相关论文: White Hole, Black Whole, and The Book

We define different notions of black holes, event horizons and Killing horizons for a general time-oriented manifold $(M,g)$ extending previous notions but without the assumption of asymptotical flatness. The notions of 'horizon' are always…

A fundamental question is whether Turing machines can model all reasoning processes. We introduce an existence principle stating that the perception of the physical existence of any Turing program can serve as a physical causation for the…

Uniform interpolation is a strengthening of interpolation that holds for certain propositional logics. The starting point of this chapter is a theorem of A. Pitts, which shows that uniform interpolation holds for intuitionistic…

This work is an extensive literature review focusing on a few of the important topics in the large-scale structure of spacetime. The work is a Bachelor's thesis submitted at the Institute of Theoretical Physics, University of Leipzig. The…

This paper is a survey of a large number of informal definitions of ``intelligence'' that the authors have collected over the years. Naturally, compiling a complete list would be impossible as many definitions of intelligence are buried…

A model of knowledge representation is described in which propositional facts and the relationships among them can be supported by other facts. The set of knowledge which can be supported is called the set of cognitive units, each having…

The notion of concept has been studied for centuries, by philosophers, linguists, cognitive scientists, and researchers in artificial intelligence (Margolis & Laurence, 1999). There is a large literature on formal, mathematical models of…

Visualization researchers and visualization professionals seek appropriate abstractions of visualization requirements that permit considering visualization solutions independently from specific problems. Abstractions can help us design,…

Conscious experience permeates our daily lives, yet general consensus on a theory of consciousness remains elusive. In the face of such difficulty, an alternative strategy is to address a more general (meta-level) version of the problem for…

As David Berlinski writes (1997), the existence and nature of mathematics is a more compelling and far deeper problem than any of the problems raised by mathematics itself. Here we analyze the essence of mathematics making the main emphasis…

By nature, transmissible human knowledge is enumerable: every sentence, movie, audio record can be encoded in a sufficiently long string of 0's and 1's. The works of G\"odel, Turing and others showed that there are inherent limits and…

The main aim of the paper is to give a full classification (up to isometry) of all metric spaces X with the following two properties: X contains a compact set with non-empty interior; and for any three distinct points a, b and c of X there…

Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces---so-called ``topological semantics''. The first is classical higher-order logic, with…

Spatial embodied intelligence requires agents to act to acquire information under partial observability. While multimodal foundation models excel at passive perception, their capacity for active, self-directed exploration remains…

Logic really is just algebra, given one uses the right kind of algebra, and the right kind of logic. The right kind of algebra is abstraction algebra, and the right kind of logic is abstraction logic.

In 1964, Paul Erd\H{o}s published a paper settling a question about function spaces that he had seen in a problem book. Erd\H{o}s proved that the answer was yes if and only if the continuum hypothesis was false: an innocent-looking question…

When modeling game situations of incomplete information one usually considers the players' hierarchies of beliefs, a source of all sorts of complications. Hars\'anyi (1967-68)'s idea henceforth referred to as the "Hars\'anyi program" is…

Contents: 1. Introduction 2. Causal Structure and Penrose Diagrams: Minkowski Space; 1+1 Dimensional Minkowski Space; Schwarzchild Black Holes; Gravitational Collapse and the Vaidya Spacetimes; Event Horizons, Apparent Horizons, and Trapped…

Humans have always constructed spaces, through Mythos and Logos, as part of an aspiration to capture the essence of the changing world. This has been a permanent endeavour since the invention of language. By doing this, in fact, Humankind…

In this chapter I focus on asking and answering the following questions: (1) What is a black hole? Answer: There are three types of black holes, namely mathematical black holes, physical black holes and astrophysical black holes. An…