An **incompressible surface** is a concept from the field of topology, specifically in the study of 3-manifolds. It refers to a two-dimensional surface that cannot be compressed into a simpler form without cutting it. This property is significant in both mathematical theory and applications, such as in knot theory and the study of 3-manifolds.
The "Self-Portrait" in the Alte Pinakothek is a painting by the Dutch artist Rembrandt van Rijn. The Alte Pinakothek is a renowned art museum located in Munich, Germany, that houses a significant collection of European masterpieces from the 14th to the 18th centuries. Rembrandt's self-portrait is one of many he created throughout his life, showcasing his mastery of light, shadow, and the human condition.
The Merten M. Hasse Prize is an award given for outstanding contributions to the field of number theory. Named after the mathematician Merten M. Hasse, the prize typically recognizes work in areas related to algebraic number theory, transcendental number theory, and related fields. The prize is often associated with a particular institution or society, such as the American Mathematical Society (AMS) or similar organizations, although specific details can vary.
The Information-Action Ratio (IAR) is a concept used to evaluate the efficiency of information in prompting action or decision-making. It highlights the balance between the amount of information acquired and the actions taken as a result of that information. The ratio can be expressed as: \[ \text{IAR} = \frac{\text{Information}}{\text{Action}} \] Where: - **Information** refers to the relevant data or insights that inform a decision or action.
Iridescence is a phenomenon in which the color of a surface changes when viewed from different angles. This effect occurs due to the interference of light waves reflected from multiple layers of a material, such as the surface of soap bubbles, peacock feathers, or certain types of opal and abalone shells. The varying thickness of these layers causes different wavelengths of light to be reflected more strongly at particular angles, creating a shifting spectrum of colors.
Neptunium (Np) has several isotopes, with the most notable ones being: 1. **Neptunium-237 (Np-237)**: This is the most stable and prominent isotope of neptunium, with a half-life of about 2.14 million years. It is produced in nuclear reactors and is of interest due to its potential use in nuclear waste management and as a source of plutonium-238.
Rhenium (Re) is a transition metal with atomic number 75. It has several isotopes, but the most notable ones are: 1. **^185Re**: This is the most stable and abundant isotope of rhenium, with a half-life of approximately 4.0 × 10^10 years. It is a non-radioactive isotope and is commonly used in various applications, including catalysts and electronics.
Thorium is a radioactive element with several isotopes, the most notable of which are: 1. **Thorium-232 (Th-232)**: This is the most abundant and stable isotope of thorium, making up about 99.98% of naturally occurring thorium. It has a half-life of approximately 14.05 billion years and is used in nuclear reactors and as a source material for nuclear fuel.
Jaakko Hintikka (1929-2015) was a prominent Finnish philosopher, logician, and epistemologist known for his contributions to the fields of logic, the philosophy of language, and the theory of knowledge. He is particularly recognized for his work in epistemic logic, which explores the implications of knowledge and belief in formal systems. Hintikka developed the concept of "possible world semantics," which has had a significant influence on modal logic and the philosophy of language.
Jakob Philipp Kulik is not a widely recognized figure in popular culture or prominent historical events, based on the information available up to October 2023. It is possible that he could be a lesser-known individual, a character, or a name that has gained significance in a specific niche or recent context after my last update.
David Lowry could refer to a few different individuals depending on the context. The most notable might be: 1. **David Lowry (Musician)**: An American musician, best known as the lead singer of the alternative rock band Cracker and as a founding member of the band Camper Van Beethoven. He has been influential in the music scene since the late 1980s. 2. **David Lowry (Film)**: A film director and writer known for his work in various genres.
Giulio Prisco is an Italian researcher and writer known for his work in the fields of science, philosophy, and technology. He has been involved in discussions surrounding topics such as transhumanism, artificial intelligence, and the philosophical implications of digital technologies. Prisco is also associated with the scientific community focused on the future of humanity, often advocating for the potential of technology to enhance human life and address existential risks.

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