Related papers: Free Lunch
The aim of this essay is to propose a conception of mathematics that is fully consonant with naturalism. By that I mean the hypothesis that everything that exists is part of the natural world, which makes up a unitary whole.
Perfectly rational decision-makers maximize expected utility, but crucially ignore the resource costs incurred when determining optimal actions. Here we employ an axiomatic framework for bounded rational decision-making based on a…
In this essay, I argue that mathematics is a natural science---just like physics, chemistry, or biology---and that this can explain the alleged "unreasonable" effectiveness of mathematics in the physical sciences. The main challenge for…
Understanding and quantifying causal relationships between variables is essential for reasoning about the physical world. In this work, we develop a resource-theoretic framework to do so. Here, we focus on the simplest nontrivial setting --…
With infinitely many high-quality data points, infinite computational power, an infinitely large foundation model with a perfect training algorithm and guaranteed zero generalization error on the pretext task, can the model be used for…
We present an approach to type theory in which the typing judgments do not have explicit contexts. Instead of judgments of shape "Gamma |- A : B", our systems just have judgments of shape "A : B". A key feature is that we distinguish free…
In this paper a conditional logic is defined and studied. This conditional logic, DmBL, is constructed as close as possible to the Bayesian and is unrestricted, that is one is able to use any operator without restriction. A notion of…
In a number of books and articles including "The Design Inference" and "No Free Lunch", W. Dembski claims to have established a robust decision process that can determine when observed structures in the natural world can be attributed to…
In this note we will show how to get consistency for first order classical logic, in a purely syntactic way, without going through cut elimination. The procedure is very simple and it uses the calculus of structures in an essential way. It…
A simple class of chaotic systems in a random environment is considered and the fluctuation theorem is extended under the assumption of reversibility.
We study the monotonicity properties of solutions in the classic problem of fair cake-cutting --- dividing a heterogeneous resource among agents with different preferences. Resource- and population-monotonicity relate to scenarios where the…
Inspired by Raychaudhuri's work, and using the equation named after him as a basic ingredient, a new singularity theorem is proved. Open non-rotating everywhere expanding universes with non-vanishing spatial average of the matter variables…
There are several formulations of the second law, and they may, in principle, have different domains of validity. Here a simple mathematical theorem is proven which serves as the most general basis for the second law, namely the Thomson…
We propose a simple "evolutionary" sandpile model exhibiting self-organised criticality and exactly $1/f$-noise (i.e. the critical exponent is equal to $-1$) and observe emergent phenomena of the same type self-organised criticality on the…
The superposition principle lies at the heart of many non-classical properties of quantum mechanics. Motivated by this, we introduce a rigorous resource theory framework for the quantification of superposition of a finite number of linear…
We show how the existence of various free vector lattices and free vector lattice algebras can be derived from a theorem on equational classes in universal algebra. A discussion about free $f$-algebras over non-empty sets is given, where…
The question what determines the structure of natural food webs has been listed among the nine most important unanswered questions in ecology. It arises naturally from many problems related to ecosystem stability and resilience. The…
The famous G\"odel incompleteness theorem says that for every sufficiently rich formal theory (containing formal arithmetic in some natural sense) there exist true unprovable statements. Such statements would be natural candidates for being…
This paper is a contribution to the study of the universal Horn fragment of predicate fuzzy logics, focusing on some relevant notions in logic programming. We introduce the notion of term structure associated to a set of formulas in the…
The ability to uncover preferences from choices is fundamental for both positive economics and welfare analysis. Overwhelming evidence shows that choice is stochastic, which has given rise to random utility models as the dominant paradigm…