Lecture XVII
Stuttgart, January 17, 1921
My Dear Friends,
May I first refer to a matter from which misunderstandings might arise
in future if some of you are thinking further along the lines we have
been indicating.*
This is essential: You must imagine the plane in which I am drawing the
Lemniscate (Figure 1) to be rotating about the Lemniscate axis, ie. about
the line joining the two foci, - call it what you will. I should therefore
have to draw the Lemniscate in space. This (Figure 1) is the projection
of it. Such is the drawing of the Lemniscate which you must have in mind
with regard to all that I have been saying, - so for example when you
are tracing the bony system or the nervous system in man. Even the blood-circulation
can be traced in this way. You must imagine it all, not in a plane but
in space. The figure eight - the Lemniscate - is therefore legitimate,
but as I said before, you are really dealing with geometrical figures
of rotation. This also underlies what I have just been saying. The forms
of our inner organisation, in the nerves-and-senses system and in the
metabolic and limb-system respectively, are mutually related upon the
principle of a lemniscate of rotation.
We were obliged to seek the criterion of the true spatial movements of
our Earth in changes that go on in man himself. We human beings are, after
all, in some way spatially united with the Earth.
So long as we merely look at the movements from outside, - then, as I
said before, we never get beyond the relativity of movements. If we ourselves
however are taking part in the movements and by so doing we perceive internal
changes in the moving body, then in these inner changes we can, as it
were, read the movements and know them to be real. This is the thing that
matters.
We pointed out that in the processes of human metabolism we have an inner
criterion of man's deliberate movement, wherein he may be said to move
his centre of gravity parallel to the surface of the Earth. Then there
are processes very similar to these metabolic processes, which accompany
our deliberate movements. They give us a criterion of a true movement
which we undoubtedly describe in cosmic space together with the Earth.
I referred to the phenomena of fatigue occurring in the course of the
day, - i.e. while the Sun changes its position in the heavens. We may
formulate it thus: - That which takes place between the head and the rest
of man in a vertical direction when man is upright, takes place in a direction
parallel to the surface of the Earth - that is, in the direction characteristics
of the animal spine - when man is sleeping. Comparing human metabolism
in sleeping and in waking respectively, we have indeed a kind of reagent
for the relations of movement of Sun and Earth.
Thence we can now pass on to the other kingdoms of Nature. We see the
plant, maintaining a radial direction, - the same direction we human beings
have in waking life. We must be clear however, when comparing our own
vertical direction with that of plant growth, that it is not permissible
to think of them with the same sign. We must give opposite signs to the
two. Many are the compelling reasons for us to do this: to give to man's
vertical direction the opposite sign to that of plant growth. I will refer
only to one such reason, mentioned before. The process of plant growth,
culminating as it does in the organic deposition of carbon, is so to speak
cancelled-out in man: It must, as it were, be negatived. The very thing
the plant consolidates into itself, man must get rid of. This and other
considerations will oblige us, if we put the direction of plant-growth
from year to year, so long as we are growing. It represents therefore,
a process in us, similar to that in the plant. Hence, my dear Friends,
we only find our way alright if we think thus: The plant grows radially
upward from the Earth, up onto cosmic space. Ourselves we must imagine
in a different way. There is our physically visible growth, but we must
think of something super-physical, invisible, growing down to meet it
- growing into us as it were, from above downward. Herein we have to seek
an understanding of the human form, - its vertical direction. We must
imagine that while man no doubt grows upward, a kind of invisible plant-formation
grows down to meet him. It is a plant-form with its roots unfolding up
towards the head and its flowers downward. It is a negative plant-forming
process, opposite to the man-forming process. In this sense we must recognize,
which movements are alike in kind. As the plant grows away from the Earth,
so have we to imagine this super-physical man-plant growing in from cosmic
space, even from the Sun, towards the centre of the Earth. This then is
what we have. (I say again, I can only indicate general directions: you
will be able to follow them up in the light of empirical phenomena) In
what we here see (Figure 2) as a line of like direction - a line of growth,
but in the one case striving positively outward, in the other negatively
back and downward - in this we have to seek the connecting line of Earth
and Sun. You cannot think of it in any other way. Nay, to imagine it thus
is comparatively simple, even trivial. You will perceive in this very
line the line of movement both of Earth and Sun. The lines of movement
both of Earth and Sun are to be looked for in the line that joins the
two. Moreover, the line will always prove to be vertical in relation to
the surface of the Earth.
What I have here been putting forward ought really to be the theme of
many lectures. I do however still want to give you something more substantial
as it were, for you to get to grips with. I want to lead you to a more
tangible result, though it will have to follow rather abruptly on the
more methodical reflections we have hitherto pursued.
We have been led to realize that Earth and Sun must be thought of as
moving in a certain sense in the identical orbit and yet again in a way
opposite to one another. You will get a more substantial line of what
this means if you recall what was said yesterday. The constitution of
the Sun, I said, - with the Sun's nucleus and then the photosphere, atmosphere,
chromosphere and corona - can be imagined in no other way than this: While
on the Earth craters are formed by outward thrusts and movements, and
we think therefore of processes that work from within outward (fundamentally
the same is true even of the tides); in the Sun on the contrary we have
to go from without inward. The Sun releases its streams and currents from
the surrounding periphery inward to the interior, to the solar nucleus.
In a sense therefore, we see what is going on the Sun's environment as
we should see things going on Earth if we were situated in the Earth's
centre and looking outward, - only we should then have bank the convex
into the concave. Looking into the Sun, it is as though we should be witnessing
earthly processes from the Earth's centre; only for this comparison the
Earth's inner surface which is concave must be bent convex, so that the
interior of the Earth becomes the exterior of the Sun. Taking your start
from this idea you will be able to realize the polar-opposite character
of Earth and Sun. This too is most important: to realize how the Sun'
s constitution derives from the Earth's once more by a turning inside-out,
- by the same process I explained for the relation of the human metabolic
and limb-system with the skull-bone. The coordination of Man and the Cosmos
is the more thoroughly revealed. The polarity in man is in its inner quality
and process like the polarity of Sun and Earth.
I shall now pursue a line of thought which may look problematical to
some of you, yet you would feel it to be thoroughly sound if we had time
to go into all the connecting links. However as I said just now, I want
to give you something more substantial. We have to look for a curve which
makes it possible or us to imagine the movements of Sun and Earth taking
their course in one and the same path and yet in some sense contrariwise.
The curve can be determined, unambiguously. If you envisage all the relevant
geometrical positions which are to be found in this way, the curve, I
say again, will be uniquely determined. You must imagine it like this
(Figure 3), - a rotating lemniscate which at the same time moves on through
space, resulting in a lemniscatory screw of spiral (as indicated in the
Figure). Imagine the Earth to be at some point of this curve and the Sun
at another, with the Earth following the Sun in movement. So then you
have the movement of the Earth up here, the Sun down here. They go past
each other. Taking all the valid criteria into account, this is the only
way to conceive the real underlying movements both of the Earth and of
the Sun. There is no other alternative than to imagine it arising on this
basis: Earth and Sun are moving, following one another, along a lemniscatory
spiral; what is projected into space arises out of this. Here is the line
of sight (ES, Figure 3). You are projecting the Sun in this position (S);
thereafter, you may assume, the Sun has gone up here(S1). You get the
apparent position, including all the relevant and necessary factors, simply
as the resulting projection when Earth and Sun move past each other along
this line. But I repeat, you must include the manifold corrections, -
the Bessel equations and so on, - if you expect your calculation to come
true. You must include in the geometrical loci all that is really given.
So too you must take into account what I mentioned before, how the Astronomy
of today uses three Suns in its calculations: the real Sun, the Dynamical
Mean Sun and the Astronomical Mean Sun. Two of them are of course imaginary;
only the real Sun is actually there. For our determination of Time however,
we reckon first with the Dynamical Mean Sun which coincides with the true
Sun at perigee and apogee and no-where else. And then we have the third
Sun which only coincides with the other at the equinoxes. You only need
correct, according to all this, the accepted notion of the Sun's apparent
path. Take all of this together and work it out; then you will certainly
get this result, - in full agreement with what we also found observing
Man's relation to the Cosmos.
We now need to relate this curve in the right way to our
solar system, I will begin by drawing the ordinary hypothetical form of
solar system (Figure 4), omitting the two outermost planets for today,
for they are not essential in this connection.
Here (disregarding the relative measures) are the orbit
of Saturn, the orbit of Jupiter, the orbit of Mars, the orbit of the Earth
with the Moon, the orbit of Venus, the orbit of the Earth with the Moon,
the orbit of Venus, the orbit of Mercury, and the Sun. Somewhere along
these orbits we should then find the respective planets. Let us assume
to begin with what this is a valid perspective from some aspect or other.
The question then is how the path of Sun and Earth as we have now described
it fits in with this picture. Work out the calculation in the way indicated
and you will find that it fits in as follows. We have to draw the path
of the Earth with the Earth tending in a sense, towards the place where
the Sun has been, and then again the Sun towards the place where the Earth
has been. We thus get the one self of the Lemniscate - Earth, Sun, Earth,
Sun. When this has been gone round, then it goes on (Figure 5). They move
past each other, as you see.
Thus we obtain the true path of Earth and Sun if we alternately imagine
the Earth to be at the place where in our usual drawings we are wont to
put the Sun, and the Sun at the place where we are wont to put the Earth.
The fact is, we do not get the true relation of movement as between Earth
and Sun if we assume either the one or the other to be at rest. We must
imagine both to be in movement, whereby the one follows the other, yet
at the same time they go past each other. So then we have to picture it.
Seen in perspective, the Sun is alternately in the middle point of our
planetary system and then again the Earth is where we normally conceive
the Sun to be. They change places, taking turns as it were. But it is
complicated, for in the meantime the planets too, needless to say, have
changed their situation, which brings in no little complication. However,
if I take this, to begin with, to be a true perspective, I shall draw
it thus (Sun in the middle point). Then as it were I get the other valid
order by drawing the ideal sequence of the planets with the Earth here
(Earth in the centre) and then Moon, Mercury, Venus, Sun Mars, Jupiter
and Saturn. You see, we are in a way misled by the perspective's, to the
establishment of an extremely simple system, whereas in fact it is by
no means simple. It is as though, with respect to the planets, Earth and
Sun were taking turns, alternately being in the centre of the system.
I confess it is not at all easy for me to be telling you these things,
which at the present stage might still be thought fantastic. We cannot
not now bring all the mathematical paraphernalia to bear on them, but
I assure you they can be calculated in all detail. The desire was for
me to explain the relations of Astronomy to other branches of Science;
hence at the end of these lectures I must try to give a resume as clear
and as complete as possible.
Tracing the path of Earth and Sun (now, once again, apart from the planetary
system as a whole) we have then to imagine a Lemniscate in which the Earth
is following the Sun. Here is it, projected (Fig.6). Incidentally, you
may also see in this a possibility of giving meaning to the idea of Gravitation.
The one draws the other after it: that is the underlying principle. Think
of it in this way, and you will no longer need the somewhat questionable
quality of gravitational and tangential forces, for they are here reduced
to a single force. Think it through thoroughly and you will find it so.
You must admit, it is a rather problematical feature in the Newtonian
conception. We are to think of the Sun in the centre and the Planets around
it - endowed, one and all, with a kind of "shove" in the tangential direction,,
one and all, without presupposing which the Newtonian system would break
down.
Taking this then (Figure ) to be the path of Earth and Sun, - if you
wish to bring out in perspective, along with the course of Earth and Sun,
the path-forms of the other planets, you must imagine the paths of the
inferior planets somewhat in this way (small Lemniscates in Figure 6).
This will enable you - if this be the line of sight - to get the perspective
of a planetary loop, for a certain position of the planet along its path.
The line of sight is here (v). In this position (s) we get the loop, while
these two branches (u) will appear to run out into the infinite. On the
other hand, taking this once more to be the path of Earth and Sun and
this the path of the inferior planets, you must imagine the corresponding
paths of the superior planets to be Lemniscates like this (Figure 7).
I should now have to go on drawing upward, but the nearest part would
be like this. And now this Lemniscate * moves on, makes its way through,
- through the Lemniscate of the superior planets.
It is a system of Lemniscates in determined order and relation. Such
are the paths of the planets; such also is the path of Earth and Sun.
Now you will easily harmonise what I have here presented in the grammatic
outline, with the fact that we see the loops of Venus and Mercury in conjunction
and those of Jupiter, Mars and Saturn in opposition. In our perspective
it is the necessary outcome. Above all, you will recognize once more what
the connection is between the planes and the human being. You need but
look at this picture and you will say to yourselves: What you have here,
in Mercury and Venus, is near in direction to the path of Earth and Sun.
It is in the cosmic neighbourhood, so to speak, of the path of Earth and
Sun. It is therefore in this relation: It has to do with the radial line
- fundamentally, the connecting line of Earth and Sun. As against this,
the other paths - those of the outer or upper planets - work more by virtue
of their lateral or spherical direction. In their effects, they more approach
what is peripherical in movement. We may then also formulate it thus:
What we behold in Venus and Mercury is far more akin to what is living
as a cosmical reality in us ourselves. Whilst, what we see in the paths
of the superior planets is more akin to the fixed-star Heavens in general.
Here too we reach a kind of qualitative valuation of what is taking place
in the Cosmos. Of course the lines I have been drawing are only meant
diagrammatically. It should really be put this way: An inferior planet
has a path, making a lemniscate loop-curve the centre of which is the
Earth-and-Sun path itself. A superior planet, on the other hand, embraces
the Earth-and-Sun path in its own lemniscate-loop. Such is the essence
of the matter; the thing itself is so complicated that the mental pictures
we can form scarcely be more than diagrammatic.
You see from this however, my dear Friends, - unwelcome as the news may
be to some, - we need to get away from a principle that crept into the
explanations of nature with the beginning of modern time. I mean the overriding
principle of simplicity. It grew to be the accepted tendency. The simple
explanation is the right one! Even today one is severely censured if one
puts forward what is not simple enough. Yet Nature is not simple. On the
contrary, it would be true to say: Nature the real World - is that which,
looking simple proves on examination to be complex. What appears simple
on the surface, is as a rule only the outward glory, only the outward
semblance of it.
It was not by any means my prime intention to let these lectures culminate
in this way. I am not pre-disposed on principle to put forward things
out of keeping with the accepted notions. We only want to get at the truth.
As it is is however, the assumptions of the modern astronomical world-picture
involves so many contradictions that in the end, having studied the current
astronomy, one comes away dissatisfied. Hypothetically, it begins by assuming
the world-picture I have also indicated in this sketch (Figure 4), - the
elliptic orbits of the planets, the Sun in one focus, and so on. The planetary
orbits are then assumed to be in different planes, inclined to one another.
For there is no alternative at this stage; the different inclinations
are given by the perspective. The complications of it are complications
of perspective. Yet the real calculations are not done to the basis of
this simple solar system which people have explained to them at school
and then retain for life. In practice, they take their start from the
Tychonic system. Then one correction after another has to be applied.
From the accepted formulae, one calculates, say, the position of the Sun
at given time, and it does not come true. Instead of the real Sun being
there, it will be the Dynamical of Astronomical Mean Sun, - something
fictitious therefore. So it is time and again: Imagined entities are there,
and more corrections must be introduced to get to what is real. In these
corrections there lies hidden that which would lead to the truth. Instead
of holding fast to the conventional formulae and being led to fictitious
entities, one should bring movement into the formulae themselves - make
them inherently mobile - and then draw curves accordingly. If one did
so, one would soon reach the system here drawn, though I repeat, the drawings
are diagrammatic.
What I have sought for above all is that a picture should arise in you
of the harmony there is between the organisation of Man and the constitution
of the Cosmos. If you have really been following thus far, you cannot
possibly regard this as offending against the scientific spirit. When
the transition emerged from the Ptolemaic to the Copernican World-picture,
a profound change was taking place in the whole way of interpreting the
connection of man with the celestial phenomenal. In very ancient times
- though from a different perspective so to speak, as mentioned a few
days ago - man still had clear and penetrating ideas of the harmony between
the movements in the Heavens and the form of Man. What they then had was
more instinctive; raised into consciousness however, it becomes the true
spirit of modern science, to which we too must be faithful, - the more
so when venturing upon this problematic ground.
Fundamentally there is no difference between the way of applying mathematics
in general and the way we are applying this qualitative mathematic (which
we have first had to develop) to man and the celestial phenomena. There
is another thing however, you need to recognise in this connection. In
the same period when the transition was developing between the old heliocentric
system and the new, the evolution of mankind suffered a certain break
in the life of knowledge, Namely the bridges were demolished between the
physically sense-perceptible or natural world-order and the ethical or
moral. I have often mentioned in other lectures, how we in our time are
thus torn asunder. On the one hand our theoretical ideas about Nature
lead us to conceive some primeval cosmic entity in the beginning, from
which the Universe was to unfold by purely natural events. So then evolved
the Earth on which we are. So it goes on again by dint of purely natural
laws and it will one day reach its end. In the midst of it are we. Out
of our inner life there arise ethical impulses; no-one knows where they
come from. And if one thinks according to this dualism, one cannot doubt
that at some future time even these impulses will suffer burial in the
universal grave.
This is the way one thinks when failing to build a bridge between the
natural world-order and the ethical. I have indicated on other occasions
how the transition is to be looked for. It can indeed be found throughout
Anthroposophical spiritual science. Here I would only draw your attention
to a specific aspect of it, - for the rift between the natural world-order
and the moral makes itself felt in diverse realms, and among others it
affects our present subject. Here too, in the evolution of mankind the
natural aspect and the ethical have in a certain way fallen asunder. The
ethical has been cultivated in Astrology; the natural in an Astronomy
bereft of spiritual values. There is no need for me to insist that Astrology
as pursued today is scientifically unacceptable. I need not prove to you
that this is an aberration on the one side. Yet on the other side our
Astronomical world-system, as we call it, also involves an abberaction.
All these perspective lines - or if you will, projective lines - that
are conventionally drawn to represent our solar system, are not to be
conceived as realities at all. Nor even are the lines that arise when
we observe a further resultant movement, built up again of many components,
namely the Sun's proper movement, the whole solar system going with it.
All these things are built up of very many components; we are in the midst
of relativities and we need some criterion to hold to. The criterion may
seem vague to many people, yet it is there and it can lead us to an understanding
of the curves in question. We have to penetrate the secret: Why is it
man has an inner need to lie down horizontally in sleep, - thus to escape
in sleep from the connecting line of Earth and Sun? Just as he can only
carry out his voluntary movements while moving his centre of gravity at
right angles to the line joining Earth and Sun, so with his involuntary
movements: He can only carry them out by lying down, putting himself in
a direction at right angles to the path of Earth and Sun. If he wants
to escape from the effects of voluntary movement - if he wants, what would
otherwise work itself out in voluntary movement, to work inside him and
bring about a metabolic interchange between his body and his head - he
must lie down, he must align himself in this way. In like manner you will
be able to find other directions that are at work in man.
From the directions ascertainable in man - derivable from man's own form
and stature - you will be able to compose the curves that are really there
in the movement of heavenly bodies. Granted, it is not so easy as what
is done with mere telescopes and measured angles. Yet it is the way, the
only way, to find the relationship between the human being and the celestial
phenomena.
* The beginning of this lecture arose out of a mistaken remark by one
of those present, which is omitted. Dr. Steiner's explanations, important
for a general understanding of the lemniscatory curves, are reproduced
apart from this.
Note by the Editor of the original edition, Dornach,
1926
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