Related papers: Agency and the physics of numbers
We show how G\"odel's first incompleteness theorem has an analog in quantum theory. G\"odel's theorem implies endless opportunities for appending axioms to arithmetic, implicitly showing a role for an agent, namely an agent that asserts an…
In this paper, we discuss different models for human logic systems and describe a game with nature. Godel`s incompleteness theorem is taken into account to construct a model of logical networks based on axioms obtained by symmetry breaking.…
The world of mathematics is often considered abstract, with its symbols, concepts, and topics appearing unrelated to physical objects. However, it is important to recognize that the development of mathematics is fundamentally influenced by…
The world runs on communicated sequences of symbols, e.g. numerals. Examining both engineered and natural communications networks reveals an unsuspected order that depends on contact with an unpredictable entity. This order has three roots.…
Is it possible to encompass the full extent of the universe within a theory based on a finite set of first principles and inference rules? The r\^{o}le of observers and observations in physics theories is considered here in the light of…
After two decades of research on indefinite causality, a philosophical lesson emerges: the tension between operational quantum theory and dynamical spacetime physics is unbridgeable if one believes both types of theories to be fundamental.…
An ultimate universal theory -- a complete theory that accounts, via few and simple first principles, for all the phenomena already observed and that will ever be observed -- has been, and still is, the aspiration of most physicists and…
We introduce some early considerations of physical and mathematical impossibility as preludes to the Goedel incompleteness theorems. We consider some informal aspects of these theorems and their underlying assumptions and discuss some the…
Agents' judgment depends on perception and previous knowledge. Assuming that previous knowledge depends on perception, we can say that judgment depends on perception. So, if judgment depends on perception, can agents judge that they have…
Although G\"odel's incompleteness theorem made mathematician recognize that no axiomatic system could completely prove its correctness and that there is an eternal hole between our knowledge and the world, physicists so far continue to work…
To operate reliably under changing conditions, complex systems require feedback on how effectively they use resources, not just whether objectives are met. Current AI systems process vast information to produce sophisticated predictions,…
I discuss three aspects of the notion of agency from the standpoint of physics: (i) what makes a physical system an agent; (ii) the reason for agency's time orientation; (iii) the source of the information generated in choosing an action. I…
Agent based systems are more common than we may think. A Promise Theory perspective on cooperation, in systems of human-machine agents, offers a unified perspective on organization and functional design with semi-automated efforts, in terms…
A new viewpoint of the G\"odel's incompleteness theorem be given in this article which reveals the deep relationship between the logic and computation. Upon the results of these studies, an algorithm be given which shows how to search a…
G\"odel's argument for the First Incompleteness Theorem is, structurally, a proof by contradiction. This article intends to reframe the argument by, first, isolating an additional assumption the argument relies on, and then, second, arguing…
G\"odel's second incompleteness theorem is standardly understood as showing that no sufficiently strong, consistent theory of arithmetic can prove its own consistency, a result typically interpreted against a model-theoretic background in…
The basic equations of physics involve a time variable t and are invariant under the transformation $t goes to -t$. This invariance at first sight appears to impose time reversibility as a principle of physics, in conflict with…
What are the physical requirements for agency? We investigate whether a purely quantum system (one evolving unitarily in a coherent regime without decoherence or collapse) can satisfy three minimal conditions for agency: an agent must be…
Despite its obvious relevance, meaning has been outside most theoretical approaches to information in biology. As a consequence, functional responses based on an appropriate interpretation of signals has been replaced by a probabilistic…
In this article, we propose to use the formalism of quantum mechanics to describe and explain the so-called "abnormal" behaviour of agents in certain decision or choice contexts. The basic idea is to postulate that the preferences of these…