<div dir="ltr"><div dir="ltr"><div dir="ltr"><div><div style="font-family:arial,sans-serif;color:rgb(7,55,99)" class="gmail_default">I think that Joseph pointed to an interesting aspect: of the dependability between space and time which goes beyond Einstein's SRT.</div><div style="font-family:arial,sans-serif;color:rgb(7,55,99)" class="gmail_default">These two (human world) concepts have been hardly investigated outside the realms of mathematics and physics. </div><div style="font-family:arial,sans-serif;color:rgb(7,55,99)" class="gmail_default"><br></div><div style="font-family:arial,sans-serif;color:rgb(7,55,99)" class="gmail_default">I am curious how you two would interpret the words of Rudolph Steiner from about the same time when Minkowski, Lorentz and Einstein put forward their rigid models of the relative reality:</div><div style="font-family:arial,sans-serif;color:rgb(7,55,99)" class="gmail_default"><br></div><div style="font-family:arial,sans-serif;color:rgb(7,55,99)" class="gmail_default"><p style="margin:0px;font-stretch:normal;font-size:15px;line-height:normal;font-family:Helvetica;font-size-adjust:none;font-kerning:auto;font-variant-alternates:normal;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-east-asian:normal;font-feature-settings:normal;color:rgb(0,0,239)">"FOUR-DIMENSIONAL SPACE</p>
<p style="margin:0px;font-stretch:normal;font-size:15px;line-height:normal;font-family:Helvetica;font-size-adjust:none;font-kerning:auto;font-variant-alternates:normal;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-east-asian:normal;font-feature-settings:normal">Berlin, November 7, 1905</p><p style="margin:0px;font-stretch:normal;font-size:15px;line-height:normal;font-family:Helvetica;font-size-adjust:none;font-kerning:auto;font-variant-alternates:normal;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-east-asian:normal;font-feature-settings:normal"><br></p>
<p style="margin:0px;font-stretch:normal;font-size:15px;line-height:normal;font-family:Helvetica;font-size-adjust:none;font-kerning:auto;font-variant-alternates:normal;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-east-asian:normal;font-feature-settings:normal">Creating dimensions through movement. Transforming a circle into a straight line. The importance of recent synthetic, projective geometry in considering space correctly. Space is self-contained. Twists in closed curves (strips of paper) as an example of intertwining dimensions. In reality, the movements of the Moon and Earth around the Sun are similarly intertwined. Enlivening our view of space. Unfolding the cube in a plane and the tessaract in three-dimensional space. A hexagon is a projection of a cube; a rhombic dodecahedron is a projection of a tessaract. The transition to reality. Time, movement, and development as expressions of the fourth dimension in plants. When time itself becomes alive, sensory ability emerges as the expression of the fifth dimension in animals. Human beings</p>
<p style="margin:0px;font-stretch:normal;font-size:15px;line-height:normal;font-family:Helvetica;font-size-adjust:none;font-kerning:auto;font-variant-alternates:normal;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-east-asian:normal;font-feature-settings:normal">are six-dimensional beings.</p></div><div style="font-family:arial,sans-serif;color:rgb(7,55,99)" class="gmail_default"><br></div><div style="font-family:arial,sans-serif;color:rgb(7,55,99)" class="gmail_default"><p style="margin:0px;font-stretch:normal;font-size:15px;line-height:normal;font-family:Helvetica;font-size-adjust:none;font-kerning:auto;font-variant-alternates:normal;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-east-asian:normal;font-feature-settings:normal;color:rgb(0,0,239)">ON HIGHER-DIMENSIONAL SPACE</p>
<p style="margin:0px;font-stretch:normal;font-size:15px;line-height:normal;font-family:Helvetica;font-size-adjust:none;font-kerning:auto;font-variant-alternates:normal;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-east-asian:normal;font-feature-settings:normal">Berlin, October 22, 1908</p><p style="margin:0px;font-stretch:normal;font-size:15px;line-height:normal;font-family:Helvetica;font-size-adjust:none;font-kerning:auto;font-variant-alternates:normal;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-east-asian:normal;font-feature-settings:normal"><br></p></div><p style="margin:0px;font-stretch:normal;font-size:15px;line-height:normal;font-family:Helvetica;font-size-adjust:none;font-kerning:auto;font-variant-alternates:normal;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-east-asian:normal;font-feature-settings:normal">Mathematicians can do no more than discuss the possibility of higher<span class="gmail_default" style="font-family:arial,sans-serif;color:rgb(7,55,99)"> </span>dimensional<span class="gmail_default" style="font-family:arial,sans-serif;color:rgb(7,55,99)"> </span>space. The cube's three dimensions of length, width, and<span class="gmail_default" style="font-family:arial,sans-serif;color:rgb(7,55,99)"> </span>height. What is a plane surface? A merely arithmetical transition to higher<span class="gmail_default" style="font-family:arial,sans-serif;color:rgb(7,55,99)"> </span>dimensions does not lead to reality. Attempting to<span class="gmail_default" style="font-family:arial,sans-serif;color:rgb(7,55,99)"> </span>understand space<span class="gmail_default" style="font-family:arial,sans-serif;color:rgb(7,55,99)"> </span>--<span class="gmail_default" style="font-family:arial,sans-serif;color:rgb(7,55,99)"> </span>for<span class="gmail_default" style="font-family:arial,sans-serif;color:rgb(7,55,99)"> </span>example, infinity--on the basis of numbers leads to confusion. Numbers<span class="gmail_default" style="font-family:arial,sans-serif;color:rgb(7,55,99)"> </span>have no relationship or a neutral relationship to space. <span class="gmail_default" style="font-family:arial,sans-serif;color:rgb(7,55,99)">O</span>bserving repeated<span class="gmail_default" style="font-family:arial,sans-serif;color:rgb(7,55,99)"> </span>disappearances and reappearances points to the existence of a fourth<span class="gmail_default" style="font-family:arial,sans-serif;color:rgb(7,55,99)"> </span>dimension. Refuting a materialistic argument. Unfolding the boundaries of<span class="gmail_default" style="font-family:arial,sans-serif;color:rgb(7,55,99)"> </span>a square and a cube. Unfolding the eight cubes of a tessaract.</p><div style="font-family:arial,sans-serif;color:rgb(7,55,99)" class="gmail_default"><span style="font-family:Helvetica;font-size:15px;color:rgb(34,34,34)"><br></span></div><div style="font-family:arial,sans-serif;color:rgb(7,55,99)" class="gmail_default"><span style="font-family:Helvetica;font-size:15px;color:rgb(34,34,34)"><u>Source:</u> "The Fourth Dimension: Sacred Geometry, Alchemy and Mathematics", </span></div><div style="font-family:arial,sans-serif;color:rgb(7,55,99)" class="gmail_default"><span style="font-family:Helvetica;font-size:15px;color:rgb(34,34,34)">A translation from the German: "Die vierte Dimension: Mathematik und </span><span style="font-family:Helvetica;font-size:15px;color:rgb(34,34,34)">Wirklichkeit (Vol. 324a in the Bibliographic Survey). </span></div><div style="font-family:arial,sans-serif;color:rgb(7,55,99)" class="gmail_default"><span style="font-family:Helvetica;font-size:15px;color:rgb(34,34,34)">First published 1995 </span><span style="font-family:Helvetica;font-size:15px;color:rgb(34,34,34)">by Rudolf Steiner Verlag, Dornach, Switzerland.</span></div>
<p style="margin:0px;font-stretch:normal;font-size:15px;line-height:normal;font-family:Helvetica;font-size-adjust:none;font-kerning:auto;font-variant-alternates:normal;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-east-asian:normal;font-feature-settings:normal">Translated by Catherine E. Creeger</p>
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<p style="margin:0px;font-stretch:normal;font-size:15px;line-height:normal;font-family:Helvetica;font-size-adjust:none;font-kerning:auto;font-variant-alternates:normal;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-east-asian:normal;font-feature-settings:normal"><br></p><p style="margin:0px;font-stretch:normal;font-size:15px;line-height:normal;font-family:Helvetica;font-size-adjust:none;font-kerning:auto;font-variant-alternates:normal;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-east-asian:normal;font-feature-settings:normal"><br></p><p style="margin:0px;font-stretch:normal;font-size:15px;line-height:normal;font-family:Helvetica;font-size-adjust:none;font-kerning:auto;font-variant-alternates:normal;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-east-asian:normal;font-feature-settings:normal"><span class="gmail_default" style="font-family:arial,sans-serif;color:rgb(7,55,99)">As for Lou's lecture, I'll need more time to digest it. I was awed by the deep symbolics of the slide with the ouroboros.</span><br></p><p style="margin:0px;font-stretch:normal;font-size:15px;line-height:normal;font-family:Helvetica;font-size-adjust:none;font-kerning:auto;font-variant-alternates:normal;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-east-asian:normal;font-feature-settings:normal"><span class="gmail_default" style="font-family:arial,sans-serif;color:rgb(7,55,99)"><br></span></p><p style="margin:0px;font-stretch:normal;font-size:15px;line-height:normal;font-family:Helvetica;font-size-adjust:none;font-kerning:auto;font-variant-alternates:normal;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-east-asian:normal;font-feature-settings:normal"><span class="gmail_default" style="font-family:arial,sans-serif;color:rgb(7,55,99)">Best,</span></p><p style="margin:0px;font-stretch:normal;font-size:15px;line-height:normal;font-family:Helvetica;font-size-adjust:none;font-kerning:auto;font-variant-alternates:normal;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-east-asian:normal;font-feature-settings:normal"><span class="gmail_default" style="font-family:arial,sans-serif;color:rgb(7,55,99)"><br></span></p><p style="margin:0px;font-stretch:normal;font-size:15px;line-height:normal;font-family:Helvetica;font-size-adjust:none;font-kerning:auto;font-variant-alternates:normal;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-east-asian:normal;font-feature-settings:normal"><span class="gmail_default" style="font-family:arial,sans-serif;color:rgb(7,55,99)">Plamen</span></p><p style="margin:0px;font-stretch:normal;font-size:15px;line-height:normal;font-family:Helvetica;font-size-adjust:none;font-kerning:auto;font-variant-alternates:normal;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-east-asian:normal;font-feature-settings:normal"><span class="gmail_default" style="font-family:arial,sans-serif;color:rgb(7,55,99)"><br></span></p><p style="margin:0px;font-stretch:normal;font-size:15px;line-height:normal;font-family:Helvetica;font-size-adjust:none;font-kerning:auto;font-variant-alternates:normal;font-variant-ligatures:normal;font-variant-numeric:normal;font-variant-east-asian:normal;font-feature-settings:normal"><br></p></div></div></div><br></div>