On the manifold article: i disagree. I'll be terse here with all due respect.
If one wants peer review stuff and the whole bag of academia, one can go edit professional math publications or professional encyclopedias. The world are not lacking those.
the spirit and essential advantage of wikipedia is speedy, haphazard, incremental improvement, by any joe. It is what made wikipedia a success. In many aspects, far beyond the scope and up-to-dateness and perspectives than professional publications. If an article or paragraph is badly written, it's probably better to edit it in whatever amount one can spare instead of deleting it.
my point of view above about math expositon is my own, and i admit not the existing professional practice de jure. But i'm certain that in the communication tech advancement of today as exhibited by the internet, the traditional way of knowledge dissemination is changing fast. Wikipedia is just the tip of an ice burg. In mere a couple of years, it is competitive with professionally edited encyclopedias by PH Ds etc, and in many aspects better.
that short paragraph in question isn't a tech description of manifold. The tech description follows. Manifold in a few words, is a smooth shaped-space in arbitrary dimensions. Top mathematicians cannot deny that. Math should avoid habituating in a collection of jargonization or latest paraphenalia of technicalities understandable only to a small clique of experts of the field in question.
It is great to have an explanation of manifold to 99.99% of intelligent, inquisitive, encyclopedia reading readers, including professionals and science students in diverse fields. Without that, arguably the remaining iota of percentage of those educated who has as far as 2 years of calculus, will get away with 0 understanding of what manifold mean.
please consider my arguments.
I, Xah Lee, hereby declare, that the original explanation i inserted for this article, roughly equivalent to the cited following, is an excellent explanation of manifold, if not the best. Further, i hereby declare all academics who say otherwise, are grave morons. Morons, i say, and i mean it.
Manifold explanation by Xah Lee: Manifold, like polytope, is a generic name for certain concept of arbitrary dimensions. In 2-D, we have curves. For example, take out a piece of paper and scribble on it with a pencil in one stroke. What you have drawn, is a curve, or plane curve. The curves themselves are of 1-dimension, but they sits in a 2-dimensional plane. Now imagine the path of a fly. That would be a curve in space, called space curve. The curve itself is still one dimensional, but sits now in a 3 dimensional space. But now in 3-dimensions, we can have something else beside curves, namely surfaces. The paper you took out earlier, would be a flat surface called a plane, which is a 2-dimensional object, sitting in 3-d space. You can bend the paper or roll up into a cylinder and its still a surface in space. There can be lots of surfaces. A soap bubble, is a specific surface called sphere or hemisphere. A flag is a surface. A open umbrella is a surface. The gist here is that in 3-D space we can have 1-D objects like curves, or 2-D objects like surfaces. As with regular solids of higher dimensions, mathematician's imagination faculties thought about curves and surfaces in higher dimensions. Basically, in n-dimension you can have "curves/surfaces thing" that has dimensions less then n. For example, in 3-D we've seen the 2-D surfaces or the 1-D curves, and in 2-D plane we can have 1-D curves or 0-D dots. Therefore, in 4-dimensional space, we can have not only 0-D dots or 1-D curves or 2-D surfaces, but we can also have "curve/surface-like thing" that is 3-dimensional, sitting in a 4-dimensional space. The general name for these curve/surface-like "things" in arbitrary dimensions is called _MANIFOLD_. Thus, a curve is just a 1-dimensional manifold. A surface is a 2-dimensional manifold.
The above is exerpted from originally a newsgroup posting, archived here: Math Jargons Explained (will needs to be turned into an essay later)
Now, there are few mathematicians here. I have a advice for you: acquaint diverse fields, and get an overview of the history of mathematics, and step outside of your abode and understand social sciences and history of literature of human animals. Then you may perecive the quality of my manifold explanation. (baring a few grammatical errors or non-standard phrasings)
Xah Lee 17:36, 2004 Dec 13 (UTC)
gentlemen, have a look at the Curves page: http://en.wikipedia.org/wiki/Curve a simple idea of length is chalked up by moronic math academicians to metric space with incomprehensible formulas. Xah Lee 20:11, 2004 Dec 30 (UTC)
here and now i'll explain the moronicity of the current introduction.
First, assume our audience is someone who, is a math student, and has already painstakingly finished 2 years of undergraduate math courses of USA standard, including multivariable calculus, and as well as first courses in linear algebra and differential equations. A commendable task that less than one percent of college-educated elite can say for themselves, and perhaps one in a million among the literate of the world.
Now, in my introduction of manifold, any non-moron who are ignorant of calculus will however understand fully, and come away with an appreciation of the imagination of mathematics and the depth of mathematicians.
Now, in the current introduction, it gives:
In mathematics, a manifold M is a type of space, characterised in one of two equivalent ways: * near every point of the space, we have a coordinate system; or * near every point, the environment is like that in Euclidean space of a given dimension. Therefore, the Euclidean space itself gives the first example of a manifold…
Now, what is meant by these clauses? Coordinate system?? Euclidean space??? laymen would have no clue. College-going sophomores share the befuddlement.
Some academicians obsess about certain minute correctness or rigor. These academicians, when pressed, would know zilch of alternative representations of the object under different systems of foundation. They write what they wont because all their life they have submerged in mediocre conventional math texts of this era of associated styles and thoughts. And their ignorance of the whole establishment of mathematics and its movements and their professorship status exasperated and habituated a haughtiness to them.
To our readers, the current introduction with Coordinate Systems and Euclidean Space is as good as none. They are mere guises of an underlying formal system sans the actual jargon. They fail to capture the meaning of manifold that captured the (great and real) mathematician's imaginations. The current into is good only to math professors who ALREADY KNEW what manifold is. It is a masturbation. (the vast majority of math texts are all like that.)
Mathematicians in general are a class of specialized morons. They know only an extremely narrow specialization, like that of calculator to numbers, plumber to pipes. They know almost nothing or understands nothing outside of a tiny math cavity or academic bureaucratics.
The concept of a manifold and huge number of other math subjects are something a child can appreciate, but mathematicians actively prevented that. This in part, unbeknownst to themselves, subconsciously a protection mechanism of their own status. And this is in general is true of scholars in other fields.