Related papers: The Mathematical Universe in a Nutshell
It is proposed that the physical universe is an instance of a mathematical structure which possesses a dual structure, and that this dual structure is the collection of all possible knowledge of the physical universe. In turn, the physical…
Some contemporary views of the universe assume information and computation to be key in understanding and explaining the basic structure underpinning physical reality. We introduce the Computable Universe exploring some of the basic…
A mathematical model of the natural origin of our universe is presented. The model is based only on well-established physics. No claim is made that this model uniquely represents exactly how the universe came about. But the viability of a…
Can mathematics help us find our way through all the wonders and mysteries of the universe? When physicists describe the laws governing the physical world, mathematics is always involved. Is this due to the fact that the universe is, at…
I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the…
The purpose of this paper is (i) to expound the specification of a universe, according to those parts of mathematical physics which have been experimentally and observationally verified in our own universe; and (ii) to expound the possible…
In this paper, we introduce a mathematical structure called Euclidean Universe. This structure provides a basic framework for Non-Archimedean Mathematics and in particular for Nonstandard Analysis.
The purpose of this paper is to discuss the various types of physical universe which could exist according to modern mathematical physics. The paper begins with an introduction that approaches the question from the viewpoint of ontic…
In a recent article, M. Tegmark poses the hypothesis that our known universe is a ``baggage free'' mathematical structure among many other possible ones, which also correspond to other physical universes --Mathematical Universe Hypothesis,…
An approach to modelling the universe based on the requisites of gravitational energy. This model is explained as it relates to the stages of the universal life cycle and the continued existence of the universe as it is known today. The…
In this talk, we touch upon the chaotic and fractal aspects of the Universe.
We present mathematical details of several cosmological models, whereby the topological and the geometrical background will be emphasized.
We investigate the most general phase space of configurations, consisting of the collection of all possible ways of assigning elementary attributes, "energies", to elementary positions, "cells". We discuss how this space defines a…
Suspicions that the world might be some sort of a machine or algorithm existing ``in the mind'' of some symbolic number cruncher have lingered from antiquity. Although popular at times, the most radical forms of this idea never reached…
Partial descriptions of the Universe are presented in the form of linear equations considered in the free (full, super) Fock space. The universal properties of these equations are discussed. The closure problem caused by computational and…
Several concrete examples in quantum information are discussed to demonstrate the importance of proper modeling that relates the mathematical description to real-world applications. In particular, it is shown that some commonly accepted…
I discuss some problems related to extreme mathematical realism, focusing on a recently proposed "shut-up-and-calculate" approach to physics (arXiv:0704.0646, arXiv:0709.4024). I offer arguments for a moderate alternative, the essence of…
We strengthen the case that the new logical perspective afforded by topos theory is suitable to the task of describing the physical world around us. In exploring some of the aspects of construction of a simple quantum-mechanical system in a…
The relationship between mathematics and physics has long been an area of interest and speculation. Subscribing to the recent definition by Tegmark, we present a mathematical structure involving the only division rings - the real,…
If our universe has appeared in a result of Big Bang or something like this, whether we have reasons to deny an existence of other universes appearing by the same or similar way? An objection that there is no anything like it, is doubtful,…