No full textThe conjecture (-1)^infinity = 0 was given in a previous paper. This paper proves this conjecture
Deciding a Bitstring of 1s is Non-Random is Impossible in General
No full textWithout domain knowledge, an algorithm given an extremely long sequence of 1s would be unsure whether the sequence is completely random. When asked to predict the next digit, the algorithm can only give an equal weighting to 0 and 1