OF DIFFERENT WORLDS
Imaginary Experiment with "Lumen."--Impossibilities.--A Destroyed
Illusion.--Is the World Infinite?--Surface Creatures and Shadow
Rambles.--What is the Beyond?--Action at a Distance.--Ideas of
Multi-dimensional Regions.--Hypnotism.--Recollections of Zöllner.--Science
and Dogma.--The Trial of Galilei.
CONVERSATION held during April 1920 destroyed an illusion which had
become dear to me.
It concerned the fantastic figure, "Lumen," conceived as an actual
human being, imagined as endowed with an extraordinary power of motion
and keenness of sight. Mr. Lumen is supposed to be the invention of the
astronomer Flammarion, who produced him in the retort of fancy, as Faust
produced Homunculus, to use him to prove the possibility of very
remarkable happenings, in particular, the reversal of Time.
Einstein declared outright: "Firstly, Lumen is not due to Flammarion,
who has derived him from other sources; and secondly. Lumen can in no
way be used as a means of proving things."
MOSZKOWSKI: "It is at least very interesting to operate with him. Lumen
is supposed to have a velocity greater than that of light. Let us assume
this as given, then the rest follows quite logically. If, for example,
he leaves the earth on the day of a great event, such as the battle of
Waterloo, and---- May I trace out this example, at the risk of tiring
you?"
EINSTEIN: Do repeat it, and act as if you were telling something
entirely new. It is clear that the Lumen-story gives you great
amusement, so please talk quite freely. But I cannot forgo the privilege
of showing later how the whole adventure and its consequences must be
demolished.
M.: Well then, the person, Lumen, sets off at the end of the battle of
Waterloo to make an excursion into space with a speed of 250,000 miles
per second. He thus catches up all the light-rays that left the field of
battle and moved in his direction. After an hour he will already have
attained a lead of about twenty minutes. This lead will be gradually
increased, so that at the end of the second day he will no longer be
seeing the end of the battle, but the beginning. What has Lumen been
seeing in the meantime? Clearly he has been observing events happening
in the reverse direction, as in the case of a cinematograph which is
exhibiting pictures backwards. He saw the projectiles leaving the
objects they had struck, and returning into the mouths of the cannon. He
saw the dead come to life, arise, and arrange themselves into battalion
order. He would thus arrive at an exactly opposite view of the passing
of time, for what he observes is as much his experience as what we
observe is ours. If he had seen all the battles of history and, in fact,
all events happening in the reverse order, then in his mind "before" and
"after" would be interchanged. That is, he would experience time
backwards; what are causes to us would be effects to him, and our
effects would be his causes; antecedents and consequents would change
places, and he would arrive at a causality diametrically opposite to our
own. He would be quite as justified in adopting his view of the
happening of things, according to his experiences, and of the causal
nexus as it appears to him, as we are justified in adopting ours.
EINSTEIN: And the whole story is mere humbug, absurd, and based on false
premises, leading to entirely false conclusions.
M.: But it is only to be taken as an imaginary experiment that plays
with fantastic impossibilities to direct our ideas on to the relativity
of time by a striking illustration. Did not Henri Poincaré adduce this
extreme example to discuss the "reversal" of time?
EINSTEIN: You may rest assured that Poincaré, even if he used this
example as an entertaining digression in his lectures, took the same
view of Lumen as I do. It is not an imaginary experiment: it is a farce,
or, to express it more bluntly, it is a mere swindle! These experiences
and topsy-turvy perceptions have just as little to do with the
relativity of time, such as it is taught by the new mechanics, as have
the personal sensations of a man, to whom time seems long or short
according as he experiences pain or pleasure, amusement or boredom. For,
in this case, at least the subjective sensation is a reality, whereas
Lumen cannot have reality because his existence is based on nonsense.
Lumen is to have a speed greater than that of light. This is not only an
impossible, but a foolish assumption, because the theory of relativity
has shown that the velocity of light cannot be exceeded. However great
the accelerating force may be, and for however long it may act, it
cannot cause this limit to be transcended. Lumen is supposed to be
equipped with the organ of sight, that is, he is supposed to have a
corporal existence. But the mass of a body becomes infinitely great when
it reaches the velocity of light, so that it is quite absurd to go
beyond this stage. It is admissible to operate with impossibilities in
imagination, that is, with things that contradict our practical
experience, but not with absolute nonsense. That is why the other
adventure of Lumen, in which he jumps to the moon, is also an absurdity.
In this, he is supposed to leap with a speed greater than light, and,
when he reaches the moon, to turn round instantaneously, with the result
that he sees himself jumping from the moon to the earth backwards! This
jump is logically meaningless; and if we try to make deductions of an
optical nature from such a nonsensical assumption, we deceive ourselves.
M.: Nevertheless, I should claim extenuating circumstances for this case
on the ground that I am enlisting the help of the conception of
impossibility. A journey even at a speed of only 1000 miles per second
is impossible for a man or a homunculus.
EINSTEIN: Yes, according to our experience, if we measure it against
facts. We cannot state definitely that a journey into the universe at an
enormous yet limited velocity is absolutely impossible. Within the
indicated bounds every play of thought that is argued correctly is
allowable.
M.: Now, suppose that I strip Lumen of all bodily organs and take him as
being a pure creature of thought, entirely without substance. A velocity
greater than that of light can be imagined, even if it cannot be
realized physically. If, for example, we think of a lighthouse with a
revolving light, and consider a beam of light about 600 miles long,
which rotates 200 times per second. Then we could represent to ourselves
that the light at the circumference of this beam travels with a speed of
nearly 760,000 miles per second.
EINSTEIN: As for that, I can give you a much better example of the same
thing. We need only imagine that the earth is poised in space,
motionless, and non-rotating. This is physically admissible. Then the
most distant stars, as judged by us, would describe their paths with
almost unlimited velocities. But this projects us right out of the world
of reality into a pure fiction of thought, which, if followed to its
conclusion, leads to the most degenerate form of imagination, namely, to
pathological individualism. It is in these realms of thought that such
perversities as the reversal of time and causality occur.
M.: Dreams, too, are confined to the individual. Reality constrains all
human beings to exist in one and the same world, whereas, in dreams,
each one has his own world with a different kind of causality.
Nevertheless, dreams are a positive experience, and signify a reality
for the dreamer. Even for waking reality it would be easy to construct
cases in which the causal relationship is shattered. Suppose a person
who has grown up in a confined retreat, such as Kaspar Hauser, looks in
a mirror for the first time in his life. As he knows nothing of the
phenomena of optical reflexion, he sees in it a new, objective world
that gives a shock to, or even subverts, his own idea of causality in so
far as it may have become developed in him. Lumen sees himself jump
backwards, whereas Kaspar Hauser sees himself performing gestures on the
wrong side of his body; should it not be possible to draw a reasonable
parallel between these two cases?
EINSTEIN: Quite impossible. However you set about it, your Lumen will
inevitably come to grief on the conception of time. Time, denoted in
physical expressions by the symbol "t," may, indeed, be given a negative
value in these equations, so that an event may be calculated in the
reverse direction. But then we are dealing with pure matters of
calculation, and in this case we must not allow ourselves to be drawn
into the erroneous belief that time itself may travel negatively, that
is, retrogressively. This is the root of the misapprehension: that what
is allowable and indeed necessary in calculations is confused with what
may be thought possible in Reality.[5] Whoever seeks to derive new
knowledge from the excursions of a creature like Lumen into space,
confuses the time of an experience with the time of the objective event;
but the former can have a definite meaning only if it is founded on a
proper causal relation of space and time. In the above imaginary
experiment the order of the experiences in time is the reverse of that
of the events. And as far as causality is concerned, it is a scientific
conception that relates only to events ordered in space and time, and
not to experiences. In brief, the experiments with Lumen are swindles.
[Footnote 5: Perhaps an analogy will serve to make this clear. Suppose
that a certain quantity of some foodstuff is consumed by ⅒ head of
population. The false inference would be that a population is possible
which has ⅒ heads! In the same way the statistics may be quite correct
in arriving at the figure ⅕ suicides, but if we leave the realms of
calculation, then the £ suicide loses its meaning entirely.]
M.: I must resign myself to giving up these illusions. I must frankly
confess that I do so with a certain sadness, for such bold flights of
constructive fancy exert a powerful attraction on me. At one time I was
near outdoing Lumen by assuming a Super-Lumen, who was to traverse all
worlds at once with infinite velocity. He would then be in a position to
take a survey of the whole of universal history at a single glance. From
the nearest star, Alpha Centauri, he would see the earth as it was four
years ago; from the Pole Star, as it was forty years ago; and from the
boundary of the Milky Way, as it was four thousand years ago. At the
same moment he could choose a point of observation that would enable him
to see the First Crusade, the Siege of Troy, the Flood, and also the
events of the present day simultaneously.
EINSTEIN: And this flight of thought, which, by the way, has been
indulged in repeatedly by others too, has much more sense in it than the
former one, because you may make an abstraction which disregards speed
altogether. It is only a limiting case of reflection.
M.: I should like to touch on other limiting cases, in particular two
that I find it impossible to interpret. Lotze mentions them in his
Logic. The first concerns the infinitely long lever whose fulcrum, or
turning-point, is at the confines of the universe. According to the Laws
of Levers, a mass of magnitude zero will suffice to keep in equilibrium
at the end of the other lever-arm any weight, no matter whether it is a
million times heavier than the earth. Our imaginations cannot even
picture this. Yet I cannot feel satisfied with the mere explanation that
it is an exceptional case, an extension of a general law to a case in
which it is no longer applicable. The second example is still more
perplexing because it does not require a journey into other worlds, but
leads us into inconceivable consequences even if we remain on the earth.
Lotze considers this second limiting case easier; to me it seems more
difficult. It is this: The force that a wedge exerts is inversely
proportional to its thickness. If it is infinitely thin, this formula
gives an infinitely great result, whereas, actually, the force exerted
is nil. This very thin wedge, transformed finally into a geometrical
plane, should be able to split in twain any wooden or even steel block.
And now, consider a special arrangement of this wedge in which it is
resting with its extremely sharp edge vertically downwards, whereas at
the top it broadens to a little ledge which supports a weight. We then
get the incredible result that this wedge, which can be imagined
concretely, should be able to cut through the whole earth with its
extremely fine edge, if placed on some base. Where is the fallacy in
this case?
EINSTEIN: The mechanical facts have not been taken sufficiently into
consideration.--He illustrated his further remarks by drawing a few
strokes with his pen, and proved from his diagram that a wedge of this
sort would be able to perform what I assumed, only if the base on which
it is placed is composed of separate laminae. Otherwise the assumption
that the force is infinitely great would be erroneous.
* * * * * * * *
After this digression to a limiting case on the earth we returned to
more general problems, and the question of the finitude or infinitude of
the universe. Shortly before, Einstein had given an address to the
Berlin Academy on this point, involving difficult calculations, and I
hoped to hear from him an easy explanation at least in general terms.
It is one of the ultimate problems. Whoever talks of the limits of the
world endeavours also to mark off the bounds of the understanding. The
average person, at first sight, almost always decides in favour of an
infinite universe, on the ground that a finite world is inconceivable.
He argues that, if it were considered finite, we should immediately be
confronted with the question: What lies _beyond_ the finite boundary?
Something must be present, even if it is only empty space. This brings
us into an inevitable conflict with the first of Kant's "antinomies,"
with the thesis and antithesis, from which there is no escape. What is
the meaning of the fact that the apprehensive understanding seeks refuge
in "Infinity"? It signifies that he gets entangled in the folds of a
negative conception, that furnishes him with no explanation at all, and
expresses merely that his first assumption of finitude cannot be thought
out to its conclusion.
Besides this, a second disturbing question arises. Is there a finite or
infinite number of stellar bodies? If this question refers to an assumed
infinite space, even if such space is inconceivable, then there are two
possible answers. For it would be possible to imagine a finite number of
stars even if no limit could be found for space.
Whereas the general question of space in the universe belongs
exclusively to speculative philosophy, the star-question is not purely
metaphysical, but is physical, too, and has accordingly been treated by
physicists. The great astronomer Herschel imagined he could solve it by
means of optical principles, and he arrived at the conclusion that the
number of heavenly bodies must be finite, as otherwise the aspect of the
starry firmament, from the point of view of illumination, would be
entirely different. But this proof did not establish itself among
scientists, for the number of stars of the type of the sun might be
finite, whilst there was an infinite number of _dark_ stars.
A further question presented itself: Would it be possible for a definite
part of the heavens (say, that north of the ecliptic) to contain an
infinite number of stars, whilst other parts contained only a finite
number? At first this sounds very extraordinary, but it is by no means
unreasonable, as a concrete example will show: If, on a scale of
temperature, we count the degrees of heat from a certain point, then
they stretch apparently to infinity in one direction, whereas they
extend only to -273° (Centigrade) in the other direction, that is, to
the absolute zero. Thus we can imagine an arrangement which stretches to
infinity only in one direction.
To get an insight into the discussion by Einstein which is about to
follow, we must first dispose of a certain arbitrariness of language,
lying in the customary indiscriminate use of the terms, infinite,
immeasurable, and unbounded. Suppose we have a globe about one foot in
diameter, the surface of which is inhabited by extremely small,
ultramicroscopic creatures that can move about freely and can think. The
surface of the sphere constitutes the world of the micro-men, and he has
a very good reason for considering it infinite, for, however far and in
whatever direction he may move, he never encounters a boundary. But we,
who live in our space, look on to this spherical surface, and recognize
that his judgment is erroneous. To us his spherical world seems
decidedly finite and quite measurable, although it has no determinable
beginning and no end, and thus must appear unbounded to the micro-man.
In fact, we ourselves may regard it as boundless, if we can succeed in
forming an abstraction that leaves out of account its limitations in our
own space.
Now, it might occur to a particularly intelligent micro-being to
undertake a voyage for the purpose of making measurements. He carefully
marks his point of departure, walks Straight ahead in a certain
direction, describing a circle on his sphere--a circle which he will
necessarily regard as a straight line. He continues ever onwards in the
firm conviction that he is getting farther and farther away from his
starting-point. Suddenly, he discovers that he has reached it again. He
discovers, by the mark he made, that he has not been describing a
straight line, but a line that merges into itself.
The micro-professor would be compelled to declare: Our world, the only
one known to me, is not infinite, although in a certain sense boundless.
Moreover, it is not immeasurable, since it can be measured in at least
one direction by the number of steps I have walked. From this we may
infer that our former geometrical view was either wrong or incomplete,
and that, in order to understand our world properly, we must build up a
new geometry.
We may assume that the majority of the remaining micro-inhabitants would
at first protest strongly against this decision. The idea that a line,
which appears to them to be pointing always in the same direction, is
curved, seems to them inconceivable and absurd. They would only
gradually overcome their scruples of thought by getting an insight into
a newly developed geometry that makes clear to them for the first time
the conception of a sphere.
In our world of space, which includes all stars, we are the
micro-inhabitants. We have been born with, or have inherited, the idea
of a straight and ever-advancing path in space, and we become filled
with the utmost astonishment if some one asks us to believe that if we
undertake a voyage in one direction out into the universe, beyond Sirius
and a million times farther, we should finally arrive at our
starting-point again, although we had not changed our direction. But the
macro-being, who belongs to a universe of higher dimensions and who
looks on our world as we looked on the above spherical world one foot in
diameter, sees the narrowness of our view. We, too, are in a position to
rise above this narrow view by means of a theory founded on our
experience, which will lead us to an extended world-geometry, just as
the micro-professor used his experience to extend his theory of the
circle to include the conception of a sphere.
After these preliminary remarks we shall endeavour to get an insight
into Einstein's reasoning, not in the form in which it was originally
presented (in the Report of the Proceedings of the Berlin Academy of
Science of 8th February 1917), but in a very easy description which was
given to me during a conversation. Here, too, I shall try to preserve
the sense of Einstein's remarks without binding myself strictly to his
words. For although I am indebted to him for his efforts to avoid
difficult points, yet the aim of this book is, if possible, to make the
explanation still easier. Any lack of accuracy arising from this last
simplification is to be debited to me. The new form of representing the
argument, which is as important as it is fascinating, is, of course, due
to Einstein.
The final result stated by Einstein was: The universe, both as regards
extent and mass, has finite limits and can be measured. If anyone asks
whether this can be pictured, I shall not deprive him of the hope. All
that is required is a power of imagination that is great enough to
follow a pictorial description and that can take up the right attitude
towards a sort of figurative representation.
Let us again imagine a sphere of modest dimensions with its
two-dimensional surface. We are concerned only with the latter, and not
with the cubical content. The sphere is to be considered as resting on
an absolutely plane white table of unlimited extent in all directions.
The sphere touches the table at a single point which we shall call its
South Pole; on the top side directly opposite, we have the North Pole.
To simplify matters we may make a sketch on paper of a vertical section
through the centre of the sphere. This profile-picture will show us the
sphere as a circle, and the white table as a straight line; the line
joining the two poles is the axis of the globe, and the sectional circle
is a meridian.
Let us further suppose a creature (resembling, say, a ladybird in shape)
having length and breadth, but no thickness, to crawl along this
meridian. Although it has no thickness, we shall imagine it to have one
property of a solid body, that of being opaque, so that it can throw a
shadow if properly illuminated. We assume the globe itself to be
transparent. At the North Pole we suppose a very strong point-source of
light, a little electric lamp, that sends out rays freely in all
directions.
The insect begins its journey at the South Pole and sets out along the
meridian to reach the North Pole. It is illuminated by the lamp all the
way, so that it continually throws a shadow on the white table. The
shadow moves along the table farther and farther from the South Pole, in
proportion as the insect moves up the meridian, with the difference that
while the insect is describing an arc of a circle, its shadow moves
along a straight line. The position of the shadow can be determined at
any moment by drawing the straight line connecting the lamp to the
insect, and producing it to meet the white surface of the table; the
point of intersection is the projection of the insect on the plane.
At the beginning of the excursion the shadow is exactly as large as the
flat insect itself, if we assume that its dimensions are negligible
compared with the surface of the sphere, for it will then coincide with
its own shadow. But when the insect crawls upwards, its shadow will
increase, because of the shortened distance between the insect and the
lamp, and because the points of projection on the table separate more
and more as their distances from their corresponding points on the
sphere become greater. There is thus a twofold increase. The shadows
move away more and more rapidly, and at the same time increase in size.
When the insect gets very near the North Pole, its shadow, now of
enormous dimensions, has moved to a very great distance; and when
finally it reaches the Pole, its shadow becomes infinitely great and
thus stretches to infinity.
But let the insect wander on along the meridian, past the North Pole,
down towards the South. At the moment when it passes the upper Pole its
shadow jumps from the right side to the left. Its shadow now emerges
from an infinite distance to the left, and, instead of being infinite
size, again becomes finite in dimensions as it approaches. It contracts
as it approaches, and, in short, the same process as occurred during the
first half of the journey now occurs in the reverse order.
[If we fix on the critical moment of the jump from the right to the
left, that is, from plus infinity to minus infinity, we may encounter
difficulties. For the surface-creature pursues its way without
interruption and continuously, and we experience a wish to ascribe to it
a shadow-path that is also unbroken and continuous. This is possible
only if we assume the two points at infinity to be connected, that is,
if we consider them identical. This assumption will seem more natural if
we reason as follows. In the profile-picture the table is represented as
a straight line, and it is along this line that the shadow travels. We
may regard this line as an infinitely great circle, for an infinitely
great circle has zero curvature, just as the straight line, from which
it is therefore indistinguishable. The infinitely great circle has,
however, only one point situated at an infinite distance, that is, it
associates together the two apparent points at infinity of the straight
line with which we identify it. Accordingly, we preserve the continuity
of the shadow-journey, too. Einstein considers it allowable to say that
the right and the left portion each represent a half of the infinite
projection, which becomes complete only when the two ends are joined.]
Now we must be prepared for an effort of thought which will need
considerable help from our imaginations. Firstly, instead of one
surface-creature, we shall suppose several crawling about on different
meridians, so that a series of shadows will be moving about along
straight lines radiating from the South Pole. Next, let us imagine the
whole picture to have its dimensions increased by one, that is, we
transform the plane-picture into a space model. The phenomena are to
remain the same, except that they are to be strengthened by one
dimension, surface conditions becoming space conditions, and surfaces
becoming solids.
What we now see are actual insects with round bodies (if we retain our
original type of creatures), or, since there is no restriction as to
their size--the shadows have assumed all possible sizes--we may assume
any solid bodies whatsoever, stars or even star-systems. Their motions
take place in exactly the same way as those of the shadows previously
thrown by the flat bodies.
This means that, if a stellar body moves, its size increases until it
reaches the spherical boundary of space, where it becomes infinitely
great, and, at the same moment, passes from plus infinity to minus
infinity, that is, it enters the universe from the opposite direction;
then, if it continues moving in its original direction (as it has been
doing all along), it gradually becomes smaller in size until, finally,
it reaches its original position and its original size. If we suppose
the body to be endowed with the power of sensation, it would not be able
to observe its own changes of size, since all its scale-measures would
be altered in the same proportion. This whole complex of phenomena would
still be taking place in an infinite world of space, but, according to
the General Theory of Relativity, the geometry that is valid in this
world would no longer be that of Euclid; it is replaced by a system of
laws that arise from physics as a geometric necessity. In this new
geometry, a circle described with unit radius is a little smaller than
it would be in Euclidean geometry, with the result that the greatest
conceivable circle in this world cannot assume an infinite size.
Thus we have to imagine that our solid bodies, say stars, arrive at a
point in their travels which we may term only "enormously distant." If
we call the directions right and left instead of positive and negative,
then the process reduces itself to this: the moving body reaches the
point, which is enormously distant on the right, and which is identical
with the point enormously distant on the left; this means that the body
never moves out of the space continuum of this world, but returns to its
initial point of departure even when it moves ever onward in what is
apparently a straight line. It moves in a "warped" space.
Einstein has succeeded in finding an approximate value for this
non-infinite universe, from the fact that there is a determinable
gravitational constant. In the constitution of the universe it denotes
the same for the mass-relationships of the earth as the gravitational
constant of the earth denotes for us, namely, the quantity from which we
can calculate the final velocity attained by a freely falling body
during a unit of time. He also assumes a probable average for the
density of distribution of matter in the universe, by supposing that it
is about the same as that of the Milky Way. On this basis Einstein has
arrived at the following result by calculation:
The whole universe has a diameter of 100 million light-years, in round
numbers. That amounts to about 700 trillion miles.
M.: Does this follow from the discussion you entered on just now?
EINSTEIN: It follows from the mathematical calculations which I
presented in "Cosmological Considerations arising from the General
Theory of Relativity," in which the figure I have just quoted is not
given. The exact figure is a minor question. What is important is to
recognize that the universe may be regarded as a closed continuum as far
as distance-measurements are concerned. Another point, too, must not be
forgotten. If, in deference to your wish, I used an easy illustration,
this must not be regarded otherwise than as an improvised bridge to
assist the imagination.
M.: Nevertheless, it will be very welcome to many, who are unable to
grasp the difficult Cosmological Considerations. The number that you
mention is overwhelming in the extreme. Indeed, it seems to me that a
diameter of 100 million light-years suggests an infinitely great
distance more than the word "infinity" itself, mentioned _per
definitionem_, which conveys nothing to the ordinary mind. It calls up a
regular carnival of numbers, particularly in those to whom the immense
number alone gives a certain pleasure. But you were going to give me the
number expressing the mass, too?
And then I learned that the weight of the whole universe, expressed in
grammes, was 10 multiplied by itself 54 times, that is 10^54 (453
grammes = 1 lb., roughly). This seems rather disappointing at first, but
assumes a different aspect when we represent to ourselves what this
figure signifies. It means that the weight of the universe in
kilogrammes is high in the octillions. The earth itself weighs six
quadrillion kilogrammes, hence the weight of the Einstein universe bears
the same relation to the weight of the whole earth as the latter bears
to a kilogramme. Again, the earth's weight to that of the sun is as 1 is
to 324,000. Hence we should have to take at least a trillion, that is, a
milliard times a milliard, suns to get the weight of the universe. And
as far as the linear extent is concerned, let us consider the most
distant stars of the Milky Way, which are at an inconceivable distance,
expressible only in light-years. If we place 10,000 such Milky Ways end
to end we shall arrive at this diameter of the universe, which,
accordingly, will have a cubical content a thousand milliard times
greater than the region accessible to astronomical observation.
Thus we have a very spacious universe. Yet it is not spacious enough to
satisfy all the demands that a mathematician interested in permutations
and combinations might make. One of such combinations is exemplified in
the so-called _Universal Book_, that originated in an imaginary
experiment of Leibniz. If we picture to ourselves the sum-total of all
books that can be printed by making all possible arrangements and
successions of our letters, each book differing from any other even if
only in one symbol, then, together, they must contain all that can be
expressed in sense and nonsense, and everything that is ever realizable
actually or in dreams. Hence, among other things, they would include all
world-history, all literature, and all science, even from the beginning
of the world to the end. If we agree to the convention of operating with
100 different printed signs (letters, figures, stops, spacings, etc.),
and of allowing each such book a million paces for signs, so that each
book will still be of a handy size, then the number of these books would
amount to exactly 10 to the two-millionth power, or, in figures, _i.e._
10^2,000,000.
This fully exhaustive universal library containing all wisdom would
consist of so many volumes that it could not be contained in a case of
the size of the entire stellar universe. And, unhappily, it must be
added that the closed universe, just described by Einstein and having a
diameter of a hundred million light-years would be much too small to
contain this library.
"Nevertheless," said I, "your universe pictures something inconceivably
great; one might call it an infinity expressed in figures. For in your
world there still remains one property of infinity, namely, that it
imposes no limitations on motion of any kind. On the other hand, the
figures proclaim a limited measure in the mathematical sense, however
great this measure may be. This calls up the old restlessness of mind,
due to the persistent question: What lies beyond? The absolute Nothing?
Or is it a something which yet does not occupy space? Descartes and many
other great thinkers have never overcome this difficulty, and have
always affirmed that a closed world is impossible. How, then, is the
average person to reconcile himself with the dimensions you have
established?"
Einstein gave an answer which, it seemed to me, offered a last escape to
apprehensive minds. "It is possible," so he said, "that other universes
exist independently of our own."
That is to say, it will never be possible to trace a connexion between
them. Even after an eternity of observation, calculation, and
theoretical investigation, no glimpse or knowledge of any of these
ultra-worlds will ever enter our consciousness. "Imagine human creatures
to be two-dimensional surface-creatures," he added, "and that they five
on a plane of indefinite extent. Suppose that they have organs,
instruments, and mental attitude adapted strictly to this
two-dimensional existence. Then, at most, they would be able to find out
all the phenomena and relationships that objectify themselves in this
plane. They would then have an absolutely perfect science of two
dimensions, the fullest knowledge of their cosmos. Independent of this,
there might be another cosmic plane with other phenomena and
relationships, that is, a second analogous universe. There would then be
no means of constructing a connexion between these two worlds, or even
of suspecting such a connexion. We are in just the same position as
these plane-inhabitants except that we have one dimension more. It is
possible, in fact, to a certain degree probable, that we shall by means
of astronomy discover new worlds far beyond the limits of the region so
far investigated, but no discovery can ever lead us beyond the continuum
described above, just as little as a discoverer of the plane-world would
ever succeed in making discoveries beyond his own world. Thus we must
reckon with the finitude of our universe, and the question of regions
beyond it can be discussed no further, for it leads only to imaginary
possibilities for which science has not the slightest use."
* * * * * * * *
Einstein left me for a while to the tumult of ideas that he had roused
up in me. After I had overcome the first shock, I sought to gain a haven
in the idea that arose out of the first shadow-argument, in which the
spherical bodies occurred that seek to escape towards infinity on the
right but reappear, instead, at enormous distances on the left. Has
anyone ever had presentiments of this kind of world? Perhaps something
of the sort is to be found in earlier books of science? If so, they have
escaped my notice. Yet, a passage of a poet occurs to me. It is to be
found in a volume by Heinrich von Kleist; it is a volume dealing only
with earthly matter and bare of astronomical ideas. Imagine a book the
subject of which is a puppet-show, containing, in the middle of it, a
section foreshadowing Einstein's universe! Quite by chance Kleist comes
to speak of "the intersection of two lines which, after passing through
infinity, suddenly appear on the other side, like a picture in a concave
mirror, which moves away to infinity and suddenly returns again and is
quite close," and, quite in accordance with our new cosmology, he
declares: "Paradise is locked and barred, and the cherub is behind us;
we must make a voyage round the world, and see whether we cannot
discover an exit elsewhere at the other end perhaps."
Perhaps poets of the future will busy themselves with this universe; not
lyrical poets, but descendants of Hesiod, Lucretius, or Rückert. They
will express in verse that Einstein's world offers a source of
consolation to tormented spirits which have sickened of Kant's
antinomies. For in this still almost immeasurable world the fateful
conception "infinite" has been made bearable for the first time. In a
certain way it relieves us from what is quite inconceivable, yet into
which we are usually driven, and forms a bridge between the thesis
"finite" and the antithesis infinite. We are brought to a common stream,
in which both conceptions peacefully flow together. There was no mention
of this in our talk, and I had good reason for being cautious about
following out the theme along these lines. I must not allow any doubts
to arise on this point: Einstein, himself, clings with unerring logic to
the strict mathematically defined conception of infinity, and allows no
compromise with the non-infinite.
When I, on some previous occasion, sought to lead him on to a
compromise, involving a transition-boundary, it availed me nothing that
I quoted Helmholtz to support the possibility of such an operation: my
effort came to an abrupt end.
* * * * * * * *
In pursuing these considerations about the universe, we arrived at
things which, in ordinary language, are usually called "occult." In
connexion with this, these remarks ensued: "I am, of course, far from
trying to trace out a connexion between the four-dimensionality that you
establish, Professor, and the four-dimensionality of certain spiritistic
pseudo-philosophers, yet it suggests itself to me that in such occult
circles efforts will be made to derive advantage from the fact that the
same word is used in both cases. This is more than a conjecture, indeed,
for there are no misgivings among the ignorant, and so we actually find
the name Einstein quoted in connexion with mediumistic experiments that
are flavoured with four-dimensionality."
"It will not be expected of me," said Einstein, "to enter into
discussion with ignoramuses and misinterpreted. Discarding them, then,
let us confine ourselves to a brief consideration of the conception
'occult,' as this has played a part in serious science. The chief
example of this in history is gravitation. Huyghens and Leibniz refused
to accept gravitation, for, so they said, according to Newton's view, it
is an action at a distance and hence belongs to the realm of the occult.
Like everything occult, it contradicts the causal order in Nature. We
must not regard Huyghens' and Leibniz's contradiction as being due to
lack of perspicacity; rather, they objected on grounds which, as
investigators, they had every right to uphold. For, as far as our
everyday experience is concerned, every mutual influence of things in
Nature occurs only by direct contact, as by pressure or impact, or by
chemical action, as when a flame is lit. The fact that sound and light
apparently form exceptions is not usually felt as a contradiction to the
postulate of contact. The case of a magnet appears much more striking
because its effect asserts itself as a direct manifestation of force. I
must mention that when I, as a child, made my first acquaintance with a
compass--and this was before I had ever seen a magnet--it created a
sensation in me, which I consider to have been a dominant factor in my
life up to the very present. There is, indeed, a fundamental difference
between pressure and impact on the one hand, and what we hear and see on
the other, even in everyday experience. In the case of light and sound,
something must be 'happening' continually, if the effect is to occur and
continue...."
"Yet another difference seems to enter here," I interposed. "Is it
possible to give a full explanation of gravitation by using only the
conceptions pressure and impact? Perhaps 'pressure at a distance' would
not have seemed to contemporaries of Newton as unintelligible as a
'tension or pull at a distance.' It seems to me that it is particularly
difficult to imagine a pull or an attraction towards a distant object."
Einstein does not consider this difference considerable, and regards it
as possible to overcome it even in a manner which can be directly
pictured. "If the force is exerted by a corpuscular transmission," he
explained, "we may imagine a 'force-shadow' into which the bombarding
corpuscles cannot penetrate. Thus if an obstacle, which produces such a
shadow, becomes interposed between a body A and a body B, then there
will be a lesser pressure on the side of B facing A, and hence B will
experience a greater corpuscular pressure on the other side, with the
result that B will be forced in the direction of A, and the observer
would gain the impression of a pull from B to A. Nowadays, when the
theory of 'fields of force' dominates our physical views, we need
trouble just as little about using corpuscular pressures and impacts as
about the vortices which Descartes once considered as the ultimate
causes of the motions of the heavenly bodies. The efforts of certain
reformers to reintroduce these vortices and whirlpools as explanations
must be regarded as futile."
"Nevertheless," I answered, "it seems admissible to say that,
ultimately, there is always an occult element in every physical
explanation, an absolutely final and elementary something which we
recognize as a principle, without concealing from ourselves that we have
reached the limit of explanation, and our knowledge avails no further.
This brings me to another question the discussion of which, as I clearly
perceive, leads us on to dangerous ground."
EINSTEIN: Don't hesitate to say what is troubling you. I cannot yet see
what you are aiming at.
M.: I am referring to certain phenomena which are also called
"occult"--with the object of discrediting them. They may at times
degenerate to hocus-pocus and fall into the category of dubious arts. It
seems to me, however, that scientists have not always drawn the line
with sufficient care, and that they have been disposed to reject as
humbug, without examination, everything inexplicable that dares to
present itself in the form of open display.
EINSTEIN: In general, they will be in the right, for investigators
cannot be expected to occupy themselves with things bolstered up by
advertisement, and which are supposed to be connected with some
fabulous, occult regions.
M.: Nevertheless, in my opinion even among such displays there sometimes
occur phenomena which scientists should not pass over with contempt. I,
myself, have experienced such cases, and have said to myself: There are
stranger happenings here----
EINSTEIN:--than are dreamt of in your philosophy, you were about to say?
M.: Exactly. These are things that in the guise of sensationalism often
hide a physical truth well worthy of study.
EINSTEIN: But you must not overlook the fact that in such cases you have
mostly played the part of an onlooker, and hence were exposed to all
possible manner of deception. You are baffled on all sides by
undiscoverable tricks and by other persons, whose collusion you do not
suspect. This renders an objective criticism impossible.
M.: This presumes that the performing artist is not entirely isolated.
It is possible to bring about conditions that positively eliminate all
tricks from the very outset.
EINSTEIN: If you have experienced any such cases, relate them by all
means.
M.: I shall be brief, and shall state only facts....
EINSTEIN: Or, expressed more accurately, only things which seem to have
been facts as far as you can trust to memory. Well then, you think that
you have grounds for saying that you caught a glimpse of a mysterious
world at that time.
M.: It is certainly long ago, more than thirty years. Hansen, the freak,
one of the most eminent of his profession, was showing hypnotic and
telepathic experiments that were partly identical with experiments that
the celebrated scientist Charcot at Paris was performing for purposes of
pathology.
EINSTEIN: Well, then, why did you hesitate before? These experiments
come under the head of science, and require no occult veil to appear in
the open.
M.: This touches the main issue. Hansen did not work in the interests of
science, but wished, above all, to earn money. Nevertheless he had in
his own way produced marvellous results that were used later for
scientific work. Unfortunately in his case, owing to the fact that he
cloaked it in occultism at the outset, he was brusquely repudiated by
scientists. The result was that Hansen was condemned to a long period of
imprisonment in Dresden, thanks to the recommendation of scientists who
declared that the experiments were only possible if deception was
practised, and hence that Hansen was an impostor who should be made
harmless by being incarcerated.
EINSTEIN: And how did you yourself seek to discover whether his
experiments were genuine?
M.: Very easily and with absolute certainty. One of my acquaintances,
the wealthy race-horse owner, von Oelschläger, had induced him by means
of a high fee to experiment at his country house, at some distance from
Berlin, in the presence of persons, not one of whom Hansen knew, and in
the case of whom there could be no question of secret collaboration. I
can assure you that everything succeeded without exception. A single
second was sufficient for him to communicate his will to each subject of
experiment. He operated like a supernatural being on those present.
EINSTEIN: I should like to hear examples.
M.: Herr von Oelschläger introduced four jockeys, and suggested a race
in the great salon. Hansen placed them astride over chairs, hypnotized
them on the spot, described the shape of the course, giving distances in
kilometres, curves, and even the value of the prizes. He then gave the
signal for starting. The jockeys immediately began treating their chairs
as race-horses, exhibiting all the signs of extreme strain which
accompany the actual ride.
EINSTEIN: This is not yet a positive proof. The subjects of experiment
may have become cognizant of the fact that they were to serve some
eccentric display. Their acquiescence in a prescribed part need by no
means signify that they were subjectively convinced of the genuineness
of the affair.
M.: There could be not the slightest doubt on this point. After a few
seconds perspiration was streaming over their faces as a result of the
exertion, a symptom that exhibits itself only when the participants are
convinced of the absolute earnestness of their undertaking. All that
gazed on this baffling ride made the acquaintance of a grotesque
reality, and were looking into a strange world of dreams, which
transformed wooden chairs into living thoroughbreds. In the course of
his following experiments in the transference of his will-power, Hansen
experimented with an actress who was famous at that time, and with whom
he had no more acquaintance than with the others. He again produced deep
hypnosis, and gave the order: I shall ask you various questions, all of
which you will be able to answer correctly, with one exception: you will
have forgotten your name. And so it happened. In her trance the actress
gave correct answers, until, when the question, "What is your name?" was
asked, her own name, Helene Odilon, had vanished from her memory. And
immediately afterwards, she told me herself that, in spite of her state
of coma, she had retained full consciousness, had understood everything,
and had been possessed of her memory until it came to the critical
moment when, in spite of extreme efforts, she could not recollect the
words Helene Odilon. But Hansen did not stop at dictating his thoughts
to others, he also transformed corporate things. By a single motion of
his hand he converted a stable-boy into a rigid block, devoid of
sensation. Never would I have thought such an intense state of cramp
possible. He placed the boy with his feet and head alone resting on two
supports, so that the body itself was poised in space. He then stood on
the body with his whole weight, without the rigid body of the boy
bending even an inch.
EINSTEIN: How did he, in all these cases, restore the normal state?
M.: Always by a single gesture, which, like everything that he did,
worked at lightning speed. I must admit that his display became a little
monotonous after a while, and that his programme did not seem capable of
much variation. Things were different, however, in the case of a man
who, some years previously, had toured the world as an exponent of
occult phenomena, and to whom scientists will some time in the future
look back with regret. When he appeared, most academicians took only
sufficient notice of him to reject him without having given him a trial.
It was Henry Slade, the American, who is not to be confused with other
Slades who appropriated his name in order to dupe people whose
insatiable curiosity was aroused.
EINSTEIN: One might almost suppose that your genuine Henry Slade served
as a model for them.
M.: For certain reasons I regard this as out of the question, mainly
because the true Slade gave "demonstrations" only occasionally, his
chief object being to interest scientists. He, himself, repeatedly
asserted that he did not understand his own achievements, and he
unceasingly requested the supervision of professional physicists and
physiologists, to whom the unusual phases in his nature were to serve as
objects of study. The result was that people like Dubois-Reymond,
Helmholtz, and Virchow refused to see him, not to mention experiment
with him.
EINSTEIN: These men cannot be reproached for acting in this way. Slade
was regarded as a representative of a four-dimensional world in the
spiritistic sense; serious scientists must avoid all humbug of this
sort, since even slight interest in it can easily be misinterpreted by
the ignorant public.
M.: Not every one was afraid of compromising himself. After closed doors
had greeted Slade in Berlin, he went to Leipzig, where he became an
object of study for one important scientist.
EINSTEIN: You are referring to Friedrich Zöllner, who undoubtedly had a
reputation as an astrophysicist to preserve. But he would have served
his reputation better if he had not entered into this adventure with the
American spiritist.
M.: Perhaps there will some day be cause for a revision of opinion on
this point. The documents are extant, even if, half forgotten, they are
reposing in various libraries. A renewed investigation of Zöllners
_Scientific Dissertations_, dating from 1878 to 1891, might lead to the
judgment that his ghostly interpretations are to be regarded as occult
in the worst sense, and yet one would marvel that a great scientist,
such as he was, should have felt himself at a complete loss with his
knowledge, so that he was forced to resort to abstruse methods in order
to escape from the mental confusion into which Slade had plunged him.
EINSTEIN: That merely shows that Slade, as a cunning practician,
surpassed him, and that Zöllner did not succeed in seeing through his
machinations.
M.: This would lead one to assume that Slade knew more physics than the
Leipzig professor. For in a great number of experiments Zöllner himself
had prescribed the conditions, including all contrivances which made
deception so much the more unlikely, since Slade himself could not know
what Zöllner's intentions were. It was a question of Electricity,
Magnetism, Optics including prepared conditions of polarization,
involved Mechanics, in short, things that Zöllner as a professional
physicist understood thoroughly, and which, moreover, were controlled by
others of his profession. Among the latter was the celebrated professor
of Electricity, Wilhelm Weber, who, like Zöllner, found himself faced
by phenomena that were utterly incomprehensible to him. It would be a
profitable undertaking to bring these dissertations to light again, and
it would easily be recognized that the things described actually deal
with scientific problems and have not the remotest connexion with tricks
of magic. For example, there is an account of an incredible anatomical
feat. On flour which had been placed carefully in a dish beforehand,
there suddenly appeared the imprint of a naked human foot, whilst Slade
was present at a certain distance, being fully clothed and subject to
careful scrutiny. The footprint showed all the surface-details of the
skin, as was confirmed by authorities, just as only a left foot could
produce them, but not an artificial copy.
EINSTEIN: And from this Zöllner inferred the intervention of
supernatural beings? He would have done better to measure the dimensions
of the foot.
M.: So he did--at once. A difference of four centimetres between the
length of Slade's foot and the copy was disclosed. This riddle, like so
many others, remained unexplained. I must repeat that I am not in the
slightest degree disposed to assert that occult phenomena really occur,
but am interested only in seeing that they are investigated carefully by
qualified persons.
EINSTEIN: Your remarks show that Leipzig scientists did so at that time
with no better result than that Zöllners mental confusion became still
greater.
M.: The conjecture remains that the Leipzig experiments, abundant as
they were, did not suffice. Allow me to ask a direct question,
Professor. Supposing another such agent of miracles should appear, would
you yourself feel impelled to test him experimentally?
EINSTEIN: Your question is misdirected. I explained above that I share
the point of view taken up by Dubois-Reymond and his colleagues.
M.: The following case may be conceived. A certain man, X, might
suddenly appear, who has control of a certain natural force that has
never before been investigated; like one who knew how to use electricity
at a time when people had never experienced any electrical phenomenon.
He would be able to give hundreds of demonstrations, all of which we
should relegate to the realm of inexplicable magic. We should, for
instance, be much astonished if he were to draw sparks from a living
person. Now, suppose two professors express an opinion. Professor A
declares the whole thing to be a farce, and refuses to look into it at
all. Professor B is ready to investigate the achievements of X only if
the latter subjects himself from the beginning to all the physical
conditions that are to be determined beforehand. And suppose the
professor arranges his conditions so that they make impossible the
occurrence of electrical phenomena. If, now, all scientists were to
behave like A and B, the consequences would be very depressing. For here
was an important field of investigation, which is cut off owing to the
distrust or obstinacy of scientists, who should have been the first to
open it up. It is quite irrelevant whether X had the character of a
charlatan or not, for behind his charlatanism there were facts which
clamoured for investigation.
EINSTEIN: The most that I can grant is that your imagined case does not
lie outside the scope of possibility. Yet the chance that there is such
a "natural force" hitherto undiscovered by Man, that is, one that is a
"secret force" as far as we are concerned, is so vanishingly small that
it may be set down as equal to impossible. I should refuse to take part
in any such practices, served up in the form of sensation, for one
reason that I should regret the waste of time, as there are better
things to do. It is a different matter if the mood takes me to visit a
variety entertainment, in order to derive amusement from such
mystifications. For example, only yesterday I was in a little theatre,
in which, among diverse items, a thought-reading woman was performing.
She correctly guessed the numbers 61 and 59 that I had in my mind. But
let no one mention this as a case of telepathic actions at a distance or
wireless communication between minds, for an intermediate person, the
manager, was present, and I had to whisper the numbers to him. The
distance to the stage was certainly too great to allow the sound to be
conveyed directly to an audible degree. Hence there must have been a
different, very cunningly arranged code of signals, which eluded the
notice of people in the stalls. The process consists actually in an
extraordinary refinement of observation, which does not, however, seem
to me any more wonderful than the training of a reckoner who extracts
cubic roots mentally, or than the practised muscles of a juggler all
working in unison to enable him to perform feats with twelve plates
simultaneously.
M.: It gives me enough satisfaction, Professor, that you conceded me
before a certain limited chance of finding a last refuge in occultism.
And even if you, yourself, as a representative of the most rigorous
research of physical reality, refuse to consider it, yet the fact that
many others are drawn irresistibly towards mysterious phenomena cannot
be denied. Should one feel shame on this account? I believe that, in
this matter, we are touching on inner confessions that are quite
independent of the standard of the mind in which they are embedded.
Newton considered the key of the universe to be a personal God, whereas
Laplace proclaimed: _Dieu--je n'avais pas besoin de cette hypothèse_:
this contrast allows no inference to be drawn as to their relative
keenness of mind. And probably the same may be said of the question
whether there are other hidden universes besides the one in which we
live. In any case, those who feel enthusiasm for such questions can
quote in their support good names from the learned world. Immanuel Kant
occupied himself seriously and intensively with the wonders of
Swedenborg, Kepler practised Astrology, in which he had a firm belief,
Roger Bacon, Cardanus, Agrippa, Nostradamus, van Helmont, Pascal, and,
among the modern, Fechner, Wallace, Crookes, are to be counted among the
mystics. No matter whether the views they held were theosophical,
occult, four-dimensional in the spiritistic sense, or coloured by any
other superstition; they proclaimed that things that could be rigorously
proved were, alone, insufficient for them. Out of presentiment and
conjecture they constructed wings with which to fly into regions _extra
naturam_. This is how it happened that, as the common folk could not
find a place in science for many extraordinary achievements, they
assigned their authors to the realm of magicians, as in the case of
Paracelsus, Albertus Magnus, Raimundus Lullus, Sylvester II, who were
regarded as sorcerers. And this coin is still current: to Edison, of our
times, the term, "sorcerer of Menlo-Park," has become attached. In the
minds of the populace discovery and invention, works of genius and
supernatural phenomena, become confused and indistinguishable; it may
even happen to you. Professor, that your works will become invested with
legend. I should not like to conjure up what your fate would have been
if your theory of relativity had originated at the time of the
Inquisition. For the views put forward by Giordano Bruno are mere
child's play compared with your theory of the universe as a
quasi-spherical closed space of hyper-Euclidean character. The tribunal
of the Inquisition would not have understood your differential equation,
gravitational potentials, tensors, and equivalence theory; they would
abruptly have declared the whole theory to be a magical formula or a
manifestation of the devil, and would have honoured it and you with a
funeral pyre.
EINSTEIN: This is clearly a slight exaggeration. Mathematico-physical
and astronomical works have never been attacked by the Papal courts,
but, on the contrary, have been much encouraged by them down to the
present day. This is abundantly clear from the fact that we can set up a
whole list of Brothers of Orders, particularly Jesuits, who have made
eminent discoveries in natural science. From my personal knowledge of
you, I foresee that you will one day sketch a fantastic trial, in which
the new world-system will have to defend itself against the _Sanctum
Officium_.
M.: This would be a very grateful task, judged from the literary point
of view. What a splendid colouring could be obtained by bringing these
two worlds of thought into conflict with one another, the Relative
against the Absolute, which has been established in tradition and dogma.
But we need not even call the historical fancy into action, for,
actually, the theory of the structure of the world is even now still at
variance with traditional ideas, that act with dogmatic violence. There
is no need to deny the fact that every person of education, who makes
the acquaintance of Lorentz's, Minkowski's, Einstein's ideas for the
first time, feels excited to offer contradictions, and becomes involved
in a tumult of pros and cons, and each one experiences in himself the
excitement of an inquisitorial tribunal. The triumph of the new theory
passes over the corpses of conceptions that lie at the cross-roads of
thought and, long after, retain a ghostly existence. Only very few of us
are aware of the further inner revolution that awaits us along the line
of development of Einsteinian ideas; we have only vague presentiments
that whisper to us that the end of forms of thought once considered as
irrefragable is drawing nigh. When once the principle of causality has
been set on a relative base, and all "properties" have been resolved
into occurrence, and all that is three-dimensional has come to be
recognized as an abstraction from the four-dimensional world that is
alone valid, then the time will have come to arrange for, the death
procession of all the philosophies that once served as the main pillars
of thought.
A retrospect of the trials of Giordano Bruno and of Galileo Galilei
offers certain parallels other than those usually discovered by
scholars. And if, to-day, we proclaim Einstein as the Galilei of the
twentieth century, it must be added that in character he is fortunately
a Bruno and not a Galilei. For it is not true that the latter came out
of the persecution as a moral victor with an _eppur si muove_, rather,
in spite of the protection of influential prelates and dignitaries, even
of the entourage of the Pope, he lacked courage and bowed his head,
betraying his science and denying himself as well as Copernicus. Are we
to picture how Einstein would have acted under similar circumstances,
even if they cannot recur again?
Whoever has even an inkling of his character will entertain no doubts.
At that time, three hundred years ago, the materials for a magnificent
scene, "one world _versus_ the other," lay ready. Only one condition was
wanting, the moral courage of the hero. The lack of this one factor
spoilt the final act for the history of that time. The fine ethical
feelings of later generations have had to be propitiated by improvising
a legend iridescent with beautiful colours.