the Dimensions of Space.
24th June, 1922.
My dear Friends,
things I shall have to explain to-day may be apparently a little far
removed from our more concrete studies of Anthroposophy. They are however
a necessary foundation for many other perceptions which we need — a
foundation on which we shall afterwards have to build in our more intimate
a certain inherent difficulty for our human power of knowledge and
understanding when we speak of the physical bodily nature of man on
the one hand, and the soul-and-spirit on the other. Man can gain
ideas about the physical and bodily with comparative ease, for it is
given to him through the senses. It comes out to meet him, as it
were, from his environment on all sides, without his having to
do very much for it himself — at any rate so far as his
consciousness is concerned. But it is very different when we
come to speak of the soul-and-spirit. True, if he is open-minded
enough, man is distinctly aware of the fact that such a thing exists.
Men have always received into their language designations,
words and phrases referring to the soul-and-spirit. The very
existence of such words and phrases shews after all, for an open-minded
consciousness, that something does exist to draw man's attention to the
reality of soul-and-spirit.
the difficulties begin at once when man endeavours to relate the world of
things physical and bodily with the world of soul and spirit. Indeed for
those who try to grapple with such questions philosophically, shall we
say, the search for this relationship gives rise to the greatest
imaginable difficulties. They know that the physical and bodily is
extended in space. They can even represent it spatially. Man forms
his ideas of it comparatively easily. He can use all that space with
its three dimensions gives to him, in forming his ideas about things
physical and bodily. But the spiritual as such is nowhere to be found
people, who imagine they are not materialistically minded — though
in reality they are all the more so — try to conceive the things of
the soul and spirit in the world of space. Thus they are led to the
well-known spiritualistic aberrations. These aberrations are in reality
materialistic, for they are an effort to bring the soul and spirit perforce
quite apart from all that, the fact is that man is conscious of his
own soul-and-spirit. He is well aware of how it works, for he is aware
that when he resolves to move about in space his thought is
translated into movement through his will. The movement is in space,
but of the thought no open-minded, unbiased thinking person can
assert that it is in space. In this way the greatest
difficulties have arisen, especially for philosophic
ask: How can the soul-and-spirit in man — to which the Ego
itself belongs — work upon the physical and bodily which is in space?
How can something essentially unspatial work upon something spatial?
theories have arisen on this point, but they all of them labour more
or less under the difficulty of bringing the soul-and-spirit, which
is unspatial, into relation with the
physical and bodily, which is spatial. Some people say: In the will,
the soul-and-spirit works upon the bodily nature. But in the first
place, with ordinary consciousness, no one can say how the
thought flows into the will, or how it can be that the will, which is
itself a kind of spiritual essence, manifests itself in outer forms
of movement, in outer activities.
other hand the processes which are called forth by the physical world
in our senses — i.e., in the bodily nature — are also processes
extended in space. Yet inasmuch as they become an experience in soul
and spirit, they are transformed into something non-spatial.
Man cannot say out of his ordinary consciousness, how the
physical and spatial process which takes place in
sense-perception can influence the non-spatial, the soul-and-spirit.
recent times, it is true, men have sought refuge in the conception,
to which I have often referred, of ‘psychophysical
parallelism.’ It really amounts to a confession that we can say
nothing of the relation of the physical and bodily to the
soul-and-spirit. It says, for example: The human being walks,
he moves his legs, he changes his position in external space. This is
a spatial, a physical-bodily process. Simultaneously, while this is taking
place in his body, a process of soul-and-spirit is enacted — a process
of thought, feeling and will. All that we know is
that when the physical and bodily process takes place in space and
time, the process of soul and spirit also takes place. But we have no
concrete idea of how the one works upon the other. We have
psycho-physical parallelism: a psychical process takes its
course simultaneously with the bodily process. But we still do
not get behind the secret — whose existence is thus
expressed — that the two processes run parallel to one
another. We gain no notion of how they work on one another. And so it
is invariably, when men try to form a conception of the existence of
the 19th Century, when the ideas of
men were so thoroughly saturated with materialism, even this question
could arise: — Where do the souls sojourn in universal space
when they have left the body? There were even men who tried to refute
spiritualism by proving that when so and so many men are dying and so
and so many are already dead, there can be no room in the whole world
of space for all these souls to find a place of abode! This absurd
line of thought actually arose more than once during the
19th Century. People said, Man cannot be
immortal, for all the spaces of the world would already have been
filled with their immortal souls.
these things indicate what difficulties arise when we seek the relation
between the bodily and physical, clearly spread out as it is in space,
and the soul and spirit which we cannot in the first place assign to
the spatial universe.
have gradually come to this pass; our purely intellectualistic thinking
has placed the bodily-physical and the soul-and-spirit sharply and
crudely side by side. For the modern consciousness they stand
side by side, without any intermediary. Nor is there any possibility
of finding a relation on the lines along which people think of
them to-day. The man of to-day conceives the spatial and
physical in such a way that the soul has no conceivable place
in it. Again, he is driven to conceive the soul-qualities
so sharply separated from the physical and bodily,
that the absolutely unspatial soul-and-spirit, as he conceives it,
cannot possibly impinge at any point upon the physical. ...
sharp contrast and division was however only developed in the course
of time. We must now begin again from an altogether different angle
of approach, which is only made possible once more by taking our
start from what anthroposophical spiritual science has to say.
first place, anthroposophical science must
consider the nature of the will. To begin with, straightforward
observation shews undoubtedly that the
will of man follows his movements everywhere. Moreover, the
movements man accomplishes externally in space when he moves about,
and those too which take place within him in the fulfilment of his
everyday functions of life, in a word, all the activities of man in
the physical world-are in the three dimensions of space. Hence the
will must also go everywhere, wherever the three dimensions extend.
Of this there can be no doubt.
if we are speaking of the will as of an element of soul-and-spirit, there
can be no question but that the will — albeit a thing of soul and
spirit — is three-dimensional. It has a three-dimensional
cannot but think of it in this way: — When we carry out a
movement through our will, the will adapts itself and enters
into all the spatial positions which are traced, for example,
by the arm and hand. The will goes with it everywhere, wherever the
movement of a limb takes place. Thus after all we must speak of the
will as of a quality of soul which can assume a three-dimensional
question is, do all the soul-qualities
assume this three-dimensional configuration?
Let us pass from the Will to the world of Feeling. To begin with, we
can make the same kind of observation. Considering the matter with
the ordinary everyday consciousness, man will say to himself,
for example: ‘If I am pricked by a needle on the
right-hand side of my head, I feel it; if I am pricked on the
left-hand side I feel it also.’ In the everyday
consciousness he can, therefore, be of opinion that his Feeling
is spread out over his whole body. He will then speak of Feeling as
having a three-dimensional configuration in the same sense as the
Will. But in so doing he gives himself up to an illusion. It is
not really so. The fact is, at this point there are certain
experiences which every man can have in his own nature, and from
these we must take our start today. Our considerations will
have to be somewhat subtle, but spiritual science cannot really be
understood without subtlety of thought.
for a moment what it is like when you touch your own left hand with your
right. You have a perception of yourself thereby. Just as in other cases
you perceive an outer object, so do you perceive yourself when
you touch your right hand with your left hand-say with the several
fingers one by one.
fact to which I am referring appears still more distinctly when you
consider that you have two eyes. To focus an object with both eyes you
have to exert your will to some extent. We often do not think of this
exertion of the will. It comes out more strongly when you try to
focus a very near object. You then endeavour to turn your left
eye towards the right and your right eye towards the left. You focus
an object by bringing the lines of vision into contact, just as you
bring your right and left hands into contact when you touch yourself.
From these examples you can see that it is of some importance
for man, with respect to his orientation in the world, to bring his
left and right into a certain mutual relation. By the contact of the
hands or the crossing of the lines of vision we can thus become aware
of an underlying fact which is of deep significance.
Though the everyday consciousness does not generally go farther
than this, it is possible to continue very much farther along
this line of study.
we are pricked by a needle on the right-hand side of our body. We
feel the prick. But we cannot really say so simply
‘where’ we feel the prick-meaning
by ‘where’ some portion of the surface
of our body. For unless the several members of our organism stood in
a living mutual relationship to one-another, —
unless they were working one upon
the other — our human nature, body and soul together, would not
be what it is. Even when our body is pricked, let us say, on the
right-hand side, there is always a connection established from
the right-hand side to the central plane of symmetry. For any
feeling or sensation to be brought about, the left half of the
body must always enter into relation with the right.
comparatively easy to realise — if this be the plane of
symmetry, seen from in front — that when the right hand touches
the left the mutual feeling
of the two hands is brought about in the plane of
symmetry. It is comparatively easy to speak of the
crossing of the lines of vision from the two eyes. But there is
always a connecting line in every case — whenever
we are pricked, for example, on the
right-hand side; — the left half of the body crosses with
the connecting line from the right. Without this process, the
sensation would never come about. In all the surging waves of feeling
and sensation, the fact that we have a right and a left half of the
body — the fact that we are built symmetrically —
plays an immense part. We always relate to the left-hand
side what happens to us on the right. In a vague groping way
something reaches over in us from the left, to cross with what is
flowing from the right.
does Feeling come about. Feeling never comes about in space, but only
in the plane. Thus the world of Feeling is in reality spread out,
not three-dimensionally, but two-dimensionally. Man
experiences it only in the plane which as a plane of section would
divide him into two symmetrical halves.
of Feeling is really like a painting on a canvas — but we are
painting it not only from the one side but from both.
Imagine that I here erect a canvas, which I paint from right to left
and from left to right, and observe the interweaving of what I have
painted from the one side and the other. The picture is only in two
dimensions. Everything three-dimensionalis
projected, so to speak, into the two dimensions.
arrive at the same idea in a somewhat different way. Suppose you were
able to project on to a flat surface shadow-pictures of objects on the
right-hand side and on the left. On the flat expanded wall you
then have shadows of left- and right-hand objects. So it is
with our world of Feeling. It is two-dimensional, not
three-dimensional. Man is a painter working from two
sides. He does not simply feel his way into space. Through his
three-dimensional will he projects on to a plane in
shadow-forms, in pictures, the influences
of feeling which meet him in the world of space. In his life of
feeling, man lives in a picture drawn two-dimensionally through his
body-only it is for ever being painted from both sides. Thus if
we would seek the transition from Will to Feeling in ourselves —
as human beings in the life of soul — we must
pass from the three-dimensional into the two-dimensional.
will already give you a different spatial relationship of the
soul-quality which is expressed in feeling, than if you merely
say of the soul-life that it is unspatial.
The plane has two dimensions, but it has no
‘space.’ Take any plane in the outer world —
the blackboard for example. In reality it is a solid body, it
has a certain thickness. But an actual plane, though it is in
space, is not in itself spatial. ‘Space’ must always be
of three dimensions; and only our Will enters into this
three-dimensional space. Feeling does not enter into the three
dimensions of space. Feeling is two-dimensional. Nevertheless it has
its own relations to space, just as a shadow-picture
has. In saying this, I am drawing your attention
at the same time to a fact of very great importance, which is not at
all easy to penetrate with clear perception, because with his
everyday consciousness man has little inclination as a rule to
perceive the peculiar nature of his world of Feeling.
is that the world of Feeling is always permeated by the Will.
Think only for a moment of this: If you really receive on the
right-hand side of your body the prick or sting of which we spoke
just now, you do not immediately sever the Feeling from the Will. You
will certainly not patiently receive the sting. Quite apart
from the fact that you will probably reach out in a very tangible
way, striking out pretty intensely with your Will into the
three dimensions of space ; inwardly too there will be a
defensive movement which does not appear externally but
shews itself in all manner of delicate disturbances of
the blood and the breathing. The defensive movement which we make,
when, stung by a gnat, we reach out with our hand, is only the
crudest and most external aspect. Of the finer aspect —
the inner defensive movement which we perform in the motion of
the blood and breathing and many another inward process — we
are generally unaware. Hence we do not distinguish what the
Will contributes from the content of Feeling as such.
content of Feeling is in fact far too shy, far too elusive. We can
only get at it by very careful meditation. If however
you can exclude, from the Feeling as such, all that belongs to
the Will, then as it were you shrink together from the right and left
and you become the plane in the middle. And when you are the central
plane, and like a conscious painter you record your inner experiences
on this plane, then you begin to understand why the real world of
Feeling is so very different from our ordinary, everyday experience.
indeed experience this plane-quality, this surface-quality of
Feeling. But it needs to be experienced meditatively. We must
feel all the shadow-likeness of our feelings as against the
robust outer experiences in three-dimensional space. We must
first prepare ourselves for this experience, but if we do so we
can really have it, and then we gradually come near the truth that
Feeling takes its course in two dimensions.
shall we characterise Thinking? To begin with we must admit with open
and unbiased mind how impossible it is to speak of a thought as
if it were in space. A thought is really nowhere there in space.
Nevertheless the thought must have some relation to space, for
undoubtedly the brain — if not the instrument — is
at least the foundation of our Thinking. Without
the brain we cannot think. Thus our Thinking takes its course in
connection with the activity of the brain. If Thinking had nothing to
do with space, we should get the following curious result: If
you were able to think well as a child of 12, your head having now
grown beyond the position in which it was when you were 12 years
old, you would have grown out of your Thinking. But that
is not the case. As we grow up, we do not leave our Thinking
behind. The very fact of growth will serve to indicate that
even with our Thinking we are somehow in the world of Space.
is this. Just as we can separate out the world of Feeling — the
world of inner experience of our Feelings — by learning
gradually to perceive our plane of symmetry, so too we can learn to
experience our Thinking meditatively, as something that only has
extension upward and downward. Thinking is one-dimensional. It takes
its course in man in the line.
a word, we must say: The Will takes on a three-dimensional configuration,
the Feeling a two-dimensional and the Thinking a one-dimensional
make these inner differentiations of space, we do not arrive at
the same hard-and-fast transition as the mere intellect. We are led
to perceive a gradual transition. The mere intellect says : The
physical is three-dimensional, spatially extended. The
soul-and-Spirit has no extension at all. From this point of
view no relationship can be discovered between them. For it goes
without saying, there is no relationship between that which has
extension and that which has none. But when once we perceive
that the Will has a three-dimensional configuration, then indeed we
find that the Will pours itself out everywhere into the
three-dimensional world. And again, when once we know that
Feeling has a two-dimensional configuration, then we must pass
from the three dimensions to the two, and as we do so we are led to
something which still has a relationship to space, though it is
no longer spatial in itself. For the mere plane — the
two-dimensional — is not spatial, but the two dimensions are
there in space; they are not entirely apart from space. Lastly, when
we pass from Feeling to Thinking we pass from the two dimensions to
the one. Thus we still do not go right out of space. We pass over
gradually from the spatial to the unspatial.
have often said, it is the tragedy of materialism that it fails to
understand the material-the material even in its
three-dimensional extension. Materialism imagines that it
understands the material, substantial world, but that is
precisely what it does not understand. Many things of real
historic importance emerged in the 19th century, which still present
an unsolved riddle to the ordinary consciousness. Think only of the
great impression which Schopenhauer's philosophic system,
The World as Will and Idea,
made on so many thinking people.
There is something unreal in the Idea, says Schopenhauer. The Will
alone has reality. Why did Schopenhauer arrive at the idea that the
world only consists of Will? Because even he was infected with
materialism. Into the world in which matter is extended
three-dimensionally, only the
Will pours itself out. To place the Feelings too into this world, we
must look for the relationship which obtains between the
three-dimensional object and the two-dimensional image on the screen.
Whatever we experience in our Feelings is a shadow-picture
of something in which our Will too is living in
its three-dimensional configuration. And what we experience in our
Thinking consists of one-dimensional configurations. Only when
we go right out of the dimensions — that is to say, when we
pass to the dimensionless point, — only then do we arrive at
our I or Ego. Our Ego has no extension at all. It is purely
may say, we pass from the three-dimensional to the
two-dimensional, to the one-dimensional and to the
‘punctual.’ So long as we remain within the
three-dimensional, there is our Will in the three dimensions. Our
Feeling and our Thinking are also there within them, only they are
not extended three-dimensionally. If we leave
out the third dimension and come down to the two dimensions, we only
have the shadow of outward existence, but in the shadow is extended
that element of soul-and-spirit
which lives in our Feeling. We are already getting
more away from space. Then, when we go on to Thinking, we come away
from space still more. And lastly when we pass on to the Ego, we go
right out of space.
are led out of space, as it were piece by piece. Now we see that it
is meaningless merely to speak of the contrast between the
soul-and-spirit, and the physical
and bodily. It is meaningless, for if we wish to discover the
relation between the soul-and-spirit
and the physical and bodily, we must ask: How are
things which are extended in three-dimensional space (our own
body, for example) related to the soul as a being of Will? How is the
bodily and physical in man related to the soul as a being of Feeling?
The bodily and physical is related to the soul as a being of Will in
such a way that one would say, it is saturated by the Will on all
sides, in all dimensions, just like the sponge is saturated by water.
Again, the bodily and physical is related to the Feeling, like
objects whose shadows are thrown upon the screen. And when we pass
from Feeling to the quality of Thought, then we must indeed
become strange painters — for we must paint on to a line
what is otherwise existing in the two dimensions of the picture.
yourselves the following question. (It will indeed make some
demands on your imagination.)
Suppose that you are standing face to face with the ‘Last
Supper’ by Leonardo da Vinci.
You have it before you in the surface. The whole
thing is two-dimensional — for we need not take into
account the thickness of the colours. The picture which you
have before you is essentially two-dimensional.
imagine to yourselves a line, drawn through the middle from top to
bottom of the picture. This line shall represent a one-dimensional
being. Imagine that this one-dimensional being has the peculiar
quality that Judas, let us say, is not indifferent to him. He
feels Judas in a certain way. He feels him more where Judas
inclines his head in that direction, and where Judas turns away
he feels him less. Likewise this one-dimensional being feels
all the other figures. He senses them differently according as the
one figure is in blue and the other in a yellow colour. He feels all
that is there, to the left and to the right of him. All that is
present in the picture is livingly felt by this one-dimensional being.
reality is our Thinking within us. Our Thinking is a
one-dimensional being of this kind, and only partakes in
the life of the remainder of our human being inasmuch as it is
related to the picture which divides us into the left- and right-hand
man. Via this two-dimensional picture, our Thinking stands
in relation to the world of Will with its threefold configuration.
wish to gain an idea of our being of soul-and-spirit
(to begin with without the Ego; only in so far as
it is willing, feeling and thinking) we must conceive it not as a
mere nebulous cloud. We must regard the soul and spirit, as it
were diagramatically. There it
appears, to begin with, as a cloud, but that is only the being of
Will. It has the constant tendency to become pressed together;
thereby it becomes a being of Feeling. First we see a cloud of light.
Then we see the cloud of light creating itself in the centre as a
plane, whereby it feels itself. And the plane in turn strives to
become a line. We must conceive this constant process — cloud,
plane and line as an inwardly living form. It
constantly tends to be a cloud, and then to squeeze together from
the cloud into the plane, and then to elongate into the line.
Imagine the plane that becomes a line and then a plane again and then
again a cloud in three dimensions. Cloud,
plane line; line, plane, cloud, and so on. Only so
can you imagine graphically what your soul is in its inner being, its
inner nature and essence. An idea that remains at rest will not
suffice. No idea that remains at rest within itself can reproduce the
essence of the soul. You need an idea with an inner activity of its
own. The soul itself, as it conceives itself, plays with the
dimension of space. Letting the third dimension vanish, it loses the
Will. Letting the second dimension vanish, it loses the Feeling. And
the Thinking is only lost when we let the first dimension vanish.
Then we arrive at the point, and then only do we pass over to the Ego.
all the difficulty in gaining a knowledge of the soul. People are
accustomed only to form spatial ideas. Hence they would like to have
spatial ideas — however diluted — of the soul's nature. But
in this form they only have the element of Will.
we make our thinking inwardly alive and mobile we can reach no
conception of the soul-and-spirit.
If we wish to conceive a quality of
soul-and-spirit, and our
conception is the same in two successive instants, we shall at most
have conceived a quality of Will. We must not conceive
the soul-and-spirit in the same form
in two successive moments. We must become alive and mobile-not by
moving from one point in space to another, but rather by
passing from one dimension to another. This is difficult for
the modern consciousness. Hence even the most well-meaning people
— well-meaning for the conception of spiritual things
— have tried to escape from Space by transcending the three
dimensions. They come to a fourth dimension. They pass from the
three-dimensional to the four-dimensional. So long as we remain
within the mathematical domain, the thoughts which we arrive at in
this way are quite in order. It is all perfectly correct. But
it is no longer correct when we relate it to the reality. For the
peculiar thing is, that when we think the fourth dimension in its
reality, it eliminates the third. Through the fourth dimension the
third dimension vanishes. Moreover, through the fifth dimension the
second vanishes, and through the sixth the first vanishes, and we
arrive at length at the point.
pass in reality from the third to the fourth dimension, we come into
the Spiritual. We eliminate the dimensions one
by one, we do not add them, and in this way we enter more and more
into the Spiritual.
such ideas we gain a deeper insight too into the human form and
figure. For a more artistic way of feeling is it not rather crude how
we generally observe a human being, as he places himself with his
three dimensions into the world? That after all is not the only
thing. Even in ordinary life we have a feeling for the essential
symmetry between the left and right halves of the body. And when we
thus comprise the human being in his central plane, we are
already led beyond the three dimensions. We pass into the plane
itself. And only thereafter do we gain a clear conception of
the one dimension in which he grows. Artistically we do already make
use of this transition, from three to two and on to one dimension. If
we cultivated more intensely
this artistic perception of the human form, we
should find more easily the transition to the soul's life. For
you would never be able to feel a being, unsymmetrically
formed, as a being of united and harmonious Feeling.
the star-fish. It has not this
symmetrical form. It has five rays. Of course you can pass it by
without any inner feeling. But if you perceive it feelingly, you
could never say that the star-fish
has a united feeling-life. The star-fish
cannot possibly relate a right-hand to a
left-hand side, or grasp a right-hand with a left-hand member.
The star-fish must continually
relate the one ray to one or two or three, or even to all four
remaining rays. What we know as Feeling cannot live in
the star-fish at all.
you to follow me along this intimate line of thought. What we know as
Feeling comes from the right and from the left, and finds itself at
rest in the middle. We go through the world by placing ourselves with
our Feeling restfully into the world. The star-fish
cannot do so. Whatever the star-fish
has, as influence of the world upon itself, it
cannot relate it symmetrically to another side. It can only relate it
to one, or two, or to the third or fourth ray. But the first
influence will always be more powerful. Thus the
star-fish has no Feeling-life at
rest within itself. When, as it were, it turns its attention to the
one side, then by the whole arrangement of its form it will
experience: ‘You are raying out in that direction, thither you
are sending forth a ray.’ The star-fish has no restfulness in
feeling. It has the feeling of shooting forth out of itself. It feels
itself as raying forth in the world.
develop your feelings in a more intimate way, you will be able to
experience this even as you contemplate the star-fish.
Observing the end-point
of any one ray and relating it to the creature as
a whole, in your imagination the star-fish
will begin to move in the direction of this ray,
as it were a streaming, wandering light. And so it is with all the
other animals which are not symmetrically built, which have no real
access of symmetry.
would only enter into this more intimate way of Feeling — instead
of giving himself up entirely to the intellectual,
merely because in the course of time he had to become an intellectual
being, — then indeed he would find his way far more intimately
into the world.
It is so
also in a certain sense for the plant world, and for all things that
True self-knowledge takes us ever farther and farther
into the inwardness of things.