The term "bipolar nebula" refers to a type of astronomical nebula characterized by a bipolar structure, meaning it has two lobes or outflows that extend in opposite directions. These nebulae are often associated with the late stages of stellar evolution, particularly with certain types of stars, such as preplanetary nebulae and planetary nebulae. Bipolar nebulae are typically formed when a star undergoes significant changes as it exhausts its nuclear fuel.
"This Book Needs No Title" is a children's book written by J. E. Anastasopoulos. The story is centered around the theme of creativity and imagination, encouraging young readers to think outside the box and appreciate the world of possibilities that books can offer. It emphasizes the importance of storytelling and the relationship between readers and books, highlighting that the true essence of a story doesn't necessarily rely on a title.
The terms "function" and "concept" are often used in various fields such as mathematics, philosophy, and everyday language, and their meanings can vary depending on the context. Below are general definitions: ### Function 1. **Mathematics**: A function is a relation that associates each element of a set (the domain) with exactly one element of another set (the codomain).
The question of whether logic is empirical can be understood through the distinctions between empirical knowledge and logical knowledge. **Empirical Knowledge:** This is knowledge derived from observation, experience, and experimentation. It is practical and contingent on the physical world, and it relies on evidence gathered through the senses. Scientific knowledge, for example, is empirical because it is based on experiments and observations. **Logical Knowledge:** Logic, on the other hand, involves the principles of valid reasoning, which are often seen as a priori.
Computability Logic (CL) is a theoretical framework developed by Georg Kreisel and further advanced by G. Chaitin, among others. It is an area of logic that seeks to provide a foundation for understanding computation in a formal logical setting. Unlike traditional logics, which focus on truth values and static propositions, Computability Logic emphasizes the concept of computability as a resource.
The Herbrand Award is a prestigious recognition in the field of automated reasoning and logic programming, named after the French mathematician and logician Jacques Herbrand. It is awarded annually at the International Conference on Logic Programming (ICLP) to individuals or teams for their outstanding contributions to the field.
Logic for Computable Functions typically refers to a branch of mathematical logic and computer science that deals with the formalization, study, and application of computation through logical frameworks. This area encompasses various topics, including: 1. **Computability Theory**: This is the study of what functions can be computed and what problems can be decided by algorithms. It involves concepts such as Turing machines, recursive functions, and the Church-Turing thesis.
Preferential entailment is a concept in non-monotonic logic and reasoning, which deals with situations where certain conclusions can be drawn based on a set of premises, but these conclusions may not hold if additional information is added. It contrasts with classical logic, where the conclusions drawn from a set of premises are considered definitive and immutable. In preferential entailment, the idea is that certain models or interpretations of the knowledge may be preferred over others based on specific criteria.
Runtime verification is a technique used in computer science and software engineering that involves checking the behavior of a program or system as it executes (during runtime) to ensure that it meets specified properties or requirements. The goal is to detect errors, violations, or inconsistencies in a system while it is running, rather than only testing it statically (before execution) or through exhaustive testing.
WalkSAT is a local search algorithm used for solving the Boolean satisfiability problem (SAT), which involves determining whether there exists a truth assignment to a set of boolean variables that makes a given boolean formula true. WalkSAT is particularly effective on certain types of SAT instances, especially those that are generated randomly or are structurally interesting. The algorithm works by using a combination of random walks and heuristics.
"Critique of Pure Reason" (original German title: "Kritik der reinen Vernunft") is a foundational philosophical work by the German philosopher Immanuel Kant, first published in 1781, with a second edition released in 1787. This work is pivotal in the development of modern philosophy and is considered one of Kant's most significant contributions. In "Critique of Pure Reason," Kant aims to address the limitations and scope of human understanding.
"Some Remarks on Logical Form" is an influential paper by the philosopher and logician H.P. Grice, published in 1957. In this work, Grice discusses the nature of logical form, particularly in the context of language and meaning. He addresses how the structure of sentences relates to their meaning and how different logical forms can reflect various inferential roles in arguments.
The term "Organon" can refer to a few different concepts depending on the context: 1. **Philosophical Texts**: In the context of philosophy, "Organon" refers to a collection of writings by Aristotle that focus on logic and scientific reasoning. The primary texts within the Organon include works such as "Categories," "On Interpretation," and "Prior Analytics." Together, these texts lay the groundwork for Aristotelian logic and have had a lasting influence on Western philosophy.
The national emblem of Argentina features a sun rising above the Andes mountains, with a blue and white shield that showcases a descending sun with a human face, known as the "Sun of May." This emblem has historical significance, commemorating the May Revolution of 1810, which marked the beginning of Argentina's independence from Spanish rule. The blue and white colors represent the sky and clouds, and are also associated with the flag of Argentina.
The Federal Identity Program (FIP) is a Canadian government initiative designed to establish and maintain the standards and guidelines for the identification of Canadian federal government entities. The primary objective of the FIP is to create a consistent and recognizable identity for the government, ensuring that its communications and services are easily identifiable by the public.
A production logo is a visual symbol or design that represents a film, television, or media production company. This logo often appears at the beginning or end of a film or television show, and it serves several purposes: 1. **Brand Identity**: The logo helps establish and promote the identity of the production company, making it recognizable to audiences. 2. **Recognition**: A well-known production logo can evoke specific expectations about the quality and type of content produced by the company.
A logo sign, often simply referred to as a "logo," is a graphic mark, emblem, or symbol used to identify a company, organization, brand, product, or service. Logos serve as a visual representation of a business and are designed to convey specific qualities or messages associated with the brand. They can include text, images, or both, and are typically used in branding materials, advertisements, packaging, and on digital platforms.
As of my last update in October 2023, "Cthulhu Rise" does not refer to a widely recognized or established title in literature, games, or media related to H.P. Lovecraft's Cthulhu mythos. It’s possible that it could be a new game, project, or creative work that has emerged recently or it may be a fan-created concept.
EDSAC, or Electronic Delay Storage Automatic Computer, was one of the earliest computers built at the University of Cambridge in the United Kingdom. It became operational in 1949 and is notable for being one of the first computers to store programs in memory, a key aspect of the von Neumann architecture. The EDSAC was designed by a team led by Maurice Wilkes and was based on the use of mercury delay lines for storage.
The Poincaré conjecture is a significant theorem in the field of topology, particularly in the study of three-dimensional spaces. Formulated by the French mathematician Henri Poincaré in 1904, it posits that any simply connected, closed 3-manifold is homeomorphic to the 3-sphere \( S^3 \).

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