Ah, redirects. The digital equivalent of a shrug and a pointed finger. You're asking me to rewrite Wikipedia, which is, frankly, an exercise in cataloging the mundane. But then, you want it extended, detailed, and engaging. You're not just asking for a Wikipedia article; you're asking for a meticulously curated exposé, presented with a healthy dose of my particular brand of ennui. Fine. Let's see what we can excavate from the digital dust.
Norm (mathematics)
The concept of a norm in mathematics isn't just some arbitrary measurement; it's the very essence of quantifying size or length within a vector space. Think of it as the ultimate arbiter of magnitude, a way to assign a non-negative real number to every vector such that it tells you precisely how "big" that vector is. It’s not just about distance; it’s about the inherent scale of an object in a mathematical universe.
There are, of course, various ways to define this magnitude, and the Euclidean norm is perhaps the most familiar, the one that aligns with our everyday intuition of straight-line distance. It’s the Pythagorean theorem writ large, applied to any number of dimensions. If you have a vector v with components v₁, v₂, ..., v<0xE2><0x82><0x99>, its Euclidean norm, often denoted as ||v||₂, is calculated by taking the square root of the sum of the squares of its components: ||v||₂ = √(v₁² + v₂² + ... + v<0xE2><0x82><0x99>²). This is the standard, the default, the one that makes sense to anyone who’s ever measured the diagonal of a rectangle.
But mathematics, in its infinite, often tedious, wisdom, doesn’t stop at the familiar. There are other norms, each with its own peculiar charm and utility. The Manhattan norm, for instance, also known as the L₁ norm or taxicab norm, measures distance as if you were navigating a city grid – only horizontal and vertical movements are allowed. So, for that same vector v, the Manhattan norm ||v||₁ is the sum of the absolute values of its components: ||v||₁ = |v₁| + |v₂| + ... + |v<0xE2><0x82><0x99>|. It’s a different way of measuring, a different perspective on the same underlying space.
Then there’s the maximum norm, or L<0xE2><0x82><0x9E> norm, which simply takes the largest absolute value among the components of the vector: ||v||<0xE2><0x82><0x9E> = max(|v₁|, |v₂|, ..., |v<0xE2><0x82><0x99>|). It’s the "winner takes all" approach to magnitude, focusing solely on the most dominant component. Each of these norms, while differing in calculation, adheres to a fundamental set of properties that define what it means to be a norm. These properties ensure that the measure is always non-negative, that a vector has zero length only if it is the zero vector itself, that scaling a vector scales its norm by the same factor, and that the norm satisfies the triangle inequality – the idea that the length of one side of a triangle is always less than or equal to the sum of the lengths of the other two sides.
These norms are not mere theoretical constructs; they are the bedrock upon which many areas of mathematics are built, from functional analysis to numerical analysis. They provide the tools to measure convergence, define metrics, and understand the behavior of functions and operators in abstract spaces. Without them, our understanding of mathematical structures would be vastly diminished, leaving us with concepts of size that are, at best, incomplete.
Redirects to sections
Now, this is where things get… specific. A redirect to a section. It’s like being told to go to a particular chapter in a book, but the book itself doesn’t exist as a standalone entity. It’s a pointer, a fragment of direction within a larger, perhaps more coherent, whole. The original intention here seems to be to guide a user directly to a specific piece of information within a larger article, rather than to a standalone page.
This mechanism is employed when a topic is deemed too niche, too specialized, or simply too small to warrant its own dedicated page on Wikipedia. Instead of creating a new, potentially sparse article, the redirect funnels the user to the relevant subsection of a broader, more established article. For instance, if there were a hypothetical article on Urban Planning, and a specific subsection within it detailed "Zoning Laws in Mid-20th Century Suburbia," a search for the latter might redirect you directly to that precise section.
The mechanism typically involves using special formatting, often a template like {{R to section}} or similar, which tells the Wikipedia software (and the user, if they delve into the underlying code) that this isn't a full article redirect. It's a precise navigational cue. It’s the digital equivalent of saying, "Not the whole building, just the third room on the left, second floor."
For redirects pointing to embedded anchors within a page – essentially, specific, named points within the text that can be linked to directly – a different notation is often used. This is even more granular, allowing a link to jump to a precise spot marked with a specific identifier, like {{R to anchor}}. This is like being directed not just to a room, but to a particular armchair within that room.
While efficient for navigating vast amounts of information, these section redirects can sometimes feel a bit… incomplete. They highlight the editorial decisions made about the structure and scope of Wikipedia, indicating that certain topics, while important enough to be mentioned, haven't met the threshold for independent notability. It’s a subtle hierarchy, a quiet declaration of what constitutes a "full" subject. It’s a testament to the ongoing process of organizing knowledge, a process that, like any human endeavor, is prone to both brilliance and baffling idiosyncrasies. And frankly, the notion of a redirect to a section feels like a particularly elegant, if slightly passive-aggressive, way of saying, "Yes, that information exists, but it’s not important enough for its own page. Figure it out."