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 Title: Lecture: Woman and Society (Die Frauenfrage)
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 Title: Jesus and Christ
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 mathematical precision when Christ must have lived in the man Jesus,
 Title: Lecture: The Moral as the Source of WorldCreative Power
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 reality a picture built up purely on the basis of mathematical
 principles, mathematicalmechanical principles. The rudiments of it
 that of today, for it was based, not upon mathematical principles but
 another in accordance with mathematical laws. To be sure, in every
 Title: Lecture: The Path to Freedom and Love and their Significance in World Events
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 mathematics. Mathematical thinking streams up entirely from our
 determined; but the mathematical thoughts in themselves are only
 They say: mathematical concepts are a priori. — A priori,
 But why are mathematical concepts a priori? Because they stream
 Title: Lecture: Search for the New Isis, the Divine Sophia: The Quest for the IsisSophia
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 built one of these pyramids with such mathematical precision that the
 luciferic world picture, at the mathematicalmechanical world picture of
 the grave of Isis, a mathematical abstraction. Then comes the search for
 Title: Lecture: The Two Christmas Annunciations
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 on, but it is merely mathematical and mechanical. It only speaks of
 mathematically, whereas the ancient wisdom of, the stars perceived in
 also in the case of such purely mathematical considerations, the
 poured into mathematical mould, that the pupil of the ancient
 thus brought to a mathematical understanding of the universe, he
 true insight into these matter the mathematical capacity is in itself
 mathematical forms and reckoning to them, we are spreading out again
 cramped into our mathematical, mechanical grasp of the heavens, so
 their phenomena. What we have in the way of mathematical astronomy is
 mathematical abstraction; and in like manner the inner must be widened
 Title: Lecture: The Threshold In Nature and In Man
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 overborne by purely mathematical pictures of the world, purely
 Title: Lecture: The Alphabet
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 music today — the mathematical physicist reckons the pitch of a note,
 In itself it is really interesting — if one has a mathematical bent
 Title: Mathematics and Occultism
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 Now Plato looked upon mathematical science as a means of training for
 mathematical images hover over the borderline between the material
 case of all mathematical pictures. They relate to the
 mathematically, I do indeed think about something my senses can
 property of mathematical perception is this: that a single
 senseperception what is spiritual. From the mathematical figure I can
 steps in mathematical knowledge for this purpose, and understand
 clearly what it is that we really gain from a mathematical figure.
 world can be based on mathematical ideas, but only that the first
 supersensible in mathematical thought. When a man reaches the stage of
 senseperception in the same way as he is able to think mathematically
 understand. He must learn through the elementary mathematical
 supersensible mathematical perception; no experience will ever
 Gnostics and all Occultists conceive mathematical science as an
 than that by reducing to mathematical formulae all natural
 only after I have reduced it to mathematical formulae. To express by
 in this sense, which may be thus mathematically expressed. As
 perception which underlies mathematical science must not be lost.
 after the pattern of mathematical science.
 Now, within the last few years, mathematical science has made
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 Title: Lecture: Elemental Beings and Human Destinies
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 diffusion of light with mathematical ideas, they will say: You see,
 Title: Lecture: Richard Wagner and Mysticism
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 mathematical concepts. Men must have patience to find their bearings
 Title: Lecture VI: Ancient Myths
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 space events take place which are calculated purely mathematically
 merely calculate, as the modern mathematical astronomer does, the
 this, even I though it is not proved mathematically, which would here
 Title: Lecture VII: Ancient Myths
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 mathematical calculations in Astronomy. But the reality is certainly
 mathematically, is there; it is only passed completely through a
 Title: Lecture: The Souls Progress through Repeated Earth Lives
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 mathematically, we develop really out of our inner being; it is the
 then one knows whence this curious mathematical knowledge springs.
 more in the purity of mathematicalgeometrical lines.
 Title: Between Death and Rebirth: Lecture Five
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 heavenly bodies purely in terms of their mathematical, spatial and
 Title: Between Death and Rebirth: Lecture Eight
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 presented as something only brought about by mathematicalphysical
 Title: Christ and the Spiritual World: Lecture Six
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 mathematical ideas and proofs, for example, are created by the soul
 come to grasp what he set out in his mathematicalmechanical laws of
 Title: Mission of FolkSouls (1929): Lecture 3
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 In order to arrive at geometrical, mathematical knowledge it is not
 only attainable by mathematical construction, then you have some
 mathematical concepts only; it is man who is so imperfect that he is
 Title: Lecture: The Inexpressible Name, Spirits of Space and Time.
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 furthest of all along the path of mathematicalgeometrical knowledge.
 mathematicalgeometrical sphere, the less transparent things become.
 Title: Lecture: The Meaning of Easter: St. Paul and the Christ Impulse
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 grasp that which is beyond the earth with mathematical and mechanical
 Title: Agriculture Course: Lecture 6
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 Stars.” Modern astronomy serves as a mere mathematical orientation,
 Title: Paths to Knowledge of Higher Worlds
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 Title: Errors in Spiritual Investigation
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 existed a kind of belief, a certain mathematicalgeometrical belief
 mathematicalanalytical, constructive thinking for that square
 thing to exist, but it is impossible to show with mathematical
 mathematical thinking does not suffice to prove something that is
 one can prove the squaring of a circle mathematically.
 Title: The Supersensible Being of Man and the Evolution of Mankind
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 presentiment of the spiritual world if clear, mathematical thinking
 Title: Lecture: The Peoples of the Earth in the Light of Anthroposophy
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 in mathematical and mechanical formulae. The Westerner must realise
 by mathematical calculation, by equally dry spectroanalysis or
 Title: Lecture: The Position of Anthroposophy among the Sciences
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 is, when actively engaged in mathematical thinking. His attitude of
 transfer, to some extent, the mathematical attitude of soul to other
 mathematical or unmathematical. What can live in us in like
 of things as mathematical perception is with mathematical
 perception. The mathematical structures we “perceive” in
 for our eternal human nature, mathematical thinking has all the
 interesting to follow such an extension of mathematical operations
 (in the mathematical sense) and quite correct. But anyone who knows
 differently. From the logical, mathematical standpoint one can
 logically, mathematically, algebraically, these things can be carried
 mathematical spaces.
 that, by penetrating the mathematical domain completely, we are led to
 world. To understand the mathematical attitude of soul is to be led
 mathematical forms. If he can then raise this activity to higher
 natural laws as valid only if they can be formulated mathematically.
 Title: Lecture: Fundamentals of the Science of Initiation
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 Title: Lecture: Cosmogony, Freedom, Altruism
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 Title: Lecture: On the Dimensions of Space
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 within the mathematical domain, the thoughts which we arrive at in
 Title: Lecture: Thinking and Willing as Two Poles of the Human SoulLife
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 that we cannot understand it by means of purely mathematically
 Title: Lecture: The Spirit in the Realm of Plants
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 thoroughly mathematical thinker, a deeply thoughtful man, who was
 Title: On the Mysteries of Ancient and Modern Times: Lecture 1
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 Title: On the Mysteries of Ancient and Modern Times: Lecture 3
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 Title: Lecture: The Supersensible in the Human Being and in the Universe
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 Title: Lecture: Foundations of Anthroposophy
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 Title: Lecture: Knowledge Pervaded with the Experience of Love
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 exact as mathematical or other scientific ideas. We do not think
 way in which mathematical or geometrical figures confront him in
 Title: Lecture: Hermes
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 mathematical concepts of Natural Science may be so deeply absorbed
 mathematical laws, in the plants with their lifefilled forms which
 mathematical sciences, geometry (which Pythagoras afterwards learnt
 for the method was really a mathematical convenience. After three
 Title: Lecture: Galileo, Giordano Bruno, and Goethe
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 Title: Lecture: On the Occasion of Goethe's Birthday
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 Title: Mission/FolkSouls (1970): 3. The inner Life of the Folk Spirits. Formation of the Races.
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 geometrical and mathematical knowledge sensedata are superfluous;
 the Archangels are not Beings who are limited to mathematical
 Title: Lecture: Wonders of the World: Lecture 3
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 mathematicalmechanical laws. Such a nature — a nature which is
 calculated according to purely external mathematicalmechanical
 as the facts which follow the physicalmathematicalchemical laws, but
 Title: Lecture: About Horses That Can Count and Calculate
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 I discovered that mathematical
 thinking, the whole mathematical conception, is something far more objective
 than one generally thinks. The whole mathematical thinking is something
 The foundation of mathematical thinking can be explained by the fact
 that all mathematical concepts are contained in the structure of the
 mathematical ability is principally dependent on three channels situated
 cord. If a human being arrives at mathematical conclusions, we are able
 we generally imagine. For mathematical conclusions are formed, as it
 connected with the Earth through a kind of mathematical automatism.
 in check the whole mathematical automatism. Now it is strange to see
 need to calculate the various mathematical problems which he gives to
 the horse, but merely touches upon something mathematical. In doing
 so, he becomes incorporated within the mathematical automaton of the
 become aware so strongly of the way in which the mathematical automaton
 the earth, in the case of the mathematical automaton, there will be a
 he was being connected in a very strange way with the mathematical automaton.
 And just because there is this connection between all mathematical things,
 Title: Tension Between East and West: Lecture 1: Natural Science
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 Title: Tension Between East and West: Lecture 2: Psychology
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 Title: Tension Between East and West: Lecture 3: East and West in History
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 Title: Tension Between East and West: Lecture 4: Spiritual Geography
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 Title: Tension Between East and West: Lecture 6: Individual and Society
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 Title: Goethe's Secret Revelation: Lecture II
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 Because regarding such truths such as mathematical truths, most
 the thoughts in us think, as we let mathematical thought do. Thus,
 Title: Purpose of the Goetheanum and Anthroposophy
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 Title: Karma of Vocation: Lecture III
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 a mathematical concept, it would not have been possible without
 Title: Mysteries of the Sun: Lecture III
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 Title: Reincarnation and Immortality: Lecture IV: Nature of Anthroposophy
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 mathematical kind, one is exclusively concerned with a simple
 Title: Necessity for Spiritual Knowledge: Lecture 2
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 Title: Eternal Soul of Man in the Light of Anthroposophy
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 Title: Necessity and Freedom: Lecture II: The Legend of the Prague Clock
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 mathematically on the basis of past ones. Ideally, scientists
 Title: The Building at Dornach (Bn/GA 289): Lecture I: The Goetheanum
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 has here been made to depart from the usual purely mathematicalgeomatricalmechanical
 and intellectual, from everything merely mechanical and mathematical,
 the merely mathematicalgeometricaldynamic column formation has been
 Title: Anthroposophy as a Demand of the Times
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 scientific result, but as the mathematical or geometric results
 sense just as a mathematician would for a mathematical problem.
 Title: Cosmic Forces in Man: Lecture I: Cosmic Forces in Man
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 attached to them because we fall back upon mathematical formulae when
 Title: Esoteric Cosmology: Lecture XVIII: The Apocalypse
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 might develop by dint of precise, minute and mathematical observation
 Title: At the Gates: Lecture XI: The PostAtlantean CultureEpochs
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 associated with logic and mathematical calculation began to develop,
 Title: At the Gates: Lecture XIII: Oriental and Christian Training
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 mathematical concepts, for example. No perfect triangle exists in the
 Title: Festivals/Easter: Lecture I: Easter: The Festival of Warning
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 mathematical and mechanical knowledge alone. In a world in which he
 Title: Lecture: Foundations of Esotericism: Lecture XXI
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 parliamentary fashion. Mathematical truth is recognised by man through
 matters was expressed so objectively, with such pure mathematical
 Devachanic plane except when he is thinking mathematically. Certain
 Title: Lecture: The Human Spirit and the Animal Spirit
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 criminologist Moritz Benedict, celebrated for his mathematical
 Title: Lecture III: Human Questions and Cosmic Answers
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 formed part of mathematical science in the course of its evolution on
 Title: First Lecture (First Scientific LectureCourse)
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 the phenomena of Nature to mathematical thinking as Goethe had.
 relation of natural phenomena to those mathematical formulations
 Increasingly in modern time, the mathematical way of studying the
 phenomena of Nature — I do not say directly, the mathematical
 the study of natural phenomena in terms of mathematical formulae
 confuse what can still be seen in purely mathematical ways, and what
 Title: Second Lecture (First Scientific LectureCourse)
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 thought. We derive mathematical formulae concerning all that can be
 Title: Eighth Lecture (First Scientific LectureCourse)
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 enough to entertain a few mathematical notions about wavemovements
 Title: Tenth Lecture (First Scientific LectureCourse)
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 real mathematical perception into that realm of phenomena which is
 mathematical certainty that air could not be liquefied. Yet air was
 Title: Macrocosm/Microcosm: Lecture 8: Mirrorimages of the Macrocosm in Man. Rosicrucian Symbols.
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 solution of a mathematical problem. It is the essence of the new
 Title: Macrocosm/Microcosm: Lecture 11: Man and Planetary Evolution
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 quoting experiments, adducing mathematical proofs and the like, so
 Title: Man/Being/Spirit/Soul: Lecture III: The Science of the Spirit and Modern Questions
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 Title: Origins of Natural Science: Lecture I
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 Title: Origins of Natural Science: Lecture II
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 1543. one century later, Copernicus, with his mathematical mind, took
 how in fact the application of this mathematical mind to nature
 conceptual systems, namely, the mathematical, is regarded as the best
 broadest sense possible. The third is mathematical. Considering the
 Title: Origins of Natural Science: Lecture III
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 depends on the way in which mathematical thinking was gradually
 perception in regard to mathematical thinking itself. We are much
 system with mathematically oriented thinking of the kind to which we
 began to apply this mathematical thought to the whole physical and
 postulates, if not in mathematical formulae — for actual
 from earlier ones, is based on the mathematical pattern. By and by it
 mathematical or geometrical system, they would thereby achieve
 Try to sense the tremendous difference between this mathematical
 feeling bound to human experience, and the bare, bleak mathematical
 understand the origin of the later mathematical way of thinking that
 mathematical structures. They have all been severed from their roots.
 mention any other mathematical category taken from algebra or
 observing how people conceived of things mathematical, we find that
 As a matter of fact, in regard to mathematics and the mathematical
 of a mystical attitude toward the mathematical method.
 mathematical, methodical lines, not specifically geometrical lines,
 but lines experienced mentally by mathematical methods. In regard to
 mathematical one. Anyone how makes such a distinction does not really
 truly mathematicalmystical way. His philosophy still reflects the
 one, in a specific mathematical case. It is an illusionary process,
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 Title: Origins of Natural Science: Lecture IV
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 no surprise therefore to discover this mathematical order in the
 some other mathematical formula on natural phenomena — even if
 such abstract mathematical concepts can be identified with
 natural phenomena is that what has first been mathematically thought
 corporeal nature the mathematical images of what one had experienced
 mathematically so much as lyrically. There is something musical in
 ancient mystics, and not because he experienced the mathematical laws
 Copernicus tried to grasp astronomy with abstract mathematical ideas.
 Here I do not mean single mathematical deductions, but mathematical
 phenomena of nature with abstract mathematical thinking. Hence, as a
 mathematicalmystical view gave way to the new
 mathematicalscientific style. The thinkers of the time find it
 common experience, can be used in my mathematical explanation of the
 my mathematical and scientific reflections. Berkeley agrees that one
 mathematically when he uses these concepts to explain the world. He
 the cosmic spirit insofar as they have mathematical forms, for that
 we cannot apply mathematical concepts in an external manner to
 Therefore he could not approve of mathematical ideas that produced
 experienced. By adopting this abstract mathematical view and these
 Therefore, owing to this mathematical approach, modern science is
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 Title: Origins of Natural Science: Lecture V
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 The isolation of man's ideas (especially his mathematical
 mathematical. He impresses the whole mathematical system upon the
 follows a mathematical method but it is not mathematics in the modern
 sense. He expounds his philosophy in a mathematical style, joining
 the former qualitative experience of quantitative mathematical
 man's inner life, we can say that his style is mathematical.
 a mathematical style to psychology, let alone ethics.
 Title: Origins of Natural Science: Lecture VI
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 These images are the mathematical geometrical, and arithmetical
 longer saw through this, mathematical forms and numbers became
 purely mathematicalmechanistic form of motion for what is supposed
 primary qualities, everything mathematicalmechanical, into
 connections. Failing to grasp how the mathematical with its
 longer produce anything other than mathematical, mechanistic,
 Title: Origins of Natural Science: Lecture VII
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 absent in the mathematicalmechanistic sphere. This sphere has been
 divorced from man, as if man were absent from the mathematical
 did not make a radical turn toward the mathematical attitude that
 Title: Origins of Natural Science: Lecture VIII
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 mathematicalmechanical element in human movement, the experiencing
 Title: Warmth Course: Lecture III
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 space you speak in mathematical terms of length, breadth, and
 anything if I remain in our threedimensional space. The mathematical
 cannot be expressed as a solid. In purely mathematical space, it is
 formula. There is such a possibility in purely mathematical formulae.
 Title: Warmth Course: Lecture V
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 the realm of the mathematical concepts. In so far as they are purely
 mathematical, there is no trace of the tonal or the visible. Now we
 greater than the part, etc. The basis of our mathematical concepts
 willconcept, that in reality you carry into the pure mathematical
 concept. That is the essential distinction between mathematical
 inner determination of mathematical concepts. This distinction arises
 from the fact that mathematical concepts are so rigidly bound up with
 subsists in the sphere of the will is brought into mathematical
 faculties, whence comes the remoteness of the mathematical and
 the mathematical or kinematical concepts.
 Title: Warmth Course: Lecture VII
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 really physical terms and not merely in mathematical terms, which
 Title: Warmth Course: Lecture IX
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 you will then, if you treat these things mathematically, have to
 Title: Warmth Course: Lecture X
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 Title: Warmth Course: Lecture XII
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 mathematical quantities merely as such if we at the same time expect
 calculation has to involve the mathematical relations expressed in
 turned, then none of the mathematical expressions so far given would
 handled mathematically and have, so to speak, more than one meaning.
 It is necessary for us to recognize how the purely mathematical leads
 one. For the purely mathematical difficulty arises of itself, and
 mathematical thinking, similar to the one du BoisReymond delivered on
 is too complicated, in this realm of the purely mathematical it must
 quantities arise from purely mathematical relations, physicists do not
 and negative signs, but only because of purely mathematical
 Title: Warmth Course: Lecture XIV
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 things further. You will be able to develop them. Our mathematical
 Title: Philosophy/Cosmology/Religion: Lecture I: The Three Steps of Anthroposophy
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 mathematical problem. The point is that at first this organization is
 Title: Philosophy/Cosmology/Religion: Lecture II: Exercises of Thought, Feeling and Volition
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 consciously exact as the mathematical and natural scientific method of
 Title: Philosophy/Cosmology/Religion: Lecture III: Methods of Imaginative, Inspired and Intuitive Knowledge or Cognition
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 thinks out a mathematical problem can be fairly certain that he is
 Title: Lecture: Rosicrucian Esotericism: Lecture I: Rosicrucian Esotericism
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 era when men's thinking would be guided by mathematical principles.
 Title: The Story of the Green Serpent and the Beautiful Lily: Lecture I
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 (dry and mathematical as he was in his other writings) — when
 Title: Lecture: Younger Generation: Lecture VIII
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 is not limitless at all. For the mechanisticmathematical way of
 Title: Lecture: Mission of Michael: Lecture IV: The Culture of the Mysteries and the Michael Impulse.
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 mathematical truths. If we have once grasped them we know they are
 These mathematical truths are different from the truths we arrive at
 The reason is to be found in the fact that mathematical truths
 then perceives them inwardly. We possess mathematical truths through
 the fact that we ourselves behave mathematically in the world. We
 we are aware of the mathematical and geometrical concepts. The middle
 significance of this matter. In reality, the whole mathematical
 Title: Lecture: Lecture I: Occult Signs and Symbols
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 built up mathematically out of simple elements. Much that at first
 I am sure will appear to mathematical astronomers as sheer madness.
 Title: Lecture: Lecture III: Occult Signs and Symbols
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 Title: Lecture: The Proclamations to the Magi and the Shepherds
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 mathematical science, speaking only of conditions and relationships in
 kind of knowledge resembling our geometrical or mathematical sciences.
 mathematical forms that the pupil of the ancient Mysteries was led.
 And when this mathematical understanding of the universe had developed
 The philosopher Kant says of the truths of mathematical science that
 engrossed in mathematical thought. For one who can truly apprehend
 these things, mathematical cognition is in itself a proof that before
 see in them the expressions of mathematical, arithmetical progression,
 has become our mathematical astronomy. The Magi possessed
 mathematicalmechanistic conception of the heavens, to the phenomena
 of which we apply only mathematical laws. What wells up from within us
 in our mathematical astronomy is the modern metamorphosis of the
 our mathematical astronomy is the child of the Magiwisdom. It was
 inward; it has become our abstract, mathematical science by which
 same forces that are unfolded in our mathematical thinking can again
 outer perception. The outer has become inward, has become mathematical
 Title: Life Between ... XV: Intercourse With the Dead
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 Today we find there a mathematical formula. Originally there was a
 Title: Lecture II: Human and Cosmic Thought
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 mathematical terms, we shall not be able to explain the simplest
 perception, but if we go outside a mathematical explanation, we shall
 materialism will become a mathematical thinker, and will recognize as
 valid only whatever can be treated mathematically. From this results
 mathematical formulae. This may be called Mathematism.
 world is ordered mathematically. If mathematical ideas are found to
 Title: Lecture IV: Human and Cosmic Thought
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 would bring to expression a mathematical worldstructure permeated by
 — and if he would inquire into the nature of mathematical
 Title: Lecture II: Human and Cosmic Thought
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 mathematical terms, we shall not be able to explain the simplest
 perception, but if we go outside a mathematical explanation, we shall
 materialism will become a mathematical thinker, and will recognize as
 valid only whatever can be treated mathematically. From this results
 mathematical formulae. This may be called Mathematism.
 world is ordered mathematically. If mathematical ideas are found to
 Title: Lecture IV: Human and Cosmic Thought
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 would bring to expression a mathematical worldstructure permeated by
 — and if he would inquire into the nature of mathematical
 Title: Inner Impulses: Lecture IV
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 mathematical knowledge, with which one can do but little harm, or
 Title: Inner Impulses: Lecture VII
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 externally, mathematically or physically as Copernicus, Kepler,
 Title: Mystery Centres: Lecture XII: The Mysteries of the Samothracian Kabiri
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 something mathematical. He begins to calculate the size of the stars
 since man learnt only to know of the heavens mathematically, which
 Title: Mystery Centres: Lecture XIV: Human SoulStrivings During the Middle Ages the Rosicrucian Mysteries
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 mathematical grandeur and mathematical movements, which can be
 Title: Fundamentals of Anthroposophical Medicine: Lecture I
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 mathematical problem, I would say the following: imagine that a
 Title: Anthroposophical Approach to Medicine: Lecture I
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 a mathematician uses figures to illustrate a mathematical problem, I
 Title: Social Future: Lecture VI: National and International Life in the Threefold Social Organism
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 subjective, and cannot be proved. Mathematical truths are also
 Title: World Economy: Lecture IV
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 our mathematical formulas in this way. True enough; for as a rule we
 only build up a mathematical formula as a result of contemplating
 Title: World Economy: Lecture VIII
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 speak mathematically — treat S and D as variables and P, the
 Title: World Economy: Lecture IX
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 mathematical formulas, but, like the ones of which I spoke before,
 Title: World Economy: Lecture X
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 well as any that can be clothed in mathematical formula. Of course
 Title: Lecture: Michaelmas VII: The Creation of A Michael Festival Out Of The Spirit (Extract)
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 time mathematically, by our earthly means alone, whereas for the real
 Title: Lecture: The Mysteries of Ephesus The Aristotelian Categories
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 to be calculated mechanically, mathematically, namely when they become
 Title: Spiritual Science and Medicine  Lecture XV
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 are mathematically inclined, i.e., are used to live much in
 mathematical shapes and to think in mathematical forms. For this way
 difference between mathematical and nonmathematical minds. And
 Title: Lecture: Curative Education: Lecture 10
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 Vreede [the original leader of the MathematicalAstronomical Section
 Title: Human Values in Education: Lecture VIII
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 and mathematical. In the Goetheanum at Dornach an attempt was
 Title: Human Values in Education: Lecture X
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 spiritual, mathematical coolness engenders enthusiasm, for
 if one is quite cool in the mathematical sense, when one has to
 Title: Study of Man: Lecture III
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 Title: Study of Man: Lecture XIV
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 perhaps not with mathematical accuracy, but in a form filled with
 Title: Lecture: Inner Nature of Music: Lecture II
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 a mathematical gift was inherited in a similar way through several
 Title: Lecture: Inner Nature of Music: Lecture III
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 family within a period of 250 years and that the mathematical talent was
 handed down through the generations just as mathematical talent was
 the mathematical sense, which is tied to these three semicircular
 musical ear. The mathematical family shows a special development of
 Title: Behind the Scenes: Lecture 1
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 nor mathematical. That is one of the things I wanted to say.
 Title: True/False Paths: Lecture Three: Form and Substantiality of the Mineral Kingdom in Relation to the Levels of Consciousness in Man
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 activities find consummation in the mathematicalspatial forms of the
 Title: True/False Paths: Lecture Eight: Potential Aberrations in Spiritual Investigation
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 mathematically. Life, however, does not proceed mechanically or
 mathematically, but dynamically. We must not say, therefore, that the
 purely mathematically and geometrically. We must say: the medium is
 Title: True/False Paths: Lecture Nine: Abnormal Paths into the Spiritual World and their Transformation
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 is that it is written like a mathematical textbook, that I sought to
 mathematical detachment the whole path of development I have been
 Title: True/False Paths: Lecture Three: Form and Substantiality of the Mineral Kingdom in Relation to the Levels of Consciousness in Man
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 activities find consummation in the mathematicalspatial forms of the
 Title: True/False Paths: Lecture Eight: Potential Aberrations in Spiritual Investigation
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 mathematically. Life, however, does not proceed mechanically or
 mathematically, but dynamically. We must not say, therefore, that the
 purely mathematically and geometrically. We must say: the medium is
 Title: True/False Paths: Lecture Nine: Abnormal Paths into the Spiritual World and their Transformation
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 is that it is written like a mathematical textbook, that I sought to
 mathematical detachment the whole path of development I have been
 Title: Art/Mystery Wisdom: Lecture Eight
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 Title: Metaporphoses/Soul One: Lecture 1: The Mission of Spiritual Science
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 justified for that period, for the time had passed when certain mathematical
 Title: The Development of Thought from the 4th to the 19th Century  1
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 never departing from the principles of mathematical calculation,
 Title: Anthroposophy Science: Lecture I
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 Title: Anthroposophy Science: Lecture II
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 Title: Anthroposophy Science: Lecture III
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 explanation of the nature of mathematical thinking.
 and on the other hand the absorption in mathematical thought.
 this, in mathematical thought, in the activity of pure
 mathematical thinking, things are different. The difference
 “high” mathematical thinking — if I may
 soul, is then found in today's mathematicallyoriented
 can say: what we experience mathematically has as such no
 natural surroundings. In this regard, mathematical thinking
 mathematical thinking only makes images of, is actually real
 and full of content; but mathematical thinking itself is
 recognize the pictorial character of mathematical thought, we
 can realize that we experience these mathematical pictures
 experience as the mathematical thinking itself.
 mathematical thinking we are right inside what actually takes
 mathematical activity, permits us to have a clear
 is the fact that in the process of mathematical thinking, one
 against mathematical thought, its highest standard. In fact,
 when we engage in mathematical thinking, there is no
 mathematically.
 mathematical thinking is in fact what a person strives for
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 Title: Anthroposophy Science: Lecture IV
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 Title: Anthroposophy Science: Lecture V
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 Title: Anthroposophy Science: Lecture VI
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 Title: Anthroposophy Science: Lecture VII
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 Title: Boundaries of Natural Science: Lecture I
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 everything that one finds in one's environment with mathematical formulae.
 One wants to translate data gathered from nature into clear mathematical
 to being able to give a mathematicalmechanical explanation of natural
 its position and momenta in mathematical formulae. They believed they
 between the various heavenly bodies in mathematical formulae, so too
 against this striving for a crystalclear, mathematical view of the
 in thought of mathematical clarity or, indeed, even of constructing
 mathematical formulae and calculate the movements of matter in terms of
 concepts, we see that it is an external, mathematicalmechanical lucidity.
 apply a mathematicalmechanical explanation, apply the theory of evolution,
 sobriety, as Herbart has done, to apply mathematical computation to
 to gain a foothold, because the mathematical formulae simply cannot
 of nature. Consciousness rejects this lucidity. This mathematical clarity
 Title: Boundaries of Natural Science: Lecture II
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 which I commenced yesterday, the modern striving for a mathematicalmechanical
 to us differently from that which we could represent as subject to mathematicalmechanical
 of touch, and that which confronts us in the mechanicalmathematical
 pose the question: how is it that we arrive at any mathematicalmechanical
 is a difference between the mathematicalmechanical qualities of external
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 between that which is still actually mathematical — as we still
 this phenomenon of mathematics as such. We comprehend mathematical truths.
 We proceed from mathematical phenomena to certain axioms. We weave the
 the poet Novalis, who underwent a good mathematical training in his
 feeling: that which you behold as mathematical harmony, that which you
 that remains just as exact as mathematical thought yet does not proceed
 not only to think in mathematical concepts but to view that which exists
 through soul faculties of a mathematical nature. It was an Inspiration.
 I would say that the mathematical atmosphere emanating from the Vedanta
 unconsciously in mathematics and the mathematical sciences and can carry
 it over into another realm, one discovers the same mathematical element
 of actual mathematical concepts and theories, he does require one thing:
 a truly mathematical spirit, that one inwardly permeate phenomena with
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 search for the axiom underlying complex mathematical constructs. Goethe,
 therefore, who himself admitted that he had no conventional mathematical
 of mathematical thinking. If one does this, one enters via a natural
 within an element of primal mathematical thought and was able to enter
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 of contemporary science, even of the mathematical sciences. He must
 one has formulated as a natural law, or perhaps mathematically.
 within them with the extended mathematical representations. Tomorrow
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 can only in mathematical, geometrical, analyticmechanical thinking. When
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 of mathematical thinking. The pursuit of philosophy is actually impossible
 without a grasp of at least the spirit of mathematical thinking. We
 have seen what Goethe's attitude was toward this spirit of mathematical
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 than the mathematical ones to understand the world; but what attracted
 Title: Colour: Part Two: The Connection of the Natural with the MoralPsychical. Living in Light and Weight.
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 line, this line could also, if we altered the mathematical equation,
 it has also only one mathematical equation; it is a simple line, only
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 transcends the abstractmathematical, or anything that is similar to
 the abstractmathematical. And so it is not surprising if our time has
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 above all when we pass from a purely mathematical conception
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 everything, even about mathematical principles. When one man
 applies a mathematical principle and gets a different result
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 The truth of a mathematical statement can be discerned in a flash,
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 have continued there into 1923, I gave the mathematical physicists an
 finding a mathematical formula to express the difference between
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 corresponds to intricate mathematical calculations prove it. But also
 Title: Spiritual Teachings of Soul/World: Course II: Lecture I: The Epistemological Basis of Theosophy I
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 are sure judgments. These are the mathematical judgments. Is the mathematical
 This is the peculiar of mathematical proofs. For everybody it is clear
 How is mathematical knowledge possible? — Kant now calls those
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 nature of the mathematical, know something about the nature of this peculiar
 mathematical theorem could never be gained by mere observation. In nature nowhere
 sentence. Those who had the biggest conquests in astronomy by their mathematical
 He knew which farreaching scope mathematical thinking has up to the most distant
 The mathematical thinking does not suffice. It is the first step where we completely
 everybody who wants to enter into my school must have gone through a mathematical
 the independence of the mathematical thinking. If one sees that the human being
 mathematical truth is. There are still savage people. Indeed, they become extinct,
 Title: Spiritual Teachings of Soul/World: Course III  Lecture III: Theosophical Teachings of the Soul. Part III: Soul and Mind
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 Why does the mathematical truth
 questions at first also uninterested, without desire and harm, as the mathematical
 pupil can look in the eye of spirit as well as somebody who delves in a mathematical
 to him as the mathematical truth speaks indifferently to him, but in such a
 way as mathematical truth also speaks in another sense. Mathematical truth namely
 state where he faces spiritual truth really as the human being faces the mathematical
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 everything by the appearance to the senses and by mathematical calculations,
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 has understood the truth of a mathematical theorem does not care whether a million
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 of the ether.’ The answer was: Purely mathematical constructions,
 Title: Novalis: On his Hymns to the Night
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 mathematical imagination became a great poem which filled him
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 proclaims mathematical truth through their official spokesmen? If I
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 just as accurately defined as the solution of a particular mathematical
 is there in the soul in the same way as mathematical, geometrical forms
 with a sense of our own reality being maintained as a mathematical soul
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 is done with the same inner clarity as that experienced in forming mathematical
 mind proceeding with the clarity of mathematical thought. The steps
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 such truths, as the mathematical ones are, most human beings
 the mathematical thoughts think in us. If we have purified the
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 horse was at simple mathematical calculations. The whole thing
 contemporary mathematical sciences, one might ask this lecturer
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 around in space, or at least something that is mathematically
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 century; for this writer tries to prove mathematically that the earth
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 was alive in ancient times, but today it is dead, it is simply mathematical
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 is mathematical reckoning. There is no need to follow the details with
 Title: Community Life: Address 2: The GoeschSprengel Situation  Part 2
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 Indeed, the mathematical field, the field of geometry seems to
 mathematically, by strict mathematical investigations that do
 That means there were mathematically thinking people who felt
 also several such geometries. Mathematically trained people
 for them! This is very indicative that even in mathematical
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 mathematically what arises from the atoms and their movements,
 difficult, if one must not have such a lot of mathematical
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 nothing but an example, a suggestion to us: the mathematical
 comparison completely suitable. The mathematical truth is
 inside. Thus, it is with all geometrical and all mathematical
 have convinced yourselves of any mathematical theorem, then two
 mathematical truths, as true it is that — if the conditions are
 of mathematical truth. However, it is long ago that one looked
 mathematically that the three angles of the triangle amount to
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 line, in that what is the ground for the mathematical head, he
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 then: this law contains nothing else than the old mathematical
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 a thinking entirely dominated by mathematical technics. We have become
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 for him as pupil to keep mathematical formulae in mind that he
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 that the pure thinking proceeds with mathematical security from
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 source of all spiritual truths. If the teacher knows the mathematical
 functioning of the semicircular organs in the ear. Mathematical
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 Mathematical talent also needs something quite specific. A particular
 space. Special development of these canals determines mathematical
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 mathematical aspect only; which amounts to nothing more, than
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 only serves as a means of mathematical orientation, and cannot
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 realise that where he could only perceive a mathematical order,
 does not really believe in this purely mathematical world, in
 the purely mathematical cosmos. His particular civilisation
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 a mathematical truth and point from certain phenomena in the present
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 principle to mathematical concepts of many kinds.
 (Great Men of Letters). There you will find his strictly mathematical
 he was really able to think only mathematically. In philosophy, in
 political economy, in mathematics itself, he thinks mathematically,
 with mathematical precision and clarity. In natural science, too, he
 Title: Karmic Relationships, Volume I: Lecture XII
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 equations for it. He knows the mathematical, calculating side of it
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 of the period. Translate it into the mathematicaldialectical mode of
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 were to produce mathematical results and, instead of testing their
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 other hand consider the stars only in mathematical calculations, but
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 veritable antipathy to the modern mathematical form of science. In the
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 that to the telescopes, the mathematical and photographic methods that
 that someone tells you a mathematical truth. If you haven't studied
 truth. No one will deny that to judge a mathematical truth the
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 vision of the great mathematical, lightwoven texture of the universe.
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 vividly in the great woman mathematician Hypatia, in whom all the mathematical
 Title: Occult History: Lecture 4
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 constructed on the clearest mathematical principles are here derived
 today once again to recognise the spiritual, mathematical law prevailing
 laws, are to be found again microcosmically in the mathematical numbers
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 Nature, especially where this knowledge is clothed in mathematical forms.
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 have so ordered things that mathematical laws appear to us as they
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 observed, with mathematical rigour, from this point of view.
 body, in the way one would demonstrate a mathematical truth.
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 ratio. Malthus expresses it somewhat mathematically. He says:
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 quality: hence the Gothic forms also produce an abstractmathematical
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 heavens only in terms of mathematical and mechanical laws. But this
 nothing but lines must remain — mathematical lines!’
 Title: Man: Hieroglyph: Lecture One
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 mathematicalmechanical calculation, to which in recent times have
 physical, and even in the physical domain, mechanicalmathematical.
 true to say that this mechanicalmathematical method of observation
 mathematicalmechanical construction of the Universe reckon? It
 in the mechanicalmathematical way in which Galileo or Copernicus
 appears as a mathematical picture only, in which the universal origin
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 mathematical astronomy. That would necessitate beginning over again
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 mechanical or mathematical means, but only through a knowledge of the
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 mathematical, geometrical way, we find that we can think out
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 doubt that mathematical truths are among the most difficult things. They
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 a mathematical problem, for instance, such as we may strain every
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 longer seen merely as objects of mathematical and mechanical
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 way to library shelves and the mathematical knowledge was not
 Title: Influences of Lucifer/Ahriman: Lecture One: The Incarnation of Lucifer in Asia in the Third Millenium B.C.
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 belief that the mechanistic, mathematical conceptions inaugurated by
 discerned in the cosmos, not merely the mathematical, mechanistic
 mathematical aspect of astronomy. Therefore he tempts many people to
 Title: Influences of Lucifer/Ahriman: Lecture Two: The Advance Preparation of Ahriman for His Future Incarnation
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 shelves and the mathematical knowledge was not much in evidence!
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 mathematical formulae what Kepler, the German astronomer, had
 Title: Old/New Methods: Lecture Fourteen: The 5th PostAtlantean Period, the French Revolution, Schiller, Goethe, the Freedom Problem, or Berlin University Course Report  2
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 clever as requiring someone who solves mathematical problems to be
 mathematical problems. To such a person it is said: If you want to
 find out whether these mathematical problems have been solved
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 manifolds in the mathematical thinking. If anybody is familiar
 supersensible world, also mathematical ideas of infinity become
 mathematical element should not be overestimated if it concerns
 Title: Truths and Errors: Lecture VII: The Questions of Life and the Riddle of Death  1
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 that he applies this mathematical method to a higher area not
 Title: Truths and Errors: Lecture IX: Spiritual Science and Natural Sciences  their Relationship to the Riddles of Life  1
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 real scourge of mathematical societies. Since they received a
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 Theosophical learning is not like the mathematical. First it was
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 Title: Lecture: The Ahrimanic Deception
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 mechanism, in fact, only to be grasped by the aid of mathematical,
 mechanistic laws. With the help of these mathematical, mechanistic
 understood and calculated by mathematical formulae. This indeed is
 these illusions of a mathematical nature about the universe, we must
 mathematicalmechanistic concepts of the universe are merely illusions.
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 gaze. In other words he made no special mathematical calculations but
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 the world mathematical thoughts are the most sensefree ones; but
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 thoughts. Aside from mathematical ones, thoughts always lead
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 developed this mathematical picturethinking in the lifeless is
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 colors in the aura, especially in those who have keen mathematical
 Title: Influence of Spiritual Beings Upon Man: Lecture IX
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 can say that he finds mathematical truths through external experience;
 If mathematical truths were not so simple and obvious then the passions
 Title: Universe, Earth and Man: Lecture II: Ancient Wisdom and the new Apocalyptic Wisdom. Temple sleep. Isis and the Madonna. Past stages of Evolution. The bestowing of the Ego. Future Powers.
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 case of a person who occupies himself much with mathematical ideas
 state of his external health. It is not, of course, as if mathematical
 anything about mathematical ideas; the other is intensely interested
 nonmathematical person whereas it might be possible to heal the other
 count on their fingers, and then follow it with pure mathematical
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 mathematical book, for instance. This will help us to fall asleep;
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 Title: Astronomy Course: Lecture I
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 they are concerned with Astronomy, in a mathematical and
 abstract mathematical science, or an abstract science of
 out that the mechanical and mathematical way of treating what
 mathematical and mechanical kind. No doubts of any kind exist
 ideas, i. e., to the mathematical, mechanical mode of
 precisely the mathematical, mechanical faculties for its
 phenomena in the picture formed by the mathematical,
 — namely, mathematical ideas — , and on the other
 attitude towards a mathematical, mechanical
 think how remote the simplest mathematical ideas are to
 nothing in the way of mathematical ideas.
 mathematical, mechanical web over them. This web of thought
 introducing mathematical ideas into his field of work. But as
 on the model of mathematical Astronomy.
 mathematical background. This is what would happen in an
 mathematician will be able, from his mathematical studies, to
 have in mind a certain mathematical handling of the process
 mathematical presentation of such a subject, but people are
 spinning of purely mathematical thoughts? What is it worth to
 mathematical process he could turn the heart inside out, and
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 been studying, he propounds peculiar mathematical formulae.
 mathematical lines. In mathematical lines he represents to
 mathematical pictures coincides in the same way with what is
 the Ptolemaic school, the mathematical imagination does not
 the mathematical thoughtpictures of the Ptolemaic school,
 mathematical lines he would comprise the logic of the
 The model he makes, the mathematical picture living in his
 Ptolemy the Mathematical picture is quite detached from what
 return to the former method, simply uniting by mathematical
 planet. These mathematical lines correspond to what was there
 mathematically, to empirical reality in general. You may
 of a priori mathematical reasoning and them applied it to the
 Heavens by mathematical lines, building it all into a system
 namely in Galileo and others, whose mathematical thinking is
 mathematical results, was able to construct his cosmic
 course of time. Then Ptolemy conceived a mathematical
 times, all they retained of this was the mathematical aspect,
 mathematical configuration there was at least some remnant of
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 We cannot not now bring all the mathematical paraphernalia to
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 mathematical or qualitative way is that one may suddenly ask
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 mathematical and other laws, how should he be able to find the laws
 beaver, carries out. They are so artistic, of such a mathematical regularity
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 inside, intuitively. Nobody could obtain a mathematical theorem only
 the mathematical in space, you get to the great mystics who inform us
 Title: Origin and Destination of Humanity: Lecture XII: Goethe's Secret Revelation I
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 mathematical knowledge. In Goethe's estate I found a notebook
 mathematical studies even during later years, even up to the highest
 Title: Origin and Destination of Humanity: Lecture XVIII: The Future of the Human Being
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 mathematical one, it is too constructivemathematical, and is not
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 service of a reform movement. Who has a mathematically trained thinking
 must arise from a basic education which is as certain as the mathematical
 for this field: the Romans did not achieve a single mathematical theorem!
 A totally unmathematical and inexact way of thinking formed the basis
 as we are able to lead back the rough matters to mathematical concepts.
 is. There is no mathematical theorem which would not have resulted from
 and forms then the mathematical theorem of the sum of the angles in
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 would faint about that. However, we know that mathematical thinking
 what can he know about mathematics? Only mathematical concepts, having
 is that the mechanics is the paradise of the mathematical sciences.
 should develop from the mathematical attitude into a spiritual direction;
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 that is either purely mathematical, or one which is equally objective
 Title: Lecture: Wonders of the World: Lecture 3
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 mathematicalmechanical laws. Such a nature — a nature which is
 calculated according to purely external mathematicalmechanical
 as the facts which follow the physicalmathematicalchemical laws, but
 Title: Esoteric Lesson: Berlin, 1903 or 1904
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 way that our mathematical theory is related to ancient math books. One
 Title: Esoteric Lesson: Berlin, December 1904
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 way that our mathematical theory is related to ancient math books. One
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 will to adopt the mathematical method of our spiritual science. This is
 experience by mathematical method appears to this author therefore to be
 mathematical clarity, perhaps indeed mathematical dryness, is what is
 Title: Social Basis For Primary and Secondary Education: Lecture III
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 mathematical concepts, for example, and concepts of physics. Here we must
 Title: Deeper Secrets: Lecture II
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 mathematical logic were both introduced through Abraham. Even until
 and measure, by mathematical logic — this human corporality was
 through mathematical logic and reasoning. But contact with the Egyptian
 was the faculty of mathematical logic — that is to say, they were
 reality in the form of a mathematical worldpicture — received
 through Moses, into the Hebrew people with their faculties of mathematical
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 that pure thought so runs with mathematical certainty from idea
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 Title: Search for the New Isis: Lecture II: The Quest for IsisSophia
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 with such mathematical precision, that its shadow disappeared in the
 mathematicalmechanical worldpicture of modern astronomy and of
 mathematical lines, then we see the grave of the world's spiritual
 into the cosmic spaces, which have become a mathematical abstraction,
 Title: Search for the New Isis: Lecture III: The Magi and the Shepherds: The New Isis
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 the brain and becomes our mathematical, mechanistic world (green
 inwards and becomes the dry, geometricalmathematical, mechanistic
 mathematical, mechanistic world. It is only outstanding persons like
 deep imagination of this inner, mathematical world. This world of
 seems to us to be dry, mathematical, mechanistic.
 What today has faded into the mathematicalmechanistic
 and their offspring are the mathematical faculties of today. The
 mathematical faculties of today will become those faculties which
 Title: Search for the New Isis: Lecture IV
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 Title: Man as a Being: Lecture 1
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 Now let us consider mathematical truths, the truths of geometry. A
 depths that mathematical thought comes, depths to which we no longer
 Title: Man as a Being: Lecture 3
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 example, he says, “Mathematical concepts are a
 evolution that most men, civilised men at any rate, bring mathematical
 process of awakening mathematical concepts and that of imparting such
 Title: Cosmic Christianity: Lecture V
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 a mathematical truth and point from certain phenomena in the present
 Title: Lecture: Reading the Pictures of the Apocalypse: Appendix: Cosmogony
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 develop itself on the field of the sense world through minute, mathematical
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 we find all such sciences — medicine, chemistry, mathematical
 Title: Impulse for Renewal: Lecture I: Anthroposophy and Natural Science
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 back to the application of mathematical methods because even
 developed, here the mathematical way of thinking forms a
 mathematical developments of concepts. However, what has been
 according to the pattern of mathematical conceptions. When
 mathematical function. For instance, if I say: X equals Y,
 Goethe couldn't achieve much with mathematical details, that he
 was not particularly talented in his time to solve mathematical
 detailed mathematical examples, if it was more algebraic. That
 mathematized nature, in the nature of building mathematical
 a mathematical proof you have simultaneously something which is
 mathematical brain. This for example also leads to the basis of
 Goethe basically had a mathematical brain, much more
 mathematical than those who develop Astronomy. That's the
 senses harmony within the experience of creating mathematical
 mathematical thinking. It is quite understandable that Du
 starry heavens to be regarded this way, through mathematical
 mathematical understanding to it. Here one must differentiate:
 phenomena with the mathematicalcausal way of thinking, or
 place those of a purely mathematicalcausal abstraction as a
 remains more of a “mathematical mind” than those
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 Title: Impulse for Renewal: Lecture II: The Human and the Animal Organisation
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 Title: Impulse for Renewal: Lecture III: Anthroposophy and Philosophy
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 on an understanding of a mathematical nature. Time was short to
 Title: Renewal of Culture
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 the universe and admiringly looks upon his mathematical conception of the
 such a way as to supply a mathematical physical picture of the universe.
 mathematicalmechanical element now appears to us in the cosmos, although in
 mathematicalmechanical cosmos, only the great machinery, as it were, when
 Title: Philosophy, Cosmology and Religion: Lecture I: The Three Steps of Anthroposophy
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 Title: Philosophy, Cosmology and Religion: Lecture III: The Imaginative, Inspirative, and Intuitive Method of Cognition
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