Twistor space is a mathematical construction that arises in the context of theoretical physics, particularly in the study of certain fundamental aspects of spacetime and quantum field theory. Introduced by Roger Penrose in the 1960s, twistor theory provides a framework for understanding the relationships between geometrical and physical entities in a novel way, combining aspects of geometry with concepts in physics.
The Proper Forcing Axiom (PFA) is a statement in set theory that relates to the concept of forcing, which is a technique used to prove the consistency of certain mathematical statements by constructing models of set theory. The PFA is a specific principle that asserts the existence of certain types of filters in the context of forcing.
Systems of formal logic are structured frameworks used to evaluate the validity of arguments and reason about propositions through a series of formal rules and symbols. These systems aim to provide a precise method for deducing truths and identifying logical relationships. Here are some key components and concepts involved in formal logic: 1. **Syntax**: This refers to the formal rules that govern the structure of sentences in a logic system.
Takeuti's conjecture is a hypothesis in the field of mathematical logic, specifically related to set theory and the study of ordinal numbers. It was proposed by the Japanese logician Genjiro Takeuti in the context of the properties of the ordinals and their representations.
Whitehead's theory of gravitation refers to the ideas developed by the philosopher and mathematician Alfred North Whitehead in the early 20th century. While he is primarily known for his work in philosophy, particularly process philosophy, he also made contributions to the understanding of physics, including gravitational theory. Whitehead's approach to gravitation is distinct from the more widely known theories of gravity, such as Newton's law of universal gravitation and Einstein's general theory of relativity.
"Works by Bertrand Russell" refers to the extensive body of literature produced by the British philosopher, logician, mathematician, and social critic Bertrand Russell (1872-1970). He was a key figure in 20th-century philosophy and made significant contributions to a variety of fields, including logic, philosophy of language, epistemology, metaphysics, and social issues.
Marcia Groszek might refer to a person, but without additional context, it's difficult to determine who she is. There may not be widely known information about her, and she may not be a public figure.
Existential quantification is a concept from mathematical logic and predicate logic that expresses that there exists at least one element in a particular domain for which a certain property or predicate holds true. It is typically denoted using the symbol ∃ (the existential quantifier).
The Age of Enlightenment, also known as the Age of Reason, was an intellectual and philosophical movement that emerged in Europe during the late 17th and 18th centuries. It emphasized reason, science, and individualism over tradition and religious authority. Prominent figures of the Enlightenment sought to challenge existing social, political, and religious norms, advocating for principles such as liberty, progress, tolerance, and the scientific method.
The European and American voyages of scientific exploration, particularly during the 18th and 19th centuries, refer to a series of expeditions undertaken by explorers, scientists, and naturalists to study various aspects of the natural world, including geography, biology, astronomy, and anthropology. These voyages were instrumental in expanding knowledge and understanding of the Earth's ecosystems, cultures, and resources.
Immanuel Kant (1724–1804) was a German philosopher who is a central figure in modern philosophy. He is best known for his work in epistemology, ethics, and metaphysics, and he significantly influenced a wide range of disciplines, including philosophy, political theory, and aesthetics.
Subreption is a term primarily used in the context of philosophy, theology, and ethics. It refers to a situation where a judgment, conclusion, or concept is formed based on misleading or incomplete information, leading to a misunderstanding or misrepresentation of the truth. In a more specific ethical context, it can involve the intentional omission of certain facts or the presentation of information in a way that could deceive or confuse someone, ultimately resulting in a flawed reasoning process.
Disposition generally refers to a person's inherent qualities of mind and character, as well as their tendency to behave in certain ways. In various contexts, it can have specific meanings: 1. **Psychology**: Disposition can refer to an individual's typical emotional state or personality traits that influence their behavior, such as optimism, pessimism, or introversion.
Post-truth politics refers to a political environment where emotional appeals and personal beliefs often outweigh objective facts and logical reasoning in shaping public opinion and political discourse. In a post-truth context, political leaders and media can prioritize subjective narratives over verifiable evidence, leading to the acceptance of misinformation and disinformation among the electorate.
Mathematics journal editors are individuals responsible for overseeing the editorial process of academic journals that publish research in the field of mathematics. Their roles typically include: 1. **Manuscript Management**: Editors manage the submission and review process of articles submitted for publication. This involves setting up a system for receiving submissions, tracking progress, and communicating with authors and reviewers.
The American Journal of Mathematics (AJM) is a peer-reviewed mathematical journal that publishes research articles in all areas of mathematics. Established in 1878, it is one of the oldest mathematical journals in the United States. The journal is known for its high-quality publications and has contributed significantly to the advancement of mathematical knowledge over the years. AJM features original research papers, survey articles, and occasional contributions in areas such as pure mathematics, applied mathematics, and mathematical education.
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!
Intro to OurBigBook
. Source. We have two killer features:
- 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-calculusArticles 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/derivativeVideo 2. OurBigBook Web topics demo. Source. - 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.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
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. - Infinitely deep tables of contents:
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





