相关论文: The Meaning of Dimensions

The problem of estimating, from a random sample of points, the dimension of a compact subset $S$ of the Euclidean space is considered. The emphasis is put on consistency results in the statistical sense. That is, statements of convergence…

The "cosmic triangle" is introduced as a way of representing the past, present, and future status of the universe. Our current location within the cosmic triangle is determined by the answers to three questions: How much matter is in the…

Astronomy and related fields are at the forefront of science and technology; answering fundamental questions and driving innovation. Although blue-skies research like astronomy rarely contributes directly with tangible outcomes on a short…

The status of angles within The International System of Units (SI) has long been a source of controversy and confusion. We address one specific but crucial issue, putting the case that the idea of angles necessarily being length ratios, and…

This article is based on papers discussing different aspects of extra dimensional environments. In addition to the results, we review some of the concepts on which models with large extra dimensions are based.

Multidimensionality of our Universe is one of the most intriguing assumption in modern physics. It follows naturally from theories unifying different fundamental interactions with gravity, e.g. M/string theory. The idea has received a great…

The universe is things which change and called events. The events are matter and field. A boundary divides a system to things and environment. The things belong to the environment have no significant effect on the things belong to the…

It is proposed that space is a four-dimensional Euclidean space with universal time. Originally this space was filled with a uniform substance, pictured as a liquid, which at some time became supercooled. Our universe began as a nucleation…

There are several notions of duality between lines and points. In this note, it is shown that all these can be studied in a unified way. Most interesting properties are independent of specific choices. It is also shown that either dual…

It is time to renew old ways of thinking about dimensional analysis. Specifically, more than $n-r$ invariants and more than one functional relation between invariants need to be considered simultaneously. Thus generalized, dimensional…

While the interpretation of high-dimensional datasets has become a necessity in most industries, and is supported by continuous advances in data science and machine learning, the spatial visualization of higher-dimensional geometry has…

Our understanding of the four basic concepts of Physics -- space, time, matter and force -- has undergone radical change in the course of work on unification, starting with Maxwell's unification of electricity with magnetism, all the way to…

Astrophysical paradoxes are the paradoxes of physics. The main motivation of a formulated paradox is clearly recognized in the scientific environment because the phenomenon of a paradox itself has become interesting. There is an explanation…

We review the idea, due to Einstein, Eddington, Hoyle and Ballard, that time is a subjective label, whose primary purpose is to order events, perhaps in a higher-dimensional universe. In this approach, all moments in time exist…

The standard picture of viable higher-dimensional theories is that extra dimensions manifest themselves at short distances only, their effects being negligible at scales larger than some critical value. We show that this is not necessarily…

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…

Pointwise tangential dimensions are introduced for metric spaces. Under regularity conditions, the upper, resp. lower, tangential dimensions of X at x can be defined as the supremum, resp. infimum, of box dimensions of the tangent sets, a…

I review the basis and limitations of plausible inference in cosmology, in particular the limitation that it can only provide fundamentally true inferences when the hypotheses under consideration form a set that is exhaustive. They never…

Motivated by string-theoretic swampland conjectures, the existence of a dark fifth dimension, whose size is roughly 1 -- 10 microns, has been proposed. A great deal of supporting evidence has been presented, and definitive experimental…

Nerd abstract: Observational constraints on spacetime are reviewed, focusing on how the underlying physics (dark matter, dark energy, gravity) can be tested rather than assumed. Popular abstract: Space is not a boring static stage on which…