Related papers: An Impossible Asylum
We utilize the technique of staircases and jagged partitions to provide analytic sum-sides to some old and new partition identities of Rogers-Ramanujan type. Firstly, we conjecture a class of new partition identities related to the…
For half a century, authors have weakened the rule of necessitation in various more or less ad hoc ways in order to make inconsistent systems consistent. More recently, necessitation was weakened in a systematic way, not for the purpose of…
In 1975, G. P\'olya suggested that if two proofreaders found $a$ and $b$ errors in a text, of which $c$ errors were found by both of them, then a reasonable approximation of the unknown number $e$ of all errors is $e\approx ab/c$. We…
The past year has seen an explosion of new and old ideas about black hole physics. Prior to the firewall paper, the dominant picture was the thermofield model apparently implied by ADS/CFT duality\cite{mal2}. While some seek a narrow…
The Prisoner's Dilemma has been a subject of extensive research due to its importance in understanding the ever-present tension between individual self-interest and social benefit. A strictly dominant strategy in a Prisoner's Dilemma…
What is the largest number accessible to the human imagination? The question is neither entirely mathematical nor entirely philosophical. Mathematical formulations of the problem fall into two classes: those that fail to fully capture the…
Situations of conflict giving rise to social dilemmas are widespread in society and game theory is one major way in which they can be investigated. Starting from the observation that individuals in society interact through networks of…
In October 2017 the Italian National Institute of Statistics (ISTAT), Italy's body for official statistics, has published the book of fairy tales Le streghe di Bayes (The witches of Bayes) written by ISTAT staff members with the commendable…
This article discusses the logical errors in the liar paradox, G\"odel's incompleteness theorems, Russell's paradox, and the halting problem. In order to avoid these errors, a redefinition of logic has been presented, which is concluded as…
Based on Lyndon words, a new Sudoku-like puzzle is presented and some relative theoretical questions are proposed.
Social sciences have accumulated a rich body of theories and methodologies for investigating the human mind and behaviors, while offering valuable insights into the design and understanding of Artificial Intelligence (AI) systems. Focusing…
We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…
Recent hype surrounding the increasing sophistication of language processing models has renewed optimism regarding machines achieving a human-like command of natural language. Research in the area of natural language understanding (NLU) in…
If no optimal propositional proof system exists, we (and independently Pudl\'ak) prove that ruling out length $t$ proofs of any unprovable sentence is hard. This mapping from unprovable to hard-to-prove sentences powerfully translates facts…
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…
In this paper, we proposed an interesting problem that might be classified into enumerative combinatorics. Featuring a distinctive two-fold dependence upon the sequences' terms, our problem can be really difficult, which calls for novel…
The paper has been withdrawn by the author, due to a fatal error. A horse stumbles that has four legs.
Pattern-Based Constraint Satisfaction and Logic Puzzles develops a pure logic, pattern-based perspective of solving the finite Constraint Satisfaction Problem (CSP), with emphasis on finding the "simplest" solution. Different ways of…
The Facility Location Problem (FLP) is a well-studied optimization problem with applications in many real-world scenarios. Past literature has explored the solutions from different perspectives to tackle FLPs. These include investigating…
The cosmic "Great Silence" revealed by the Fermi paradox remains a central puzzle in contemporary science. Existing explanations such as the "Big Filter," "Zoo Hypothesis," and "Dark Forest" theory are trapped in isolated frameworks of…