Related papers: An Impossible Asylum
In 1942 Haskell B.Curry presented what is now called Curry paradox which can be found in a logic independently of its stand on negation.In recent years there has been a revitalised interest in non-classical solutions to the semantic…
For a $k$-ary predicate $P$, a random instance of CSP$(P)$ with $n$ variables and $m$ constraints is unsatisfiable with high probability when $m \gg n$. The natural algorithmic task in this regime is \emph{refutation}: finding a proof that…
In this expository note, we discuss a ``balls-and-urns'' probability puzzle posed by Daniel Litt.
The consistency problem for a class of algebraic structures asks for an algorithm to decide for any given conjunction of equations whether it admits a non-trivial satisfying assignment within some member of the class. By Adyan (1955) and…
The following conjecture was proposed in 2010 by S. Lando. Let M and N be two unions of the same number of disjoint circles in a sphere. Then there exist two spheres in 3-space whose intersection is transversal and is a union of disjoint…
The paper is an extended version of the talk in the Logic Colloquium-2000 at Paris. We discuss a series of results and problems around Hrushovski's construction of counter-examples to the Trichotomy conjecture.
We revive an old lateral-thinking puzzle by Michael Rabin, involving poisons with strange properties. We show that the puzzle admits several unintended solutions that are just as interesting as the intended solution. Analyzing these…
This is a collection of variants of Schanuel's conjecture and the known dependencies between them. It was originally written in 2007, and made available for a time on my webpage. I have been asked by a few people to make it available again…
Black hole complementarity, as originally formulated in the 1990's by Preskill, 't Hooft, and myself is now being challenged by the Almheiri-Marolf-Polchinski-Sully firewall argument. The AMPS argument relies on an implicit assumption---the…
The Monty Hal problem is an attractive puzzle. It combines simple statement with answers that seem surprising to most audiences. The problem was thoroughly solved over two decades ago. Yet, more recent discussions indicate that the solution…
Crossword puzzles are popular word games that require not only a large vocabulary, but also a broad knowledge of topics. Answering each clue is a natural language task on its own as many clues contain nuances, puns, or counter-intuitive…
Gr\"atzer asked in 1971 for a characterization of sublattices of Tamari lattices (associahedra). A natural candidate was coined by McKenzie in 1972 with the notion of a bounded homomorphic image of a free lattice---in short, bounded…
This is a typeset version of Alan Turing's declassified Second World War paper \textit{Paper on Statistics of Repetitions}. See the companion paper, \textit{The Applications of Probability to Cryptography}, also available from arXiv at…
The standard iterated prisoner's dilemma is an unrealistic model of social behaviour because it forces individuals to participate in the interaction. We analyse a model in which players have the option of ending their association. If the…
We present Russell's antinomy using three distinct deductive systems, which are then compared to deepen the logical deductions that lead to the contradiction. Some inferential paths are then presented, alternative to the commonly accepted…
We analyze the problem of matching asylum seekers to member states, incorporating wait times, preferences of asylum seekers, and the priorities, capacities, and burden-sharing commitments of member states. We identify a unique choice rule…
The purpose of this paper is to clarify the (non-Bayesian and Bayesian) two-envelope problems in terms of quantum language (or, measurement theory), which was recently proposed as a linguistic turn of quantum mechanics (with the Copenhagen…
In this note, we show that a "Toy Conjecture" made by (Boyle, Ishai, Pass, Wootters, 2017) is false, and propose a new one. Our attack does not falsify the full ("non-toy") conjecture in that work, and it is our hope that this note will…
The U.S. Supreme Court is currently deliberating over whether a proposed mathematical formula should be used to detect unconstitutional partisan gerrymandering. We show that in some cases, this formula will only flag bizarrely shaped…
Natural languages can express some logical propositions that humans are able to understand. We illustrate this fact with a famous text that Conan Doyle attributed to Holmes: 'It is an old maxim of mine that when you have excluded the…