Related papers: Conway's cosmological theorem and automata theory
Within the quantum mechanical treatment of the decay problem one finds that at late times $t$ the survival probability of an unstable state cannot have the form of an exponentially decreasing function of time $t$ but it has an inverse…
The cosmological constant $\Lambda$ is a measure of the energy density of the vacuum. Therefore properties of the energy of the system in the metastable vacuum state reflect properties of $\Lambda = \Lambda(t)$. We analyze properties of the…
We present a categorical theory of the composition methods in finite model theory -- a key technique enabling modular reasoning about complex structures by building them out of simpler components. The crucial results required by the…
Almost forty years ago, C.T.C. Wall systematically analyzed the set of "thickenings" of a finite CW complex. Of the results he obtained, probably the most computationally important is the "suspension theorem," which is an exact sequence…
An overview is given of the current status of the theory and observations of the acceleration of the expansion of the observable part of the Universe. Contents 1. Historical Introduction 2. Friedmann equations and cosmological acceleration…
The current cosmological model, known as the $\Lambda$-Cold Dark Matter model (or $\Lambda$CDM for short) is one of the most astonishing accomplishments of contemporary theoretical physics. It is a well-defined mathematical model which…
We formulate physically-motivated axioms for a physical theory which for systems with a finite number of degrees of freedom uniquely lead to Quantum Mechanics as the only nontrivial consistent theory. Complex numbers and the existence of…
The interplay between string theory and cosmology is very promising. Since string theory will yield a quantum theory of space-time and unify all forces of nature, it has the potential of addressing many of the conceptual problems of the…
Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…
In this paper we consider a variant of Conway's sequence (OEIS A005150, A006715) defined as follows: the next term in the sequence is obtained by considering contiguous runs of digits, and rewriting them as $ab$ where $b$ is the digit and…
A simple quantum model describing the onset of time is presented. This is combined with a simple quantum model of the onset of space. A major purpose is to explore the interpretational issues which arise. The state vector is a superposition…
In cosmology, we would like to explain our observations and predict future observations from theories of the entire universe. Such cosmological theories make ontological assumptions of what entities exist and what their properties and…
The cosmological principle says that the Universe is spatially homogeneous and isotropic. It predicts, among other phenomena, the cosmic redshift of light and the Hubble law. Nevertheless, the existence of structure in the Universe violates…
A Conway semiring is a semiring $S$ equipped with a unary operation $^*:S \to S$, always called 'star', satisfying the sum star and product star identities. It is known that these identities imply a Kleene type theorem. Some computationally…
An interpretation and re-formulation of modern physics which removes the presumption of the space-time continuum, and bases physical theory on a small number of rational and empirical principles. After briefly describing the philosophical…
The compositionality of meaning extends beyond the single sentence. Just as words combine to form the meaning of sentences, so do sentences combine to form the meaning of paragraphs, dialogues and general discourse. We introduce both a…
Besides their use for efficient computation, quantum computers are a base for studying quantum systems that create valid physical theories using mathematics and physics. An essential part of the validation process for quantum mechanics is…
We describe a technique for mechanically proving certain kinds of theorems in combinatorics on words, using automata and a package for manipulating them. We illustrate our technique by solving, purely mechanically, an open problem of Currie…
Sequence theories are an extension of theories of strings with an infinite alphabet of letters, together with a corresponding alphabet theory (e.g. linear integer arithmetic). Sequences are natural abstractions of extendable arrays, which…
This article is a sequel to a recent article by Eric Rowland and Reem Yassawi, presenting yet another approach to the fast determination of congruence properties of `famous' combinatorial sequences. The present approach can be taught to a…