相关论文: Algorithmic Theories of Everything

Algorithmic information theory studies description complexity and randomness and is now a well known field of theoretical computer science and mathematical logic. There are several textbooks and monographs devoted to this theory where one…

Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some…

I will propose the notion that the universe is digital, not as a claim about what the universe is made of but rather about the way it unfolds. Central to the argument will be the concepts of symmetry breaking and algorithmic probability,…

Is the universe computable? If so, it may be much cheaper in terms of information requirements to compute all computable universes instead of just ours. I apply basic concepts of Kolmogorov complexity theory to the set of possible…

Kolmogorov complexity and algorithmic probability are defined only up to an additive resp. multiplicative constant, since their actual values depend on the choice of the universal reference computer. In this paper, we analyze a natural…

Everettian Quantum Mechanics, or the Many Worlds Interpretation, lacks an explanation for quantum probabilities. We show that the values given by the Born rule equal projection factors, describing the contraction of Lebesgue measures in…

Solomonoff unified Occam's razor and Epicurus' principle of multiple explanations to one elegant, formal, universal theory of inductive inference, which initiated the field of algorithmic information theory. His central result is that the…

In cosmology, we would like to explain our observations and predict future observations from theories of the entire universe. Such cosmological theories make ontological assumptions of what entities exist and what their properties and…

Increasingly encompassing models have been suggested for our world. Theories range from generally accepted to increasingly speculative to apparently bogus. The progression of theories from ego- to geo- to helio-centric models to universe…

We introduce the framework of general probabilistic theories (GPTs for short). GPTs are a class of operational theories that generalize both finite-dimensional classical and quantum theory, but they also include other, more exotic theories,…

General relativity treats spacetime as dynamical and exhibits its breakdown at singularities. This failure is interpreted as evidence that quantum gravity is not a theory formulated within spacetime; instead, it must explain the very…

We propose a test based on the theory of algorithmic complexity and an experimental evaluation of Levin's universal distribution to identify evidence in support of or in contravention of the claim that the world is algorithmic in nature. To…

Toda's Theorem is a fundamental result in computational complexity theory, whose proof relies on a reduction from a QBF problem with a constant number of quantifiers to a model counting problem. While this reduction, henceforth called…

We introduce a hierarchical classification of theories that describe systems with fundamentally limited information content. This property is introduced in an operational way and gives rise to the existence of mutually complementary…

We propose a measure based upon the fundamental theoretical concept in algorithmic information theory that provides a natural approach to the problem of evaluating $n$-dimensional complexity by using an $n$-dimensional deterministic Turing…

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…

We produce a probabilistic space from logic, both classical and quantum, which is in addition partially ordered in such a way that entropy is monotone. In particular do we establish the following equation: Quantitative Probability = Logic +…

We argue using simple models that all successful practical uses of probabilities originate in quantum fluctuations in the microscopic physical world around us, often propagated to macroscopic scales. Thus we claim there is no physically…

The aim of this paper is to present an elementary computable theory of random variables, based on the approach to probability via valuations. The theory is based on a type of lower-measurable sets, which are controlled limits of open sets,…

In the modern quantum mechanics of cosmology observers are physical systems within the universe. They have no preferred role in the formulation of the theory nor in its predictions of third person probabilities of what occurs. However,…