Related papers: Extracting a Paradox by the Roots
Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful to the study of chaos since no analytical…
The concepts of symmetry and its breakdown are investigated in two different terms according to whether the resulting asymmetry is universal or only obtained for a special configuration: we shall illustrate this by considering in the first…
The definition of probabilities in eternally inflating universes requires a measure to regulate the infinite spacetime volume, and much of the current literature uses a global time cutoff for this purpose. Such measures have been found to…
Some possible (re)sources of indeterminism and randomness encountered in physics are enumerated. These gaps in the physical laws, if they exist, could possibly be exploited for dualistic interfaces. We also speculate that physical laws and…
From classical mechanics to quantum field theory, the physical facts at one point in space are held to be independent of those at other points in space. I propose that we can usefully challenge this orthodoxy in order to explain otherwise…
Time-asymmetric behavior as embodied in the second law of thermodynamics is observed in {\it individual macroscopic} systems. It can be understood as arising naturally from time-symmetric microscopic laws when account is taken of a) the…
Two paradoxical aspects of the prevailing kinetic equations are presented. One is related to the usual understanding of distribution function and the other to the usual understanding of the phase space. With help of simple counterexamples…
We set up a model for reasoning about metric spaces with belief theoretic measures. The uncertainty in these spaces stems from both probability and metric. To represent both aspect of uncertainty, we choose an expected distance function as…
Consider the following story: A teacher announces to her students a test for the following week, such that the test will be ``surprising''. The students use this as the basis for a ``logical derivation'' and reach a contradiction, which…
Component systems - ensembles of realizations built from a shared repertoire of modular parts - are ubiquitous in biological, ecological, technological, and socio-cultural domains. From genomes to texts, cities, and software, these systems…
The Erd\H{o}s discrepancy problem, now a theorem by T. Tao, asks whether every sequence with values plus or minus one has unbounded discrepancy along all homogeneous arithmetic progressions. We establish weighted variants of this problem,…
According to the quantum Zeno effect, the frequent observations of a system can dramatically slow down its dynamical evolution. We show that the Zeno dynamics is the result of projective measurements among quantum states which are…
From bird flocking to neural dynamics, complex systems generate fascinating structures and correlations. Often, seemingly simple dynamics lead to intricate emergent properties. Despite their visceral appeal, defining complex systems lacks…
Curiously overlooked in physics is its dependence on the transmission of numbers. For example the transmission of numerical clock readings is implicit in the concept of a coordinate system. The transmission of numbers and other logical…
``No one has ever touched Zeno without refuting him''. We will not refute Zeno in this paper. Instead we review some unexpected encounters of Zeno with modern science. The paper begins with a brief biography of Zeno of Elea followed by his…
Substitution systems evolve in time by generating sequences of symbols from a finite alphabet: At a certain iteration step, the existing symbols are systematically replaced by blocks of $N_{k}$ symbols also within the alphabet (with…
Paradoxes that can supposedly occur if a time machine is created are discussed. It is shown that the existence of trajectories of ``multiplicity zero'' (i.e. trajectories that describe a ball hitting its younger self so that the latter…
One of the most discussed peculiarities of Einstein's theory of relativity is the twin paradox, the fact that the time between two events in space-time appears to depend on the path between these events. We show that this time discrepancy…
A new approach to the phenomenon of large numbers coincidence leads to unexpected results. No matter how strange it might sound, the exact value of cosmological parameters and their analytical expression through fundamental constants have…
One of the presuppositions of science since the times of Galileo, Newton, Laplace, and Descartes has been the predictability of the world. This idea has strongly influenced scientific and technological models. However, in recent decades,…