相关论文: The Error in the Two Envelopes Paradox

The envelope theory is an easy-to-use approximation method to obtain eigensolutions for some quantum many-body systems, in particular in the domain of hadronic physics. Even if the solutions are reliable and an improvement procedure exists,…

The reversibility and recurrence paradoxes are key issues that have been left unsolved in researches on the foundation of thermodynamics since the 19th century. This article shows that (1) the reversibility paradox can be overcome if we pay…

The Doomsday argument and anthropic reasoning are two puzzling examples of probabilistic confirmation. In both cases, a lack of knowledge apparently yields surprising conclusions. Since they are formulated within a Bayesian framework, they…

I'll discuss how Goedel's paradox "This statement is false/unprovable" yields his famous result on the limits of axiomatic reasoning. I'll contrast that with my work, which is based on the paradox of "The first uninteresting positive whole…

There has been a considerable amount of work on uncertainty in knowledge-based systems. This work has generally been concerned with uncertainty arising from the strength of inferences and the weight of evidence. In this paper we discuss…

Previous work finds that recent long-context language models fail to make equal use of information in the middle of their inputs, preferring pieces of information located at the tail ends which creates an undue bias in situations where we…

Current QA systems can generate reasonable-sounding yet false answers without explanation or evidence for the generated answer, which is especially problematic when humans cannot readily check the model's answers. This presents a challenge…

The Stokes paradox is the statement that in a viscous two dimensional fluid, the "linear response" problem of fluid flow around an obstacle is ill-posed. We present a simple consequence of this paradox in the hydrodynamic regime of a Fermi…

We present a few charge distributions for which the application of Gauss' law in its integral form, as typically outlined in standard textbooks, results in a contradiction. We identify the root cause of such contradictions and put forward a…

There are reasons to believe that implications of a certain paradox introduced by Ginzburg and related problems have not been fully recognized. Pertinent issues remain open and unresolved. There are instances when the current widely used…

Double descent is a surprising phenomenon in machine learning, in which as the number of model parameters grows relative to the number of data, test error drops as models grow ever larger into the highly overparameterized (data…

The EPR paradox and the meaning of the Bell inequality are discussed. It is shown that considering the quantum objects as carrying with them ''instruction kits'' telling them what to do when meeting a measurement apparatus any paradox…

In 1967, Frederick Lord posed a conundrum that has confused scientists for over half a century. Subsequently named Lord's 'paradox', the puzzle centres on the observation that two different approaches to estimating the effect of an exposure…

Attempts to replicate probabilistic reasoning in expert systems have typically overlooked a critical ingredient of that process. Probabilistic analysis typically requires extensive judgments regarding interdependencies among hypotheses and…

An inductive logic can be formulated in which the elements are not propositions or probability distributions, but information systems. The logic is complete for information systems with binary hypotheses, i.e., it applies to all such…

We identify a choiceless variation of the box game paradox, in which players predict unknown real numbers with near-perfect accuracy despite lacking any useful information. We also verify that choice is necessary in the solution of the…

Two paradoxical aspects of the prevailing kinetic equations are presented. One is related to the usual understanding of distribution function and the other to the usual understanding of the phase space. With help of simple counterexamples…

Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…

Asking questions is a pervasive human activity, but little is understood about what makes them difficult to answer. An analysis of a pair of large databases, of New York Times crosswords and questions from the quiz-show Jeopardy,…

An argument, perhaps originating with Feyerabend a half century ago, and repeated many times since, purporting to establish that an "ignorance interpretation" of a bipartite pure entangled state leads to logical inconsistency, is incorrect:…