A law, in the context of principles, refers to a rule or guideline that governs behaviors, actions, or processes within a specific context. It can be applied in various fields, including science, mathematics, philosophy, and social sciences. Here are a few perspectives on what constitutes a law as a principle: 1. **In Science**: A scientific law is a statement that describes a consistent and universal relationship observed in nature. It is often expressed mathematically and supported by empirical evidence.
Neurath's boat is a philosophical metaphor introduced by the Austrian philosopher Otto Neurath in the early 20th century. It is often used to illustrate the idea of scientific knowledge and theory change. The metaphor describes a situation where we are trying to build a boat while out at sea; we cannot return to shore to construct a new one, nor can we fully build a new boat while at sea.
Artillery operation refers to the use of large-caliber guns, howitzers, mortars, and missile systems to deliver destructive force on a battlefield or target area. Artillery is a critical component of military operations, providing indirect fire support to ground troops, conducting bombardments, and engaging enemy positions from a distance.
Philosophy of physics is a subfield of philosophy that explores the foundational, conceptual, and interpretative issues arising in the field of physics. It examines the implications of physical theories and phenomena, as well as the philosophical underpinnings of the methods and assumptions employed in physics. Key areas of inquiry within philosophy of physics include: 1. **Nature of Space and Time**: Philosophers investigate the nature of space and time as described by various physical theories, particularly in the framework of relativity.
Aristotle's concept of physics, as articulated in his works such as "Physics" (or "Physica"), encompasses a broad exploration of the natural world and fundamental principles governing it. While modern physics is a highly specialized field involving mathematics and empirical testing, Aristotle's approach was more philosophical and observational.
Universal causation is a philosophical concept that posits that every event or phenomenon in the universe has a cause. This principle suggests that all events are part of a causal chain, where causes lead to effects, and there are no occurrences that happen without an underlying reason or cause. This concept is deeply intertwined with discussions on determinism, free will, and the nature of reality. In different philosophical traditions, universal causation may take on various interpretations.
Chemical affinity refers to the tendency of certain substances to combine or react with each other due to the attractive forces between their atoms or molecules. This concept can be thought of in several contexts: 1. **Thermodynamic Perspective**: In thermodynamics, chemical affinity relates to the change in free energy of a reaction.
The term "liquid junction interface" often refers to the boundary that exists between two different electrolyte solutions in electrochemical cells. This interface plays a crucial role in various electrochemical processes, particularly in the context of measuring ion concentrations, pH, or carrying out electrochemical reactions. ### Key Aspects of Liquid Junction Interface: 1. **Formation**: The liquid junction is formed when two electrolyte solutions come into contact.
Cirism by Ciro Santilli 40 Updated 2025-07-16
Welcome to the wonderful world of Cirism!
Followers of Cirism call themselves Cirists, and their primary goal in life is to obtain Cirocoins.
Enlightened Cirists donate money to the cause at: Section "Sponsor Ciro Santilli's work on OurBigBook.com". It is totally optional of course, your soul will just be eternally damned if you don't.
Ciro Santilli once proclaimed:
Thou shalt eat thy watermelon in the morning, and thy melon in the evening. Thou shalt not eat thy watermelon in the evening, nor shalt thou eat thy melon in the morning.
Function space by Ciro Santilli 40 Updated 2025-07-16
Most notable example: .
Constructs the quaternions from complex numbers, octonions from quaternions, and keeps doubling like this indefinitely.
Bilinear form by Ciro Santilli 40 Updated 2025-07-16
Analogous to a linear form, a bilinear form is a Bilinear map where the image is the underlying field of the vector space, e.g. .
Some definitions require both of the input spaces to be the same, e.g. , but it doesn't make much different in general.
The most important example of a bilinear form is the dot product. It is only defined if both the input spaces are the same.
The P51 is a bit too heavy, and the battery could be better!
We can then immediately see that the matrix is symmetric, then so is the form. We have:
But because is a scalar, we have:
and:

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