GA 324a - Revision history

Odyssee at 07:48, 12 September 2021

2021-09-12T07:48:08Z

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	Six connected lectures, Berlin 24 March to 7 June 1905, two individual lectures, Berlin 7 Nov. 1905 and 22 Oct. 1908. Question answers from 1904 to 1922.		Six connected lectures, Berlin 24 March to 7 June 1905, two individual lectures, Berlin 7 Nov. 1905 and 22 Oct. 1908. Question answers from 1904 to 1922.

			The point, line, plane and solid objects represent the first three dimensions, but a kind of reversal of space is involved in the ascent to a fourth dimension. Steiner leads us to the brink of this new perspective—as nearly as it can be done with words, diagrams, analogies, and examples of many kinds. In doing so, he continues his lifelong project of demonstrating that our objective, everyday thinking is the lowest rung of a ladder that reaches up to literally infinite heights. The talks in this series and the selections from the question-and-answer sessions on many mathematical topics over the years are translated into English for the first time in The Fourth Dimension. They bring us to tantalizing new horizons of awareness where Steiner hoped to lead his listeners.

	The first part of this volume is a series of lectures on the problem of the real existence of a fourth dimension, which was much discussed in the cultural world at the time. A large part of it is devoted to the geometry of four-dimensional bodies. The more extensive second part contains answers to questions on topics such as projective geometry, the speed of light, fluid geometries between the original image and the image, positive and negative numbers, imaginary and super-imaginary numbers, the third Copernican law and, in particular, Albert Einstein's theory of relativity.		The first part of this volume is a series of lectures on the problem of the real existence of a fourth dimension, which was much discussed in the cultural world at the time. A large part of it is devoted to the geometry of four-dimensional bodies. The more extensive second part contains answers to questions on topics such as projective geometry, the speed of light, fluid geometries between the original image and the image, positive and negative numbers, imaginary and super-imaginary numbers, the third Copernican law and, in particular, Albert Einstein's theory of relativity.

Odyssee at 07:46, 12 September 2021

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			[[File:GA324a en 2001.jpg\|thumb]]
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	== The Fourth Dimension. Mathematics and Reality ==		== The Fourth Dimension. Mathematics and Reality ==
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	== Literature ==		== Literature ==
			* [[Rudolf Steiner]], C. E. Creeger (Translator): ''The Fourth Dimension: Sacred Geometry, Alchemy and Mathematics: Sacred Geometry, Alchemy, and Mathematics''. '''CW 324a'''. ‎ Anthroposophic Press 2001. ISBN 978-0880104722; eBook {{ASIN\|‎B006VIMNB4}} {{rsarchive\|324a}}

	=== German ===		=== German ===
	* [[Rudolf Steiner]]: ''Die vierte Dimension'', [[GA 324a]] (1995), ISBN 3-7274-3245-4 {{Lectures\|324a}}		* [[Rudolf Steiner]]: ''Die vierte Dimension'', [[GA 324a]] (1995), ISBN 3-7274-3245-4 {{Lectures\|324a}}

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Created page with "thumb == The Fourth Dimension. Mathematics and Reality == === Die vierte Dimension. Mathematik und Wirklichkeit === Listener's notes from lectures on mult..."

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[[File:GA324a.jpg|thumb]]
== The Fourth Dimension. Mathematics and Reality ==
=== Die vierte Dimension. Mathematik und Wirklichkeit ===

Listener's notes from lectures on multi-dimensional space and from question answers on mathematical topics.

Six connected lectures, Berlin 24 March to 7 June 1905, two individual lectures, Berlin 7 Nov. 1905 and 22 Oct. 1908. Question answers from 1904 to 1922.

The first part of this volume is a series of lectures on the problem of the real existence of a fourth dimension, which was much discussed in the cultural world at the time. A large part of it is devoted to the geometry of four-dimensional bodies. The more extensive second part contains answers to questions on topics such as projective geometry, the speed of light, fluid geometries between the original image and the image, positive and negative numbers, imaginary and super-imaginary numbers, the third Copernican law and, in particular, Albert Einstein's theory of relativity.

== Literature ==
=== German ===
* [[Rudolf Steiner]]: ''Die vierte Dimension'', [[GA 324a]] (1995), ISBN 3-7274-3245-4 {{Lectures|324a}}

{{GA}}

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