Related papers: The Computable Universe Hypothesis
Are minds subject to laws of physics? Are the laws of physics computable? Are conscious thought processes computable? Currently there is little agreement as to what are the right answers to these questions. Penrose goes one step further and…
A basic concept of Type Two Theory of Effectivity (TTE) is the notion of an admissibly represented space. Admissibly represented spaces are closely related to qcb-spaces. The latter form a well-behaved subclass of topological spaces. We…
We define the notion of ordinal computability by generalizing standard Turing computability on tapes of length $\omega$ to computations on tapes of arbitrary ordinal length. We show that a set of ordinals is ordinal computable from a finite…
With the great success in simulating many intelligent behaviors using computing devices, there has been an ongoing debate whether all conscious activities are computational processes. In this paper, the answer to this question is shown to…
To better understand the deep significance of our best physical theories it could be interesting to compare our Universe with its models. It may happen that the differences between the model and reality can be made indistinguishable, to the…
The theory that all processes in the universe are computational is attractive in its promise to provide an understandable theory of everything. I want to suggest here that this pancomputationalism is not sufficiently clear on which problem…
To scrutinize notions of computation and time complexity, we introduce and formally define an interactive model for computation that we call it the \emph{computation environment}. A computation environment consists of two main parts: i) a…
The notion of computability is stable (i.e. independent of the choice of an indexing) over infinite-dimensional vector spaces provided they have a finite "tensorial dimension". Such vector spaces with a finite tensorial dimension permit to…
We investigate the theory of thermodynamic formalism from the perspective of computable analysis, with a special focus on the computability of equilibrium states. Specifically, we develop two complementary general approaches to verify the…
In this paper, a computably definable predicate is defined and characterized. Then, it is proved that every separable infinite-dimensional Hilbert structure in an effectively presented language is computable. Moreover, every definable…
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…
This article reviews the history of digital computation, and investigates just how far the concept of computation can be taken. In particular, I address the question of whether the universe itself is in fact a giant computer, and if so,…
This article is a fundamental study in computable analysis. In the framework of Type-2 effectivity, TTE, we investigate computability aspects on finite and infinite products of effective topological spaces. For obtaining uniform results we…
Although there is a somewhat standard formalization of computability on countable sets given by Turing machines, the same cannot be said about uncountable sets. Among the approaches to define computability in these sets, order-theoretic…
The central idea of this work is the concept of prespace, a hypothetical structure that is postulated to underlie the fabric of space or space-time. I consider how such a structure could relate to space and space-time, and the implications…
In this article, we establish the foundations of a computational field theory, which we term Topological Kleene Field Theory (TKFT), inspired by Stephen Kleene's seminal work on partial recursive functions and drawing parallels with…
We study the computational complexity theory of smooth, finite-dimensional dynamical systems. Building off of previous work, we give definitions for what it means for a smooth dynamical system to simulate a Turing machine. We then show that…
This article addresses the question of when physical laws and their consequences can be computed. If a physical system is capable of universal computation, then its energy gap can't be computed. At an even more fundamental level, the most…
A fundamental question is whether Turing machines can model all reasoning processes. We introduce an existence principle stating that the perception of the physical existence of any Turing program can serve as a physical causation for the…
The long lasting discussion on the completeness of quantum theory (QT) has not yet come to an end. The discussion is impeded by the lack of a clear understanding of what makes up the contents of a theory of physics in general and of QT…