A **permutation group** is a mathematical structure consisting of a set of permutations that can be combined in a way that satisfies the properties of a group. Specifically, if you have a set \( X \), a permutation is a bijective function that rearranges the elements of \( X \). The collection of all possible permutations of a finite set \( X \) of size \( n \) is called the symmetric group, denoted as \( S_n \).
Phonocentrism is a philosophical and linguistic concept that prioritizes spoken language over written language. The term arises from the critique of the traditional Western metaphysical idea that speech is the primary and most authentic form of communication. This view tends to value the immediacy and perceived authenticity of oral communication over the more mediated and artificial nature of written language. The concept has been notably discussed by philosopher Jacques Derrida, particularly in his deconstruction of language and meaning.
Landau's function typically refers to concepts or mathematical functions related to Landau's theory in various fields, particularly in physics and mathematics. One prominent example involves Landau's theory of phase transitions, where critical phenomena are studied. In statistical physics, Landau's theory often introduces a free energy functional expressed in terms of order parameters, which are quantities that describe the different phases of a system.
The concept of "autonomy of syntax" refers to the idea that the syntactic structure of a language operates independently of its semantic (meaning-related) and pragmatic (context-related) aspects. This notion is particularly associated with certain theories in linguistics, especially generative grammar, which was notably advocated by Noam Chomsky.
The term "mental space" can refer to several concepts, depending on the context in which it's used. Here are some common interpretations: 1. **Cognitive Psychology and Mental Representation**: In cognitive psychology, mental space refers to the cognitive structures and processes that allow individuals to represent, store, and manipulate information in their minds. This can include visualizing scenarios, remembering places, or thinking about abstract concepts.
The Lexical Hypothesis is a concept in personality psychology that suggests that the most important personality traits are encoded in the natural language of a culture. In other words, it posits that people have developed a way to describe their personalities and the personalities of others through the words they use. This hypothesis is central to the development of various personality models, particularly the Five Factor Model (FFM) or the Big Five personality traits.
A **monogenic semigroup** is a particular type of algebraic structure in the field of abstract algebra. Specifically, a semigroup is a set equipped with an associative binary operation. In the case of a monogenic semigroup, there is a specific defining feature: the semigroup is generated by a single element.
Predictive power refers to the ability of a model or tool to accurately forecast future outcomes based on past and present data. In various fields such as statistics, machine learning, finance, and social sciences, predictive power is a crucial measure of how well a model can predict unknown data points. Key aspects of predictive power include: 1. **Accuracy**: The degree to which predictions made by the model match actual outcomes.
Antiscience refers to attitudes, beliefs, and actions that reject or oppose scientific reasoning, methods, and evidence. It encompasses a wide range of phenomena, including skepticism towards scientific consensus, the promotion of pseudo-science, misinformation, and beliefs that contradict established scientific understanding. Antiscience can manifest in various forms, such as: 1. **Rejection of Scientific Consensus**: Dismissing established scientific views in fields like climate change, vaccines, evolution, and healthcare without credible evidence.
The 158th meridian east is a line of longitude that is 158 degrees east of the Prime Meridian, which is located at 0 degrees longitude. This meridian runs from the North Pole to the South Pole and passes through several territories and regions. In the northern hemisphere, the 158th meridian east crosses through parts of Russia and other countries in the Pacific Ocean. In the southern hemisphere, it primarily runs through the Pacific Ocean, south of major landmasses.
The term "resacralization of knowledge" refers to a process in which knowledge, particularly scientific or secular knowledge, is imbued with spiritual or sacred significance. This concept can emerge in various contexts, including philosophy, sociology, and educational theory. It often involves a critique of the secularization of knowledge that occurred during the Enlightenment and modernity, where knowledge became increasingly viewed as objective, empirical, and separate from moral or spiritual considerations.
The term "Logic alphabet" typically refers to the symbols and notations used in formal logic and mathematical logic to represent logical expressions, propositions, and operations. Here are some common components of a logic alphabet: 1. **Propositional Variables**: Often denoted by letters such as \( P, Q, R \), etc., these represent basic propositions that can be either true or false. 2. **Logical Connectives**: These symbols are used to connect propositional variables.
São Paulo City by Ciro Santilli 40 Updated 2025-07-16
Although Ciro Santilli lived in São Paulo City nominally during his studies, it would be more precise to say that he lived in University of São Paulo-land, because Ciro was cheap, didn't have a car, and did nothing but study, stay at home, go back to Santos to see his parents and the beach.
But the little he saw of the city made a deep impression on him.
The unreasonable size.
The unbearable contrasts.
Caetano's Sampa is the ultimate description of the city!
Chinese scholar by Ciro Santilli 40 Updated 2025-07-16
On Wikipedia we only find the term Scholar-official. But the idea of the ancient Chinese scholar is a bit wider as a concept, and even people who were not trying to be officials could thrive to follow certain aspects of the scholar way of life.
Logical consequence, often referred to in formal logic as entailment, is a relationship between statements whereby one statement (or set of statements) necessarily follows from another statement (or set of statements). In other words, if a set of premises logically entails a conclusion, then if the premises are true, the conclusion must also be true. In more formal terms, we can express this using symbolic logic.
Water Margin quote by Ciro Santilli 40 Updated 2025-07-16
Something along:
If two men are destined to meet, they will come together from thousands of miles apart. If they aren't, they will pass by in front of one another and never know about one another's existence.
TODO find Chinese.

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    Figure 3.
    Visual Studio Code extension installation
    .
    Figure 4.
    Visual Studio Code extension tree navigation
    .
    Figure 5.
    Web editor
    . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
    Video 4.
    OurBigBook Visual Studio Code extension editing and navigation demo
    . Source.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact