"[…] the intrinsic value of a small-scale model is that it compensates for the renunciation of sensible dimensions by the acquisition of intelligible dimensions." (Claude Levi- Strauss,"The Savage Mind", 1962)
"It is always extremely difficult to express thoughts. Words and phrases are so many fretters by which our spirit is bound. Words are mere symbols of reality, and the written word is not more than a one-dimensional fl ow across the two-dimensional page of a three-dimensional book." (Charles-Noël Martin, "The Role of Perception in Science", 1963)
"In all of natural philosophy, the most deeply and repeatedly studied part, next to pure geometry, is mechanics. […] The picture of nature as a whole given us by mechanics may be compared to a black-and-white photograph: It neglects a great deal, but within its limitations, it can be highly precise. Developing sharper and more flexible black-and-white photography has not attained pictures in color or three-dimensional casts, but it serves in cases where color and thickness are irrelevant, presently impossible to get in the required precision, or distractive from the true content." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)
"The plane is the mainstay of all graphic representation. It is so familiar that its properties seem self-evident, but the most familiar things are often the most poorly understood. The plane is homogeneous and has two dimensions. The visual consequences of these properties must be fully explored." (Jacques Bertin, Semiology of graphics [Semiologie Graphique], 1967)
"A diagram thus enables us to discover the internal categorization which characterizes the information being processed in a much shorter time than does a map. […] A diagram permits the rapid and precise internal processing of information having three components, but it does not permit introducing the information into a universal system of visual memorization and geographic comparison. It is a closed graphic system, limited solely to the information being processed. […] In a diagram, one begins by attributing a meaning to the planar dimensions, then one plots the correspondences." (Jacques Bertin, "Semiology of graphics", 1967)
"There is one metaphor in the physicist’s account of space-time which one would expect anyone to recognize as such, for metaphor is here strained far beyond the breaking point, i.e., when it is said that time is ‘at right angles to each of the other three dimensions’. Can anyone really attach any meaning to this - except as a recipe for drawing diagrams?" (Clement W K Mundle, "The Space-Time World", Mind, 1967)
"In the definition of a coordinate system we have required that the coordinate neighborhood and the range in Rd be open sets. This is contrary to popular usage, or at least more specific than the usage of curvilinear coordinates in advanced calculus. For example, spherical coordinates are used even along points of the z axis where they are not even 1-1. The reasons for the restriction to open sets are that it forces a uniformity in the local structure which simplifies analysis on a manifold" (there are no 'edge points') and, even if local uniformity were forced in some other way, it avoids the problem of. spelling out what we mean by differentiability at boundary points of the coordinate neighborhood; that is, one-sided derivatives need not be mentioned. On the other hand, in applications, boundary value problems frequently arise, the setting for which is a manifold with boundary. These spaces are more general than manifolds and the extra generality arises from allowing a boundary manifold of one dimension less. The points of the boundary manifold have a coordinate neighborhood in the boundary manifold which is attached to a coordinate neighborhood of the interior in much the same way as a face of a cube is attached to the interior. Just as the study of boundary value problems is more difficult than the study of spatial problems, the study of manifolds with boundary is more difficult than that of mere manifolds, so we shall limit ourselves to the latter." (Richard L Bishop & Samuel I Goldberg, "Tensor Analysis on Manifolds", 1968)
"The idea of knowledge as an improbable structure is still a good place to start. Knowledge, however, has a dimension which goes beyond that of mere information or improbability. This is a dimension of significance which is very hard to reduce to quantitative form. Two knowledge structures might be equally improbable but one might be much more significant than the other." (Kenneth E Boulding, "Beyond Economics: Essays on Society", 1968
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