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The Rudolf Steiner Archive

a project of Steiner Online Library, a public charity

Search results 321 through 330 of 941

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324a. The Fourth Dimension (2024): Fifth Lecture 31 May 1905, Berlin

Rudolf Steiner
It is therefore half of an octahedron because it intersects half of the faces of the octahedron. It is not the case that you cut the octahedron in half. If you bring the other four faces of the octahedron to the cut, the result is also a tetrahedron, which together with the first tetrahedron has the octahedron as a common intersection.
But this applies only to the cube. The rhombic dodecahedron, cut in half, also gives a different spatial structure. Figure 38 Now let us take the relation of the octahedron to the tetrahedron.
For this purpose, let us take a tetrahedron, which we cut off at one vertex (Figure 38). We continue this process until the cut surfaces meet at the edges of the tetrahedron; then what remains is the indicated octahedron.
324a. The Fourth Dimension (2024): Sixth Lecture 07 Jun 1905, Berlin

Rudolf Steiner
Such a change can indeed be made, and it corresponds exactly to the change that a three-dimensional being undergoes when it passes into the fourth dimension, when it develops through time. If you cut a four-dimensional being at any point, you take away the fourth dimension, you destroy it. If you do that to a plant, you do exactly the same thing as if you were to make a cast of the plant, a plaster cast.
324a. The Fourth Dimension (2024): Four-Dimensional Space 07 Nov 1905, Berlin

Rudolf Steiner
I pin the paper tape together tightly with pins and cut it in half. Now one tape is firmly stuck inside the other. Before that, it was just one tape. So here, by merely intertwining the tapes within the three dimensions, I have created the same thing that I would otherwise have to reach out into the [fourth] dimension to achieve."
324a. The Fourth Dimension (2024): On Higher-Dimensional Space 22 Oct 1908, Berlin

Rudolf Steiner
Those who are not capable of very sharp abstractions will already falter here. For example, you cannot cut the boundaries of a wax cube as a fine layer of wax. You would still get a layer of a certain thickness, so you would get a body.
326. The Origins of Natural Science: Lecture III 26 Dec 1922, Dornach
Tr. Maria St. Goar, Norman MacBeth

Rudolf Steiner
Hence they felt that if they could express the world in thoughts arranged in the same clear-cut architectural order as in a mathematical or geometrical system, they would thereby achieve something that would have to correspond to reality.
305. Spiritual Ground of Education: The Organisation of the Waldorf School 23 Aug 1922, Oxford
Tr. Daphne Harwood

Rudolf Steiner
Or children bring their own fantasy into play: they make a cat, not just a nice cat, but as it strikes them: humped, without more ado and very well carried out.
306. The Child's Changing Consciousness and Waldorf Education: Lecture I 15 Apr 1923, Dornach
Tr. Roland Everett

Rudolf Steiner
For example, you may have witnessed—I am not implying that as teachers you have actually carried out this experiment yourselves, for present company is always excluded when negative assertions are being made—you may have witnessed how the rotation of the planets around the Sun was graphically illustrated even to a class of young children. A piece of cardboard is cut into a disc and its center is pierced with a pin. A drip of oil is then put onto its surface before the disc is floated on water.
306. The Child's Changing Consciousness and Waldorf Education: Lecture II 16 Apr 1923, Dornach
Tr. Roland Everett

Rudolf Steiner
The activities of the legs, in a certain way, have the effect of producing in the physical and soul life a stronger connection with what is of the nature of beat, of what cuts into life. In the characteristic attunement of the movements of right and left leg, we learn to relate ourselves to what lies below our feet.
306. The Child's Changing Consciousness and Waldorf Education: Lecture IV 18 Apr 1923, Dornach
Tr. Roland Everett

Rudolf Steiner
For example, children of preschool age are told to make parallel cuts in strips of paper and then to push multi-colored paper strips through the slits so that a woven colored pattern finally emerges.
For a leg is only a leg as long as it is part of a whole organism. If cut off, it ceases to be a leg. Such things have to become flesh and blood again so that, by progressing from the whole to the parts, we comprehend reality.
306. The Child's Changing Consciousness and Waldorf Education: Lecture VI 20 Apr 1923, Dornach
Tr. Roland Everett

Rudolf Steiner
Whether the teacher enters the classroom in a dignified manner, or whether the teacher tries to cut a fine figure, speaks directly to the child. Likewise, whether the teacher is always fully awake to the classroom situation—this will show itself in the child's eye by the way the teacher handles various objects during the lessons—or, during wintertime, whether it could even happen that the teacher absent-mindedly walks off with the blackboard towel around his or her neck, mistaking it for a scarf—all of this speaks volumes to the child.
6 This leads to a complete absurdity, because, from the perspective of energy output, it makes no difference whether someone cuts a certain quantity of firewood within a given time, or whether—if one can afford to avoid such a menial task—one expends the same energy and time on treading the pedals of a wheel specially designed to combat incipient obesity.

Results 321 through 330 of 941

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