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 this new perspective with words, diagrams, analogies, and examples of many kinds. In doing so, he continues his life-long project of demonstrating that our objective, everyday thinking is the lowest rung of a ladder that reaches up to literally infinite heights. Translated into English [from GA 324a] for the first time, these talks and the other selections on many mathematical topics bring us to tantalizing new horizons of awareness. They discuss: -- The relationship between geometric studies and developing direct perception of spiritual realities -- Constructing a fourth-dimensional hypercube -- Creating dimensions through movement -- Six dimensions of the self-aware human being -- The relationship of the Trinity and the angelic hierarchies to physical space
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