相关论文: The Infinite in Sciences and Arts
There are infinite processes (matrix products, continued fractions, $(r,s)$-matrix continued fractions, recurrence sequences) which, under certain circumstances, do not converge but instead diverge in a very predictable way. We give a…
If we assume that there is the ultimate thoery at all, how should the concept of the spacetime be formulated? The following essay is my consideration on such a question. The use of mathematical expressions is suppressed as long as possible.…
Through-out human history the new generations have sought to create their own artistic style while trying to avoid repeating, for example, earlier generations' music. If we assume that this search occurs in a multi-dimensional but confined…
In this article we address the mystery of dark matter. We expound the various evidences, astrophysical and cosmological, leading to hypothesize the existence of an invisible form of matter, whose attempts at detecting it have so far all…
In this speculative analysis, interdimensionality is introduced as the (co)existence of universes embedded into larger ones. These interdimensional universes may be isolated or intertwined, suggesting a variety of interdimensional intrinsic…
We describe constructions of infinite graphs which are not representable as integral graphs in the plane, addressing a question of Erd\H{o}s. We also mention some related problems.
After discussing two senses in which the notion of undecidability is used, we present a survey of undecidable decision problems arising in various branches of mathematics.
What do we do when cosmology raises questions it cannot answer? These include the existence of a multiverse and the universality of the laws of physics. We cannot settle any of these issues by experiment, and this is where philosophers…
The topic of diversity is an interesting subject, both as a purely mathematical concept and also for its applications to important real-life situations. Unfortunately, although the meaning of diversity seems intuitively clear, no precise…
The infinite numbers of the set M of finite and infinite natural numbers are defined starting from the sequence 0\Phi, where 0 is the first natural number, \Phi is a succession of symbols S and xS is the successor of the natural number x.…
Four constructions result from a desire to create enhancements to Cantor's infinite real set cardinality. Each continues to keep Cantor's cardinality formulation in place while providing new comparisons of arbitrary infinite sets. To…
The physics of matter in the condensed state is concerned with problems in which the number of constituent particles is vastly greater than can be easily comprehended. The inherent physical limitations of the human mind are fundamental and…
The difference between the terms additivity and extensivity, as well as their respective negations, is critically analyzed and illustrated with a few examples. The concepts of subadditivity, pseudo-additivity, and pseudo-extensivity are…
We discuss cosmological models for an eternal universe. Physical observables show no singularity from the infinite past to the infinite future. While the universe is evolving, there is no beginning and no end - the universe exists forever.…
Time is one of those issues about which many thinkers and scientists have tried to pronounce their finest thoughts, but the discourse about time has remained vague and often inconsistent. In this paper we put forward a conceptual framework…
These notes collect results about algebraic correspondences and adapt them to the setting of correspondences on projective lines. The focus lies on finite orbits of algebraic correspondences. The main result is a field theoretic…
We discuss recent developments related to certain blow up methods suitable for the analysis of cosmological singularities and asymptotics. We review results obtained in a variety of currently popular themes and describe ongoing research…
This paper deals with the philosophical issues of the notion of nothingness and pre-inflationary stage of the universe in physical cosmology. We presuppose that, in addition to cosmological limits, there may be both anthropic and…
The notion of geometric version of an infinitely divisible law is introduced. Concepts parallel to attraction and partial attraction are developed and studied in the setup of geometric summing of random variables.
In this paper we investigate complex dynamics in infinite dimensions.