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 Title: Lecture: Mathematics and Occultism.
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 Lecture: Mathematics
 Mathematics and Occultism
 of Mathematics, from participating in the teachings of the Master.
 to mathematics within the domain of human knowledge. Plato intended to
 “Learn to emancipate thyself from the senses by mathematics,
 of mathematics to natural science. Kant and many others like him, for
 mathematics in our knowledge of Nature. This implies nothing else
 sense that Extension must be understood, the science of Mathematics
 Science as there is Mathematics in It, so it is true that on all the
 realm of mathematics itself, towards the supersensible. This has come
 the mathematics of the infinitely small; nevertheless to the Occultist
 from such perception. And such is the case in mathematics. The latter,
 figures. For them vague faith begins where mathematics end; and
 mathematics itself who can most thoroughly value the true enlightened
 research which advances in the spirit of mathematics even where
 overrating of mathematics. He did not want to have the qualitative
 open to him. Through the schooling in the spirit of mathematics lies
 mathematics is able to understand how the mathematician builds up the
 Title: Mission of Spiritual Science and Its Building at Dornach
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 mathematics, because we are dealing with external space. The lifegerm,
 Title: Lecture: Mathematics and Occultism.
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 Mathematics and Occultism
 of Mathematics, from participating in the teachings of the Master.
 to mathematics within the domain of human knowledge. Plato intended to
 “Learn to emancipate thyself from the senses by mathematics,
 of mathematics to natural science. Kant and many others like him, for
 mathematics in our knowledge of Nature. This implies nothing else
 sense that Extension must be understood, the science of Mathematics
 Science as there is Mathematics in It, so it is true that on all the
 realm of mathematics itself, towards the supersensible. This has come
 the mathematics of the infinitely small; nevertheless to the Occultist
 from such perception. And such is the case in mathematics. The latter,
 figures. For them vague faith begins where mathematics end; and
 mathematics itself who can most thoroughly value the true enlightened
 research which advances in the spirit of mathematics even where
 overrating of mathematics. He did not want to have the qualitative
 open to him. Through the schooling in the spirit of mathematics lies
 mathematics is able to understand how the mathematician builds up the
 Title: Oswald Spengler: Article I: Spengler's "Perspectives of World History"
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 as transparent as those of mathematics, he has moved toward
 Title: History of the Middle Ages: Lecture I: Celts, Teutons, and Slavs
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 Mathematics and Physics, so also we see everywhere in actual History
 Title: History of the Middle Ages: Lecture VI: Culture of the Middle Ages
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 — such as Mathematics, Natural Science, etc. — were not
 Title: Spiritual Teachings of Soul/World: Course IV: Lecture I: Theosophy and Spiritism
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 become a competent mechanic must study mathematics. Who wants to be at home
 Title: Spiritual Teachings of Soul/World: Course III: Lecture I: Theosophical Teachings of the Soul. Part I: Body and Soul
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 anybody to his philosophers’ school who had not learnt mathematics first,
 mental activity which the human being exercises if he does mathematics. However,
 this is clear also to Aristotle that it does not depend on doing mathematics
 rather than on understanding: the human being is able to do mathematics.
 but in mathematics we investigate these, and we apply the world which we have
 soul in the same way as mathematics gets out the truth of the starry heaven
 course first. — Not mathematics is necessary, but a knowledge which has
 described it as the spirit of mathematics as nous which results easily like
 Title: Spiritual Teachings of Soul/World: Course III: Lecture III: Theosophical Teachings of the Soul. Part III: Soul and Mind
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 penetrated into the spirit of mathematics before they tried to take up his teachings
 disciple should have understood the spirit of mathematics. We heard in the first
 lecture what this spirit of mathematics offers. It offers truths in the most
 this way. Mathematics only gives the most trivial supersensible truth, but it
 that they learn in mathematics how one gets to the supersensible truth. What
 in the spirit of mathematics. After they had got used to looking up to truth
 field sees in the eye of pure objective mathematics: without passion, without
 most trivial supersensible truth. Mathematics is widely avoided just because
 is true and eternal in certain way. What appears to us in the language of mathematics,
 Title: Spiritual Teachings of Soul/World: Course V: Lecture II: What Do Our Scholars Know about Theosophy?
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 you can see through the telescope and what you can achieve with mathematics.
 Title: Spiritual Teachings of Soul/World: Course V: Lecture IV: Is Theosophy Buddhist Propaganda?
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 anybody who wants to teach mathematics today does not teach what he himself
 mathematics or physics. What is announced as a principle of wisdom becomes immediate
 mathematics or natural sciences, but it is a lively life. What the science of
 Title: Origin and Destination of Humanity: Lecture XI: Origin and Goal of the Human Being
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 knows this thought only in one single field, in the field of mathematics,
 about soul and spirit. Hence, the mystic also calls mysticism “mathematics”
 – mathesis , not because mysticism is mathematics, but because
 it is built up corresponding to the sample of mathematics.
 to the higher spheres like the thought in mathematics, then you experience
 Title: Origin and Destination of Humanity: Lecture XII: Goethe's Secret Revelation I
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 one does not feel any passion with the truths of mathematics, no quarrel
 Title: Esoteric Development: Lecture VII: The Great Initiates
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 highest thoughts of mathematics and geometry, that have an eternal
 Title: Origin and Destination of Humanity: Lecture XVI: The Great Initiates
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 of mathematics and geometry to which the human being dedicates himself
 Title: Origin and Destination of Humanity: Lecture XX: The Divinity Faculty and Theosophy
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 physics, chemistry, botany, zoology, mathematics etcetera. Not before
 Title: Origin and Destination of Humanity: Lecture XXI: The Faculty of Law and Theosophy
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 of mathematics and mechanics and of that what enables us from the start
 of thinking in all fields as it exists between mathematics, the differential
 one must have studied mathematics before one constructs a bridge. Theosophy
 The natural sciences still go back to mathematics, of course, go back
 that mathematics has real significance only, since the thinking of the
 the social ethics if it is as clear as it is with mathematics which
 some concepts to a clear shape similar to mathematics. Everybody has
 as mathematics proceeds with the bridge building. Nevertheless, life
 Mathematics also does not
 to the legal life, that is positioned to life like mathematics to nature,
 However, the knowledge exists that there is a kind of mathematics, a
 Mathematics is nothing else
 than an internal experience. You can nowhere learn externally what mathematics
 It is not mathematics what we apply to life, but something similar.
 and mathematics.
 in all fields of life according to the pattern of mathematics. If this
 view of law is as impossible as a historical view of mathematics. It
 mathematics, but that one puts together three rods, measures the angles
 Title: Origin and Destination of Humanity: Lecture XXIII: The Arts Faculty and Theosophy
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 in it. Why does one study botany, mathematics, history, for example?
 professor of theology and of mathematics in Vienna. Today, a professor
 in the way that he exercises some mathematics, learns to think quite
 what can he know about mathematics? Only mathematical concepts, having
 no inkling of the fact that mathematics introduces in the great principles
 of arguing. In the Middle Ages, mathematics was regarded as the basis
 world the paradise of mathematics! Where he built bridges, thoughts
 of mathematics from bridge building. The gods want free beings, they
 Title: Two Essays on Haeckel: Essay II: Haeckel, "The Riddle of the Universe," Theosophy
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 know is true, and all higher mathematics are only imaginary
 Title: Riddles of the World: Lecture I: Haeckel, the Riddles of the World and Theosophy
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 true, and the higher mathematics is only a fantastic stuff.
 Title: Riddles of the World: Lecture III: Basic Concepts of Theosophy. Soul and Spirit of the Human Being
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 trivial I can say that mathematics is something that is
 Title: Lecture: Brotherhood and the Fight for Survival
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 had to come, but as little as one can vote in mathematics to obtain a
 Title: Riddles of the World: Lecture VIII: Fraternity and the Struggle for Existence
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 Title: Esoteric Development: Lecture I: Inner Development
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 preconditions are truly necessary. Just as higher mathematics would
 Title: Riddles of the World: Lecture IX: Inner Development
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 incomprehensible as higher mathematics is for the usual farmer
 Title: Riddles of the World: Lecture XVI: German Theosophists at the Beginning of the Nineteenth Century
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 mathematics like a religion. It is something sacred to him.
 something like music with the abstract lines of mathematics and
 Novalis speaking about mathematics. However, you can only take
 space. Mathematics is the access to the infinite truth.
 Title: Supersensible Knowledge: Lecture XII: Richard Wagner and Mysticism
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 Title: Knowledge of Soul and Spirit: Lecture I: The Mission of Occult Science in Our Time
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 mathematics, but because this occult science has the character
 occult science just as mathematics is an occult
 Title: Knowledge of Soul and Spirit: Lecture IV: Initiation
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 today. I can produce evidence. Mathematics, geometry, can
 This is thinking free from sensuousness. Mathematics is not
 mathematics free from sensuousness and create as one can do it
 between the dry abstractions that one puts in mathematics or in
 Title: Knowledge of Soul and Spirit: Lecture VI: The SoCalled Dangers of Initiation
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 Title: Where/How/Spirit: Lecture I: Where and How Does One Find the Spirit?
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 mathematics, for example, gives us something spiritual, for
 example, in mathematics. Nobody can understand by experience
 Title: Goethe's Secret Revelation: Lecture II
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 everyone can in mathematics. But there are methods of purifying
 civilization, in history, in mathematics and all other sciences can
 Title: Where/How/Spirit: Lecture III: Goethe's Secret Revelation  Esoteric
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 Title: Where/How/Spirit: Lecture IV: Bible and Wisdom I
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 mathematics regardless how it has developed in the course of
 Title: Metaporphoses/Soul One: Lecture 3: The Mission of Truth
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 mathematics that humanity in general has reached the goal of truth, for here
 as far with them as they have with mathematics. The truths of mathematics are
 Title: Metamorphoses/Soul Two: Lecture 6: Positive and Negative Man
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 geometry and mathematics cannot be accepted on the authority of another
 Title: Answers to Big Questions: Lecture I: The Nature of Spiritual Science and Its Significance for the Present
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 anybody can allege that the statements of mathematics, of
 who have soared to invent geometries, mathematics purely
 mathematics and geometry and could invent a geometry that
 Title: Answers to Big Questions: Lecture VII: How Does One Attain Knowledge of the Spiritual World?
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 anyhow? Transfer this example on mathematics that somebody may
 say of it: the incomprehensibility of mathematics mostly
 Mathematics, geometry teaches the human being the knowledge of
 what is dry outer science, dry outer philosophy, mathematics,
 Title: Lecture: Galileo, Giordano Bruno, and Goethe
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 Science to Mathematics, which has continued on his lines from
 to any single field; to the field of Mathematics. We see at
 about Mathematics, he will have or to toil at Mathematics for
 years. Then, as you know, man's conception of Mathematics
 Title: Lecture: Hermes
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 was brought down by Hermes into mathematics and geometry and he
 mathematics, geometry, the science of landsurveying and
 Title: Turning Points: Lecture 2: Hermes
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 the people the elements of the science of mathematics, while he
 script, our Mathematics, Geometry, Surveying, our general conduct
 Title: Human History: Lecture XII: Copernicus and His Time in the Light of Spiritual Science
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 that summarised by logic and mathematics what spread out in
 Title: Lecture: Errors in Spiritual Investigation
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 the circle is considered not to know mathematics in this realm.
 Title: Spirit and Matter: Lecture III: Immortality, the Forces of Destiny, and the Course of Life
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 Title: Spirit and Matter: Lecture VI: Life, Death, and Immortality in the Universe
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 of mathematics stop. As absurd as it sounds, but it is true. I
 Title: Truths and Errors: Lecture III: How Does One Defend Spiritual Science?
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 such a way, as I have just characterised: mathematics. Already
 takes place after the same principle as in mathematics that one
 mathematics can decide on whether beings really exist who carry
 of reality. This is the difference, the fact that mathematics
 Title: Truths and Errors: Lecture IV: Truths of Spiritual Research
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 is familiar with mathematics at the same time, for that many
 better mathematics if one possibly wants to count in the things
 real, in particular things of the border area of mathematics. I
 the supersensible world. Mathematics is useful only formally;
 it cannot get to reality. However, mathematics can be
 applied to any other human being. Mathematics has this in
 Title: Truths and Errors: Lecture V: Errors of Spiritual Research  1
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 chemistry, mathematics, or any other science is something that
 Title: Truths and Errors: Lecture VII: The Questions of Life and the Riddle of Death  1
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 medallion. Mathematics shows such symbols of regularities
 Title: Freedom/Immortality/Social: Lecture VIII: How Natural Sciences Justify the Supersensible Knowledge
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 hours that I did the very best progress in mathematics or
 Title: Thomas Aquinas: Lecture III: Thomism in the Present Day
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 mathematics, but in the proof develop ourselves at the same
 gets in mathematics? And he gets such certainty in a manner
 Title: Redemption of Thinking: Lecture III:
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 certainty, as it exists in mathematics? He gets to such
 Title: Fruits/Anthroposophy: Lecture 6: From Imaginative Knowledge to Inspirational Knowledge
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 spirit and with the lucidity we know in mathematics, not with a dreamy,
 working with geometry and mathematics. The work which has to be done
 Title: Lecture: Paths to Knowledge of Higher Worlds
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 mathematics above all as an excellent example for the scientific
 What particular result can the human soul gain through mathematics?
 mathematics can be inwardly surveyed, is inwardly transparent, and
 that mathematics contains, as it were, nothing to which we submit
 The spiritual science of Anthroposophy is naturally not mathematics.
 penetrates into mathematical thought. It is not mathematics in itself
 Title: Lecture: The World Development in the Light of Anthroposophy
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 mathematics, so that it is out of the question to speak of
 Title: Foundations of Anthroposophy: Lecture III: World Development in the Light of Anthroposophy
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 study of mathematics, so that it is out of the question to
 Title: Lecture: The Renewal of Culture
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 through mathematics and natural science — there is spirituality.
 Title: for Renewal: Lecture I: Anthroposophy and Natural Science
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 where pure mathematics aren't applied, but thoughts steered
 of mathematics. The Kantian saying claims that there is only as
 much certainty in a science as there is mathematics contained
 within it. Now obviously mathematics can be introduced into
 I have in mathematics, when I created a concept of function. It
 mathematics has been brought into the sphere of science.’
 previous inner scrutiny. That is so with all mathematics.
 is this particular kind of mathematics which Goethe regarded as
 mathematics fruitfully to all natural phenomena. This resulted
 Title: for Renewal: Lecture II: The Human and the Animal Organisation
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 we create mathematics and we believe we have a purely apriori
 science. However, mathematics is no pure apriori science. We
 in our earliest childhood reflects later in us as mathematics;
 visible as mathematics and mechanics. We often take mathematics
 Title: Lecture: The Position of Anthroposophy among the Sciences
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 of mathematics among the sciences has already been mentioned. Kant's
 mathematics, is widely known. Now I have not to deal here with
 mathematics itself, with its value for the other sciences and in
 characterise it by speaking, first, of that branch of mathematics
 mathematics, although it remains unnoticed. (I have given a
 (in which mathematics is our sure guide), and will open up a new
 mathematics in the right frame of mind, we come to see precisely in
 For mathematics is simply the first stage of supersensible
 now describing is not formal mathematics, but the reality of spiritual
 mathematics — which does not, of course, work in a material way
 applies mathematics as it has been elaborated to date. But anyone who
 branches of mathematics are related to their axioms. The primary
 the formalism of mathematics, while it nevertheless learns from
 mathematics inner certainty and exact observation, regarding
 what is most certain: namely, mathematics, recognised as
 Title: Tension Between East and West: Lecture 1: Natural Science
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 mathematics to natural processes. Why is this? It is
 mathematics. This is exaggerated if we are thinking of ordinary
 mathematics. And yet, when we apply these to lifeless natural
 with mathematics what otherwise stands outside us. Why? Because
 mathematics is experienced inside us with immediate certainty:
 of mathematics, we can penetrate into the facts and
 that of mathematics with which to penetrate into the higher
 we have mathematics, geometry; for the organic, the
 them: not with the ordinary mathematics of numbers and figures,
 penetrating with mathematics of this kind into worlds that we
 quantitative mathematics, in the broadest sense, that can
 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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 comprehended with ordinary mathematics and geometry: living
 outlook, yet one as exact as ever mathematics or mechanics can
 creation, and unless from a qualitative mathematics we
 Title: Lecture Series: What was the Purpose of the Goetheanum
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 Title: Spiritual Development: Lecture I: The Inner Experience of the Activity of Thinking
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 exercises if one has had some practice in mathematics,
 field of mathematics if, for instance, one makes a mental
 Title: Theosophic/Esoteric Cosmology: Spiritual Cosmology
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 mathematics you don't have the necessary knowledge to verify this
 Title: Lecture: Richard Wagner and Mysticism
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 thought to be akin to mathematics but because it was known that the
 Title: Temple Legend: Lecture 7: The Essence and Task of Freemasonry from the Point of View of Spiritual Science  1
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 knowledge of our presentday mathematics. We behold the wonderful
 Title: Temple Legend: Lecture 11: Concerning the Lost Temple and How It Is To Be Restored  1
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 mathematics. Then he will have to learn how it is to be made,
 Title: Temple Legend: Lecture 20: The Royal Art in a New Form
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 want to learn mathematics, I must occupy myself with it, and gain an
 Title: Foundations of Esotericism: Lecture XXI
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 thoughts, that is in mathematics. When people calculate, their
 they have no love for mathematics. Here one cannot vote in
 emotion, as objectively, as in mathematics. In Europe one can only
 thoughts and introduce the spirit of mathematics into higher regions.
 Title: Third Lecture: The Gospel of St. John
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 teaching them higher mathematics, I would be teaching them
 Title: Theosophy/Rosicrucian: Lecture I: The New Form of Wisdom
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 teacher of mathematics to his students. Can it be said that the
 student of mathematics depends upon his teacher simply out of belief
 in authority? No! And can it be said that the student of mathematics
 little accept them on authority as in mathematics he need accept on
 mathematics, in philosophy, or in practical life. The difference in
 Title: Theosophy/Rosicrucian: Lecture VII: The Technique of Karma
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 talent — herein lies the gift for mathematics. This is a physical
 Title: Theosophy/Rosicrucian: Lecture XIV: The Nature of Initiation
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 Study in the Rosicrucian sense is the ability to immerse oneself in a content of thought not taken from physical reality but from the higher worlds. This is called the life in pure thought. Modern philosophers for the most part deny this; they say that every thinking must have a certain vestige remaining from sense perception. This, however, is not the case, for no one, for example, can see a true circle; a circle must be seen in the mind; on the blackboard it is only a collection of tiny particles of chalk. One can only attain to a real circle if one leaves aside all examples, all actual things. Thus thinking in Mathematics is a supersensible activity. But one must also learn to think supersensibly in other fields.
 Title: Theosophy and Rosicrucianism: Lecture XIII: The Rosicrucian Training
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 mathematics must be grasped independently of all sensory
 with the circle. Through mathematics we learn to think of the
 Title: The Influence of Spiritual Beings Upon Man: Lecture IX
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 of mathematics alone, for these are the most trivial of all. No one
 Title: Gospel of John: Lecture IX: The Prophetical Documents and the Origin of Christianity
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 just as anyone wishing to learn mathematics at present does
 mathematics have first been communicated. What, for example,
 Title: Gospel of John: Lecture X: The Effect of the Christ Impulse Within Mankind
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 mathematics. Men agree upon these mathematical truths at
 Title: Apocalypse of John: Introductory Lecture
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 instruction is related to the books on mathematics which have
 history versed in mathematics, namely, the geometry of
 been taught mathematics and geometry will value and
 Title: Universe/Earth/Man: Lecture II: Ancient Wisdom and the new Apocalyptic Wisdom
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 applying himself to mathematics and one who does not. Suppose two
 difference between a man who likes mathematics and one who does not.
 Title: Universe/Earth/Man: Lecture XI: The Reversing of Egyptian Remembrance by way of Arabism.
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 mathematics to him; it gave him the musical secrets of the world in
 the harmony of numbers. Mathematics, which is only something abstract
 Title: Egyptian Myths: Lecture 9: The Influence of the Sun and Moon Spirits, of the Isis and Osiris Forces. The Change in Consciousness. The Conquest of the Physical Plane.
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 arose geometry, mathematics. With the help of this, man could rule the
 Title: Lecture Series: Novalis
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 knowledge of law and mathematics was necessary. He became a
 spiritual being allowed mathematics to penetrate into his inner
 When mathematics showed him how it is suitable for the
 when he dived into numbers and sizes. For him mathematics
 power and crystallize out there. Mathematics became for his
 people, who only know mathematics from outside, it remains
 Title: Lecture: The Theory of Categories / Kategorienlehre
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 only arrived at pure concepts in mathematics. Most men, of
 Title: Principle/Economy: Lecture IV: Results of Spiritual Scientific Investigations of the Evolution of Humanity: I
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 Title: The East in the Light of the West: Lecture II
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 mathematics or geography today by means of old documents, written in
 Title: The East in the Light of the West: Lecture IV
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 present time can be studied at its source; even mathematics may also
 Title: Macrocosm/Microcosm: Lecture 8: Mirrorimages of the Macrocosm in Man. Rosicrucian Symbols.
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 entrusts himself to a tutor in mathematics. If he did not assume that
 case of those given by a tutor in mathematics, only now our whole soul
 Title: Mission/FolkSouls (1929): Lecture 3
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 only able by means of abstractions such as the truths of mathematics,
 Title: Mission/FolkSouls (1970): 3. The inner Life of the Folk Spirits. Formation of the Races.
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 the logic of mathematics you will have some idea of how the
 mathematics. These truths are the normal experiences both of man and
 Title: Excursus Mark: Part I: A Retrospect
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 path leading to mathematics, to botany, or any other branch of
 Title: Background/Mark: Lecture One: On the Investigation and Communication of Spiritual Truths
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 let us say, that of mathematics or botany or some other
 Title: Excursus Mark: Part III: Excursus: Lecture III
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 the case of mathematics, for instance, or any other science, that
 Title: Background/Mark: Lecture Five: The Two Main Streams of PostAtlantean Civilisation
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 for granted that in mathematics and science some grounding is
 Title: Lecture: The Concepts of Original Sin and Grace
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 inherited the principles of mathematics or other such concepts from
 Title: Wonders of the World: Lecture 3
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 could not explain according to the strict laws of mathematics and
 Title: Wonders of the World: Lecture 3
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 could not explain according to the strict laws of mathematics and
 Title: Lecture: On the Occasion of Goethe's Birthday
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 in our day, — I mean mathematics, although even here we
 carried on in certain branches of mathematics during the
 Title: Esoteric Christianity: Jeshu ben Pandira  Lecture 1
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 study a book of mathematics, for instance. This will help us to fall
 Title: Lecture: Jesuit and Rosicrucian Training
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 Title: From Jesus to Christ: Lecture I: Jesuit and Rosicrucian Training
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 dispute over mathematics, because we have raised mathematics entirely
 Title: Evolution/Aspect: Lecture 1: Introductory Lecture
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 distinguish an Eastern and a Western system of mathematics; yet some
 Title: Introductory Lecture. Winter Session
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 and Western mathematics. But on account of intrinsic characteristics,
 Title: FormCreating Forces
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 individuality. Mathematics in itself is an illustration of this fact.
 no different from a teacher of mathematics, who quite obviously has
 his function. But mathematics are not accepted merely on the authority
 of the teacher of mathematics; every individual accepts mathematics
 an affair of humanity, like mathematics — not the affair of any
 Title: Reincarnation and Karma: Lecture I
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 for mathematics at all. If we wish to discover what gifts we may
 may happen that a man had a special talent for mathematics in a
 with a talent for mathematics and this will represent a continuation
 mathematics. I knew a man who had so little gift for mathematics that
 a gift for mathematics.
 to be appointed Professor of Mathematics in the University of
 Title: Reincarnation and Karma: Lecture V
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 chemistry or mathematics. How an individual assimilates Anthroposophy
 Title: Lecture 3: Spiritual Beings in the Heavenly Bodies and in the Kingdoms of Nature
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 mathematics, numbers and calculation. The fact that three times three
 inner being. In dry, prosaic mathematics begins what we may call
 begins with dry mathematics, because most people take dry mathematics
 Indeed education through mere mathematics is very good. For instance,
 individual, but mathematics and moral obligations do not depend on
 Title: Man/Light of Occultism: Lecture I.
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 symbols. Those of you who know mathematics will readily
 occultism, — any more than there are different mathematics. It is
 we can imagine there might be different standpoints in mathematics.
 Title: Effects of Occult Development: Lecture IV
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 to mathematics, the evening hours to poetry. We are now living
 Title: Secrets/Threshold: Lecture IV
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 mathematics. At one time the university Math departments were
 the realm of mathematics. What actually is he demanding? If we know
 Title: Human and Cosmic Thought: Lecture II
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 real science as there is mathematics. This means that from being a
 Title: Human and Cosmic Thought: Lecture Two
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 real science as there is mathematics. This means that from being a
 Title: Presence of the Dead: Lecture One: Understanding the Spiritual World (Part One)
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 mathematics, not only as far as we know it today, but also everything
 read the mathematics contained there and read it consciously, we
 Title: Presence of the Dead: Lecture Seven: Robert Hamerling: Poet and Thinker
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 examination. He had good grades in Greek, Latin, and mathematics.
 Title: Esoteric Development: Lecture X: The Three Decisions on the Path of Imaginative Cognition
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 same time. Nor can ordinary calculation, physical mathematics, be
 Title: Destinies of Individuals and Nations: Lecture 8: Three Decisions on the Path to Imaginative Perception
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 Title: Destinies of Individuals and Nations: Lecture 10: Problems on Spiritual Path  National Characteristics in Europe Moulded by Folk Spirits
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 Title: Lecture Series: Meditation and Concentration
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 our head. Instead of mathematics, logic metaphysics, we
 Title: Chance/Necessity/Providence: Lecture 1: Probability and Chance
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 been what is called in mathematics the calculus of probability. It's
 Title: Necessity and Freedom: Lecture V: The "I" is Found on the Physical Plane in Acts of Will
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 more a matter of mathematics and geometry. Just as today we can
 Title: Things Past and Present: Lecture V: Comenius and the Temple of PanSophia
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 external is geometry and mathematics. That person who today
 allows geometry and mathematics to work upon him in a true
 mathematics, a different kind of knowledge from the other
 something within geometry and mathematics which one can
 mathematics goes back to a much more ancient knowledge than
 Title: Toward Imagination: Lecture 6: The Feeling For Truth
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 professor of physics and mathematics at the Vienna Agricultural College,
 Title: Karma of Vocation: Lecture VIII
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 instruments, was also familiar with geometry and mathematics,
 humanities with a monk, learned mathematics from his father
 mathematics and mechanics, he continued to excel in these
 country, teaching mathematics and also practicing medicine, of
 he lectured on mathematics for sixty scudi a year and also
 lectured with great distinction on mathematics and related
 Title: Karma of Untruthfulness II: Lecture Twenty Five
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 As yet they are unable to do this. They attend lectures on mathematics,
 Title: Fall/Darkness: Lecture 13: The Fallen Spirits' Influence in the World
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 Goethe's Faust, mathematics, mechanics and technology at
 again in the late 70s. In between he spoke only on mathematics,
 teaching the exact sciences of mathematics, physics and
 that someone who had used physics, mechanics, mathematics and
 Title: Mysteries of Ancient and Modern Times: Lecture 1
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 Mathematics. The latter were strictly preserved and guarded;
 Title: Mysteries of Ancient and Modern Times: Lecture 2
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 mathematics, it is no doubt impossible to stir your heart and
 an abstract mathematics. Yet this is what humanity needs to
 Title: Ancient Myths: Lecture VII
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 calculate by mathematics or mechanics. But what was formerly
 often quoted it — ‘Mathematics is in truth a great poem’.
 But in order to see how mathematics, by which one also calculates the
 poetry of mathematics. For mathematics is phantasy. Mathematics is
 with the immediate external reality. Mathematics in fact is Maya
 but learns to know mathematics in its substance, learns to know
 Title: The Earth As Being with Life, Soul, and Spirit: Lecture 2
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 Mathematics is certainly spirit, indeed pure spirit; but employed
 world, as there is mathematics. But from the other point of view,
 Title: Life Gifts: Lecture II: The Relativity of Knowledge, and Spiritual Cosmology
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 Certainly mathematics do belong to the realm of the spirit, pure
 world as there is mathematics.” But one might also say, from
 Title: Life Gifts: Lecture III: Thoughts about the Life Between Death and Rebirth
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 Science as we might perhaps take up mathematics, but we shall
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 put everything into terms of mathematics, which really can only be rightly understood if we take
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 mathematics, physics, chemistry and especially for projective
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 mathematics, and I can, therefore, build a great railway
 of mathematics, of mechanics, of dynamics. Thus must a person
 Title: How Can Mankind Find Christ Again?: Lecture 5
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 through mathematics. In saying this, no particular objection is intended
 to external mathematics; it can even shed light on many things —
 Title: How Can Mankind Find Christ Again?: Lecture 8
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 people love mathematics. Certain rules are established and the rest
 is on mathematics or botany or politics or socialism or anarchy; that
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 say, of chemistry, physics, mathematics, is of course true and these
 the point is not that the truths of chemistry and mathematics are true
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 earth's environment in terms of mathematics, but they have
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 earth's environment in terms of mathematics; but they have not
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 of friends bought themselves books on mathematics. A kind of
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 Title: Social Basis For Primary and Secondary Education: Lecture III
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 convenience of the college of teachers, let us say mathematics,
 but mathematics from morning to evening; I mean it in the sense of what I
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 Title: Lecture: The Ahrimanic Deception
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 with mathematics, with the science of mechanics. What lies around the
 worldmathematics, mere worldschematism of a mechanical order, does not
 instructing men in mathematics, but not in instructing them that
 Title: Mission of Michael: Lecture IV: The Culture of the Mysteries and the Michael Impulse.
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 such as mathematics and geometry, which are employed in the endeavor
 receive the inner perception of mathematics. Mathematics arises below
 mathematics — this is the purely Ahrimanic element, which arises
 we know that mathematics is correct; but this sovereign correctness of
 mathematics we owe to Ahriman who sits in us. The most uncertain
 through logic and the Ahrimanic wisdom through mathematics, geometry,
 Title: Knowledge of Healing: Lecture II
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 knowledge, developed by man himself, chiefly in mathematics, knowledge,
 unconcerned attitude usually adopted towards mathematics. It is not
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 most that which is given him in mathematics and mechanics, and now in
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 most that which is given him in mathematics and mechanics, and now in
 Title: Roman Catholicism: Lecture I
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 free scientist. After having argued at length that even mathematics
 of science because one is bound by the truths of mathematics, he goes
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 In mathematics it is a matter of indifference whether some object is a
 Title: Man: Hieroglyph: Lecture Five
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 There simply does not exist such a thing as mathematics calls
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 the truths of mathematics. These are certainly evident though
 Title: Lecture Series: Hegel, Schopenhauer, Thought, Will
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 natural laws and we can practically only use mathematics to
 Title: Lecture: The Souls Progress through Repeated Earth Lives
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 the following: All that we conceive as mathematics, all that comes
 into some kind of unintelligible expression. Mathematics is said to
 The astral body has gone through the mathematics of the whole
 Title: The Moral as the Source of WorldCreative Power
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 machine in terms of mathematics and the principles of mechanics, or
 Title: Young Doctors Course: Bridge Lecture 2: The Moral as the Source of WorldCreative Power
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 exactitude we envisage a machine in terms of mathematics and
 Title: The Path to Freedom and Love and their Significance in World Events
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 mathematics. Mathematical thinking streams up entirely from our
 inner being, but it has a mirrorexistence only. Through mathematics
 had a dim inkling that we bring mathematics with us from our existence
 before birth, and therefore they called the findings of mathematics
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 Title: Search for the New Isis: Lecture I: A Christmas Lecture
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 it has become cold and gray mathematics and geometry. Today we see
 mathematics. This is the last remnant of that which in the
 mathematics again through inner experience to that glory which the
 Title: Search for the New Isis: Lecture III: The Magi and the Shepherds: The New Isis
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 mechanics, of mathematics.
 into our modern mathematics and mechanics.
 mathematics and mechanics. The faculties of outer and inner
 faculty that is now dry mathematics may intensify pictorially to
 into mathematics, into geometry, into the science of mechanics. But
 from mathematics, phoronomy and geometry, this means the finding of
 Title: Search for the New Isis: Lecture IV
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 mathematics being fulfilled in the cosmos and to which every star was
 mathematics, abstract mechanics or phoronomy — the
 spiritfilled vision of the heavens has become abstract mathematics
 Kepler, as if they were intelligible as a mere object of mathematics
 mathematics’ which is none other than ancient astronomy or, if
 developed, and the mathematics and mechanics into which the old
 consciousness that otherwise occurs only in mathematics with its
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 mathematics. What plays with a higher significance into man's inner
 possible. Nor could mathematics or geometry be grasped in the way they
 in mathematics which, in utter contrast to the vast majority today,
 described as the three Magi from the East. The mathematics of the
 through the mathematics imparted to them?
 mathematics comes from within ourselves, rises into consciousness from
 origin of mathematics.
 mathematics. In that other existence my own inner forces led me from
 birth. In our mathematics this has become pure abstraction. But the
 None really comprehend mathematics who do not undertake the study
 "Mathematics and physics are the two theoretical sciences of reason
 Title: Lecture: The Two Christmas Annunciations.
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 mathematics as we know them could not then exist. The whole of life
 our geometry and mathematics. Euclid was the first to give geometry to
 sensed when he felt mathematics to be like great poetry —
 The mathematics of the universe, which have become so thoroughly
 introduction of mathematics into their soulcondition, when this was
 found especially mature and ready? Kant speaks of mathematics as being
 mathematics is something that rises up within us, that rises to
 that when he does mathematics, experiences of the time before
 mathematics is.
 symbolize in mathematics. With my innermost forces I moved from star
 Magi? It has become our mathematics, with its knowledge of the
 that we apply nothing but the laws of mathematics and mechanics to
 but slight resemblance to its mother. And our mathematics, our
 The wisdom of the Magi too has become dry mathematics, perceiving the
 has become abstract in our mathematics. But the very same forces out
 of which we develop mathematics can be brought back to life, and
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 Mathematics, — can be furnished by the intellect, but not
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 all that developed as mathematics, as modern natural science
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 mathematics out of his head, or from somewhere or other (ideas on the
 subject are not very precise). But it is not so. Mathematics derives
 you will get to know the sphere from which mathematics comes. It is
 mathematics lives at a deeper level than our ordinary soullife. And
 thus we see that mathematics is really rooted in that part of us which
 Title: Man as a Being: Lecture 2
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 the scientific spirit that tries to apply mathematics to everything.
 Mathematics, as I explained to you yesterday, comes from the senses of
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 partiality for mathematics, for geometry, for mechanics.
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 terms of mathematics and mechanics. We look at the stars through
 worldmachinery which can be expressed in terms of mathematics.
 the Earth can be explained in terms of mathematics and mechanics. In
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 or, over and above that, in mathematics. Here we really do restrict
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 which at present holds good only for mathematics; we shall be able to
 What we do today only when we are thinking in terms of mathematics, we
 the human soul. The study of mathematics does not, as a rule, give
 mathematics. For Novalis, the science of mathematics was a great and
 devout mood of soul when studying mathematics!
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 mathematics all the numbers were contained in the unit. This
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 Or he could say to himself: When I do mathematics I create
 thoughts purely out of myself. Properly understood, mathematics is
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 become only a superstructure of Natural Science gained by Mathematics,
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 way that mathematics or natural science is exact. But I should
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 the scientific thinking we utilize in mathematics or natural
 of mind as is only developed in mathematics or the exactness of
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 nineteenth century, it was wellnigh only mathematics. That was the
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 mathematics; but the human being must bring along something, for
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 in mathematics because method alone has been followed, is
 Title: Preparing for a New Birth
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 of numbers. The other was a mathematics student. Now, we know
 that at certain moments in the study of mathematics, you do
 pleased with himself, while the mathematics student was not,
 student woke up and saw the mathematics student get out of bed
 when they both got up, the mathematics student said, “We didn't
 Title: Lecture: Gnostic Doctrines and Supersensible Influences in Europe
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 mathematics and its kindred sciences, all of which are the legacy of
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 spiritual world we find that our mathematics and geometry are no
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 in relation to space and time we can grasp through mathematics. When
 nature and from the laws of mathematics — from the latter laws
 threedimensional space. It has its own mathematics, following
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 Yes, the mathematics, the intellectual element, was the same in the
 Title: Karmic Relationships, Volume I: Lecture VII
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 mathematics, including branches of knowledge such as political
 on a variety of subjects: national economy, philosophy, mathematics.
 political economy, in mathematics itself, he thinks mathematically,
 thinks with clarity but, again, in terms of mathematics. He is not a
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 physics and mathematics, especially by the treatise Neue
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 onesided. A geometrician knows the whole of mathematics; when he
 generally realised) that man does not get geometry or mathematics out
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 sciences or mathematics. But the very curious thing is this, so curious
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 — mathematics, philosophy, architecture, commerce, industry,
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 deeply versed in mathematics. He lived at a time when all descriptive
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 understood), Geography, Mathematics, Poetry, Chemistry, Medicine,
 Title: True/False Paths: Lecture Nine: Abnormal Paths into the Spiritual World and their Transformation
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 along and say: I understand nothing about mathematics so I cannot say
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 along and say: I understand nothing about mathematics so I cannot say
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 conversant with the whole range of higher mathematics at that
 “differential” in mathematics is the atomic, the
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 rationalistic science of today, particularly mathematics, which is
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 objective mathematics, objective chemistry, that it is working toward
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 objective mathematics, objective chemistry, that it is working toward
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 complete rebirth of chemistry, physics, mathematics, and so on,
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 corresponding fashion any truth from the realms where mathematics and
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 regions, where mathematics are no longer valid and the senses
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 has become purely a business in which physical mathematics is simply
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 that men carry the mathematics of earth up into the stars of
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 to encompass mathematics and astronomy. And the last, for the
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 realm of mathematics and astronomy it comes from her. You,
 instruction — by means of mathematics. Everything which
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 currencies, down to what in mathematics is termed the
 point, as they say in mathematics, will have a definite part
 Title: Esoteric Lesson: Berlin, 1903 or 1904
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 can understand mathematics out of one's own intellectual forces and
 mathematics as one tries to develop one's intellectual forces. The
 Title: Esoteric Lesson: Berlin, December 1904
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 can understand mathematics out of one's own intellectual forces and
 mathematics as one tries to develop one's intellectual forces. The
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 sphere of knowledge, unless it be Mathematics, that there
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 its own particular medium. In speaking about mathematics, mechanics,
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 in the depths just as it contains the secrets of mathematics,
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 reality which transcends all abstract mathematics or systems
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 those which approach, one might say, the most abstract Mathematics,
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 lifeless mathematics. It is true Hegel used more pregnant concepts
 Title: Colour: Part Two: The Connection of the Natural with the MoralPsychical. Living in Light and Weight.
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 possibility does not exist; things especially like Mathematics, etc.,
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 Mathematics or Mechanics or Physics from artistic sensibility, but
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 In physical mathematics it is a matter of indifference to divisions
 Title: Practical Course/Teachers: Lecture XII: How to Connect School with Practical Life
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 Title: Education as a Social Problem: Lecture VI: The Inexpressible Name, Spirits of Space and Time, Conquering Egotism
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 Title: Spiritual Ground: Lecture III: Spiritual Disciplines of Yesterday and Today
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 To be sure the multiplication table is not the whole of mathematics,
 and integral calculus is built up on elementary mathematics, — it
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 working at mathematics I evolve thoughts purely out of myself.
 Mathematics in the real sense is a web which I spin out of my
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 intellectual element can be given the child too soon. Mathematics as
 operations of mathematics are not foreign to human faculty in the way
 arithmetic and mathematics in the right way. And what this is can
 with mathematics in the right way during these past years we should
 Title: Child's Changing Consciousness: Lecture IV
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 pervades every subject, even mathematics. This fundamental
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 essentially the same as the principles of mathematics and
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 mathematics and physics at the Waldorf school in Stuttgart.]
 effects. Mathematics is built on purely causal sequences, so it
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 cases until about the age of twenty — so mathematics and
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 geometry, indeed all mathematics, occupy a unique position in education.
 physics and mathematics written by Dr. von Baravalle (a teacher at the
 chiefly with higher mathematics. If we penetrate to its underlying
 essence, it is a splendid guide for teaching mathematics in a way
 teaching mathematics and physics from earliest childhood up to the
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 name or another: Diploma in Geometry or Mathematics or whatever
 mathematics for instance, who boasted of the fact that when
 Title: Human Values in Education: Lecture X
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 Title: Kingdom of Childhood: Lecture 5
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 in spiritual life isdone from the body. Mathematics are done by the
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 There are indeed points of view better than the mathematics of
 Title: Lecture XV ...... Spiritual Science and Medicine
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 other hand, individuals with a certain aversion to mathematics,
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 physics, mathematics, chemistry, physiology, biology, anthropology.
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 mathematics the point has been reached of hatching such hypotheses or
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 maybe to the attainment of mathematics or geometry. In fact we
 same way as we do with regard to mathematics or geometry, only
 Title: Art of Healing: Lecture I
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 as any method leading maybe to the attainment of mathematics or
 mathematics or geometry, only in Anthroposophy we are not
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 he knew what is the only possible relation of Mathematics to Natural
 Science, though Mathematics be ever so idolized even for this domain
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 mathematics, in our geometry, in our ideas of movement. These
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 sort of thing. I mean all that is obtained from pure mathematics. Such
 priori, to speak of them as we do in mathematics. When you go over to
 Title: Warmth Course: Lecture VII
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 see that in this way we can suffuse mathematics with vitality? The
 Title: Warmth Course: Lecture XI
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 heat is related to the application of mathematics and how it affects
 Title: Warmth Course: Lecture XII
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 interesting parallelism between thinking in mathematics and thinking
 different. Within mathematics, unless the matter slips us because it
 cannot apply mathematics if we wish to enter reality unless we keep in
 mathematics of physics, and aside from the cases where negative
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 formulae, into the transparent language of mathematics.
 movements wholly intelligible in terms of mathematics. Hence there arose
 of lucid mathematics. This was a striving that climaxed in the last
 mathematics, in all explanations, proceeding all the way up to the explanation
 world view within the lucid realm of mathematics, while on the other
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 man into a cog in a social order modeled on mathematics or mechanics
 mathematics, of the number, weight, measure, or temporal relation that
 within our systematic science of nature as a whole do mathematics, do
 judgment? How do we arrive at a science of mathematics, at a science
 of mechanics? How is it, then, that this mathematics, this mechanics,
 Title: Boundaries of Natural Science: Lecture III
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 to our use as an immediate necessity: mathematics and that part of mechanics
 comprehended by mathematics and analytical mechanics, we have before
 the notions of mathematics and analytical mechanics, this process within
 manner and the more inward mode of apprehension we find in mathematics
 conceive mathematics today — and that which leads over into
 this phenomenon of mathematics as such. We comprehend mathematical truths.
 fabric of mathematics out of these axioms and then stand before an
 we must see in this fabric of mathematics something that arises through
 experience. We thus must ask: where does mathematics originate? Nowadays
 how is this inner activity of the soul that we need in mathematics,
 in the wonderful architecture of mathematics — how is this inner
 is it, then, that we acquire when we engage in mathematics? We want
 is that which manifests itself as the ability to perform mathematics
 as the ability to perform mathematics and something like mathematics
 to the change of teeth, the soul faculties enabling one to perform mathematics
 same way we must be entirely clear that the capacity to perform mathematics,
 the nature of mathematics — mathematics taken, of course, in the
 seventh year there works an inner mathematics, an inner mathematics
 not abstract like our external one but full of active energy, a mathematics
 “latent mathematics”
 Maximum number of matches per file exceeded.
 Title: Boundaries of Natural Science: Lecture IV
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 pellucid is that of mathematics and analytical mechanics.
 in the soul as mathematics, as analytical mechanics, actually rests
 the same spirit from which we now draw only mathematics and analytical
 training, nevertheless sensed the essence of mathematics so clearly
 reveals the same inner necessity as mathematics and analytical mechanics.
 Goethe did have this — of the true inner structure of mathematics.
 discipline, as, for example, mathematics or analytical mechanics.
 to consciousness in the same way that mathematics or the faculties and
 structure of mathematics, I flew in the face of every kind of philosophy
 can be experienced when one performs mathematics in the right way, when
 this performance of mathematics itself becomes an experience that can
 his experiences of an inner mathematics in the Vedanta. This path is
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 occurs unconsciously), when one enters into this “living mathematics,”
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 as mathematics and analytical mechanics. On the other hand, spiritual
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 philosophers who maintain this have never really studied mathematics
 in mathematics. Many thus would deny the existence of the very faculty
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 have never really studied mathematics, or gone into the
 himself to any special training in mathematics. Many would deny
 Title: Astronomy Course: Lecture I
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 Biology, of Mathematics, and so on. Special branches have
 mathematics and mechanics. In observing the phenomena, men
 fashion without understanding mathematics or mechanics, we
 Mathematics satisfies this requirement, at least in most
 in mathematics and mechanics men think they
 only so much real science as there is mathematics in
 mathematics. We may talk to him perhaps of the need for a
 we have seen, everything outside mathematics, mechanics and
 i.e., one who is master of higher mathematics —, and a
 now suppose that you have become an expert at mathematics,
 were taught to use his mathematics in actual life, then he
 Title: Astronomy Course: Lecture II
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 grasped through mathematics and mechanics, while
 dealing with them anything of the nature of mathematics or
 phenomena merely through the mathematics which we apply to
 mathematics, can thus be foretold. One system is as well
 Mathematics is something that ascends from our inner
 being; in mathematics we lift ourselves out of external
 Title: Astronomy Course: Lecture III
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 the cosmic Mathematics indwells man. Man is himself in the
 midst of the living Mathematics. Of this we shall speak more
 Title: Astronomy Course: Lecture IV
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 mathematics reminds me of a scene in which I was once a
 sciences, Mathematics, to the celestial phenomena, and in the
 Mathematics in Astronomy we come at one point into chaos. And
 the standpoint of Mathematics. It appeared that at one point
 encounters too in purely formal Mathematics. Now there is
 application of mathematics to reality. How do we proceed? We
 develop Mathematics as a formal science and it appears to us
 see that Mathematics is only applicable to outer reality on
 to continue Mathematics beyond certain limits. First, certain
 inductive laws, developed within Mathematics. They
 those encountered by anyone who studies Mathematics. In
 Mathematics of today, and are used as a basis for further
 if I take Mathematics as constituting reality, for
 Title: Astronomy Course: Lecture V
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 Title: Astronomy Course: Lecture VII
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 do, in quantitative treatment? Mathematics is the obvious
 world with the premises of Phoronomy and Mathematics, and we
 of our Euclidean Mathematics would be at most a kind of
 indeed a kind of qualitative Mathematics. How, then, shall we
 modern Mathematics, but a form of space derived from the
 Title: Astronomy Course: Lecture IX
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 mathematics and to show you how, in a different domain from
 Mathematics itself this element of the incomprehensible, the
 where the mathematics itself confronts us with what I called
 cannot remain in space. So you see, Mathematics itself
 of space. Even in Mathematics therefore we are confronted
 that most people who concern themselves with mathematics take
 treatment of Mathematics as subject matter for education any
 Mathematics, where — as in Synthetic Geometry —
 dear friends, when you apply Mathematics in one way or
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 first. In this way you can create, even in mathematics
 mathematics capable of dealing with realities; and it is
 Title: Astronomy Course: Lecture XI
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 kind of qualitative mathematics, learned from the human form
 still farther. Ordinary mathematics, reckoning in the main on
 mathematics and geometry as such, by thinking of the
 Title: Astronomy Course: Lecture XII
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 fresh extension of mathematics. You are led to recognise a
 Title: Astronomy Course: Lecture XV
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 in mathematics generally. It cannot be objected that the
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 mathematics in general and the way we are applying this
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 Title: Anthroposophy Science: Lecture I
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 nature, experimentation, and the use of mathematics to establish
 entire field of natural science through mathematics, and with
 mathematics.
 mathematics must be introduced. Through this, one feels
 accompanying the use of mathematics will lead us to
 only so much real knowledge as there is mathematics? How
 modern psychology, by the use of mathematics, has developed
 introduce mathematics into actual knowledge.
 mathematics to the facts of the outer senseaccessible world?
 mathematics.”
 mathematics, or in the field of analytical or synthetic
 mathematics? — how is this knowledge related to
 mathematics contained in it. And, I repeat, this is a
 permeate empirical facts with mathematics, our activity
 mathematics in relation to the outer world, but if we are
 correct use of mathematics. It was not for nothing that Plato
 good grounding in the knowledge of geometry and mathematics.
 what really happens in a man when he does mathematics or
 did not mean by this that God just created with mathematics,
 he who understands the place of mathematics in the whole
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 nature, experimentation, and the use of mathematics to establish
 science that is free of mathematics to one that includes it.
 Title: Anthroposophy Science: Lecture III
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 nature, experimentation, and the use of mathematics to establish
 our mathematics can be characterized as purely pictorial. One
 why we really know that when we work in mathematics we are in
 field of pure mathematics.
 mathematics to outer nature (at first we can hardly do
 with mathematics — not so much in order to reach
 usually applied with the help of mathematics to the external
 manner as with mathematics in the inorganic realm, I can
 ordinary mathematics are in the face of what is taking place
 Title: Anthroposophy Science: Lecture IV
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 nature, experimentation, and the use of mathematics to establish
 and algebraic mathematics to approach plant growth and plant
 it we can proceed. We experience clarity as in mathematics
 possibility, through a higher kind of qualitative mathematics
 Title: Anthroposophy Science: Lecture V
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 nature, experimentation, and the use of mathematics to establish
 processes are understood through mathematics. Nor will one
 study of mathematics can give. Of course, it would be a very
 Title: Anthroposophy Science: Lecture VI
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 nature, experimentation, and the use of mathematics to establish
 Title: Anthroposophy Science: Lecture VII
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 nature, experimentation, and the use of mathematics to establish
 mathematics. When we seek for the realm in which mathematics
 of fanciful or dilettante activity. For even in mathematics,
 receive a training in geometry and mathematics. In a similar
 Title: Anthroposophy Science: Lecture VIII
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 nature, experimentation, and the use of mathematics to establish
 Title: Development of Thought: Lecture 1
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 It is the same in mathematics, when objective truths are proclaimed,
 Title: Origins/Natural Science: Lecture I
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 that come to a man who immerses himself in mathematics. Thus he was
 pursuit of mathematics. But he shies away, as it were, from applying
 mathematics. He says to himself: Mathematics is the last remnant left
 when I apprehend mathematics with my mind. — At the same time,
 later on, but he dared not try to grasp with mathematics what
 realm has withdrawn. Mathematics, the most reliable of the sciences,
 with the admission that even with mathematics one can no longer
 removed from human perception that even mathematics can approach it
 1440. “Conceive of mathematics as so powerful and reliable that
 Title: Origins/Natural Science: Lecture II
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 theology nor the precise perceptions of mathematics can lead any
 ideas and concepts. These may have the certainty of mathematics, but
 faintly, in symbols taken from mathematics, did Cusanus want to
 fully grasp, not even symbolically, with mathematics. Today, we see
 from outside with mathematics although mathematics cannot penetrate
 into the inner essence. For this reason, Cusanus applied mathematics
 Title: Origins/Natural Science: Lecture III
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 position today in regard to mathematics and to the relationship of
 mathematics to reality. We assume that this is the way it has to be
 felt differently concerning mathematics. We need only recall what
 appeared selfevident to the men of that time that in mathematics
 through the special way in which man relates to mathematics and
 mathematics relates to reality. Mathematics had gradually become what
 The mathematics existing in the age of Descartes
 mathematics that has been thoughtout but not experienced. As an
 the selfexperienced mathematics of a bygone age. Mathematics in
 unconscious. As a matter of fact, man even now produced mathematics
 demonstrated by the fact that mathematics, mathesis, and mysticism
 and mathematics are one, though only in a certain connection. For a
 one experienced more inwardly in the soul. Mathematics was the
 actual mysticism was soul mysticism and that mathematics, mathesis,
 As a matter of fact, in regard to mathematics and the mathematical
 time when mathematics, mathesis, and mysticism were felt as one and
 mathematics, of geometry, is brought up out of our limb system of
 mathematics, was still felt to be something close to mysticism, the
 existence. But in the age when mathematics, mathesis, was still
 mathematics spoke quite differently about the triangle and the
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 Title: Origins/Natural Science: Lecture IV
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 the formrelated or geometrical elements of mathematics, the
 mathematics — is originally experienced by man in direct
 The kind of mathematics prevalent today, by means of which man wants
 mathematics as something that he experienced within himself together
 The most that can be said of such an imposition of mathematics on
 nature — one experienced as mathematics through one's own
 were images of the divine spiritual. The instant that mathematics is
 Only when man severed himself from mathematics, only then was it
 possible also to sever mathematics from the earth and to found an
 order to do this, mathematics would have had to be also mysticism,
 On the other hand, Newton shows mathematics completely on its own.
 mathematics that has been severed from man. We find that he
 hand, one pictures space in terms of Cartesian mathematics, without
 abstracted mathematics and geometry, and therefore he penetrates
 spatial phenomena and processes of nature with abstract mathematics.
 whenever mathematics was observed, the intentions of God were also
 By Newton's time mathematics has become abstracted. Man has
 forgotten that originally he received mathematics as an inspiration
 mathematics to the study of space. As he writes his Principia, he
 simply applies this abstracted mathematics, this idea of space (which
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 Title: Origins/Natural Science: Lecture V
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 this view because, as I have said, a man experienced mathematics by
 If man is to apply mathematics, for example, to the world, then it is
 follows a mathematical method but it is not mathematics in the modern
 Title: Origins/Natural Science: Lecture VI
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 Therefore they did not find either mathematics or the primary
 itself to the body if it is to comprehend mathematics. Nor was it
 indispensable. A healthy and open mind can feel that mathematics
 Title: Origins/Natural Science: Lecture VII
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 divorced from man. This is most evident in the case of mathematics.
 mathematics, a way of thinking which from then on was combined with
 physics was divorced from man, along with mathematics. The progress
 By permeating all external phenomena with abstract mathematics, this
 Title: Origins/Natural Science: Lecture VIII
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 Title: The Social Question: Lecture V: The Social Will as the Basis Towards a New, Scientific Procedure.
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 Certainly mathematics doesn't have a state characteristic, but
 Title: The Social Question: Lecture VI: What Significance Does Work Have for the Modern Proletarian?
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 such a superstructure. Certainly chemistry or mathematics can't
 Title: Social Future: Lecture VI: National and International Life in the Threefold Social Organism
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 individuals can confirm the truths of mathematics. Anyone acquainted
 Title: Lecture: The Peoples of the Earth in the Light of Anthroposophy
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 cold, barren mathematics is the only science which remains to him for
 Title: Art of Lecturing: Lecture I
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 whether we can teach mathematics or geography well, the very,
 Title: Art of Lecturing: Lecture I
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 whether we can teach mathematics or geography well, the very,
 Title: Lecture IV
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 Mathematics we only have to take what is given as number; but when we
 Title: Book of Revelation: Lecture Six
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 little bit of abstract geometry or mathematics but to that
 Title: The Apocalypse: Lecture VI
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 doesn't mean our rather abstract geometry or mathematics, but
 Title: Man/Being/Spirit/Soul: Lecture III: The Science of the Spirit and Modern Questions
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 mathematics, astronomy, physiology, biology, in history,
 Title: Lecture: Esoteric Christianity: The Gospel of St. John and Ancient Mysteries
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 Mathematics as elaborated by Leibnitz, Newton and others, such works
 Title: Lecture: About Horses That Can Count and Calculate
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 were, by themselves, and particularly in the sphere of mathematics the
 of mathematics that we really feel impelled to develop it as it were
 very large numbers together. A famous professor of mathematics once
 the horse the programme; this will be enough, for the whole of mathematics
 Title: Lecture: How Can We Gain Knowledge of the Supersensible Worlds?
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 mathematics. Consequently one must say that at the present time
 Title: Lecture: Jesus and Christ
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 mechanical forces through mathematics, so is it possible to understand
 Title: Lecture: The Supersensible in the Human Being and in the Universe
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 try to solve problems in mathematics. This fact has given rise to
 which natural science contains mathematics. For this reason,
 apply to mathematics and natural science, so that thought is
 Title: New Spirituality: Lecture 5: The New Spirituality and the Christ Experiance of the Twentieth Century  4
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 being quite abstractly. He works with them in an entirely abstract way. He has his mathematics,
 could in fact already show how psychology, and, indeed, even mathematics, point towards spiritual
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