answer but that he was wont to ponder again and again on a subject; and
similar utterances are accredited to D'Alembert and Helmholtz.
Scientists and artists both recommend persistent labor. After the
repeated survey of a field has afforded opportunity for the
interposition of advantageous accidents, has rendered all the traits
that suit with the mood or the dominant thought more vivid, and has
gradually relegated to the background all things that are inappropriate,
making their future appearance impossible; then from the teeming,
swelling host of fancies which a free and high-flown imagination calls
forth, suddenly that particular form arises to the light which
harmonises perfectly with the ruling idea, mood, or design. Then it is
that that which has resulted slowly as the result of a gradual
selection, appears as if it were the outcome of a deliberate act of
creation. Thus are to be explained the statements of Newton, Mozart,
Richard Wagner, and others, when they say that thoughts, melodies, and
harmonies had poured in upon them, and that they had simply retained the
right ones. Undoubtedly, the man of genius, too, consciously or
instinctively, pursues systematic methods wherever it is possible; but
in his delicate presentiment he will omit many a task or abandon it
after a hasty trial on which a less endowed man would squander his
energies in vain. Thus, the genius accomplishes[91] in a brief space of
time undertakings for which the life of an ordinary man would far from
suffice. We shall hardly go astray if we regard genius as only a slight
deviation from the average mental endowment--as possessing simply a
greater sensitiveness of cerebral reaction and a greater swiftness of
reaction. The men who, obeying their inner impulses, make sacrifices for
an idea instead of advancing their material welfare, may appear to the
full-blooded Philistine as fools; yet we shall scarcely adopt Lombroso's
view, that genius is to be regarded as a disease, although it is
unfortunately true that the sensitive brains and fragile constitutions
succumb most readily to sickness.
The remark of C. G. J. Jacobi that mathematics is slow of growth and
only reaches the truth by long and devious paths, that the way to its
discovery must be prepared for long beforehand, and that then the truth
will make its long-deferred appearance as if impelled by some divine
necessity[92]--all this holds true of every science. We are astounded
often to note that it required the combined labors of many eminent
thinkers for a full century to reach a truth which it takes us only a
few hours to master and which once acquired seems extremely easy to
reach under the right sort of circumstances. To our humiliation we learn
that even the greatest men are born more for life than for science. The
extent to which even they are indebted to accident--to that singular
conflux of the physical and the psychical life in which the continuous
but yet imperfect and never-ending adaptation of the latter to the
former finds its distinct expression--that has been the subject of our
remarks to-day. Jacobi's poetical thought of a divine necessity acting
in science will lose none of its loftiness for us if we discover in this
necessity the same power that destroys the unfit and fosters the fit.
For loftier, nobler, and more romantic than poetry is the truth and the
reality.
FOOTNOTES:
[Footnote 81: Inaugural lecture delivered on assuming the
Professorship of the History and Theory of Inductive Science in the
University of Vienna, October 21, 1895.]
[Footnote 82: The phrase is, _Er hat das Pulver nicht erfunden_.]
[Footnote 83: "Quod si quis tanta industria exstitisset, ut ex
naturae principiis at geometria hanc rem eruere potuisset, eum ego
supra mortalium sortem ingenio valuisse dicendum crederem. Sed hoc
tantum abest, ut fortuito reperti artificii rationem non adhuc satis
explicari potuerint viri doctissimi."--Hugenii Dioptrica (de
telescopiis).]
[Footnote 84: I must not be understood as saying that the fire-drill
has played no part in the worship of fire or of the sun.]
[Footnote 85: Compare on this point the extremely interesting
remarks of Dr. Paul Carus in his _Philosophy of the Tool_, Chicago,
1893.]
[Footnote 86: Möbius, _Naturwissenschaftlicher Verein für
Schleswig-Holstein_, Kiel, 1893, p. 113 et seq.]
[Footnote 87: I am indebted for this observation to Professor
Hatscheck.]
[Footnote 88: Cf. Hoppe, _Entdecken und Finden_, 1870.]
[Footnote 89: See the lecture "Sensations of Orientation," p. 282 et
seq.]
[Footnote 90: This story was related to me by Jolly, and
subsequently repeated in a letter from him.]
[Footnote 91: I do not know whether Swift's academy of schemers in
Lagado, in which great discoveries and inventions were made by a
sort of verbal game of dice, was intended as a satire on Francis
Bacon's method of making discoveries by means of huge synoptic
tables constructed by scribes. It certainly would not have been
ill-placed.]
[Footnote 92: "Crescunt disciplinae lente tardeque; per varios
errores sero pervenitur ad veritatem. Omnia praeparata esse debent
diuturno et assiduo labore ad introitum veritatis novae. Jam illa
certo temporis momento divina quadam necessitate coacta emerget."
Quoted by Simony, _In ein ringförmiges Band einen Knoten zu machen_,
Vienna, 1881, p. 41.]
ON SENSATIONS OF ORIENTATION.[93]
Through the co-operation of a succession of inquirers, among whom are
particularly to be mentioned Goltz of Strassburg and Breuer of Vienna,
considerable advances have been made during the last twenty-five years
in our knowledge of the means by which we ascertain our position in
space and the direction of our motion, or orient ourselves, as the
phrase goes. I presume that you are already acquainted with the
physiological part of the processes with which our sensations of
movement, or, more generally speaking, our sensations of orientation,
are connected. Here I shall consider more particularly the physical side
of the matter. In fact, I was originally led to the consideration of
these questions by the observation of extremely simple and perfectly
well-known physical facts, before I had any great acquaintance with
physiology and while pursuing unbiasedly my natural thoughts; and I am
of the conviction that the way which I have pursued, and which is
entirely free from hypotheses, will, if you will follow my exposition,
be that of easiest acquisition for the most of you.
No man of sound common sense could ever have doubted that a pressure or
force is requisite to set a body in motion in a given direction and that
a contrary pressure is required to stop suddenly a body in motion.
Though the law of inertia was first formulated with anything like
exactness by Galileo, the facts at the basis of it were known long
previously to men of the stamp of Leonardo da Vinci, Rabelais, and
others, and were illustrated by them with appropriate experiments.
Leonardo knew that by a swift stroke with a ruler one can knock out from
a vertical column of checkers a single checker without over-throwing the
column. The experiment with a coin resting on a piece of pasteboard
covering a goblet, which falls into the goblet when the pasteboard is
jerked away, like all experiments of the kind, is certainly very old.
With Galileo the experience in question assumes greater clearness and
force. In the famous dialogue on the Copernican system which cost him
his freedom, he explains the tides in an unfelicitous, though in
principle correct manner, by the analogue of a platter of water swung to
and fro. In opposition to the Aristotelians of his time, who believed
the descent of a heavy body could be accelerated by the superposition
of another heavy body, he asserted that a body could never be
accelerated by one lying upon it unless the first in some way impeded
the superposed body in its descent. To seek to press a falling body by
means of another placed upon it, is as senseless as trying to prod a man
with a lance when the man is speeding away from one with the same
velocity as the lance. Even this little excursion into physics can
explain much to us. You know the peculiar sensation which one has in
falling, as when one jumps from a high springboard into the water, and
which is also experienced in some measure at the beginning of the
descent of elevators and swings. The reciprocal gravitational pressure
of the different parts of our body, which is certainly felt in some
manner, vanishes in free descent, or, in the case of the elevator, is
diminished on the beginning of the descent. A similar sensation would be
experienced if we were suddenly transported to the moon where the
acceleration of gravity is much less than upon the earth. I was led to
these considerations in 1866 by a suggestion in physics, and having also
taken into account the alterations of the blood-pressure in the cases in
question, I found I coincided without knowing it with Wollaston and
Purkinje. The first as early as 1810 in his Croonian lecture had touched
on the subject of sea-sickness and explained it by alterations of the
blood-pressure, and later had laid similar considerations at the basis
of his explanation of vertigo (1820-1826).[94]
Newton was the first to enunciate with perfect generality that a body
can change the velocity and direction of its motion only by the action
of a force, or the action of a second body. A corollary of this law
which was first expressly deduced by Euler is that a body can never be
set _rotating_ or made to cease rotating of itself but only by forces
and other bodies. For example, turn an open watch which has run down
freely backwards and forwards in your hand. The balance-wheel will not
fully catch the rapid rotations, it does not even respond fully to the
elastic force of the spring which proves too weak to carry the wheel
entirely with it.
Let us consider now that whether we move ourselves by means of our legs,
or whether we are moved by a vehicle or a boat, at first only a part of
our body is directly moved and the rest of it is afterwards set in
motion by the first part. We see that pressures, pulls, and tensions are
always produced between the parts of the body in this action, which
pressures, pulls, and tensions give rise to sensations by which the
forward or rotary movements in which we are engaged are made
perceptible.[95] But it is quite natural that sensations so familiar
should be little noticed and that attention should be drawn to them only
under special circumstances when they occur unexpectedly or with unusual
strength.
[Illustration: Fig. 45.]
Thus my attention was drawn to this point by the sensation of falling
and subsequently by another singular occurrence. I was rounding a sharp
railway curve once when I suddenly saw all the trees, houses, and
factory chimneys along the track swerve from the vertical and assume a
strikingly inclined position. What had hitherto appeared to me perfectly
natural, namely, the fact that we distinguish the vertical so perfectly
and sharply from every other direction, now struck me as enigmatical.
Why is it that the same direction can now appear vertical to me and now
cannot? By what is the vertical distinguished for us? (Compare Figure
45.)
The rails are raised on the convex or outward side of the track in order
to insure the stability of the carriage as against the action of the
centrifugal force, the whole being so arranged that the combination of
the force of gravity with the centrifugal force of the train shall give
rise to a force perpendicular to the plane of the rails.
Let us assume, now, that under all circumstances we somehow sense the
direction of the total resultant mass-acceleration whencesoever it may
arise as the vertical. Then both the ordinary and the extraordinary
phenomena will be alike rendered intelligible.[96]
I was now desirous of putting the view I had reached to a more
convenient and exact test than was possible on a railway journey where
one has no control over the determining circumstances and cannot alter
them at will. I accordingly had the simple apparatus constructed which
is represented in Figure 46.
In a large frame _BB_, which is fastened to the walls, rotates about a
vertical axis _AA_ a second frame _RR_, and within the latter a third
one _rr_, which can be set at any distance and position from the axis,
made stationary or movable, and is provided with a chair for the
observer.
[Illustration: Fig. 46.
From Mach's _Bewegungsempfindungen_, Leipsic, Engelmann, 1875.]
The observer takes his seat in the chair and to prevent disturbances of
judgment is enclosed in a paper box. If the observer together with the
frame _rr_ be then set in uniform rotation, he will feel and see the
beginning of the rotation both as to direction and amount very
distinctly although every outward visible or tangible point of reference
is wanting. If the motion be uniformly continued the sensation of
rotation will gradually cease entirely and the observer will imagine
himself at rest. But if _rr_ be placed outside the axis of rotation, at
once on the rotation beginning, a strikingly apparent, palpable,
actually visible inclination of the entire paper box is produced, slight
when the rotation is slow, strong when the rotation is rapid, and
continuing as long as the rotation lasts. It is absolutely impossible
for the observer to escape perceiving the inclination, although here
also all outward points of reference are wanting. If the observer, for
example, is seated so as to look towards the axis, he will feel the box
strongly tipped backwards, as it necessarily must be if the direction of
the total resultant force is perceived as the vertical. For other
positions of the observer the situation is similar.[97]
Once, while performing one of these experiments, and after rotating so
long that I was no longer conscious of the movement, I suddenly caused
the apparatus to be stopped, whereupon I immediately felt and saw myself
with the whole box rapidly flung round in rotation in the opposite
direction, although I knew that the whole apparatus was at rest and
every outward point of reference for the perception of motion was
wanting. Every one who disbelieves in sensations of movement should be
made acquainted with these phenomena. Had Newton known them and had he
ever observed how we may actually imagine ourselves turned and displaced
in space without the assistance of stationary bodies as points of
reference, he would certainly have been confirmed more than ever in his
unfortunate speculations regarding absolute space.
The sensation of rotation in the opposite direction after the apparatus
has been stopped, slowly and gradually ceases. But on accidentally
inclining my head once during this occurrence, the axis of apparent
rotation was also observed to incline in exactly the same manner both as
to direction and as to amount. It is accordingly clear that the
acceleration or retardation of rotation is felt. The acceleration
operates as a stimulus. The sensation, however, like almost all
sensations, though it gradually decreases, lasts perceptibly longer than
the stimulus. Hence the long continued apparent rotation after the
stopping of the apparatus. The organ, however, which causes the
persistence of this sensation must have its seat in the _head_, since
otherwise the axis of apparent rotation could not assume the same motion
as the head.
If I were to say, now, that a light had flashed upon me in making these
last observations, the expression would be a feeble one. I ought to say
I experienced a perfect illumination. My juvenile experiences of vertigo
occurred to me. I remembered Flourens's experiments relative to the
section of the semi-circular canals of the labyrinths of doves and
rabbits, where this inquirer had observed phenomena similar to vertigo,
but which he preferred to interpret, from his bias to the acoustic
theory of the labyrinth, as the expression of painful auditive
disturbances. I saw that Goltz had nearly but not quite hit the bull's
eye with his theory of the semi-circular canals. This inquirer, who,
from his happy habit of following his own natural thoughts without
regard for tradition, has cleared up so much in science, spoke, as early
as 1870, on the ground of experiments, as follows: "It is uncertain
whether the semi-circular canals are auditive organs or not. In any
event they form an apparatus which serves for the preservation of
equilibrium. They are, so to speak, the sense-organs of equilibrium of
the head and indirectly of the whole body." I remembered the galvanic
dizziness which had been observed by Ritter and Purkinje on the passage
of a current through the head, when the persons experimented upon
imagined they were falling towards the cathode. The experiment was
immediately repeated, and sometime later (1874) I was enabled to
demonstrate the same objectively with fishes, all of which placed
themselves sidewise and in the same direction in the field of the
current as if at command.[98] Müller's doctrine of specific energies now
appeared to me to bring all these new and old observations into a
simple, connected unity.
[Illustration: Fig. 47.
The labyrinth of a dove (stereoscopically reproduced), from R. Ewald,
_Nervus Octavus_, Wiesbaden, Bergmann, 1892.]
Let us picture to ourselves the labyrinth of the ear with its three
semi-circular canals lying in three mutually perpendicular planes (Comp.
Fig. 47), the mysterious position of which inquirers have endeavored to
explain in every possible and impossible way. Let us conceive the nerves
of the ampullæ, or the dilated extensions of the semi-circular canals,
equipped with a capacity for responding to every imaginable stimulus
with a sensation of rotation just as the nerves of the retina of the eye
when excited by pressures, by electrical or chemical stimuli always
respond with the sensation of light; let us picture to ourselves,
further, that the usual excitation of the ampullæ nerves is produced by
the inertia of the contents of the semi-circular canals, which contents
on suitable rotations in the plane of the semi-circular canal are left
behind in the motion, or at least have a tendency to remain behind and
consequently exert a pressure. It will be seen that on this supposition
all the single facts which without the theory appear as so many
different individual phenomena, become from this single point of view
clear and intelligible.
I had the satisfaction, immediately after the communication in which I
set forth this idea,[99] of seeing a paper by Breuer appear[100] in
which this author had arrived by entirely different methods at results
that agreed in all essential points with my own. A few weeks later
appeared the researches of Crum Brown of Edinburgh, whose methods were
even still nearer mine. Breuer's paper was far richer in physiological
respects than mine, and he had particularly gone into greater detail in
his investigation of the collateral effects of the reflex motions and
orientation of the eyes in the phenomena under consideration.[101] In
addition certain experiments which I had suggested in my paper as a test
of the correctness of the view in question had already been performed by
Breuer. Breuer has also rendered services of the highest order in the
further elaboration of this field. But in a physical regard, my paper
was, of course, more complete.
In order to portray to the eye the behavior of the semi-circular canals,
I have constructed here a little apparatus. (See Fig. 48.) The large
rotatable disc represents the osseous semi-circular canal, which is
continuous with the bones of the head; the small disc, which is free to
rotate on the axis of the first, represents the mobile and partly liquid
contents of the semi-circular canal. On rotating the large disc, the
small disc as you see remains behind. I have to turn some time before
the small disc is carried along with the large one by friction. But if I
now stop the large disc the small disc as you see continues to rotate.
[Illustration: Fig. 48.
Model representing the action of the semi-circular canals.]
Simply assume now that the rotation of the small disc, say in the
direction of the hands of a watch, would give rise to a sensation of
rotation in the opposite direction, and conversely, and you already
understand a good portion of the facts above set forth. The explanation
still holds, even if the small disc does not perform appreciable
rotations but is checked by a contrivance similar to an elastic spring,
the tension of which disengages a sensation. Conceive, now, three such
contrivances with their mutually perpendicular planes of rotation joined
together so as to form a single apparatus; then to this apparatus as a
whole, no rotation can be imparted without its being indicated by the
small mobile discs or by the springs which are attached to them.
Conceive both the right and the left ear equipped with such an
apparatus, and you will find that it answers all the purposes of the
semi-circular canals, which you see represented stereoscopically in Fig.
47 for the ear of a dove.
Of the many experiments which I have made on my own person, and the
results of which could be predicted by the new view according to the
behavior of the model and consequently according to the rules of
mechanics, I shall cite but one. I fasten a horizontal board in the
frame _RR_ of my rotatory apparatus, lie down upon the same with my
right ear upon the board, and cause the apparatus to be uniformly
rotated. As soon as I no longer perceive the rotation, I turn around
upon my left ear and immediately the sensation of rotation again starts
up with marked vividness. The experiment can be repeated as often as one
wishes. A slight turn of the head even is sufficient for reviving the
sensation of rotation which in the perfectly quiescent state at once
disappears altogether.
We will imitate the experiment on the model. I turn the large disc until
finally the small disc is carried along with it. If, now, while the
rotation continues uniform, I burn off a little thread which you see
here, the small disc will be flipped round by a spring into its own
plane 180°, so as now to present its opposite side to you, when the
rotation at once begins in the opposite direction.
We have consequently a very simple means for determining whether one is
actually the subject or not of uniform and imperceptible rotations. If
the earth rotated much more rapidly than it really does, or if our
semi-circular canals were much more sensitive, a Nansen sleeping at the
North Pole would be waked by a sensation of rotation every time he
turned over. Foucault's pendulum experiment as a demonstration of the
earth's rotation would be superfluous under such circumstances. The only
reason we cannot prove the rotation of the earth with the help of our
model, lies in the small angular velocity of the earth and in the
consequent liability to great experimental errors.[102]
Aristotle has said that "The sweetest of all things is knowledge." And
he is right. But if you were to suppose that the _publication_ of a new
view were productive of unbounded sweetness, you would be mightily
mistaken. No one disturbs his fellow-men with a new view unpunished. Nor
should the fact be made a subject of reproach to these fellow-men. To
presume to revolutionise the current way of thinking with regard to any
question, is no pleasant task, and above all not an easy one. They who
have advanced new views know best what serious difficulties stand in
their way. With honest and praiseworthy zeal, men set to work in search
of everything that does not suit with them. They seek to discover
whether they cannot explain the facts better or as well, or
approximately as well, by the traditional views. And that, too, is
justified. But at times some extremely artless animadversions are heard
that almost nonplus us. "If a sixth sense existed it could not fail to
have been discovered thousands of years ago." Indeed; there was a time,
then, when only seven planets could have existed! But I do not believe
that any one will lay any weight on the philological question whether
the set of phenomena which we have been considering should be called a
sense. The phenomena will not disappear when the name disappears. It was
further said to me that animals exist which have no labyrinth, but which
can yet orientate themselves, and that consequently the labyrinth has
nothing to do with orientation. We do not walk forsooth with our legs,
because snakes propel themselves without them!