Ancient Mysteries and Christianity
GA 87 — 16 November 1901, Berlin
5. The Pythagorean
Highly Esteemed Attendees!
I must apologize for my cold; it will be difficult to hear me.
I have tried to show that this Pythagoreanism, which lived in southern Italy in the sixth century BC - this strictly self-contained and yet not self-contained school - had a great influence in all the centuries following Pythagoreanism, and that this whole direction was acquired in a difficult course of study that lasted many years. You really had to do a lot of exercises before you could grasp things in a purely spiritual way. I [wanted] to show that it is a pity not to have such a school today. I [wanted] to show that the Pythagorean is not so isolated, but that in Novalis we have a personality who thought in quite the same way. But there is something else.
It can seem somewhat strange when we hear that the Pythagoreans sought something in the strange harmony of numbers, in numbers and in the combination of numbers that represents the primal causes of things. It will not surprise us if we make the assertion that our science, ordinary natural science, insofar as it is physics and chemistry today, is on the way to becoming Pythagoreanism. In the course of the nineteenth century, only a certain group of sensual views prevented natural science from merging into Pythagoreanism. Today we are facing the reformation of natural science. We are on the verge of chemistry and physics becoming completely materialistic because only scientific ideas have been adopted. But perhaps in a few years' time we will no longer be able to think only materialistically about chemical and physical matters. Helmholtz, despite his merits and enormous inventions, and although he never got beyond a certain materialistic presentation at the end of his life, adopted a kind of idealism. At the Naturforscher-Versammlung he announced a lecture on "Apparent substance and true movement". Unfortunately, no notes remain in his estate. However, we can imagine what Helmholtz wanted to say. The physicist only gives a lecture [with such a title] when he has to. Having to give a lecture on "Apparent substance and true motion", on the fact that everything substantial is only apparent, and then the spiritual, the motion is the true, is of great importance. For it is not immediately possible for the physicist to ascend to the spirit. But it is already something if the physicist does not regard matter as the real, but only as something apparent. That is a symptom.
Our entire natural science is basically out to confirm the old Pythagorean theorem that everything that exists in space can be traced back to numerical relationships. To indicate what I mean when I say that natural science is Pythagoreanism, that it is on the way to seeing the decisive factor precisely in numbers, let us take the chemical substances: oxygen, hydrogen, nitrogen, lead or any of the various other elements. They form compounds, as we know. For example, when lead and oxygen combine, what is the decisive factor? The number! The number is the decisive factor when these two substances combine to form lead oxide. I can't go into this in detail, nor can I go into how the two substances can be separated again, because it would be going too far. However, it is enough for us to know that when lead and oxygen combine, they always combine according to a certain numerical ratio.
But this goes even further. Suppose mercury combines with oxygen. For example, 103 grams of mercury only combine with 8 grams of oxygen. You can see beforehand that if you want to combine 8 grams of oxygen, you need 103 grams of mercury.
But now it's like this: oxygen always combines with all other elements in such a way that certain parts by weight of other elements combine with eight parts by weight of oxygen. This is the case with all elements. For each of the seventy-three known elements there is a number that indicates the weight fraction with which it combines with all the others. The chemist must recognize this from a wealth of facts. That is just it: We have many more facts than the ancients. They had the same thoughts, but fewer facts!
Lead oxide combines 103 parts by weight of lead with 8 parts by weight of oxygen. If we combine lead with sulphur, 103 parts by weight of lead combine with 16 parts by weight of sulphur.
So, if you construct the whole world materially, you do not have something chaotic and arbitrary, but - as the Pythagoreans thought - something ordered according to the harmony of numbers.
And the further we go in science, the more we see that the organization and construction [of nature] can be expressed by numbers. Today's science provides confirmation of the correctness of the Pythagoreans' spiritual construction that we are dealing with numbers in nature.
Helmholtz seems to have wanted to say the same thing in his lecture. We are ultimately dealing with the spirit. Whether the mind is expressed by numbers or viewed in some other way, we will leave that aside for now. If we extract everything that lies dormant in the substance, then we finally come to the conclusion that we are dealing with spirit.
Science also provides us with proof of this. Science is disproving materialism more and more every day. The opinion that natural science needs materialism may still exist in some people's minds, but the truth is that nothing disproves materialism more than natural science. I would like to give you an example from contemporary natural science to show you how this natural science is overcoming materialism bit by bit day by day.
You know that the human eye consists of a displaced spherical envelope or shell filled with a glassy, watery liquid, the vitreous body, and that seeing an object is made possible by the fact that embedded in this mass is a small crystal lens that images the image on the background. Light penetrates through the black in the eye. This light is refracted in the lens, creating a small image, and this image becomes the cause of our vision. The various animals, vertebrates and also a number of invertebrates have similarly constructed eyes.
The octopus also has an eye that appears to be similar to that of humans. It has an eye with a vitreous body, embedded in the vitreous body is a lens that mediates vision. The interesting thing is that in humans, the crystalline lens grows in a completely different way to the octopus, even though both are crystalline lenses. In the octopus, the crystalline lens is formed because the crystalline lens has grown within the aqueous fluid of the eye [through excretion and thickening]. Now you can say to yourself: the eye with the aqueous fluid and the lens resembles a camera obscura. In humans, however, the lens is not formed by excretion and thickening, but by the surface pulling the lens out of itself and then pushing it into the eye. This crystalline lens emerged once from the eye and the other time in a different way from the outside and was then pushed into the vitreous body!
Can we still say, when we see how a material structure can arise in so many different ways, that it is the material that forms nature? Should we not say that nature is not built up according to material powers, but according to purely spiritual powers? The natural substance does not matter at all. One time it is formed from the inside, the other time from the outside. The substance as such is therefore basically the same for the construction of organisms. The mind constructs things.
The further we get in natural science, the more we find that we can never say what would come into being if we [only] took the substance into account. It is the spirit that uses matter to create forms. That is why the Pythagoreans divide the world into these two components: On the one hand, they conceive of the world as that which makes it perceptible/and then again as that which is not perceptible in the world, or let us say better, that which is only perceptible, recognizable to the mind; they have there clearly set apart two things in the human and animal eye; they see how the same eye is constructed in the one and in the other case.
This law - in general the whole spiritual that makes use of the material - cannot be perceived with the senses, it can only be perceived in a spiritual way. But space could not be fulfilled if the spirit could not make use of the perceptible.
The Pythagorean separates these two things: on the one hand, he has the eternally creative, the spiritual, which uses matter to create countless forms; on the other hand, he has matter, which is not active for itself, but only to make visible something that cannot be perceived by the senses.
The Pythagorean composes the whole world from the perceptible and the imperceptible. For him, the one is the number one. It forms the boundary for him. Something exists for us because it becomes one, because it becomes individual. But this is only apparent; it is connected to all other things in the world. And the "how" is conveyed by the number symbolism and the number context. And so we can understand it, because the Pythagoreans had this connection, they saw how much the number rules when it comes to material things and objects. But they also saw how the Pythagoreans endeavored to find the wonderful connection within the numbers and to find what they had found internally confirmed externally.
Whoever does not pay attention to this, whoever does not realize that it was the harmony of the inner and outer, whoever does not take this into account, that it was the delight for the Pythagorean, can very easily find gimmicks in the Pythagorean number teachings. But this only lives in the minds if they cannot become aware of the inner rapture, if they cannot understand, if they cannot grasp how for the Pythagoreans the whole counting becomes different when we have arrived at the ten.
If you don't understand this purely in the way the Pythagoreans understood it, you won't understand what the Pythagoreans meant. As long as we count to ten, we are dealing with units where we add one number to another. But when we reach ten, we continue counting. But we don't just count units, we count the tens: 10 = 1 x 10, 20 = 2 x 10, 30 = 3 x 10. While we have 10, we add 10 others. So we count in a spiritual way what we used to count materially. We count the numbers themselves from 10 onwards, so that when we count to 10, we are actually counting materially in the Pythagorean sense. But if we continue counting the tens, we can disregard the material. We do this by saying: 1 x 10, 2 x 10 and so on. And then we come to the hundreds. The further we count up, the more we forget the material basis and what we used to count. According to the Pythagoreans, it is precisely in counting that we have a means of raising ourselves more and more into the spiritual realm.
You have to consider what he understands by the so-called "gnomons". He understands this to mean nothing other than the inner lawfulness that prevails in our world of numbers if we study this world of numbers in the right way.
Take the following: If you take the consecutive numbers and multiply them, each number by itself, you get the so-called square numbers: 2 x 2 = 4, 3 x 3 = 9, 4 x 4 = 16, 5 x 5 = 25.
So if we multiply the individual numbers by themselves, we get the square numbers. However, there is a strange relationship between the numbers and the square numbers. This relationship was first explored by the Pythagoreans.
If you now take what is not yet in 2x2, take what is new for the 4; the 5, and add to it, you get the second square number. Strangely enough, this law applies continuously through the whole square numbers. 4 is the first square number, 9 is the second, 16 is the third.
2 + 2 = 4; the next new number is 5, so plus 5 = 9.
Take 3 + 3 = 6, the next new number is 7, so 3 x 3 = 9, plus 7 = 16.
You can continue like this. And this is what the Pythagoreans called the "gnomons".
Take 4: 4 x 4 = 16.16 + ( 4 + 4 + 1 =9 ) = 25, the square number of 5.
Take the 5: 5 x 5 = 25. 25 + ( 5 + 5 + 1 = 11) = 36, the square number of 6.
Take the 6: 6x 6 = 36. 36 + ( 6 +6 + 1 = 13 ) = 49[, the square number of 7].
You can find this inner regularity throughout the entire number range. Here you get an inner insight into the context itself. This was what compelled the Pythagorean to believe that the numerical has an inner regularity of its own. He found this in things like gnomons, so that the Pythagorean could say to himself: The same thing that I form within my mind I find outside in the cosmos, and the same thing that forms the inner context is in an inner harmony with the cosmos. If we have 3 x 3 things outside [in the cosmos] and have arranged them in this way, they correspond to what we have brought out in the spirit. We can form the whole of mathematics in our minds, we can form the whole of the theory of numbers, we don't need to know anything about the outside world. If we then close our eyes, the outside world will obey the laws we have devised! Lothar Meyer gave an interesting lecture on these things at a meeting of natural scientists about lithium, potassium and sodium, which combine with the other elements in the following weight ratios:
This is what led Pythagoras to recognize a numerical law - and everything else that lies within it.
I would just like to draw attention to the great chemical discoveries of Lothar Meyer and the Russian Mendeleev, which are a complete confirmation of what the Pythagorean wanted with his views. I have said that the elements all combine in certain numerical ratios: Hydrogen always combines with oxygen in such a way that it is in a ratio of 8 or a multiple of 8. If we now examine the space between the individual given numbers, we get a complete regularity. We ascend from the oxygen with 16 or also from the element which has 7. The elements cannot combine with others according to a numerical ratio other than their own, but there is a regularity in these combinations.
- Lithium in a weight ratio of 7,
- Sodium in a weight ratio of 23.
- Potassium in a weight ratio of 39.
If you put these figures together, you get some strange correlations. If we take the weight ratio of 7 to 23, we get a difference of 16. If we take the weight ratio of 23 to 39, we get a difference of 16 again. There are many such consecutive triads of three consecutive substances in chemistry. We could also take other three elements and we would find that the same number spaces arise between them.
If we took the whole elements, we would always find spaces that can be expressed in numbers. We have certain substances that are grouped together quite nicely. But a number is missing in between. Let's assume we have lithium and sodium, we also have other substances and we know that there is a certain space between them; but then we are missing something in between! Now the chemist has become accustomed to something; he no longer says: There is an irregularity here, but he says: It is because we do not yet know the substance that has this numerical ratio. Many substances have been found recently. At first, we only suspected that they must exist. But later they were found. Trusting that the spirit would find it led to the spirit really finding it out.
[Uranus was found through observation. Neptune was predicted on the basis of calculations]. The laws according to which the planets move were seen. These laws did not apply to Uranus, and they said to themselves: there must be another body at a certain point in space [that deflects Uranus from its calculated orbit]. One has more confidence in the spiritual law than in sensory reality, and this has completely confirmed the spirit, has proved the spirit right.
This harmony between spirit and matter, as established by the Pythagoreans, is confirmed bit by bit by natural science. It will increasingly overcome what we see as material. It will increasingly come to the point where the apparent substance dissolves into spiritual relationships.
Matter is not merely frozen spirit, is not merely appearing spirit. It dissolves piece by piece, so that the spirit does not perceive something else, but itself. So what is emphasized today by the most diverse sides, natural science provides us with proof of this.
Annie Besant has drawn attention to similar relationships between her views and natural science. Starting from these basic views, the Pythagorean immersed himself in the world and now arrived at a view that must be particularly valuable to us because Goethe, in turn, arrived at a similar view in recent times, based on his scientific principles!
The Pythagoreans imagined the constitution of the world in such a way that this spirit, which they sought to capture in number, is limited by the unlimited and becomes perceptible by being limited.
Now the Pythagoreans imagined that all this becoming is the continuous interpenetration of the limited and the unlimited. The appearance of the unlimited as a boundary [they imagined] as a kind of matter. Matter is the indifferent that does nothing other than make the spirit visible. In order to form the entities out of matter, the spirit breathes in matter and breathes it out again into the world space. Therefore, the spirit [works] in a continuous inhalation and exhalation, a breathing process.
Goethe also uses this image, imagining this process as inhaling and exhaling the air. Goethe imagines that the earth influences itself from the outside with the air space, that it literally contracts into itself, breathes in what it needs in terms of world space and then breathes out again what it has processed within itself. It is a different air pressure when you inhale and exhale, a becoming stronger and also a becoming weaker. People left this path because they didn't want to believe in such regular ideas. [Goethe] wanted to show that the fluctuations of the barometer are not arbitrary, but essentially point back to basic fluctuations, to something that is quite regular. In the seemingly irregular processes, one can see regularity that stems from the fact that the earth breathes in air and then breathes it out again, a regularity that then produces regular fluctuations that indicate that we are dealing with inhalation and exhalation on the earth.
Goethe shows us this in an interesting way. I do not regard this as indifferent, but it seems to me that it is tremendously important that our ideas are spiritualized by such ideas. We can follow the processes in the outside world all the time, such as barometer fluctuations. If we have not grasped them, at least in terms of direction, we will not be aware of them at all. Such regular fluctuations are also found when we examine the irregular
and then subtract the regular. What remains is then irregular.
I wanted to point out that what the Pythagoreans taught is not something outdated, but that it is used in today's natural science. [The Pythagoreans approached astronomy in such a way that they also applied the spatial view of the bounded and unbounded to the cosmos.
Each time can only understand the various perceived things in the way that the state of the relevant perceptual science - astronomy, for example, and so on - is at that time. Research is carried out in the field of experience. The Pythagoreans also had to reckon with [the ideas of their time]. They placed themselves before the central fire, which represents the unity, the primordial ground of the world; that which continually breathes matter in and out and therefore brings the world into being. The stars with their regular movement represented to them a regular multiplicity, which was expressed in the numerical relationships. And what took place in the sphere below the moon was an irregularity, a continual struggle between the limited and the unlimited. But in that which lies above, the struggle is balanced to a great harmony. There the world bodies move in regular orbits. This has resulted in the regular orbits taking the place of the point, the sharply defined One. We are no longer dealing with the One, but with unity. This battle, which is constantly taking place before our eyes, is taking place between the earth and the moon, is taking place as an eternal battle. On earth, harmony and disharmony are constantly alternating. Man stands in this struggle because he is a unity. He seeks to reconnect, since he is torn out of the harmony of the world, by trying to come back into harmony with the world through what the Pythagoreans call virtue. You see that the Pythagorean penetrates from the lowest phenomena to those of human life with numerical ideas.
Now we are left with the most important things from the Pythagorean world of ideas, namely those elements of spiritual life to which the ethical sphere rises by the spirit attempting the deepest immersion into its own inner being. The Pythagoreans also had certain views on this, which were taken from cosmological ideas.
In that the Pythagoreans sought to establish an extraordinarily deep harmony with the world, with that which separates man from the whole universe, they arrived at the idea of reincarnation, of the connection between the various embodiments of all beings.
This is a matter that will occupy us in particular next time. I wanted to discuss the basic question, which was first communicated through Pythagorean physics and ethics, which was formed through such a world of ideas as has just been described, after a long period of training. One must not imagine that the communication of reincarnation or re-embodiment took place immediately! The pupil was first trained through things such as those expressed in the regularity of the world of numbers, which then led him deep into the matter. Then he was also shown what he had to do to achieve world harmony, to eliminate the so-called original sin from the world. The problem: How can the separation of the individual soul from the universe be justified? - became the great Pythagorean question.
And this question led the Pythagoreans to solve it within Pythagoreanism, and this is the basic feature of the Pythagorean training that we will talk about next time.
Question answer:
Question: [?]
Dr. Steiner's answer: The way a person breathes is intimately connected with the fact that a person can speak. If humans did not have a vertically positioned lung and a vertically
positioned larynx, they could not speak. A dog could never speak words. In general, dogs are more intelligent than parrots and starlings, but parrots and starlings can be made to speak more easily than dogs. This has to do with the whole constitution of the human lungs and larynx, and in particular with the fact that the lungs and larynx are upright. The production of articulated sounds can only take place with an upright larynx and upright lungs. Monkeys cannot produce articulated sounds, even if they can be made to walk upright. The organism is not built that way. The upright larynx exhales and inhales air in a peculiar way. This exhalation and inhalation produces articulate speech. And if we know that articulated speech is connected with the spirit, then we have the scientific possibility of the spirit taking hold in the organism. This possibility is only given in upright walking beings. Only when the body [knew how to walk] upright could the spirit take hold. Beings who still use their front limbs to move forward cannot harbor a spirit. In the Tertiary Period, namely in the Diluvial Period, we had gibbons, highly intelligent creatures. After it became colder, they migrated, but came back again and then had to live in colder climates where the plant life was not so abundant. They had to use their front legs as tools, then gradually learned to walk upright, and the spirit was then able to take possession of the brain.
Question: Can an octopus see like a human?
Answer: Kurd Laßwitz has written a fairy tale that deals with this question. It is highly probable that what comes about in the eye of a human also comes about in the eye of an octopus. One makes the crystal lens from glass, the other from rock crystal or another similar
material, and the same thing comes about through the crystal lens. In humans, the same thing is formed in another substance as in the octopus. But even if the octopus has the same image as the human being, the image must first be spiritualized, processed. Because you have a red circle in your eye, you do not yet have an object. It has to be connected with other images. We don't know whether the octopus can do this.
One could assume that the same animal is created in completely different ways. In the case of the dog, we are dealing with organically structured matter that is permeated by laws. The indifference of matter is what physicists see in the conservation of force or substance. What is used for the eye today can be used for something else tomorrow. Matter is the indeterminate. It would be different if matter had laws within itself. The same thing can consist of different material preconditions. The lawfulness does not depend on matter, but can be devised by us. That is the delightful thing for the Pythagoreans. The matter of the eye is the same as the matter of the ear. On the other hand, if one could make each of them, one would have to demand that one could see with the ears and hear with the eyes! Disharmonies arise that balance each other out again.
Question: [2] Answer: We no longer know the sublunary circle today.
[Question:] How is it that people fall so completely out of harmony?
[Answer:] The Pythagorean view is that there is no perfect harmony on earth, but a becoming of the harmonious out of disharmony. There is only a continual falling out and a drawing back into harmony. This is what forms the individual being. In the individual being we have the detached being that longs to return to harmony. The
world bodies as a whole describe their paths, which do not disturb each other. This is perfect harmony. There is also harmony and disharmony in hunger and satiety: the balance is life. There are beings at rest in themselves as opposed to those in motion. The [individualists] have restlessness within themselves. Christ says: "Where two or three are together, I am in their midst." That is a Pythagorean idea. And it is this: The Pythagorean sees the beginning in the one, in the two he sees the indeterminate added, and the completed being is where the three is added. Think of two points, connect them and you have a line. With three points you have a plane, the triangle. Something planar is only determined by the three. The three has a center, the two only has a side by side. The three has to achieve a balance. It is the spirit that connects them.
Question: [?]
Answer: The Bible is made up of the whole world. Nothing is easier than interpreting the Bible. With the esoteric interpretation, you can get it about right, but you can't know if you're getting it historically [right].
Question: [2]
Answer: Neptune would not be the last planet. In 1839, [Dawes] already communicated this. Kunowsky is a pleasing apparition.