Related papers: It From Bit and The Unsmooth Reality
In order to reject the notion that information is always about something, the "It from Bit" idea relies on the nonexistence of a realistic framework that might underly quantum theory. This essay develops the case that there is a plausible…
I argue that, on the subjective Bayesian interpretation of probability, "it from bit" requires a generalization of probability theory. This does not get us all the way to the quantum probability rule because an extra constraint, known as…
In his famous 1989 It from Bit essay, John Wheeler contends that the stuff of the physical universe, or it, arises from information or bits, encoded in yes or no answers. Wheeler's question and assumptions are reexamined from a post Aspect…
We believe that the hypothesis `it from bit' originates from the assumption that probabilities have a fundamental, irremovable status in quantum theory. We argue against this assumption and highlight four well-known reformulations /…
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…
The "unit theorem" to which the present mini-course is devoted is a theorem from algebra that has a combinatorial flavour, and that originated in fact from algebraic combinatorics. Beyond a proof, the course also addresses applications, one…
Chaitin's incompleteness theorem states that sufficiently rich formal systems cannot prove lower bounds on Kolmogorov complexity. In this paper we extend this theorem by showing theories that prove the Kolmogorov complexity of a large (but…
This article deals with plausible reasoning from incomplete knowledge about large-scale spatial properties. The availableinformation, consisting of a set of pointwise observations,is extrapolated to neighbour points. We make use of belief…
The aim of this paper is to enlight the emerging relevance of Quantum Information Theory in the field of Quantum Gravity. As it was suggested by J. A. Wheeler, information theory must play a relevant role in understanding the foundations of…
I discuss several aspects of information theory and its relationship to physics and neuroscience. The unifying thread of this somewhat chaotic essay is the concept of Kolmogorov or algorithmic complexity (Kolmogorov Complexity, for short).…
A selection of the relevant theorems of Probability Theory that comes directly from Kolmogorov's axioms, Set Theory basic results, definitions and rules of inference are listed and proven in a systematic approach, aiming the student who…
While Kolmogorov's probability axioms are widely recognized, it is less well known that in an often-overlooked 1930 note, Kolmogorov proposed an axiomatic framework for a unifying concept of the mean -- referred to as regular means. This…
In this article we discuss the formal structure of a generalized information theory based on the extension of the probability calculus of Kolmogorov to a (possibly) non-commutative setting. By studying this framework, we argue that quantum…
Is our world just information? We argue that our current notion of information has one serious shortcoming: It is quite literally meaningless. We suggest a meaningful extension of the notion of information that is dynamic, internal,…
The use of algorithmic information theory (Kolmogorov complexity theory) to explain the relation between mathematical probability theory and `real world' is discussed.
Kolmogorov Complexity constitutes an integral part of computability theory, information theory, and computational complexity theory -- in the discrete setting of bits and Turing machines. Over real numbers, on the other hand, the…
The incompressibility method is a counting argument in the framework of algorithmic complexity that permits discovering properties that are satisfied by most objects of a class. This paper gives a preliminary insight into Kolmogorov's…
We will focus on the Quantum theory and starting from simple philosophical conjectures, we infer possible different physical realities. Also we argue of possible wavefunction emerging under specific conditions of the physical reality.…
We present several application of simple topological arguments in problems of Kolmogorov complexity. Basically we use the standard fact from topology that the disk is simply connected. It proves to be enough to construct strings with some…
In this essay I develop quantum contextuality as a potential candidate for Wheeler's universal regulating principle, arguing -- \textit{contrary} to Wheeler -- that this ultimately implies that `bit' comes from `it.' In the process I…