相关论文: Resolution of the Surprise Exam Paradox

All the already known results on self descriptive numbers, together with the demonstration of the uniqueness for bases greater than 6, are here obtained through a systematic scheme of proof and not trial and error. The proof is also…

Paradoxes are a relatively frequent occurrence in physics. The nature of their genesis is diverse and they are found in all branches of physics. There are a number of general and special classifications of paradoxes, but there are no…

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…

The purpose of this paper is to show the magic of physics by showing the physics of magic. What usually makes magic tricks interesting is that something unexpected occurs. Similarly, demonstrations are interesting inasmuch as they produce…

We conduct an incentivized experiment on a nationally representative US sample \\ (N=708) to test whether people prefer to avoid ambiguity even when it means choosing dominated options. In contrast to the literature, we find that 55\% of…

Developing a better understanding of surprising or counterintuitive phenomena has constituted a significant portion of deep learning research in recent years. These include double descent, grokking, and the lottery ticket hypothesis --…

Peculiar measurements can be obtained on systems that undergo both pre- and post-selection. We prove a conjecture from [1] on logical Pre- and Post-Selection (PPS) paradoxes for a restricted case. We prove that all of these paradoxes admit…

Type-free systems of logic are designed to consistently handle significant instances of self-reference. Some consistent type-free systems also have the feature of allowing the sort of general abstraction or comprehension principle that…

We present an astonishingly simple and elegant proof of the celebrated Basel problem.

It is sometimes claimed that the twin "paradox" requires general relativity for a resolution. This paper presents a simple, exact resolution using only special relativity and the equivalence principle. Two earlier approximate solutions are…

After pointing out the historical avatar at the origin of a would be twin or clock paradox, we argue that, at least on a local scale, the (re-qualified) paradox is but a necessary consequence of the sole principle of causality.

The halting problem is considered to be an essential part of the theoretical background to computing. That halting is not in general computable has supposedly been proved in many text books and taught on many computer science courses, in…

We formulate a paradox in relation to the description of a joint entity consisting of two subentities by standard quantum mechanics. We put forward a proposal for a possible solution, entailing the interpretation of density states as pure…

In the Story Cloze Test, a system is presented with a 4-sentence prompt to a story, and must determine which one of two potential endings is the 'right' ending to the story. Previous work has shown that ignoring the training set and…

The well-known Simpson's Paradox, or Yule-Simpson Effect, in statistics is often illustrated by the following thought experiment: A drug may be found in a trial to increase the survival rate for both men and women, but decrease the rate for…

Russell's paradox is the most easily understandable way to illustrate the inconsistency of na\"ive set theory. This note proposes a direct encoding of Russell's paradox with type-in-type universe, sigma types, and either extensional…

Zeno's paradoxes are explained as being the result of inappropriate combination of discrete and continuous mathematical systems. It is proposed that the source of this confusion lies in the course of development of the number system, which…

I discuss how five reasonably sounding assumptions lead to a dilemma -- the Page-time paradox -- , which appears to challenge a conventional statistical mechanical underpinning of black hole thermodynamics. By inspecting the conceptual…

A perfect number is a number whose divisors add up to twice the number itself. The existence of odd perfect numbers is a millennia-old unsolved problem. This note proposes a proof of the nonexistence of odd perfect numbers. More generally,…

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…