![...the stereographic projection of the spherical surface. From the north pole P we draw radial lines to project every point of the surface of the sphere upon the horizontal plane [below, perpendicular to a line joining it to P and the sphere's center]. In general this transformation is unique and continuous, although the metrical relations are distorted; for the point P, however, it shows a singularity. Point P is mapped upon the infinite; i.e., no finitely located point of the plane corresponds to it. It can be shown that every transformation possesses a singularity in at least one point. The surface of the sphere is therefore called topologically different from the plane. Only a "sphere without a north pole" [point] would be topologically equivalent to a plane. ...such a sphere has a point-shaped hole without a boundary and is no longer a closed surface. (Hans Reichenbach)](https://cdn.quotesdtb.com/img/quotes_images_webp/18/hans-reichenbach-boundary-center-429318.webp)
...the stereographic projection of the spherical surface. From the north pole P we draw radial lines to project every point of the surface of the sphere upon the horizontal plane [below, perpendicular to a line joining it to P and the sphere's center]. In general this transformation is unique and continuous, although the metrical relations are distorted; for the point P, however, it shows a singularity. Point P is mapped upon the infinite; i.e., no finitely located point of the plane corresponds to it. It can be shown that every transformation possesses a singularity in at least one point. The surface of the sphere is therefore called topologically different from the plane. Only a "sphere without a north pole" [point] would be topologically equivalent to a plane. ...such a sphere has a point-shaped hole without a boundary and is no longer a closed surface.
Hans ReichenbachRelated topics
boundary center different draw equivalent general hole horizontal infinite joining least line longer map north perpendicular plane point pole project projection radial show singularity sphere surface transformation unique relations linesRelated quotes
Our sense of touch is a fundamental sensibility which comes into action at birth – our stereognostic sense – the ability to feel weight and form and assess its significance. The form which have had special meaning for me since childhood have been the standing form (which is the translation of my feelings towards the human being standing in the landscape) the two forms (which is the tender relation of one living thing besides another); and the closed form, such as the oval, spherical or pierced form (sometimes incorporating colour) which translates for me the association and meaning of gesture in landscape; in the repose of say a mother and child.... In all these shapes the translation of what one feels about man and nature must be conveyed by the sculptor in terms of mass, inner tension, and rhythm, scale in relation to our human size and the quality of surface which speaks through our hands and eyes.
Barbara Hepworth
Since one cannot create 'depth' by carving a hole in the picture, and since one should not attempt to create the illusion of depth by tonal gradation, depth as a plastic reality must be two dimensions in a formal sense as well in the sense of color. 'Depth' is not created on a flat surface as an illusion, but as a plastic reality. The nature of the picture plane makes it possible to achieve depth without destroying the two-dimensional essence of the picture plane.. A plane is a fragment in the architecture of space. When a number of planes are opposed one to another, a spatial effect results. A plane functions in the same manner as the walls of a building... Planes organized within a picture create the pictorial space of its composition... The old masters were plane-consciousness. This makes their pictures restful as well as vital...
Hans Hofmann
The earth has no doubt wobbled through the years. The North Pole has moved around. Today the earth is tilted over 23.5 degrees. That is why they always mount the globe on that 23.5 degree angle. Stonehenge is an interesting stone building. Apparently it was built to worship the sun at summer solstice. But today, Stonehenge does not line up. The Egyptian Temple Amen Ra was apparently built to worship the sun at summer solstice, the longest day of the year. But it doesn't line up. Eudoxus, same thing. The earth is tilted over today, and that's what causes the seasons. [...] Today the earth is pretty stable. The North Pole doesn't move around very much. But could it be that something actually struck Planet Earth about the time of Noah's flood? Well that's what the scientific evidence points towards. Today the earth is tilted over and that's what causes the seasons.
Kent Hovind
In the Vietnam War, the leaders of the White House claimed at the time that it was a necessary and crucial war, and during it, Donald Rumsfeld and his aides murdered two million villagers. And when Kennedy took over the presidency and deviated from the general line of policy drawn up for the White House and wanted to stop this unjust war, that angered the owners of the major corporations who were benefiting from its continuation. And so Kennedy was killed, and al-Qaida wasn't present at that time, but rather, those corporations were the primary beneficiary from his killing. And the war continued after that for approximately one decade. But after it became clear to you that it was an unjust and unnecessary war, you made one of your greatest mistakes, in that you neither brought to account nor punished those who waged this war, not even the most violent of its murderers, Rumsfeld.
Osama bin Laden
Every measurable thing except numbers is imagined in the manner of a continuous quantity. Therefore, for the mensuration of such a thing, it is necessary that points, lines, and surfaces, or their properties, be imagined. For in them... measure or ratio is initially found... Therefore, every intensity which can be acquired successively ought to be imagined by a straight line perpendicularly erected on some point of the space or subject of the intensible thing, e. g., a quality... And since the quantity or ratio of lines is better known and is more readily conceived by us-nay the line is in the first species of continua, therefore such intensity ought to be imagined by lines... Therefore, equal intensities are designated by equal lines, a double intensity by a double line, and always in the same way if one proceeds proportionally.
Nicole Oresme
