Related papers: Three Aspects of Typicality in Multiverse Cosmolog…

We reconsider a well known problem of quantum theory, i.e. the so called measurement (or macro-objectification) problem, and we rederive the fact that it gives rise to serious problems of interpretation. The novelty of our approach derives…

The aim of this article is to promote the use of probabilistic methods in the study of problems in mathematical general relativity. Two new and simple singularity theorems, whose features are different from the classical singularity…

We consider the properties of an ensemble of universes as function of size, where size is defined in terms of the asymptotic value of the Hubble constant (or, equivalently, the value of the cosmological constant). We assume that standard…

Supervised machine learning and predictive models have achieved an impressive standard today, enabling us to answer questions that were inconceivable a few years ago. Besides these successes, it becomes clear, that beyond pure prediction,…

We argue that the many-worlds of quantum mechanics and the many worlds of the multiverse are the same thing, and that the multiverse is necessary to give exact operational meaning to probabilistic predictions from quantum mechanics.…

The problem of characterizing a multivariate distribution of a random vector using examination of univariate combinations of vector components is an essential issue of multivariate analysis. The likelihood principle plays a prominent role…

Classical probability theory supports probability measures, assigning a fixed positive real value to each event, these measures are far from satisfactory in formulating real-life occurrences. The main innovation of this paper is the…

Probabilities in quantum theory are traditionally given by Born's rule as the expectation values of projection operators. Here it is shown that Born's rule is insufficient in universes so large that they contain identical multiple copies of…

We present the possibility that the gravitational growth of primordial density fluctuations leads to what can be considered a week version of the cosmological principle. The large scale mass distribution associated with this principle must…

Using the idea of regularisation of singularities due to the variability of the fundamental constants in cosmology we study the cyclic universe models. We find two models of oscillating and non-singular mass density and pressure…

How can probabilities make sense in a deterministic many-worlds theory? We address two facets of this problem: why should rational agents assign subjective probabilities to branching events, and why should branching events happen with…

The universal validity of the second law of thermodynamics is widely attributed to a finely tuned initial condition of the universe. This creates a problem: why is the universe atypical? We suggest that the problem is an artefact created by…

There is strong expectation that cities, across time, culture and level of development, share much in common in terms of their form and function. Recently, attempts to formalize mathematically these expectations have led to the hypothesis…

In calculations of the probability distribution for the cosmological constant, it has been previously assumed that the a priori probability distribution is essentially constant in the very narrow range that is anthropically allowed. This…

I discuss an issue arising in analyzing data from astronomical surveys: accounting for measurement uncertainties in the properties of individual sources detected in a survey when making inferences about the entire population of sources.…

We investigate a number of simple toy models to explore interesting relationships between dynamics and typicality. We start with an infinite model that has been proposed as an illustration of how non-ergodic dynamics can produce interesting…

Contrary to an oft-made claim, there can be observational distinctions (say for the expansion of the universe or the cosmological constant) between "single-history" quantum theories and "many-worlds" quantum theories. The distinctions occur…

Attempts to derive the Born rule, either in the Many Worlds or Copenhagen interpretation, are unsatisfactory for systems with only a finite number of degrees of freedom. In the case of Many Worlds this is a serious problem, since its goal…

Randomness in scientific estimation is generally assumed to arise from unmeasured or uncontrolled factors. However, when combining subjective probability estimates, heterogeneity stemming from people's cognitive or information diversity is…

In this paper we investigate how observational effects could possibly bias cosmological inferences from peculiar velocity measurements. Specifically, we look at how bulk flow measurements are compared with theoretical predictions. Usually…