Ancient Mysteries and Christianity
GA 87 — 9 November 1901, Berlin
4. The Pythagorean Doctrine
Highly Esteemed Attendees!
The last time I drew attention to the fact that I wanted to talk about Pythagorean teaching. Pythagoras had founded a school in Lower Italy. It was not so much a school, but rather a discipleship whose spiritual leader was Pythagoras. He formed a doctrine. We can no longer say how much of it belonged to Pythagoras and how much to his disciples.
The world view of the Pythagoreans emerges before us, and this shows itself to be one of the most profound world views we have. Since it is very important for us to really introduce the things we are dealing with, I would like to introduce a modern Pythagorean before I mention Pythagoras himself, a Pythagorean who lived in Germany himself and whose world view always seems to me like a forecourt to Pythagoras.
You can understand this world view much better if you are familiar with the works and views of Baron von Hardenberg - Novalis, a poet of a thoroughly mystical nature. No one who knows his writings will doubt this.
Take his "Apprentices at Sais". This is something that can only be understood in its esoteric meaning. But anyone who knows the personality of Novalis - he was born in 1772 and died in 1801, so he was 29 years old - will understand this. This Novalis seems to have remained the most innocent youth throughout his life. He seems to us more like the revelation of an unearthly individuality than an earthly personality. It is quite impossible to understand that this immersion, this contemplation, could have been acquired in his immense youth.
When we read his "Heinrich von Ofterdingen", we find that he drew from direct sources, from the sources of mysticism. He then incorporated these into his novel "Heinrich von Ofterdingen" and thus showed that he understood the mysticism of the twelfth and thirteenth centuries. If we look at his basic ideas, we will find a certain similarity with other mystics.
He searched for the "Blue Flower. People have often mocked this "Blue Flower. We will understand each other better if we remember Goethe's "Prophecies of Bakis", where he speaks of the serpent's thread and the flower, where he says that man can walk the path that is long and narrow. When man then walks this path, he sees knots before him. He also sees the knot in which lives are tied together. Behind him, he trails a snake. The snake disappears and the knot transforms into a flower in front of him.
This image, which Goethe repeatedly refers to, is egoism, the approach to the highest spirituality or deepest knowledge. The symbol for this is the "blue flower. It is also a symbol of that which arises for man as an entanglement of life when he progresses along the path of knowledge. It is this "Blue Flower" that Novalis has in mind for his Heinrich von Ofterdingen.
We also find this flower in Master Klingsohr, who can prophesy. The future lies open before him. Goethe says: The future also lies open before him who really has a complete overview of the past. [...] - Master Klingsohr reveals the future to Heinrich von Ofterdingen. This satisfies him to such an extent that he is able to see the individualized Blue Flower in the daughter, as he has progressed so far that he can see the highest in the female being.
Matilda dies away from Henry of Ofterdingen. He decides to die after his beloved. For him, reality turns into a dream. What he was previously inclined to regard as a dream, the higher spiritual world, is now reality. He no longer finds this highest in the individual being, but he
finds it in other beings as well. He finds a second girl. It is the same for him. He finds Mathilde again in Cyane. She is like a new embodiment of him. He lives a life of the afterlife.
We find the idea of this in his "Apprentices of Sais". A beautiful fairy tale is woven into it about the boy Hyacinth, who loves the girl Rosenblüthe. Only the trees and birds of the forest know of this love. Then we find Hyacinth changed. He is overcome by a longing to seek something deeper. He leaves Rosenblüthe without sufficient reason. Then he comes to the evil old man, who plants in him the longing to seek the mother of all things, or the veiled maiden. He sets off on his journey to the temple of Isis, comes upon an image, and when he unveils it, he finds nothing but roses. [He finds the beloved as the solution to the riddle, as the veiled image of Sais.
This is reminiscent of the higher concept of "Know thyself", as he expressed it in an epigram. He stands before the veiled image at Sais. He lifts the veil and - wonder of wonders - he finds himself. A magical individualism consists in the fact that one can find the infinite in the finite, [that one can turn the spirit into immediate reality].
So in Novalis we undoubtedly find a mystical personality. So if we assume that in Novalis we are dealing with a deep-seated, mystical nature, and if we then get to know him, he does not appear to us as a mystic, as he has just been described, but as a resurgent old Pythagorean disciple.
When we let Novalis pass us by, when he seems more like a memory, and when we then see how this touch of the earthly, how this personality nevertheless stands firmly in life, has tendencies that we would least expect to find in such romantically inclined natures, then we are referred to the Pythagoreans as to fleeting ghosts.
We must by no means equate this view and philosophical contemplation, as we have it of Romanticism in him, with the view of the other Romantics, with contemporaries of his who lack any depth. Friedrich Wilhelm Schlegel or Tieck, [E-T.A.] Hoffmann and so on must not be confused [with him]. But anyone who allows Novalis to have an effect on them will not be tempted to make such a confusion. What is astonishing about Novalis - despite his [poetic] nature - is that he is one of the most enthusiastic admirers of everything mathematical. He has a thoroughly educated, mathematical psyche, an immediate revelation of what he calls the magical in nature. In this he finds the law of the spirit. That which he who wishes to enter the higher regions would like to leave behind, we find in Novalis as the main thing, as that which led him to emphasize the magical in his [idealism]. In the concatenation of basic mathematical concepts he sees the most intriguing revelation of the mystery of the world. He sees free matter at the bottom of things. Mathematics is the foundation on which existence rests, it is therefore nothing other than the highest form, the purest form of spirituality.
If we find this as the basis of his view, then he appears to us as a representative of Pythagoreanism. We can understand Pythagoreanism much better if we imagine it like Novalis. The Pythagorean soul must be imagined in this way, then we arrive at where Novalis stands; [just as] Pythagoras was able to arrive at the view that the basic structure, the basic essence, the basic spirit of the universe is actually given in the connection between numerical quantities and spatial quantities in this harmony.
If we want to gain an insight into a Pythagorean soul from the first elementary beginnings, we must imagine it in the following way. The pupil was led up step by step to the knowledge to which he was to come. He was guided in a very careful way. The first was mathematical knowledge, the second astronomical. Astronomy was preferably mathematical. The regularity resulted from the numerical relationship in the universe. He was first introduced to these numerical relationships. Then he was gradually led on to the knowledge of man himself. The fulfillment of the desire "Know thyself" [came] last. First he was introduced to mathematics.
How can one imagine that man can actually come to the idea that mathematics is the spiritual foundation of the entire universe? How can this be imagined in the form of harmony, formed in space and time? If we immerse ourselves in those areas of space and time which outwardly already show a regular grouping, such as the movement of the celestial bodies, if we immerse ourselves in that, then we have basically given nothing other than an embodied mathematics, an embodied arithmetic, in this construction of the celestial vault that we perform in our minds.
No human being can actually find anything of a mathematical structure, of a spatial structure of geometric figures in the world and in reality, if he has not first formed these mathematical figures in his mind. If someone described a circle or an ellipse, we would not know what it is that he is describing as an object. We would be able to trace the line in the various places in space and connect these places. But we would not be able to connect a concept with the whole line that describes the object if we had not already formed the concept. We can draw a star and then think about what kind of line the star describes. But only then can we find the figure if we already have it in our minds. The same is also the case with other things, even if we take the numerical relationships. We will only recognize the objects outside in space in their certain mutual numerical relationships, in their numerical diversity, if we have formed these relationships in our minds. If we know that 2 x 2 = 4, then we can also recognize it outside in space. We would not be able to connect any concepts with reality, we would not be able to grasp them at all, they would pass us by like nothing, they would not be there for us at all, if we had not formed the images in a purely spiritual way in our psyche.
So it is that the Pythagoreans could say: That which I see outside must also be contained in a certain way in my mind. What emerges from the source point of my soul is the same as what I perceive outside as the primordial ground of the world itself. The Pythagoreans thought about this more deeply and said to themselves: "It is impossible that two things that are completely separate from each other, spirit outside and world inside, [merely] exist side by side [and do not agree]. The coincidence would only have meaning if what is in the spirit is exactly the same as what is outside in space. If the circle, the ellipse that I perceive within me, the numerical relationships, are the same as those outside, which I see in the outer world, then it makes no sense at all if [the Pythagorean] does not have something that he forms within himself. If he sees the spirit of things and has it within him, then it has only one meaning.
Therefore the Pythagorean did not initially think like the philosophers of the nineteenth century under the influence of Kant. He did not ask: How is it that my imagination inside me corresponds to the things outside? My experience is quite different. That is the unquestionable unity of what is outside and what is in my mind. This is how the Pythagorean thinks.
It makes no difference whether I take the ideas of the Pythagoreans' astronomy or apply the new ones. It doesn't matter at all. So when the Pythagorean sees the celestial body describing an orbit in the form of an ellipse, it is a direct experience for the Pythagorean that the ellipse that he perceives within himself and the ellipse that exists outside as the orbit of a star are not two ellipses, but only one. And that is experience.
Schelling also expressed this, and this makes the matter clear in the simplest way. He has taken up the "power of attraction that physicists have always [known]. They imagined that objects exert a force of attraction on each other. The earth attracts the moon, the sun attracts the earth. When the sun attracts the earth, it acts on the earth. It is difficult to attribute an effect to a body where it does not exist. But the fact is that when a body acts on the earth, it is on the earth. A body is where it acts. The boundary of light is not the boundary of the real sun. The sun is in the entire space where it exerts its gravitational pull. The space that the earth fills is also part of solar space.
Imagine this Schellingian idea as [already] underlying the Pythagorean doctrine. The human spirit fills the entire world space. It is not enclosed in a single organism. The spirit is where it perceives.
For the philosophers of the nineteenth century who followed Kant, the question is this: How is it that the mind perceives what is outside it? - The Pythagorean does not say this at all: How is it that the mind perceives that which is apart from it? The Pythagorean says: If the mind perceives an ellipse in the sky, then it is a fact that the mind is not enclosed in the organism, that it is not there where it perceives with the senses, but that it is there where it perceives [mentally]. The limit of the spirit is not the sense, but the spirit is where it perceives. - There is a separation between the numerical relationships in space and what exists in our head as numerical relationships, which does not exist for the Pythagoreans. The Pythagoreans do not recognize the idea that man is initially a sensual, finite being, enclosed with the psyche in a fabric that connects the senses with the outside world. This gives people today the impression that the mind is also enclosed in [a] housing.
When other philosophers take this for reality and ask: "How is it that we perceive external things?", the Pythagoreans take the opposite view. They do not ask: How is it that the mind is enclosed in such an organism? - It is perhaps better that I do not say "individual", but "individual being". This then leads to an understanding of a world view such as the Pythagorean one. It leads to an understanding that can only be grasped if one sees in the mathematical that which constitutes the basic structure in the universe, and which, if one thinks of the whole world as filled with spirit, constitutes the basic structure of the spirit itself.
So we actually have in the basis of the thing that can be perceived with the senses deep down, on a lower level, in the spatial-temporal of the universe, commonalities that can be expressed through spatial sizes and numerical ratios, that which appears to the spirit on a higher level. The spirit has a numerical, geometrical basis. The spirit has its origin where things are regular. The spirit grows out of the mathematically constructed world. Therefore [the Pythagorean] seeks the primordial grounds of existence in the mathematically constructed world.
I have pointed out that there is a difference between the Greek worldview, as represented by Heraclitus, and the Pythagorean one. At the time, I constructed my remarks in such a way that they came back to Goethe's basic view. I said then that Goethe says that the seed and the plant are one and the same being. The material seed contains everything that is still in it in complete concealment. It is the same as the fully developed plant. The plant is not in it, but it has the sense that in a spiritual way the plant is the same in every form as in another form, so that the plant with its foliage and petals, with its whole fruit and with all that is in it, is to be regarded as that which has become material, materially, which is in the seed in an ideal way. Goethe therefore says that the seed is the whole plant, except that the spirit is still concealed behind it. That which is ideal in the seed becomes material reality in the whole plant.
The same image can be applied to the whole world. One can understand the world by observing it in its highest state, by immersing oneself in its blossom and fruit, in the human soul, by studying the "Know thyself" and going to the human being. There, where the purely spiritual-soul then appears directly, i.e. in the deepening, in the direct immersion into the self, one can first look for a world view, a world view. But you can also examine a seed. You can find ways and means to examine the seed. One can assume that what lies in the seed is already indicated and that the world view that is gained from the human being is the highest. The Pythagoreans do not seek man where he is soul, nor where he appears as spirit, but where he is apparently not spirit at all, where he apparently is not at all. The Pythagorean seeks certain reality through indifferent numbers. And that is why he seeks the spirit where he already knows the spirit. That is why he also finds the primal source, the basic structure of existence, in mathematics.
I just wanted to say that this world view of the Pythagoreans can only be understood if one understands the immersion of Novalis, which must be understood mathematically - of Novalis, who was of a thoroughly poetic nature and as such was what literary history calls a "Romantic", yet was rooted in such laws that he could see strict mathematics as the primal source of existence. That is why the Pythagoreans, because their spirit was powerful enough, were able to find spirit in the relationships of numbers. They started from the lowest level of the spiritual. Just as the seed is not yet a plant, but can become a plant, so they ascended from the seemingly unspiritual to the spiritual.
This is what can make us understand the whole world view of the Pythagoreans. The Pythagorean worldview is usually presented as if it were the numerical aspect of the world that led the Pythagoreans to regard number as the origin of things. And one cannot quite imagine what they meant by that. I must confess that if we follow what is written in the textbooks and read that the Pythagoreans regarded number as the origin of all things, it would seem meaningless to me. Only if I imagine how it is in reality, if I assume that they grew up in a completely different theory of knowledge, can I understand what they meant. Their view is simply described by the word: the Pythagorean did not look for the spirit where it appears to be a sensual entity, but where he perceives it as something that fills the whole of space.
That is one side of the Pythagorean world view, that is the reason why they descended to numbers and geometric shapes. On the other hand, the reason is also because they found something in these numbers and geometric figures that they could address as spirit.
What do geometric or mathematical ratios mean? Anyone who can only imagine a circle or an ellipse when they are drawn on the blackboard cannot be said to have any idea of the real geometric or mathematical relationships. If he has to put five peas or beans on the table when he wants to imagine the number <>, we cannot say that he has an idea of the real numbers.
On the contrary, we are aware that what we call a circle, what we call an ellipse, can only be represented approximately in material reality. We know that the material circle we draw is only an approximation of what we can create in our minds. We also know that what the celestial bodies in outer space describe is only an approximation of a circle. However, it is the same law that governs the creation of the world as the law that governs us when we imagine a circle in our minds, when we no longer need to deduce the spiritual from the sensual. That is why mathematics would be the best thing to introduce us to the spiritual. This is also why the Pythagoreans placed the highest value on mathematics. So if you really want to recognize the spirit, you have to be able to disregard everything sensual. You must be able to realize that it is not what you draw on the blackboard with chalk that is a real circle, but what remains for the spirit without the chalk drawing on the blackboard. Using the salt cube, it was possible to show that the cube is something completely different from the [salt] cube. In this way, the pupils could be shown that the spiritual - also of other things - can only be understood if the sensual remains absent. This is easy to show with the salt cube. The spiritual content is not the same as the outer cube.
But if we understand this for the whole sum of world phenomena, if we understand that the spiritual can be detached from the material, then this leads us up to higher levels. Everyone admits that mathematics has nothing to do with the things of the world, but with the spiritual. But if this goes further up, people confuse the spirit with reality
A strange document on the confusion of the spirit with reality has just come out these days. A book has been published entitled "Kritik der Sprache" (Critique of Language) by Fritz Mauthner, which aims to show how all our knowledge floats in the air, how nothing is given to us but the sensory world, and if we disregard the sensory world, we have nothing more in our imaginary world than empty words.
Now, ladies and gentlemen, this is something that someone who is unable to detach the spirit of things at a higher level of reality, as he can do with mathematical entities, can very easily come to. He who has no intuition, who does not really have from the source point of his spirit what he has to hold up to things, who is sterile and barren, who cannot fill his soul with spiritual realities, believes that he has nothing more when he goes beyond [the sense world] than words. Instead of a "critique of knowledge, he writes a "critique of language.
The book comprises two volumes. It seems to me as if someone wanted to write a critique and had not mastered what he wanted to criticize. He confuses what the mind adds to the formations. What Mauthner gives would be - compared to what spiritual content can and should give - a critique of pencil drawing. It shows how much the pencil is capable of depicting circles. Thus sterile views cling to those who are unable to feel the true content. He does not know that the spirit gradually acquires the ability to ascend to the higher realms of existence and is aware of its difference from material things at every stage of spiritual life, just as the mathematician is able to detach the spiritual, the spiritual from things, i.e. to advance from what is not yet spirit to the immediate God in the world.
This was something that the Pythagoreans sought to achieve step by step by trying to lead the student from the lower to the higher. They were convinced that by ascending from the lower to the higher, man was not merely having an experience within himself, but was fulfilling a task in the universe itself. They were convinced that he was doing something in the world, they were so convinced that they only compared the ascent with the numerical relationships themselves. They said to themselves: The individual human being who perceives is apparently a duality. The perceiver and the perceived. These two great opposites stood for the Pythagoreans at the basic level of their table of knowledge.
But they said to themselves: All this is only apparent because man does not stand on the highest level of perfection, but on the lower levels. The perceiving and the perceived must be overcome if they are to become one. Thus the Pythagorean imagines that, just as now in human cognition, unity triumphs over duality, over what is separate in the world, the Pythagorean must imagine everything according to numerical relationships and specifically again in such a way that what is separately a duality presents itself to him as unity.
Now the Pythagorean is convinced that the whole multiplicity of the world, the fact that there are many things in the world, derives only from the fact that man first sees the appearance, not the thing, that he does not see things as they are, but that he sees them as they are not, because of the limitations of his own existence. He sees that this multiplicity, when he overcomes appearance, then presents itself in reality, in truth, as unity. What man ultimately achieves is the primordial unity, the primordial One of the world, and the Pythagorean also sees this as the foundation from which everything springs.
This is what makes it possible for man to perceive something in space. This is the general unity of the world, but man can only gradually ascend to it. What is revealed last is there first, and that is because it is a member of this multiplicity. After it has been placed in a corner for a while, it integrates itself into the world structure and becomes one with the world harmony. The numerical harmony, the geometric regularity of the world view embraces the human being. And so he finds it by integrating himself into the structure of numbers. Therefore, the Pythagorean can say that all good, all virtue consists in man overcoming appearances and finding numerical, geometric regularity, whereby he integrates himself into the great world existence.
Thus man appears to himself like a tone in harmony, and because he appears to himself like a tone in harmony, he has to give himself the right tone and the right proportion. He does not fulfill a task for himself, but fulfills a moral task. If he does not fulfill it, then he is not in the right numerical proportion. He has something to [contribute] not to himself, but to the whole structure of the world. Through every transgression, man brings upon himself an unlimited responsibility, and, recognizing this, he should strive more and more to attain the mood that he has to fulfill in the great music of the world.
So to the Pythagorean, what is spread outside in space and time appears as a moral task itself. For the Pythagoreans, the moral task is not to be understood as a mathematical one on a higher level. The mathematical task is that he discovers the world space, but in such a way that he is thereby integrated, that he is thereby integrated like a tone in the world music, like a number in the law of numbers. He then discovers that when he does something - because he is not just his own redeemer - it is not just important for himself, but something that concerns the whole universe. The spirit is not only in me, but also where it works. He then sees that the spirit not only has to work on its own moral perfection, but also on the harmonization of the whole universe. When the Pythagorean imagines the harmony of the universe in such a way that he thinks of the world as permeated by musical tones, by music of the spheres analogous to music itself, this happens because music is based on tonal relationships.
The Pythagorean translates this by saying: Just as the tonal relationships become perceptible to our senses as a harmony of tones, there is also a harmony of tones, a music of the spheres in the world, which acts like the numerical relationships in the world. But if it does not find the right numerical relationship, the right tonal relationship to the world within itself, then it disturbs the harmony of the world.
This is why the insights of the Pythagoreans had to lead to the strictest educational system. The Pythagorean is aware, when he teaches the individual this or that, that he is taking upon himself a responsibility, not only towards that person, but towards the whole universe.
Answer to the question:
Everyone's special disposition enables them to gain knowledge of the spirit. The Pythagoreans endeavored to create this possibility for everyone.
[Mathematical ideas are only easy to prove because they are simple, almost without content.
For those, however, who are not at all suited from the outset to immerse themselves in the content of the world, the best and safest school will be to go through mathematics. Plato therefore demanded a thorough knowledge of mathematics from his students. Otherwise it might not have worked for everyone. I would like to explain this to someone who has gone through the Pythagorean school: Let's imagine a person who can only feel. Such an organism would be able to perceive geometric shapes and also be able to conceive of numbers. In fact, blind and deaf people have been taught these relationships and turned into accomplished mathematicians. Such an organism can also arrive at music in a mathematical way. The numerical relationships only appear to him in a shadowy way. Now let us imagine that such a person suddenly hears. He will then perceive the same thing that he had previously understood. He now perceives it with his ears. It is the same with the blind. Through an explanation of the vibrations of the world, he can get an idea of the colors through the numerical relationships. The Pythagorean should now also bring the higher senses to rise. It is the same thing as when a mathematician comes to a musician who is constructing his work himself and calculates it for him. Then the musician can say: "Stay away from that. If you have the necessary receptivity, you can have perceptions even without mathematical representation.
I have contrasted two currents. One current within Hellenism, which starts from Heraclitus, and the other, which starts from Pythagoras. Heraclitus and Pythagoras stand before us as two who have the same object. Heraclitus, as it were, as the composer, Pythagoras as the one who mathematically calculates his subject. It is the same with us as with Pythagoreanism. You first have to teach the blind and the deaf and then you can lead them to higher levels.
Mathematical concepts devised by humans are often confirmed in the outside world. In the case of electricity, people calculate that this or that must be one way or the other. If you then carry it out in reality as an experiment, it must agree [with the calculation].
I would like to cite a famous conversation between Schiller and Goethe. Goethe and Schiller left a scientific lecture together and got into a conversation about what they had heard. In the course of the conversation, Goethe took a piece of paper and drew a symbolic plant, an ideal plant, saying: "This plant is actually in every plant. Every plant is actually an individual embodiment of this general plant. To which Schiller replied: Yes, but that's just an idea! To which Goethe replied: But then I see my ideas with my eyes.
[Or let's take a] triangle [it is presumably drawn]: The angles add up to 180 degrees. Because we have seen a triangle, we can form a quadrilateral by connecting the blue one with the green one. This can be extended in the mind. We can move from the triangle to the square. But we cannot go from one shade of color to another. We can only perceive sensually what belongs to the world of the senses. In mathematics, the spiritual is the easiest to grasp. The mathematical is the most spiritual.
You don't know how to perceive sounds from numerical relationships? Sounds are not perceived [with the ears], only thought. Composers who become deaf therefore only have a surrogate. It is the same as when we deduce one mathematical entity from another. It is not [sensory] perception, but a mental experience.
The sensual is transformed [into the spiritual], it is elevated.
Studying mathematics makes no difference, but recognizing the essence of mathematics does. The most superficial person just splashes and splashes around in the primordial being. Someone can also have studied mathematics. Goethe studied little mathematics. But no one understood the essence of mathematics more than he did. Goethe arrived at his magnificent world of metamorphoses precisely because he had such a great idea of the nature of mathematics, even though he was only able to arrive at the [gap in the transcript] theorem.
He who can make razors may not be able to shave, and he who can shave usually cannot make razors. Thus the mathematician who knows mathematics [only] in form need not know its meaning and its application to the primal being.