Related papers: A Computational Anthropic Principle: Where is the …
The uncertainty principle is a fundamental principle in quantum physics. It implies that the measurement outcomes of two incompatible observables can not be predicted simultaneously. In quantum information theory, this principle can be…
Arrow's Impossibility Theorem establishes bounds on what we can require from voting systems. Given satisfaction of a small collection of "fairness" axioms, it shows votes can only exist as dictatorships in which one voter determines all…
We prove that given a computable metric space and two computable measures, the set of points that have high universal uniform test scores with respect to the first measure will have a lower bound with respect to the second measure. This…
By nature, transmissible human knowledge is enumerable: every sentence, movie, audio record can be encoded in a sufficiently long string of 0's and 1's. The works of G\"odel, Turing and others showed that there are inherent limits and…
It is possible that there may be differences in the fundamental physical parameters from one side of the observed universe to the other. I show that the cosmological constant is likely to be the most sensitive of the physical parameters to…
Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also…
Hypercomputation or super-Turing computation is a ``computation'' that transcends the limit imposed by Turing's model of computability. The field still faces some basic questions, technical (can we mathematically and/or physically build a…
Predictive coding has emerged as an influential normative model of neural computation, with numerous extensions and applications. As such, much effort has been put into mapping PC faithfully onto the cortex, but there are issues that remain…
Evidence for fine-tuning of physical parameters suitable for life can perhaps be explained by almost any combination of providence, coincidence or multiverse. A multiverse usually includes parts unobservable to us, but if the theory for it…
This paper deals with the philosophical issues of the notion of nothingness and pre-inflationary stage of the universe in physical cosmology. We presuppose that, in addition to cosmological limits, there may be both anthropic and…
Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…
We devise a hierarchy of computational algorithms to enumerate the microstates of a system comprising N independent, distinguishable particles. An important challenge is to cope with integers that increase exponentially with system size,…
Quantum mechanics introduces the concept of probability at the fundamental level, yielding the measurement problem. On the other hand, recent progress in cosmology has led to the "multiverse" picture, in which our observed universe is only…
A cosmological constant fits all current dark energy data, but requires two extreme fine tunings, both of which are currently explained by anthropic arguments. Here we discuss anti-anthropic solutions to one of these problems: the cosmic…
Here we deconstruct, and then in a reasoned way reconstruct, the concept of "entropy of a system," paying particular attention to where the randomness may be coming from. We start with the core concept of entropy as a COUNT associated with…
[Abridged] Some cosmological theories propose that the observable universe is a small part of a much larger universe in which parameters describing the low-energy laws of physics vary from region to region. How can we reasonably assess a…
Quantum information theory and the multiverse are two of the greatest outcomes of the XX century physics. The consideration of entanglement between the quantum states of two or more universes in a multiverse scenario provides us with a…
I argue that various derivations of the Born probability rule within strictly unitary quantum mechanics implicitly use anthropic constraints on the properties of the probabilities, but without proposing an ensemble from which those…
In theories in which different regions of the universe can have different values of the the physical parameters, we would naturally find ourselves in a region which has parameters favorable for life. We explore the range of anthropically…
Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and…