Related papers: The Infinite in Sciences and Arts
Numerous observations and studies suggest that the universe has some sort of overall rotation. We consider this matter and provide a new angle.
We investigate the theory of finite observables, i.e., resolutions of the finite-dimensional identity by means of positive operators, that have a physical interpretation in terms of measurement schemes. We focus on extremal and rank-one…
When a proposition has no proof in an inference system, it is sometimes useful to build a counter-proof explaining, step by step, the reason of this non-provability. In general, this counter-proof is a (possibly) infinite co-inductive proof…
Contrary to popular misconception, the question in the title is far from simple. It involves sets of numbers on the first level, sets of sets of numbers on the second level, and so on, endlessly. The infinite hierarchy of the levels…
One main goal of argumentation theory is to evaluate arguments and to determine whether they should be accepted or rejected. When there is no clear answer, a third option, being undecided, has to be taken into account. Indecision is often…
We continue the study of how one can define means of infinite sets. We introduce many new properties, investigate their relations to each other and how they can typify a mean. We collect the properties in property groups e.g. for…
Cosmological models which predict a large amount of antimatter in the Universe are reviewed. Observational signatures and searches for cosmic antimatter are briefly considered. A short discussion of new long range forces which might be…
A speculative discussion on the role of various symmetries in physics.
The physical nature of most of the gravitating mass in the universe is completely mysterious. The astrophysical evidence for the presence of this dark matter and astrophysical constraints on its properties will be reviewed. The most popular…
This is a survey of results on definability and undefinability in models of arithmetic. The goal is to present a stark difference between undefinability results in the standard model and much stronger versions about expansions of…
The mathematical universe discussed here gives models of possible structures our physical universe can have.
The observational evidence for dark matter on progressively larger cosmic scales is reviewed in a rather pedagogical fashion. Although the emphasis is on dark matter in galaxies and in clusters of galaxies, its cosmological evidence as well…
In our previous articles ("The Information and the Matter", v1, v5; more systematically the informational conception is presented in arXiv paper "The Information as Absolute", 2010) it was rigorously shown that the Matter is some…
We consider ways of conceptualizing, rendering and perceiving quantum music, and quantum art in general. Thereby, we give particular emphasis to its non-classical aspects, such as coherent superposition and entanglement.
It goes without saying that we are stuck with the universe we have. Nevertheless, we would like to go beyond simply describing our observed universe, and try to understand why it is that way rather than some other way. Physicists and…
We review recent developments in the field of string cosmology with particular emphasis on open problems having to do mainly with geometric asymptotics and singularities. We discuss outstanding issues in a variety of currently popular…
Mathematical conception of infinite quantities forms a cornerstone of many disciplines of modern mathematics --- from differential calculus to set theory. In fact, it could be argued that the most significant revolutions in mathematics in…
Are time-travels possible? is the past still existing? and is the future already existing? We try to give an answer to these an other questions concerning the properties of time and the close connection (but deep physical difference)…
It is a widespread belief that results like G\"odel's incompleteness theorems or the intrinsic randomness of quantum mechanics represent fundamental limitations to humanity's strive for scientific knowledge. As the argument goes, there are…
We are used to the fact that most if not all physical theories are based on the set of real numbers (or another associative division algebra). These all have a cardinality larger than that of the natural numbers, i.e. form a continuum. It…