相关论文: The Infinite in Sciences and Arts

The end (for human scientists) is nigh? The posit of this discourse is that the majority, if not all, scientific research will eventually be undertaken by one, or a number of, weak artificial intelligences.

Some classical and recent results on the Euler equations governing perfect (incompressible and inviscid) fluid motion are collected and reviewed, with some small novelties scattered throughout. The perspective and emphasis will be given…

We present evidence that the number of string/$M$ theory vacua consistent with experiments is a finite number. We do this both by explicit analysis of infinite sequences of vacua and by applying various mathematical finiteness theorems.

The 20th century has revealed two important limitations of scientific knowledge. On the one hand, the combination of Poincar\'e's nonlinear dynamics and Heisenberg's uncertainty principle leads to a world picture where physical reality is,…

Despite the extraordinary successes the two great bastions of $20^{th}$ century science (Quantum Theory and General Relativity) are troubled with serious conceptual and mathematical difficulties. As a result, further growth of fundamental…

We determine the finite groups whose real irreducible representations have different degrees.

The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real…

Science is a crowning glory of the human spirit and its applications remain our best hope for social progress. But there are limitations to current science and perhaps to any science. The general mind-body problem is known to be intractable…

Universes with multiconnected spatial sections predict multiple images of cosmic sources. A confusing terminology exists in the naming of these images as real ones vs. ghosts. Here an attempt is made to clarify the situation.

This paper proposes a new definition of science based on the distinction between the activity of scientists and the product of that activity: the former is denoted (lower-case) science and the latter (upper-case) Science. These definitions…

Generalized entropies and relative entropies are the subject of active research. Similar to the standard relative entropy, the relative $q$-entropy is generally unbounded for $q>1$. Upper bounds on the quantum relative $q$-entropy in terms…

This article deals with empty spacetime and the question of its physical reality. By "empty spacetime" we mean a collection of bare spacetime points, the remains of ridding spacetime of all matter and fields. We ask whether these geometric…

The hypothesis concerning the off-site continuum existence is investigated from the point of view of the mathematical theory of sets. The principles and methods of the mathematical description of the physical objects from different off-site…

Despite great advances in computation, materials design is still science fiction. The construction of structure-property relations on the quantum scale will turn computational empiricism into true design.

Some hypotheses in modern theoretical physics that have not any experimental verification are listed. The goal of the paper is not to criticize or be lawyers any of these hypotheses. The purpose is focus physicists attention on that now…

The nature of the scientific method is controversial with claims that a single scientific method does not even exist. However the scientific method does exist. It is the building of logical and self consistent models to describe nature. The…

Doing research is fighting, what any other thing the human being could do? Fight against powers or to get powers, that depends on us. Science can be a revolution or deadlocked idleness. Still waters, without hitting the stones along their…

A careful look at an allegedly well-known century-old concept reveals interesting aspects in it that have generally avoided recognition in literature. There are four different kinds of physical observables known or proclaimed as…

We survay some nice result concerning the irrationals with a metric space point of view.Here is ofcourse nothing new may be or an expert in this field.

In this paper I propose a new principle in physics: the principle of "finiteness". It stems from the definition of physics as a science that deals (among other things) with measurable dimensional physical quantities. Since measurement…