Abraham ibn Ezra (1089–1164) was a prominent Jewish scholar, poet, and philosopher of the medieval period. Born in Spain, he later traveled extensively throughout Europe, including to France and Italy, where he became known for his contributions to various fields, including philosophy, astronomy, mathematics, and biblical exegesis. Ibn Ezra is well-known for his commentaries on the Hebrew Bible, which reflect his deep understanding of Jewish texts and his influences from both Jewish and Islamic thought.

The John Dewey Society is an organization dedicated to promoting progressive education and the educational philosophy of John Dewey, an influential American philosopher, psychologist, and educational reformer. Founded in 1935, the society serves as a platform for educators, scholars, and researchers who are interested in the principles of democratic education, experiential learning, and the importance of critical thinking and problem-solving in education.

"Twilight of the Idols," also known as "Twilight of the Idols, or: How to Philosophize with a Hammer," is a philosophical work by the German philosopher Friedrich Nietzsche, published in 1888. This essay is one of Nietzsche's later works and serves as a critical examination of various philosophical and moral concepts prevalent in Western thought.

Joseph Solomon Delmedigo (1591–1655) was a notable figure in the fields of philosophy, mathematics, and science during the early modern period. He was born in Crete and later moved to Italy, where he became involved in the intellectual circles of the time. Delmedigo was known for his work in mathematics, particularly his interest in the mathematical sciences and astronomy, and he corresponded with several prominent thinkers of his time.

Conway triangle notation is a method introduced by mathematician John Horton Conway for representing ordinal numbers, particularly transfinite ordinals, in a compact and structured way. This notation is an extension of his earlier work with `surreal numbers` and the `Conway chained notation` for ordinals. In Conway triangle notation, ordinals are represented within a triangular array, where each entry corresponds to a specific ordinal.

The Free Will Theorem is a concept arising from the intersection of quantum physics and philosophy, formulated by physicists John Conway and Simon Kochen in 2006. The theorem explores the implications of quantum mechanics on the notion of free will and determinism.

Kisrhombille, also known as the kisrhombic dodecahedron, is a type of geometric structure classified as a polyhedron. Specifically, it belongs to a family of Archimedean solids, which are highly symmetrical, convex polyhedra composed of two or more types of regular polygons.

Jigsaw puzzle manufacturers are companies that produce jigsaw puzzles, which are puzzles consisting of oddly shaped interlocking pieces that, when assembled, form a complete picture or design. These manufacturers create puzzles in a variety of themes, difficulties, sizes, and materials to appeal to different audiences, from children to adults. Some well-known jigsaw puzzle manufacturers include: 1. **Ravensburger**: A German company known for high-quality puzzles with unique pieces and a wide range of images.

The 2022 World Jigsaw Puzzle Championship was a competitive event where puzzle enthusiasts from around the world gathered to compete in assembling jigsaw puzzles. This championship typically features individual and team competitions, where participants race against the clock to complete a given puzzle as quickly as possible. The event not only showcases skill and speed but also fosters a sense of community among puzzle aficionados.

The 2023 World Jigsaw Puzzle Championship is an annual competitive event where participants from various countries come together to compete in assembling jigsaw puzzles. This championship typically involves teams and individuals racing against the clock to complete puzzles in the shortest time possible. The event may include various categories and types of puzzles, showcasing not only speed but also teamwork and puzzle-solving skills.

The World Jigsaw Puzzle Championships is an annual competitive event that brings together puzzle enthusiasts from around the globe to compete in assembling jigsaw puzzles under timed conditions. Established in 2002, this championship typically involves teams or individuals racing against the clock to complete a specified jigsaw puzzle as quickly as possible. Participants are usually given a standard puzzle, and the competition is often structured in heats leading to a final where the fastest teams or individuals compete for titles and prizes.

"Works by John Dewey" typically refers to the extensive body of writings by John Dewey, an influential American philosopher, psychologist, and educational reformer associated with pragmatism and progressive education. Dewey's work spans a wide array of topics, including philosophy, education, psychology, and social theory.

Instrumental and value-rational action are concepts introduced by the sociologist Max Weber as part of his framework for understanding social actions. 1. **Instrumental Rational Action (Zweckrational)**: This type of action is characterized by the systematic pursuit of a specific goal using the most efficient means available. It is essentially about calculating the best way to achieve a desired outcome. In instrumental rationality, the actor weighs the costs and benefits of different actions to maximize efficiency and success.

In mathematics, "involution" refers to a function that, when applied twice, returns the original value. Formally, if \( f \) is an involution, then: \[ f(f(x)) = x \] for all \( x \) in its domain. This property means that the function is its own inverse. Involutions can be found in various mathematical contexts, including algebra, geometry, and operators in functional analysis. ### Examples of Involutions 1.

"On Numbers and Games" is a book written by mathematician John H. Conway, published in 2001. The work delves into the field of combinatorial game theory, exploring how games can be analyzed mathematically. Conway introduces concepts such as surreal numbers and various types of games, including impartial games (where the allowed moves depend only on the state of the game and not on which player's turn it is) and partisan games (where the allowed moves depend on whose turn it is).

Sprouts is a two-player pencil-and-paper game that involves strategy and spatial reasoning. The game begins with a certain number of "dots" (or "spots") drawn on a sheet of paper, and players take turns connecting these dots with lines. Each line must be drawn under specific rules: 1. A line must connect two dots (or a dot to itself). 2. A line cannot cross any existing lines. 3. Each dot can have a maximum of three lines connected to it.

The concept of "epic cycles of incarnations" is not a widely recognized term in religious or philosophical literature, but it seems to relate to ideas about reincarnation and the spiritual journey of the soul through multiple lifetimes. This idea is found in various spiritual and philosophical traditions that propose that souls undergo a series of incarnations or rebirths, learning and evolving through different experiences across various lifetimes.

The ATLAS of Finite Groups is a comprehensive reference work that provides detailed information on the finite simple groups and their characteristics. Published in 1986 by Daniel G. Higman, John Conway, and Robert W. Curtis, the ATLAS is significant in the field of group theory, particularly in the classification of finite groups.

The Alexander polynomial is an important invariant in the field of knot theory, which studies the properties of knots and links in three-dimensional space. It provides a way to distinguish between different knots and links. ### Definition For a given knot or link, the Alexander polynomial is constructed using a presentation of the knot or link's fundamental group. Specifically, it is derived from the first homology group of the knot complement, which can be computed using a Seifert surface.

**Architectonic tessellation** and **catoptric tessellation** are terms related to specific types of geometric patterns or arrangements, though they might not be widely recognized in all fields of study. Let's break these down: 1. **Architectonic Tessellation**: - This refers to a type of tessellation that is inspired by architectural forms and structures. It often involves the arrangement of shapes that can suggest elements of architecture, such as walls, roofs, or other building components.