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The relative importance of space and mass can change very quickly: in 1872, Viollet-le-Duc wrote his book, Entretiens sur l'architecture, completely avoiding the use of the word "space" in its modern meaning; just 20 years later August Schmarsow was declaring the primacy of German: Raumgestaltung, "forming the space". [9]
The Nature of Order: An Essay on the Art of Building and the Nature of the Universe (ISBN 0-9726529-0-6) is a four-volume work by the architect Christopher Alexander published in 2002–2004. In his earlier work, Alexander attempted to formulate the principles that lead to a good built environment as patterns , or recurring design solutions.
Forms are aspatial in that they have no spatial dimensions, and thus no orientation in space, nor do they even (like the point) have a location. [17] They are non-physical, but they are not in the mind. Forms are extra-mental (i.e. real in the strictest sense of the word). [18] A Form is an objective "blueprint" of perfection. [19]
"Witt's theorem" or "the Witt theorem" may also refer to the Bourbaki–Witt fixed point theorem of order theory.. In mathematics, Witt's theorem, named after Ernst Witt, is a basic result in the algebraic theory of quadratic forms: any isometry between two subspaces of a nonsingular quadratic space over a field k may be extended to an isometry of the whole space.
Bohm, his co-worker Basil Hiley, and other physicists of Birkbeck College worked toward a model of quantum physics in which the implicate order is represented in the form of an appropriate algebra or other pregeometry. They considered spacetime itself as part of an explicate order that is connected to an implicate order that they called pre-space.
A subset of a vector space is called a cone if for all real >,.A cone is called pointed if it contains the origin. A cone is convex if and only if +. The intersection of any non-empty family of cones (resp. convex cones) is again a cone (resp. convex cone); the same is true of the union of an increasing (under set inclusion) family of cones (resp. convex cones).
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Laws of Form (hereinafter LoF) is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy. LoF describes three distinct logical systems : The primary arithmetic (described in Chapter 4 of LoF ), whose models include Boolean arithmetic ;