Related papers: Spurious, Emergent Laws in Number Worlds
Skill acquisition is a key area of research in cognitive psychology as it encompasses multiple psychological processes. The laws discovered under experimental paradigms are controversial and lack generalizability. This paper aims to unearth…
What distribution of graphical degree sequence is invariant under ``scaling''? Are these graphs always power-law graphs? We show the answer is a surprising ``yes'' for sparse graphs if we ignore isolated vertices, or more generally, the…
Much of philosophical logic and all of philosophy of language make empirical claims about the vernacular natural language. They presume semantics under which `and' and `or' are related by the dually paired distributive and absorption laws.…
Zipf's law is the most common statistical distribution displaying scaling behavior. Cities, populations or firms are just examples of this seemingly universal law. Although many different models have been proposed, no general theoretical…
When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf's law or the Pareto distribution. Power laws appear…
Physics seeks to uncover the laws of Nature and express them through mathematical equations. Despite the vast diversity of natural phenomena, physical equations exhibit structural regularities that set them apart from arbitrary mathematical…
We present a simple mathematical model in which a time averaged pattern emerges out of spatio-temporal chaos as a result of the collective action of chaotic fluctuations. Our evolution equation possesses spatial translational symmetry under…
Cosmology has come a long way from being based on a small number of observations to being a data-driven precision science. We discuss the questions "What is observable?", "What in the Universe is knowable?" and "What are the fundamental…
Pairs of numerically computed trajectories of a chaotic system may coalesce because of finite arithmetic precision. We analyse an example of this phenomenon, showing that it occurs surprisingly frequently. We argue that our model belongs to…
We extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom. While the previous systems were linear and exploded exponentially for…
We address the question of why particular laws were selected for the universe, by proposing a mechanism for laws to evolve. Normally in physical theories, timeless laws act on time-evolving states. We propose that this is an approximation,…
There is a property of a quantum state called magic. It measures how difficult for a classical computer to simulate the state. In this paper, we study magic of states in the integrable and chaotic regimes of the higher-spin generalization…
Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism - mathematics exists and is…
A core problem in learning semantic parsers from denotations is picking out consistent logical forms--those that yield the correct denotation--from a combinatorially large space. To control the search space, previous work relied on…
Disordered many-body systems exhibit a wide range of emergent phenomena across different scales. These complex behaviors can be utilized for various information processing tasks such as error correction, learning, and optimization. Despite…
We review a cosmology in which particles are fluctuationally created from a background Zero Point Field. This cosmology is consistent with recent observations of an ever expanding and accelerating universe, as also the recently confirmed…
It is a common belief that in any environment where life is possible, life will be generated. Here it is suggested that the cause for a spontaneous generation of complex systems is probability driven processes. Based on equilibrium…
The emergence of cosmic structure is commonly considered one of the most complex phenomena in Nature. However, this complexity has never been defined nor measured in a quantitative and objective way. In this work we propose a method to…
The mechanism responsible for the emergence of chaotic behavior has been identified analytically within a class of three-dimensional dynamical systems which generalize the well-known E.N. Lorenz 1963 system. The dynamics in the phase space…
The unreduced, universally nonperturbative analysis of arbitrary interaction process, described by a quite general equation, provides the truly complete, "dynamically multivalued" general solution that leads to dynamically derived,…