Related papers: Is independent choice possible?
The role of complex quantities in quantum theory has been puzzling physicists since the beginnings. It is thus natural to ask whether, in order to describe our experiments, the mathematical structure of complex Hilbert spaces it is built on…
The concept of determinism for a classical system is interpreted as the requirement that the solution to the Cauchy problem for the equations of motion governing this system be unique. This requirement is generally assumed to hold for all…
We consider an infinite system of particles in one dimension, each particle performs independant Sinai's random walk in random environment. Considering an instant $t$, large enough, we prove a result in probability showing that the…
Transfinite set theory including the axiom of choice supplies the following basic theorems: (1) Mappings between infinite sets can always be completed, such that at least one of the sets is exhausted. (2) The real numbers can be well…
Consider a finite renewal process in the sense that interrenewal times are positive i.i.d. variables and the total number of renewals is a random variable, independent of interrenewal times. A finite point process can be obtained by…
What makes a paper independently reproducible? Debates on reproducibility center around intuition or assumptions but lack empirical results. Our field focuses on releasing code, which is important, but is not sufficient for determining…
We assess how physically realistic the ''simulation hypothesis'' for this Universe is, based on physical constraints arising from the link between information and energy, and on known astrophysical constraints. We investigate three cases:…
We propose a new nonparametric test for the supposition of independence between two continuous random variables. The test is based on the size of the longest increasing subsequence of a random permutation. We identified the independence…
Decisions are often based on imprecise, uncertain or vague information. Likewise, the consequences of an action are often equally unpredictable, thus putting the decision maker into a twofold jeopardy. Assuming that the effects of an action…
Starting from the assumption that general relativity might be an emergent phenomenon showing up at low-energies from an underlying microscopic structure, we re-analyze the stability of a static closed Universe filled with radiation. In this…
In this paper the author presents some non-conventional thoughts on the complexity of the Universe and the algorithmic reproducibility of the human brain, essentially sparked off by the notion of algorithmic complexity. We must warn that…
A software product line models the variability of highly configurable systems. Complete exploration of all valid configurations (the configuration space) is infeasible as it grows exponentially with the number of features in the worst case.…
The prime numbers look like a randomly chosen sequence of natural numbers, but there is still no strict theory to determine 'Randomness'. In these years, cryptography has developed a battery of statistical tests for randomness. In this…
We investigate initial information, unbounded memory and randomization in gathering mobile agents on a grid. We construct a state machine, such that it is possible to gather, with probability 1, all configurations of its copies. This…
Environment induced decoherence, and other quantum processes, have been proposed in the literature to explain the apparent spontaneous selection - out of the many mathematically eligible bases - of a privileged measurement basis that…
We review possible measures of complexity which might in particular be applicable to situations where the complexity seems to arise spontaneously. We point out that not all of them correspond to the intuitive (or "naive") notion, and that…
The issue of whether we make decisions freely has vexed philosophers for millennia, Resolving this is vital for solving a diverse range of problems, from the physiology of how the brain makes decisions (and how we assign moral…
As observers of the universe we are quantum physical systems within it. If the universe is very large in space and/or time, the probability becomes significant that the data on which we base predictions is replicated at other locations in…
Many have proposed that free will would use quantum indeterminism. Strict adherence to the Born rule, which follows from the no-signal condition, seems to block this possibility. I propose here that if state collapse really does occur then…
In this work we show that the prime distribution is deterministic. Indeed the set of prime numbers P can be expressed in terms of two subsets of N using three specific selection rules, acting on two sets of prime candidates. The prime…