The Value of Thinking for Satisfying our Quest for Knowledge

GA 164 — 20 August 1915, Dornach

Episodic Observation On Space, Time, Movement

I thought that at most a dozen people would be here today and wanted to say something, as is to be expected, that is not part of our usual considerations, but which may be important for some who can immerse themselves in the matter, for the assessment of some things that currently play a role in relation to certain concepts of space and time and movement.

There are theoretical physicists today who believe that a profound revolution is taking place in relation to the simplest conceptions of the world. Among these simple conceptions of the world, on which theoretical physics is based, we want to look today at a small part that relates to time, space and motion. This will provide the basis for a more extensive consideration to be undertaken in the near future, which can lead us deeper into what is currently being sought in fundamental physical considerations.

You will all have heard that what is known as the theory of relativity is prevailing in modern physics. The theory of relativity – and here there are also many variations – is today advocated by countless theoretical physicists. It is expected to bring about a complete revolution in all the concepts that physicists, when they have been engaged in elementary theoretical considerations, have hitherto recognized as correct and which, after all, go back essentially to Newton. Now, however, the newer theoretical physicists of today believe that all these Newtonian concepts, which were still accepted as absolutely incontrovertible during our time as students, must undergo a revolution, indeed that, to a certain extent, the entire theoretical basis of physics, as it has been believed and is still believed, is actually false. Now, the reason why I have to relate the observation I want to make to this newly emerging theory of relativity will become clear later.

In order for what I have to say not to remain completely incomprehensible, I would like to start from very simple, elementary concepts in order to show you immediately what kind of idea can be associated with the concept of time. Let us start, as I said, with very elementary things. Let us assume that some object, which I will call (a) for the sake of argument, a rolling ball or something similar, moves in a direction that I will indicate with this line; so (a) moves along the straight line in the direction of (b):

Now, as you all know, the distance traveled by such a moving object in one second is called the speed. So let us assume that (a) would come here in one second, up to (a_1). In physics, this distance (a) up to (a_1) would be called the speed and denoted by (c). And if we further assume that the moving object continues through the following seconds, then, if it were to perform a uniform motion – and we only want to talk about such a motion – it would be at (a_2) at the end of the second second, where (aa_1 = a_1a_2) , that is, with the same speed (c). During the second second, the moving object goes from (a_1) to (a_2), during the third second from (a_2) to (a_3), during the fourth second from (a_3) to (a_4), and so on. Now, let us assume that we observe this movement for a certain period of time and that our movable object travels a certain distance. If it moves from (a_5)

then, when this movable has rolled from (a) to (a_5), the piece of space - which we understand here in its one dimension - is called the way; so that (a) to (a_5) is the way that it has traveled; (c) is the speed; the distance traveled is denoted by (s); and one says: the movable (a) has traveled the distance (s) at a speed (c) in a certain time - here five seconds. This transit time is denoted by (t).

Now there is a certain relationship between distance, time and speed. The simplest relationship that has been found is that one would say here: (s) - the distance - is five times from ( )to (a_1), that is, once the distance (a) to (a_1) times (5), which is (5) seconds, so that is the time ; so we have to multiply what we have called the speed – this piece of (aa_1) – by (5), and then we get the distance (s = c \cdot t) (distance = speed (\cdot) time). So there are three terms in this formula: (s), (c), (t).

Now you know that an infinite amount has been written about time by a number of philosophers, mathematicians and also theoretical mechanics. People believe that they have an idea, a concept, of time, but if they had to explain and reflect on what they understand by time, everyone would very soon realize that they do not really have a proper idea of this concept of time, which is one of the most commonly used concepts in mechanics. In order to be able to study anything about the concept of time, let us stick to this formula, which, after all, initially sets the concept of time into a uniform, rectilinear motion. But even though this formula can be found in every physics book, in physics it is surrounded by a whole host of – I won't say ambiguities, but a lack of clarity, a lack of will to go deeper into the matter. And this is due in particular to the fact that in our schools, the teaching with regard to something that we all learn does not teach us certain distinctions, but these are important if one wants to arrive at more precise concepts in a certain direction. In our schools, we learn to speak of four types of calculation: addition, subtraction, multiplication and division. But when it comes to division, I don't think we are often made aware that there are actually two completely different things involved in the usual calculation operation. I will show you this in a very simple way.

Let us assume that we have an ordinary apple and divide it. We can divide it into five, into ten parts and so on, then, when we have divided it, we get a so-and-so-many-parts of the apple. If we want to distribute the parts, what we distribute is just a piece of the apple. We are actually performing a division here. I want to write it as a fraction, because that is the same as a division. I can say: an apple is divided into, say, ten parts, and the result is one tenth of an apple. Now take a look at what I have written on the blackboard:

$$\frac{1 apple (thing)}{10 (number)} = \frac{1}{10}apple (thing)$$

In the numerator or dividend, we have a quality, something real; in the divisor or denominator, we have nothing real, but a mere number; (10) is a mere number here; and in the quotient, we have something real again: one tenth of an apple.

This fact does not change if we divide twenty apples instead of one. If we divide (20) apples by (10), we get (2) apples instead of one tenth of an apple:

$$\frac{20 Apfel}{10} = 2 Apfel$$

The (20) apples are again a thing; below is only the number and as a quotient we get again a thing. That is a division.

But dividing can have a completely different meaning. I can have (20) apples in the dividend above, but below as the denominator or divisor, let's say (2) apples, then I have a thing above and below. What do I get as a result? In this case, I do not get a real thing as a result, but I find out how often (2) apples are contained in (20) apples, I get (10), that is, I get a number:

$$\frac{20 apple (real thing)}{2 apple (real thing)} = 10 (number)$$

Again, I am dealing with a division, but this time it has a completely different meaning than the division in the first case. In the first case, I divide a thing and get another thing in return; in the second case, I don't divide at all, but set myself the task of exploring how often a thing is contained in another thing, and that's where I get a number.

We can therefore say that division is not always the same as dividing, but that there are two types of division that are strictly different from each other. When teaching, it is therefore always necessary to explain that there are two types of division. In the first, the task arises for me to investigate what comes out when you divide a thing; in the second, the task arises to investigate how often a thing is contained in a similar thing – they must be similar, because of course you can't ask how often (2) apples are contained in (20) pears – and then we get a number out.

This must be borne in mind when studying the formula (s = c \cdot t).

Now this formula can also be written differently. I don't always have to look for the (s), but I can also look for the (c) or (t), then the formula changes. If I look for the (c), then I get it by dividing the (s) by (t). By dividing the whole space by (t), I get the space that has been traversed in (5) seconds, by (5), which is the speed (c): $$c= \frac{s}{t}$$ Likewise, you can get (t): the time. Let's assume that you divide (s) by (c). If you ask: how often is the distance of one second included in the whole distance, then it is included five times. So you get the time:

Let's take a closer look at these formulas. First, let's take the second one and compare: (s), which is the distance here, the length (a) to (a_5), we have that in the numerator; here in the denominator we have (c). What is (c)? Well, that's the distance in one second. Distances are this: (s) is a distance, (c) is a distance. What form of division does that resemble? Well, it resembles this form (20) apples : (2) apples = (10). Here (in the numerator) you have apples and here (in the denominator) you have apples; here (in the numerator of (\frac{s}{c})) you have distance and here (in the denominator) you have distance. What should be in front of that? Just a number. That is, (t) turns out to be nothing more than a number in our physical considerations. For if I regard (s) and (c) as distance, that is, as a thing - both are, after all, distance or a piece of distance -, then, from the nature of the division, time (t) can only figure as a number. Just as the number (10) ((20) apples : (2) apples = (10)) is a number and nothing less or more, so in this division (t), time, can also be nothing but a number.

You can also take the division form (1 apple: 10 = \frac{1}{10} apple), then this is the same as the formula (c = \frac{s}{t}). On the other hand, if we divide a thing by a thing, what must come out? A number like here (t = \frac{s}{c}), where with (t) we are dealing with a mere number. That is, both formulas indicate that - insofar as we stop at physics - we get nothing more than a number for the time after the nature of the division. And in this case ((20) apples: (2) apples = (10)) it is a number that refers to apples and shows how often (2) apples are contained in (20) apples, and here, in the case of time, (\frac{s}{c} = t) is a number that shows how often the velocity is contained in space.

Now, none of you will see the number as such as a thing. If you give any boy or girl not (3) apples, but only (3) as a number, they will not be satisfied. So in the number you cannot see a thing, but just a mere abstraction, something that merely indicates relationships in the external world.

From this consideration, we can see that time itself slips through our fingers through the physical consideration; it shrinks to a mere number. Just as we cannot philosophize about the number, we cannot philosophize about time either, that is, it has been reduced to the idea of a number. That is why we cannot find time in things, no matter how long we search everywhere, because it only appears as a number. What is the connection? Well, I don't think a boy or girl needs to be particularly old to give a healthy gut feeling answer to the question: What interests you, the apples or the number? Of course, someone could speak sophistically and say, “I am interested in the number because I prefer (8) apples to (6)”; but that is only because (8) apples are more than (6). So the number is not what it is about, but the apples are, the tangible is.

But from this it follows that we must adhere to the material and not to the number when we speak of time, space and speed. And if we now consider the material, time is eliminated from the outset, that is, it is a number and not a material thing. So you can say to yourself: we have (s), we have space, we have the piece of space that our movable passes through. If it continues to roll, it can still cover a great deal of space. Space is something material outside. But that is not what is most important, because space can be thought of as continuing forever. But there is something else that is very important to us, and that is (c). How (a) travels through space depends entirely on whether it travels, say, (20) or (25) or (50) cm in one second, and so on. In turn, how much it travels depends on how fast it moves. But how fast it runs, that is inside it, that is peculiar to it inside. And the whole process depends on what is peculiar to the movable inside. So it depends on the speed of the movable, which belongs to the movable as such, is an inner quality of the movable. And if we look at the world in terms of mechanical processes, then, when we speak of reality, we must speak of the intrinsic speed of the bodies or atoms or molecules. And the whole process forces us to speak of intrinsic speed as belonging to things, just as red color belongs to the rose.

So the fundamental concept is speed; it is what matters. It follows that we must not adhere to the formula that has (c) here (c = \frac{s}{t}), and must not believe that with space and time we have something particularly real, but what is real in things is speed, not time. Time, in turn, is only abstracted from the concept of speed because things have different speeds. If we look at the different speeds and want to reduce them to a common denominator, we get the concept of time. This is an abstraction, just as the generic term “apple” is an abstraction and only the particular, the concrete apple, is real. So if we look at the mechanical reality of things, we have to look at speed and must not believe that we can put the concept of time in the foreground. That is the big mistake that is made everywhere in physics, that one does not consider that one must start from the speed that is inside things, that belongs to them as life belongs to living bodies.

So, my dear friends, remember: not time but velocity is what must underlie mechanics. You might say that making these distinctions is mere madness. But it is not madness. These things are fundamental to our understanding of certain aspects of reality, and I will point out to you in a moment something that shows how fundamentally significant they are.

In the various discussions about the theory of relativity, people were struggling to come to terms with the concepts of time and speed. Now I would like to show you, by means of two speculations, the way in which certain people think and formulate their thoughts when they talk about time and speed. I have to introduce you to a strange character, Mr. Lumen, who plays a certain role in the theory of relativity. What kind of strange gentleman is he? Yes, you see, this is an, I would say, “imaginary acquaintance” that Flammarion has made. This Mr. Lumen has a very strange ability, which we can understand in the following way.

You all know from your physics lessons that light has a certain speed; it travels 300,000 km per second. (c), so everything that, in our view, is mechanically inherent in light is a speed of 300,000 km per second. Let us assume, for example, that here is the earth and that a beam of light goes out into space from the objects and events that happen on earth (as schematically indicated on the board) and one says yes, because the light goes out, one sees the things. Let us now assume the following. We have had a somewhat abstruse mathematical-physical lesson, and, let us say, a eurythmy lesson from three to four o'clock. From all this, the light goes out into space and one can observe from outside what is happening here. And since light travels at a speed of 300,000 km per second, what happened here between three and four o'clock this afternoon also went out into space at a speed of 300,000 km a second, so that if you imagine an observer 300,000 km away, he will see what is happening here on Earth only after one second.

Now Flammarion assumes that Mr. Lumen rushes out into space even faster than the speed of light, namely at a speed of 400,000 km per second. What will be the result of this? He will continually overtake the light, because after the light has traveled one second, he is already 100,000 km further away. When he rushes out and looks back, he must come to the manifestations of light, where he sees what has happened here now and between three and four o'clock. But since he not only catches up with the light, but overtakes it, it must follow that he does not perceive the eurythmy lesson first and then our lesson, but everything in reverse, first the end and then the earlier. It is a strange spectacle that this Mr. Lumen experiences. He sees everything in such a way that he first sees the end and then the beginning, because he overtakes the light.

As I said, such ideas have played a certain role in the discussions about the theory of relativity. I would like to present you with yet another idea, which has also played a certain role and which the naturalist Baer formed. He said to himself: One could imagine that man does not live his life in about 70 or 80 years, but in 70 or 80 seconds. His pulse would simply have to beat so much faster that one second would contain a year. This could cause man to be not just like a mayfly, but like a 70-second animal, if only his pulse beat fast enough. What would be the result? Such a person would experience tremendous things in 70 seconds. If, for example, he looks at a plant that has remained true to its species, he would never come to the conclusion that a plant grows out of the earth, but he would come to the conclusion that plants are eternal beings. Thus, such a person would have a completely different view of the world, simply because the speed of his life could be thought of as increasing in the same measure as the speed of his pulse compared to the rest of us. Or, says Baer, let us imagine that man does not live 80 seconds or 80 years, but 80,000 years, and that the pulse rate is so much slower, then the whole world would be different again. For example, the sun, which appears to move at a certain speed to us, would race across the sky like a fiery wind; we would not distinguish the individual sun, but would see it racing around like a reddish wheel. Plants would shoot up quickly and then fade away at breakneck speed, and so on.

Baer presents this as a possible idea to show how the world view depends on the subjective constitution of the organism. You see, everything, absolutely everything, is called into question.

If we consider the type of thinking that underlies such ideas as those of Mr. Lumen or Baer's Flammarions, one thing is important to note. Let's take Mr. Lumen again. It is assumed that Mr. Lumen would be able to fly 400,000 km per second, thus overtaking light and catching up with later light images. But now take what you can really take when you delve deeper into our spiritual scientific concepts. We can even disregard the coarser physical body altogether and go straight to the etheric body. Yes, when we go into the etheric body, what is it? It is ether, light ether, it is itself weaving light. Hold on to that, because what follows from it? It follows that when we move in space, we can move at the highest speed that is peculiar to light. So if someone says that a person like Mr. Lumen moves at a speed of 400,000 km per second, then we have to ask – I will even leave out the physical body and just assume that an etheric body could move out – how fast could he possibly move? Well, at most at a speed of 300,000 km per second, the speed of light. We cannot say that the etheric body overtakes light, because it is itself movable light. So Mr. Lumen cannot be woven out of anything that exists in space; in other words, he is an unreal conception, he is a pure fantasy. For to the tangible or the substantial in the world, its speed is immanent or inherent. It is inside of it. It is its property. We cannot tear it out. We cannot say: we separate the speed from the thing – but it is a property of the thing. We cannot speak of a property that exists separately outside the thing. So we must also say, in the face of Baer's ideas: in the moment when one realizes that the speed of the pulse beat belongs to the essence of every human being, one also realizes that we cannot have any other speed than that of our pulse beat. We are human because we have a certain pulse rate, and we cannot imagine it being any different, because we would cease to be human if, for example, our pulse were a thousand times faster than it actually is. Speed belongs to the material world.

It is important to see how spiritual science leads to the essence of things, and what the thinking that has developed into our time leads to without engaging in spiritual science. It leads to the formation of ideas such as those of Mr. Lumen or the pulse rate that has accelerated a thousand times, which are simply impossible or unreal. One calculates with fantastic concepts if one does not realize that time is a mere number. Thus, so-called rational mechanics has led to completely unreal concepts. Spiritual science leads us to say: Yes, what is such a Mr. Lumen, who races 400,000 km while he would at most travel 300,000... [gap in the transcript]... He is nothing more than the famous gentleman who pulls himself up by his own hair.

From this point of view, then, spiritual science is there to bring human thinking, which has lapsed into fantasy, back to reality, not to dissuade it from reality. You see, while people accuse spiritual science of being fantastic, it is actually there to guide the fantastic ideas and concepts of physics back to reality. And it will be extremely important for healthy thinking in the future that children are really taught something like the two types of division, so that they do not calculate with all kinds of ambiguities, but with definite concepts. When it comes to ideas and concepts that have a bearing on reality, there is no other way than to face reality squarely, that is, to think with spiritual science, because only then do real, not fanciful, concepts emerge.

Before the theory of relativity, physics had Newton's idea that space is an emptiness, a vessel, so to speak – whether it is infinite or not, we will not examine that now – and time flows like a uniform stream; things are in space and processes run in time, and depending on whether a thing needs this or that time to cover a certain space, it is given a certain speed. This idea is untrue because it does not look at the essence of space and time and thus divides speed, which is actually an inner property, into the two unreal ideas of space and time. Speed is truly the original, while physics always regards speed as a function of space and time. But what belongs to things is their essential nature, and spiritual science shows that one must take certain paths in order to avoid fantasies about space and time - such as that of infinite space or that of time as a flowing stream - but to arrive at the real reality of speed. The entire field of mechanics, which we absorbed in our youth as something tremendously secure, as the most secure there is in science after mathematics, operates with very vague concepts because it does not know what the nature of speed is and does not know how to regard it as fundamental.

Now the impetus for the theory of relativity from Minkowski, Einstein, Planck, Poincaré, the late mathematician and physicist and so on, came precisely because they could no longer cope with this childish Newtonian idea of empty space and regularly flowing time and things that move at a certain speed. Certain experiments led to concepts that did not agree with what had been considered the most certain.

Recently, I have developed a concept here that is purely related to spiritual science, which may have come as a surprise to some. I have developed the concept that it is not true at all to believe that the most important thing in the head is substance, matter, because precisely where we suspect matter, it is hollow and, from a spiritual point of view, we are all hollow-headed. I used the comparison with the air bubbles in a bottle of Selters water. There it is also the case that where we believe we perceive something real, there is nothing. All around is the spiritual reality and in it there are holes everywhere; you see them, just as you only see the bubbles in the Selters water, which are air, you do not see the water. And if people believe that there is something where I touch the table, that is not true either, because there is actually nothing there. I touch the hollow space and because there is nothing there, that is why I cannot go further.

We arrived at this conclusion quite systematically on the basis of spiritual scientific premises. Certain insightful and perceptive physicists have now been pushed to a similar conclusion by other means, because certain processes in nature simply do not agree with the concepts of Newtonian mechanics, which are considered so certain. And these things include, for example, the processes at work in the cathode rays that you are familiar with, which, as you know, can be observed in certain evacuated glass tubes. Here we are dealing with something that, as a moving part, has speed, with electrons, figuratively speaking, with flowing electricity. And through observation, through the experiment of observing the cathode rays in the tubes, which are flowing electricity, the physicists have come to very peculiar ideas. And I would like to read you one such idea. It can be found in a lecture by Poincaré on “The New Mechanics”. He ties in with the ideas that arise from the cathode ray experiment, because this does not agree with the Newtonian concept of speed. And after rather confused trains of thought, he sees himself compelled to make the following concession:... [gap in the transcript] ..., and there the physicist feels compelled to say the following:

“Matter has now become completely passive. The property of resisting the forces that seek to change its motion no longer applies to it in the true sense of the word. When a cannonball moves at high speed and thereby becomes the carrier of a living force, of a tremendous energy that spreads death and destruction, it is no longer the iron molecules that are the seat of this energy, but this seat is to be sought in the ether that surrounds the molecules. One could almost say that there is no longer any matter, only holes in the ether.” - Well, what more do you want, my dear friends? — “And as far as these holes seem to play an active role, it consists in the fact that these holes cannot change their location without affecting the surrounding ether, which reacts against such changes.”

Matter is holes in the ether! Physics is therefore compelled to admit this based on its current experience. And building on such experiences, another physicist, Planck, uttered a sentence that is highly remarkable, namely the sentence that says: We experienced in the forties of the 19th century that Helmholtz approached a certain problem in such a way – it wasn't Helmholtz, but Julius Robert Mayer, but we don't want to get into this important question of priority now – as someone who doesn't put the cart before the horse, but before the horse. People had always said before that the distribution of forces in space had to be studied in a certain way. Helmholtz turned the matter around. He said that one must study the universe in such a way that only the whole universe can be a perpetuum mobile, whereas no individual process in the universe can ever be a perpetuum mobile. The people before Helmholtz had tried to explain the world without any perpetuum mobile at all. But now Planck says that a similar process must occur with regard to the ether. There are countless theories about the ether, ranging from the idea that was held in the past, when the ether was thought of as rarefied matter, to the idea of Lord Kelvin or J. J. Thompson, who imagined the ether to be a rigid liquid - of course, it is not to be thought of as a liquid like water - all intermediate stages are represented. And now Planck says as a physicist: Physics will only be cured when we start from the principle that no conception of the ether gives a tenable physics that attributes material properties to the ether. That is the sentence that one of the most important physicists of the present day has uttered. This means that if the ether is to be a tenable basis for physics, only spiritual properties may be attributed to it. And from this it follows that today's physicists are urged to think of matter as holes surrounded by ether, which, however, must be imagined as having no material but only spiritual properties. So: holes surrounded by spiritual ether, that is what must be taken as a basis in order to arrive at a tenable physics. This is being prepared today; it exists.

Now one can raise the question: Yes, but where does that leave the possibility of establishing a materialistic world view when physicists talk about matter consisting of holes and the ether can only have spiritual properties? One is almost forced to say: there is no longer any matter, there are only holes in the spiritual ether, and matter cannot change its location without exerting an influence on the surrounding ether, a reaction in the spiritual ether. That is what physics comes to.

However, one will need a sharp logic and must not be afraid to tackle such questions as to how the concept of speed is really to be grasped if it is not to contradict what the experiment expresses.

Take these things as something that should be said to prove that the humanities, so reviled as being unscientific, are in their foundations infinitely more scientific than that which is considered science today, because they approach things, I would say get to grips with them, in the sharpest logic. And that is what we must seek above all: a sharp grasp of the concepts, a definite conception of what otherwise confronts us as a vague thing in the world.