| Here
under follows the transcription of the chapter Leonardo of
Houston
Stewart Chamberlain's Immanuel Kant, published by John Lane,
The
Bodley Head, 1914.
LEONARDO DA
VINCI
Painted by
himself
Drawn and
engraved
by Charles Townley
|
99
LEONARDO
CONCEPTION AND
PERCEPTION
WITH AN EXCURSUS UPON PHYSICAL OPTICS
AND THE DOCTRINE OF COLOUR
Our soul is composed of harmony,
and harmony is never bred save
in moments when the proportions
of objects are seen or heard.
Leonardo.
100
(Blank page)
101
LEONARDO
THAT
Seeing is a
passive as well as an active function is a maxim as old as Aristotle.
But
the difference between passivity and activity in different men repeats
itself in the degree and the more delicate qualities of both. It must
be
our business to bring into relief those personal peculiarities of
Kant's
way of Seeing which differentiate him from other Seers. It is with this
object in view that we resort to comparison. We desire ourselves to
observe
and See the most important of the Seers, in the
profound
conviction that this will carry us further and to greater advantage
than
if we were to go into abstract theories about them, and hedge in their
doctrines with finely pointed fences of definition.
From our first
comparison,
— that with Goethe, — we have won a significant and lasting advantage.
The intellectual individuality of Kant revealed itself in striking
contrast
to that of Goethe. In Kant we saw a peculiar quality of intuition
developed
to an absolutely astounding degree. We saw the power of appreciating
mentally
that which has been described: and that which is described is something
which has been brought to our minds parcel-wise, or, to use the
technical
expression, analytically: for it is only by degrees that words can
present
a Whole, whereas the Eye first gives us a Whole, and only by degrees
separates
it into Parts. Moreover, in Kant we found an important development of
that
method of perception which is projected from within to without,
geometrically
in accordance with formula, humanly
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LEONARDO
speaking
creative, — namely the
mathematical
method. In Goethe, on the contrary, we found as a characteristic the
insatiable
hunger of the Eye, and in connection therewith the impulse to treat
even
matters of theory as something actually seen. In spite of this,
inasmuch
as the Doctrine of Metamorphosis had furnished us with a clear
demonstration
of the relationship between passivity and activity in Goethe's manner
of
Seeing, we recognised its harmony with Kant's mental vision and his
analytical
distinction between Experience and Idea.
To-day I wish to
carry this comparison with Goethe further, for it still contains a
whole
store of instruction. I hope to convince you that without the help of
Kant
we could hardly succeed in correctly grasping Goethe's view of nature,
while at the same time no other man leads us so directly and patently
to
Kant, as does Goethe. This consideration, then, will give you a twofold
advantage. Still, I wish to associate with these two men a third, —
another
great artist. I hit upon my choice without any reference to chronology;
— simply with the intention of avoiding the ever-present danger of
allowing
our lazy thoughts to crystallise, and of contenting ourselves with some
idle phrase about the antagonism between art and philosophy.
Unfortunately
no lesser man than Schopenhauer has given encouragement to so stark a
fallacy:
he is the most read of all philosophers, and in so far justly as he is
by a long way the most readable; pity, that among his many perversities
of thought, (I can find no other word for them,) there should be the
asseveration
that “Genius and a head for mathematics“ should be contradictions. 1
It is not possible here to enter upon a refutation of this detestable
asseveration,
to which, in the very first place, the whole phenomenon of Hellenism
would
have to fall a sacrifice: it would be easy and entertaining to carry
out
such a refutation with no other help than that of Schopenhauer's own
writings:
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LEONARDO
but
one feels almost
ashamed
to enter the lists against this much too clever man when one hears him
in an important passage cite Alfieri as having been unable to master
the
fourth proposition of Euclid, and again bringing forward some unnamed
French
mathematician who, on reading through Racine's Iphigénie,
shrugged his shoulders, and asked, “Qu'est-ce que cela prouve?“ 2
If those are arguments then one might, with equal force, come to the
conclusion
that because a certain nineteenth-century poet at the age of forty, and
in spite of living in the country, did not yet know that tadpoles turn
into frogs, therefore no Poet is gifted with the power of observing
nature.
The mischief of such phrases, when they are presented with the
seductive
eloquence of a Schopenhauer, is that they are scattered far and wide,
and
establish themselves as dogmas, and so it comes to pass that to-day we
find many men who because, like Alfieri, they are incapable of
something,
pose as men of genius, and who, not content with the fact that “the
pride
of the human intellect,“ as Kant calls mathematics, is none of theirs,
plume themselves upon their impotence. Nay more, these mental waifs who
cannot even grasp the simple problem of the equilateral triangle, look
down from the height of their superiority on the most important men if
only they show any aptitude for mathematics, and catalogue them as
second-rate
goods. But we need not dwell upon this, though it is difficult to
prevent
our wrath from blazing up over the impertinence of so fundamentally
perverted
a dogma. It is time for us to enter at once upon the heart of our
subject.
3
Schopenhauer's thesis
affects genius in general. Sometimes, however, he propounds it in a
narrower
and therefore more plausible form: in this sense he writes, “Experience
has proved that men of great genius in art have no aptitude for
mathematics.“
That is an important limitation, for even in his eyes it is not the
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LEONARDO
artist
alone who can lay claim to
genius:
indeed, he is fond of quoting himself as an example, and certainly he
had
no artistic sense. Nevertheless this contention, which is to be found
in
the thirty-sixth paragraph of the first volume of his principal work,
is
so fundamentally false, that one asks oneself how Schopenhauer could
have
been blind enough to let it stand unaltered from the year 1818 to the
day
of his death. If we only think of German artists, the very first that
comes
to our thoughts is the man who was so specially admired even by Goethe,
the great, the only, I had almost said the holy, Albrecht Dürer.
He
is one of those great “men of genius in art“ of whom one can say that
they
were the beginning and the end and the culminating point, all in one.
Of
course historically they spring from what has gone before, and they
lead
to what is to follow after, but that association hangs about their
noble
forms like a mantle. Like the goddess from the sea-foam, the individual
rises out of the mass, something new, something incomparable, that
never
was before, and never can be again. At the sight of such men we are
struck
by Schopenhauer's fine saying, “Art is everywhere triumphant.“
Perfection
it is that blazes out upon us out of all the feverish struggles of
these
artists, — Peace that smiles upon us, full of trust, and resting from
the
hurry of the eternal strife for something higher. And where labour and
thought and prayer have wrought together as tireless journeymen, there
at last reigns Harmony, divinely restful, incapable of failure. Among
these
giants is Dürer — and mark this. Not only had he an aptitude for
mathematics,
but that aptitude was something quite out of the common. Dürer is
the author of the first textbook of applied geometry in the German
language!
Besides that, he devoted a whole work to the hopelessly dry, and only
mathematically
interesting, subject of Fortification; and his lectures on the
proportion
of the human figure are a little miracle
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LEONARDO
of
intricate
geometrical
descriptions. In his partiality for mathematics, in his sure eye for
the
study, and the weight that he lays upon it for the educational
equipment
of the artist — as he writes, “mensuration is the right foundation of
all
painting“ 4
—
we have the special characteristic of this great artist. This one
example
is enough to prove that Schopenhauer's contention that the great artist
has no aptitude for mathematics is an untenable generalisation from
single
instances. Further, you will easily understand that I must have it at
heart
to refute the insinuation that Kant belonged to the class of inferior
minds
lacking genius, because he had a talent for mathematics: far rather do
we see that the possession of that talent gives us no right to infer a
lack of artistic feeling.
Now, at last, I call
up the man whose radiant name I should be loath to cloud with polemics
— Leonardo da Vinci. No greater painter ever lived; and this great
painter
was like Dürer, and even more than Dürer, a pre-eminent
mathematician
and mechanician. At the same time — as we see every day more clearly —
a man of an all-embracing intellect, a Seer who penetrated all that his
eye saw, a Discoverer so inexhaustible that the world has perhaps never
seen his like, a deep, bold Thinker. Let us compare his method of
Seeing
with the methods of Goethe and Kant: that, I hope, will save us from
all
future danger of the crystallisations of the phrase-mongers.
Like Goethe, this
man is all Eye. He calls the Eye the Window of the soul, finestra
dell'
anima, 5
whose
precious qualities he is never weary of praising; the Eye is signore
de' sensi, “Lord of the senses,“ 6
the Eye is the Source of all Knowledge. Those who rely solely on the
study
of learned writings, instead of becoming acquainted with the works of
Nature
by means of their own Eyes, are only grandchildren not Sons of Nature,
that one
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LEONARDO
teacher
of all
teachers.
All Arts, all Sciences, all Thought, are according to Leonardo
“daughters
of the Eye,“ and so it is that the painter is nipote à Dio,
“the grandson of God.“ The Eye of this remarkable man is nevertheless,
like Goethe's, far from being an exclusively artistic organ, — it has
also
the power of penetrating the universe. A brilliant light radiates from
his Eye — for it is the special characteristic of the Eye of such men
that
it not only takes up light as others do, but also sends out rays of
light
illuminating the darkness, glowing through the impenetrable until it
becomes
transparent. A ray of light radiates, I say, from Leonardo's Eye so
brilliantly,
that even the most prosaic historians must admit that in him the
intuitive
power of divination of this organ verges upon the fabulous. Leonardo
anticipated
our whole modern natural science, — that is to say so far as this was
possible,
relying upon the Eye alone and without the help of the higher
mathematics,
— which were not then known, — of the new instruments, and of the mass
of observations which had to be mastered by whole generations. For
example,
this man who died in 1519, who had been brought up in the strict belief
of the Church in a flat earth laid between Heaven and Hell, knew the
principles
of the Cosmic system as Copernicus developed them thirty years later.
How
he gained this knowledge, and in what connection it came to him, we
know
not. For his observations, up to the present time far from being all
deciphered
and published, are for the most part aphoristic, often forming an
unsolvable
tangle of the most various thoughts, jotted down in the midst of, or
under,
or across his sketches, or on the backs of his sheets of drawings —
thoughts
often occurring to him in the midst of his painting, which he evidently
seizes in a hurry, in order to use them elsewhere. Sometimes he writes
expressly, “This is how I must deal with the matter in my work,“ or
something
of the same sort: or they are
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LEONARDO
clear
and neat
preparations
for books which he seems never to have written, and it is only from the
outline that we can make a guess at the direction of his thought. So in
Leonardo's writings we find no astronomical system. Yet on one sheet,
under
a number of mathematical calculations, we find written in unusually
large
letters, il sole non si muove, “the sun does not move.“ Not
another
word. Here we have clearly a sudden inspiration. But Leonardo is no
visionary:
his was throughout a positive intellect, never weary of seeking the certezza
delle scientie by the strictly empirical and mathematical road. Sperientia
è commune madre di tutte le scientie e arti. “Experience is
the common mother of all the arts and sciences,“ — and nissuna
humana
investigatione si po dimandare vera scientia, s'essa non passa per le
matematiche
dimostrationi, “no human investigation can lay claim to being true
science, unless it can stand the test of mathematical demonstration.“
Experiment,
therefore, and calculation must be brought into court as tests of the
correctness
of any assumed fact. In the same way on other sheets we find a
succession
of investigations and deductions all circling round this central idea
of
a stationary sun and an earth which is in motion. Take, for instance,
the
important recognition come la terra non è nel mezzo del
cerchio
del sole, ne nel mezzo del mondo, 7
“that the earth is not in the centre of the sun's orbit, nor in the
centre
of the universe.“ In this connection we over and over again find the
remark
that the sun is greater than the earth, together with the assertion
that
there are many stars that are many times bigger than the star which is
the earth. Molte stelle vi sono che son moltissime volte maggiore
che
la stella che è la terra. 8
The recognition of the fact that the dark earth reflects light leads
him
to the further assumption that the light of the planets is also
reflected
light, and that our earth seen from the moon would have
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LEONARDO
exactly
the same
appearance
as that which the moon gives us. 9
From this recognition there was but one step to the affirmation that
the
earth must be nearly spherical in shape and revolve round its axis.
Certainly,
so far as I know, we possess no written proof that Leonardo in any of
his
abrupt sentences ever gave expression to the further fundamental
thought
of the heliocentric system; but a great portion of his work is as yet
unpublished,
and this idea of motion follows so necessarily from the tenets which I
have cited, that we are compelled to accept the belief that it was
known
to him. If now we turn our attention from the movements of the
constellations
to the hidden inner movements of the body, we find that Leonardo with
the
help of a like magical power of vision suspected, and even had a clear
idea of, the circulation of the blood. This has been denied on the
ground
that in one passage Leonardo compared the movements of the blood with
the
ebb and flow of the tide. But the objection breaks down, because the
notes
which we possess of Leonardo's thoughts date from the most various
periods
of his life, and nothing can blot out the words which we have in his
own
hand, in black and white, concerning il continuo corso che fa il
sangue
per le sue vene, “the continuous course of the blood racing through
its veins,“ and over and above this that the blood which flows back to
the heart, il sangue che torna indirieto, differs from that
which,
when the blood is driven out, closes the valves of the heart, che
riserra
le porte del core. 10
These words suffice to prove a deep insight into the mechanism of the
circulation,
which at that time was unsuspected and not discovered until a century
later:
for Leonardo knows that the blood “runs an uninterrupted course through
the veins,“ he knows that it proceeds from the heart, and finds its way
back to the heart, and he makes a distinction between the venous blood
and the arterial blood. And here we must bear in mind that the most
important
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LEONARDO
works
of Leonardo in
this
connection, as in others, are up to the present unpublished. They lie
idle
in the dust of libraries.
I have chosen these
two examples, the astronomical and the physiological, out of the great
mass of material. Leonardo seems to have interested himself in every
branch
of science, and everywhere, through the mere penetrating power of his
sight,
coupled with the sagacity of his judgment, he appears to have
forestalled
science — often by centuries. Think only of his right appreciation of
the
significance of petrifactions and of the geological strata at a time
when
people used to explain the one as the playful products of a vis
plastica,
while for the other at best the Deluge was made responsible! But to my
regret I can give no more time to this captivating subject. If you want
more particulars I must refer you to the books upon Leonardo. 11
I must be content if, by quoting typical instances, I have made you
familiar
with the wonderful quality and astounding penetration of this power of
perception. Words are insufficient, what we need is facts — and these
facts
patent to every man, even to the unlearned, point to an intellect whose
kinship with that of Goethe is at once striking: the same ever-open
Eye,
never satiated, the Eye of the warder Lynceus (as he called it in my
first
lecture), surveying the whole world, and uninterruptedly entertaining
the
monarch imprisoned in the Tower with new pictures: at the same time it
is an Eye which creates. Yet we are struck by two important
differences.
Leonardo sees more exactly than Goethe, his Eye is sharper, and he can
do what Goethe never could: he can reproduce what he has seen so that
it
becomes something seen by others: he is a painter, and for that reason
still further removed from Kant than Goethe. But just as the outer
sense
is more refined in Leonardo than in Goethe, so it is too in the case of
that inner schematic power of perception, which Goethe hardly
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LEONARDO
possessed,
but which in
Kant was conspicuously developed. In this respect the relationship is
reversed:
Leonardo is nearer to Kant than Goethe was; in mechanics, indeed, he is
as richly gifted with genius as he is in Art. Take up the six beautiful
volumes into which Ravaisson-Mollien has divided all Leonardo's
manuscripts
in the Bibliothèque de l'Institut, in facsimile and deciphered,
and you will see that nine-tenths of these notes refer to mathematics
and
mechanics. Leonardo never ceased to calculate. His mind was busy with
the
squaring of the circle, and with groping attempts at infinitesimal
calculation;
from the flight of birds to the observation of a waterfall, in every
direction
the interest in mathematics and mechanics forces itself upon him side
by
side with that of the painter. In one place he speaks of mechanics as
“a
Paradise,“ and says of it, “the science of machinery or mechanics is
the
noblest of all the sciences“ — La scientia strumentale over
machinale
è nobilissima. On the sheet which contains perhaps the very
first sketch for the Last Supper, we find immediately under the subject
a geometrical problem drawn and solved in ciphers, and another sheet
which
contains studies for the Apostles and a pathetic sketch for the Christ,
shows under these figures a plan for a piece of machinery with
explanatory
notes. So if Leonardo and Goethe are two men in whom, in
contradistinction
to Kant, the Eye is the organ of life, still two very different
intellects
must be looking out from this finestra dell' anima, two very
different
modes of activity, to quote Aristotle, and therefore at the same time
two
very different systems of philosophy. Starting from the outward and
visible
signs we shall reach the very core of the question if we pay attention
to one thing, — that Goethe wished to paint and could not, whilst
Leonardo
presents such a culminating point of pictorial genius, that few can
reach
his level, none surpass him.
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LEONARDO
Goethe's
lack of capability in the plastic arts would be less striking if we did
not see him from childhood so passionately striving to attain mastery
in
this very direction. We know that as a student in Leipzig he painted
more
than he read. It was Oeser's studio, not the lecture-rooms of the
juristic
Faculty, that he haunted. And with what touching industry did he carry
on this struggle for the impossible!
- Doch unvermögend Streben,
Nachgelalle,
- Bracht' oft den Stift, den Pinsel
bracht's
zu Falle;
- Auf neues Wagnis endlich blieb
doch nur
- Vom besten Wollen halb und halbe
Spur.
In
the end Goethe himself was bound to
confess,
“I was lacking in the true plastic power,“ and he adds the precious
words
of irony against himself, “my attempts at representing nature were more
like distant suspicions of given forms, and my figures resembled the
light
vaporous beings in Dante's Purgatorio, shadowless themselves, and
terror-stricken
at the shadows of real bodies.“ What this defect meant Goethe
accurately
realised; for in a conversation with Eckermann he quotes with praise
words
of our Leonardo, — “If your son lacks the sense to make what he draws
stand
out in relief by powerful shadowing, so that one might grasp it in
one's
hand, then he has no talent.“ And do you know why Goethe had no talent
for drawing? Why his copies were mere “distant suspicions of given
forms“?
Because he was deficient in the sense of Geometry. Because we men are
so
built that we are incapable of accurately grasping any form which
nature
presents to us, unless, consciously or unconsciously, we have held
before
it by way of comparison the complex network of possible forms which is
innate in us, and have in this way assimilated that which is outside
all
rule, incalculable, and which has never existed, by contrasting it with
that which is regular, calculated and for ever unalterable. This happens
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LEONARDO
without
our thinking of
it during every second of our life: we are incessantly schematising.
Later
on you will learn from Kant to what degree our whole intellectual being
is under the domination of Scheme. “This schematising of our
understanding,
when we are face to face with phenomena,“ he writes, “is an art hidden
in the depths of the human soul.“ For the images which we receive from
without, that is to say the complex of the impressions of our senses,
cannot
be grasped directly, but our intellect — the “activity“ of Aristotle —
must first, as Kant says in a happy figure of speech, have impressed
its
monogram upon them. “It is only by means of the Scheme that images and
conception can be brought into union.“ You see that from without to
within
there is an intermediary action similar to that which takes place from
within to without. Our ideas, as you will remember from the
metamorphosis,
were only able to reach the Eye by borrowing a symbol, e.g. the leaf,
from
the world of the senses: but this world of the senses — so runs the new
creed — can penetrate the thinking consciousness in no other way than
by
the intermediary of schemes of the understanding; and these schemes
coincide
with the perceptions with no more exactitude than the symbols coincided
with the ideas. It is not my intention at this moment to weary you with
metaphysical disquisitions; on the contrary, I wanted only to call your
attention to the fact that the plastic artist shows us this secret
domination
of the “hidden art“ of schematisation in bright daylight, and so
smooths
the way for the understanding of one of the most difficult passages of
Kant's Critique of the Doctrine of Perception. For the great
painter,
consciously and in the sight of all men, puts into concrete form that
which
in others exists in the unconscious “depths of the soul.“
That is why
Dürer
wrote those words which perhaps may have struck you as strange a little
while ago — “The
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LEONARDO
art
of mensuration is the true
foundation
of all painting,“ and the same order of thought gives rise to what he
writes
on the next page: “The outer (practical) work must be the indication of
the inner understanding.“ And in order that you may realise how
powerfully
the geometrical and schematic principle is developed in so pre-eminent
a modeller, and how busily it is at work, I would beg you to take up
another
work of Dürer's, “the four Books of human proportion,“ — not in a
modern abbreviated edition, but in the original small folio of 1528,
with
all the charts and tables, as they left the master's hands. You will be
astounded at the world of numbers and geometrical figures in which
Dürer
lived; they are enough to make you giddy. Indeed, every complication
can
be solved by figures, yielding of its own accord without any involving
of the imagination: but one can hardly grasp how any man should have
been
able to carry in his head, as something visible, such complicated
geometrical
figures, as Dürer was obviously able to do. In the two first books
the many charts of figures and the painful precision of the
measurements
will strike you as imposing. But now look at the third book! Here
Dürer
teaches us how we may at will change the fixed proportions; for
instance,
he takes a woman of average proportions that he has already shown us,
and
makes her first long and thin, then short and monstrously fat; or else
he changes one part of the body, leaving the other parts as they were,
etc., and all this he does without ever departing from the established
foundations of geometrical schemes, and with the help of instruments
which
he calls “the perverter,“ “the falsifier,“ etc. The fourth book is
almost
more interesting: it shows “how you may distort the previously
described
images,“ and yet it is no simple doctrine of perspective in our sense
of
the word, but rather what mathematicians call the geometry of position,
bound up with that of projection. You need
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LEONARDO
only
look at the
figures
on page Y4, Z, and those that follow, in order to arrive at the
understanding
of what Dürer expects of the art-disciple.
Leonardo's brain
was organised in like fashion. To be sure he was not so self-tormenting
— for instance, look at his doctrine of perspective, how bright it
seems
by the side of Dürer's, — yet always and everywhere he paid
respect
to the mathematical relations, always bringing calculation into play,
always
displaying the geometrical Scheme between the Eye and the Object. One
hundred
and
fifty years ago, Charles Bonnet, the
Genevan botanist, introduced the so-called doctrine of Phyllotaxy, that
is to say, the exact observation of the relative position of the leaves
on the stalk.
To the most widely
spread form of this relative position he gave the name of Quincunx:
in this the sixth leaf after the stalk has been twice encircled
invariably
stands immediately above the first; accordingly every cycle of leaves
consists
of five leaves. This discovery was the result of years of study by an
experienced
professed botanist. But two hundred and fifty years earlier Leonardo's
artist-eye had observed the Quincunx, and
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LEONARDO
had
drawn it with the most painful care, and that too in his Book on
Painting.
12
You see with what mathematical precision the painter observed! and not
only with precision but also with schematisation, for as a matter of
fact
this 2/5 position is only approximatively existent. But in order that
you
may also see the geometrician at work, I have copied here a little
sketch
out of Ravaisson-Mollien — (M.S. M. f. 78 overleaf). To this Leonardo
has
added the note “all twigs possess lines which work towards the central
point of the tree.“ In order to understand him you must naturally only
take into consideration the youngest twigs, and you must realise how
this
so-called central point year by year moves upwards, quickly at first,
then
slowly. Even so there is great boldness in such a schematisation. On
other
pages you will see how Leonardo was at pains to apply to the human head
a similar law of relationship to the line of circumference. His
comparative
studies of various human heads, including monstrous deformities, are so
well known that I need do no more than allude to them. *
This cursory outline
may suffice to show you what special qualities must be at work in a man
who is capable of reproducing that which he has seen. Where these
qualities
are lacking there can be no painter, because there is no organ for the
correct assimilation of form, and every attempt yields nothing but
“distant
suspicions.“ Of such men who are willing but incapable, Leonardo says,
Multi
sono gli uomini chi anno desiderio e amore al disegno ma non
disposizione
— “many are the men who
*
Leonardo
drew a circle, by the help of which he fixed every point of the human
head
in a Scheme — nose, chin, ears, eyes, etc.
116 LEONARDO
have
the wish to draw
and
who take delight in it, but who have not the capability“ — the disposizione
lies in the aptitude for schematising. Naturally the geometrical
quality
by itself is not enough: yet it must not be wanting. The man who keeps
the scheme steadily before his Eye, notes every deviation in the form,
whereas on the other hand a Goethe, as we have seen, was rather
inclined
to underestimate points of difference, and in everything to see the
points
of union. “I was born in the school of identity,“ is his confession,
but
that is no school of painting. On the other hand, it is certainly
interesting
to discover that the thinker with closed eyes, whose stupendous
schematic
power of representation thought out the theory of the Heavens, showed
in
this respect a true intellectual relationship with a Dürer and a
Leonardo.
However much the science of mathematics may on one side root itself in
logic, and signify in many of its adepts a purely abstract logical
exercise
of the intellect, — still the living water that gives nourishment to
the
tree is the power of the Eye, and so it may happen that a Kant may in
certain
respects stand in closer relationship to Leonardo than Goethe. In order
to keep up the association of ideas in what I have to say, I shall
return
to this subject later, but I shall beg you once for all not to forget
that
the power of schematisation is a true formative power.
In the meantime we
must still linger awhile over the comparison between Leonardo and
Goethe.
I wish to show you how far-reaching is the difference that we have here
observed in the Eye at work. For this purpose Leonardo's judgments on
the
essence of Art will be of service to us. According to him the senses
are
the true agents in real art, and the man who, like the poet, excites
the
conceptions of the senses by descriptions alone, makes use of a
subordinate
and indirect species of Art. Leonardo exclaims proudly, se'l
pittore
vol vedere bellezze
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LEONARDO
che
lo innamorino
egli
n'è signore di generarle. That the poet is equally master of
producing beauty that shall be capable of exciting his love, that
Leonardo
denies. For il senso piu nobile is the Eye, and next to this
noblest
sense follows the Ear, la musica si deve chiamare sorella minore
della
pittura, whereas the artist in words is only indirectly and not
really
an artist, because he can only produce forms by roundabout ways, and by
steering clear of the impressions of the senses: e per questo il
poeta
resta, inquanto alla figurazione delle cose corporee, molto indietro al
pittore, e delle cose invisibili rimane indietro al musico, “the
Poet
in the representation of bodily things remains far behind the painter,
and in that of invisible things, behind the musician.“ But the
strongest
objection that Leonardo has to make against the poet, is che non ha
potestà in un medesimo tempo di
dire diverse cose, “that he has not
the power of saying several things at one and the same time“; but it
must
be the aim of Art to waken that Harmony of many tones which lies
slumbering
in the human soul, and that must take place with lightning rapidity,
like
an inspiration of the Deity: for armonia non
s'ingenera se non in istanti, nei quali le proportionalità degli
obietti si fan vedere, o'udire.
“Harmony cannot be bred otherwise than in instants in which the
relative
proportions of things are seen or heard.“ Here, obviously, it is the
plastic
artist who is master, for he alone reveals his whole work in one single
moment, and that is why Leonardo speaks of his art as a Divinity, una
Deità. But the musician too gives in every moment a
multiform
perfect Harmony, while on the contrary the word-poet is forced to build
up bit by bit, l'una parte nasce dall' altra successivamente, e non
nasce la succedente, se l'antecedente non muore, “one part is born
from the other in succession, and the following part is not born unless
the previous part is dead.“ It is not my intention here to discuss the
aesthetic doctrines of Leonardo: I
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LEONARDO
have
only felt
compelled
to show you with what a passionate bias this clear-sighted man paid
respect
to the Eye, and, beside the Eye, to the direct impressions of the
senses
in general as opposed to all mere reflection. The point of contact with
Richard Wagner is clear, and in any other connection would give
occasion
to useful considerations.
Here, however, we
have one immediate and special interest — Leonardo, the man whose Eye
at
once reminded us of Goethe's Eye, is not only the antipodes of Goethe
in
respect to the scientific observation of Nature, but he comes very near
to refusing altogether to recognise as true art that very art in which
Goethe rendered immortal services. From the point of view which we are
for the moment adopting, Goethe and Leonardo stand so far apart that we
should hardly bring them into relationship, were it not for Kant who
holds
out the hand to both. For as a matter of fact, Kant, whom a while ago
we
found to be of so near kin to Leonardo that the two viewed from the
distant
Goethe appeared like brothers, now, seen from point of view of
Leonardo's
aesthetics, seems to move close up to Goethe. In this method of
constructing
“parcel-wise“ — una parte nasce dall' altra — we were able to
discover
a characteristic of Kant's method of perception; now it is Leonardo who
shows us, that it is equally characteristic of every professor of the
art
of thinking, even of the Poet — and instinctively these words, una
parte
nasce dall' altra, call to our recollection Goethe's Doctrine of
Metamorphosis.
Of course Goethe examines nature with an Eye differing from that of
Kant,
yet he too is forced to construct, and in order to put the phenomena of
nature perspicuously into form and to embody them in his memory, he
cannot
help allowing one part to arise from another. That is the exact purport
of Metamorphosis. Practically there is, then, in Goethe's intellectual
personality, exactly as in
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LEONARDO
Kant's,
a preponderant
quality that we might well indicate with Kant as “understanding“ in
contradistinction
to “Sense,“ or perhaps still better as Reason (in the Kantian sense of
“the whole higher power of recognition,“) in contradistinction to the
power
of observation. In both these men, Goethe and Kant, — however various
may
have been the sources at which they drew their impressions, — the
insistence
upon the idea of dallying with theory forms a common feature. However
different
from the path trodden by Kant may be that by which Goethe reached his
Ideas,
— he is only quite at borne, only quite the master, quite the creator,
in that domain which Kant calls the Higher Power as opposed to a Lower
Power; while Leonardo looks upon this so-called Lower Power as the
Higher
Power, and takes no account of any knowledge that has not, “born of the
experience of the senses, made its way through mathematical exposition,
and found its final conclusion in experiment.“ That is why he exhorts
us
to put no faith in authors who have wished by the force of imagination
alone to make themselves interpreters between nature and man: non
vi
fidate degli autori che anno solo colla imaginatione voluto farsi
interprete
fra la natura all' uomo, and warns us not to give ourselves up to
those
things of which the human mind is incapable and which cannot be
demonstrated
by any natural example: Quelle cose di che la mente umana non
è
capace
e non si possono dimostrare per nessuno esemplo naturale. As you
see,
Leonardo will only accept in relation to Nature the most strict
empiricism
knitting together effect and cause, whereas formation by Ideas as
practised
by Goethe, and defended by Kant, seemed to him to be idle imagination,
or as he also called it bugiarda scientia, a science of lies.
Here then we discover
how far-reaching is the difference between Goethe and Leonardo; for it
is not merely con-
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LEONARDO
cerned
with art alone,
but extends to the whole method of contemplating nature. In the
previous
lecture we saw that Goethe was working with ideas when he believed
himself
to be in possession of experiences: that at once gives you an example
of
the dominant power of Reason — of the Higher Power of Recognition in
contradistinction
to empirical contemplation. For, as we saw in our investigation of the
doctrine of metamorphosis, Ideas are certainly something seen, but not
empirically seen; in other words, they are not given to us by mere
experience.
It is true that they are rooted in Impressions of the senses, though
that
is only the field which gives them nourishment: the air which surrounds
them is that of Reason, and the daylight in which we see them, radiates
from within out of a focus imaginarius.
There is a saying
of Kant's which will render us good service at this moment: for it
describes
exactly what it is that divides Goethe and Leonardo, and at the same
time
affords us a deep insight into Kant's own method of seeing; by abstract
study we might perhaps have failed altogether in understanding his
view;
but in the light and shade of Leonardo's and Goethe's methods, his view
stands out in plastic form. Kant is speaking of the essential nature of
the Poet. After having, in diametrical opposition to Leonardo, assigned
the highest of all artistic rank to the art of Poetry, he gives the
poet
the credit of encouraging “a free, personal and independent Power,
untrammelled
and unhampered, of observing and judging Nature as phenomenon,
according
to views which She herself affords neither to the senses nor to the
understanding,
and therefore to make use of her in the interests, and for the
Schematisation
of that which is transcendental“ (i.e. beyond the senses). The poet,
then,
teaches us to look upon Nature from points of view which direct
experience
does not offer us, and opens up in us a power to make use of what is
clear
to our Senses for the benefit
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LEONARDO
of
the schematisation
of
that which transcends them. This definition of the poet gives us an
exact
idea of Goethe's position in regard to Nature. In his method of
observation
there is a continual exchange between that with which the senses
furnish
us and that in which the experience of the senses only acts as a
spring-board.
Goethe is a good, trusty and, where necessary, a sober observer of
Nature;
in spite of which it is in the noblest sense of the word a poetical
longing
— I must add a yearning and a formative power — which impels him to
observation:
he wishes to put in practice that “free, personal and independent
power,“
and unconsciously he flies far beyond the boundaries of empirical
experience.
His Orphische Urworte with
its last line:
Ein
Flügelschlag! Und hinter
uns
Aeonen!
“One stroke of the wings! And behind
us aeons!“ appeared first in the Morphologie
of which the masterly Athroismos
belongs to the osteology, and here in the midst of illustrations of
bones
and comparative tables he cries out:
Nimm
vom Munde der Muse,
Dass du
schauest, nicht schwärmst,
die liebliche volle Gewissheit.
“Take from the mouth of the muse the
sweet full certainty that thou art seeing and under no delusion.“ So it
is the Muse that is to be our guardian goddess in the domain of the
investigation
of nature. Goethe, indeed, in certain moments is fully conscious of his
own method of procedure; for in his legacy of notes upon natural
science
we find the following most noteworthy passage: “Phantasy is far nearer
to nature than the senses: the latter are in nature, the former hovers
over her. Phantasy can hold its own with nature, the senses are
mastered
by her.“ There you see at work the free, personal power, of which Kant
spoke; at the same time you see the exact opposite of Leonardo's
convictions
and principles. For
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LEONARDO
according
to Leonardo
all forms of knowledge
are vain and full of errors, — vane e piene di errori, — unless
they be created from the experience of the senses and tested by
scientific
experiment. Leonardo is such a strict empiric, that he goes so far as
to
warn the artist that he must know no other aim than to gareggiare colla
natura, — literally “to compete with nature.“ How differently
the Eyes
of Goethe and Leonardo work we see not only in the Doctrines to which
their
method of Seeing gives occasion, but also in the success of their
activity.
Not only can Leonardo say of himself, “in painting I can stand
comparison
with any other man, be he who he may,“ 13
while Goethe, after toiling for
years, is obliged to confess the contrary, but Leonardo's contributions
to science are throughout of a different nature from those of Goethe. I
am far from underrating Goethe's doctrine of metamorphosis, — his
doctrine
of colour, — his other scientific thoughts; rather am I deeply
convinced
that his whole method of observing Nature possesses for the culture of
the human intellect a significance of which we are only just beginning
to be aware. In many respects Goethe is even now hardly born. But this
significance is one of culture and not of true science in the strict
sense
of the word. Goethe will teach us “to cast a free Eye upon the wide
field
of nature“ — a free Eye, that is to say the Eye of the conscious human
creator, who no longer stands in dull obedience at the command of idle
Matter, but who is able “to hold his own with Nature“: and that means
at
the same time the eye of the man who is no longer dazzled by his own
compelling
hallucinations, but who, thanks to Kant's efforts, has won together
with
his own freedom, the freedom of Nature. All this, — to which I propose
to return to-day, so soon as our observations shall have ripened
sufficiently,
— we can perceive, and yet must admit that it was Goethe's part to
excite
and spur on exact natural science rather than really to
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LEONARDO
further
it himself:
while Leonardo, on
the contrary, who saw as a schematiser, and thought as a mechanician,
was
such a master of the art of gaining knowledge, that in his guesses he
anticipated
the triumphant course of our natural history. As Kant proclaimed to us,
“experience alone is the fountain of truth in the observation of
Nature.“
Leonardo knew that full well: gareggiare
colla natura, “to compete with
nature“ — that was his maxim not only in art, but also in science; it
was
his delight and the cause of his success. That the earth revolves is no
symbolical idea, like Goethe's doctrine of metamorphosis, but a
concrete
theory; that the blood is chased from the heart through the veins, is
not,
like the discovery of the intermaxillary bone, an inference from an a priori
admission, but a fact discovered by painstaking autopsy and
observation.
In respect of pure natural science, I think we may say that Leonardo
surpassed
Goethe almost as much as he did in painting. He knows the only true
method:
one sees that in him at once: and that says everything. Observation,
experiment,
mathematical calculation, — these are the three principles which he
again
and again impresses as the foundation of all knowledge. If beyond this
we remember that he devoted a passionate interest to the technics of
instruments
(he built himself a sort of telescope for the observation of the moon a
century before Galilei), we must admit that he possessed all the
qualities
which go to make the born investigator of Nature.
By working up with more
and more
sharpness the contrast between Leonardo and Goethe, we have now reached
the critical point, that is to say the point where we shall be rewarded
if we sink a deep shaft, confident of coming upon a vein of the
precious
metal of discernment. Whoso thoroughly understands the difference
between
the value for science set upon mathematics by Leonardo and that set by
Goethe, has gained much, not only in the
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LEONARDO
estimate
of the two
great intellects,
but for his own thought-life in general. At the same time this point is
one of those which are of primary importance for the understanding of
the
intellect of Kant. For if a little while ago we saw Kant near — very
near
to Goethe — we see him quickly move back to Leonardo as soon as stress
is
laid not upon Art and Idea, but upon Science and Mathematics. Here it
is
not only the analogy of qualities between Leonardo and Kant which is
dominant,
— as it was just now in the case of the observation of schematising, —
but a true close kinship in the whole manner of looking upon the
universe.
There, at a great distance, Goethe stands aloof.
I have already spoken of
Leonardo's
love for mathematics; but I must still claim your patience for a few
moments.
Non mi legga chi non è
matematico, “let no man read me who is not
a mathematician“! Such forcible language as this should be enough! but
we have still got to learn that in Leonardo this is no question of a
mere
predilection, nor even of an instrument indispensable to the practical
artist, but the insight of a philosopher into the essence of the human
intellect. “The man who undervalues mathematics nourishes himself upon
confusion,“ says Leonardo, chi
biasima la somma certezza della matematica,
si pasce di confusione e mai porrà silentio alle contraditioni
delle
soffistiche scientie, colle quali s'inpara uno eterno gridore.
“For truth
and the power of knowledge are contained in the mathematical sciences.“
That is a very important saying, “the power of knowledge.“ Goethe would
not have subscribed to it: Kant would have done so with both hands. And
because practical knowledge is joined to the mathematical way of
thinking,
therefore Leonardo lays down the dogma that “no human investigation can
lay claim to be considered as true science unless it will stand the
test
of mathematical demonstration.“ For the criterion of
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LEONARDO
true
science — vera scientia — is
incontrovertible
certainty, and knowledge in the sense of certainty is only afforded by
mathematics. The consequence of this is that nessuna certezza è, dove non
si puo applicare una delle scientie matematiche over che non sono unite
con esse matematiche, — therefore no investigation can lay the
foundation
of true science, unless it can and does follow the path of mathematical
exposition, that is Leonardo's impregnable conviction. It is with the
clear
recognition of the relationship between mathematics and knowledge that
this miracle of a man forestalled Kant, in the same way that in his
discoveries
he anticipated Copernicus and Harvey. In one of his ripest works, Die Anfangsgründe
der Naturwissenschaft, Kant writes in the same way, “I maintain
that in
every special nature-doctrine there will be found only so much exact
science
as it contains of mathematics.“ Certainly Kant, the thinker, analysed
more
exactly than Leonardo. The whole tenour of Kant's general philosophy
teaches
us to distinguish between “exact“ and “inexact“ science; he has shown
us
that a science which rests upon empirical observation alone, is only
worthy
of the name and dignity of a “science,“ so far as it does not deviate
from
experience, ordering its discovered facts systematically, and
dissecting
them in accordance with the relationship between cause and effect; but
that such science should preferably be called systematic art (giving as
an example the chemistry of his time), because the apodictic certainty
of any true knowledge needs something more than empirical experience.
This
Something, which Kant calls the “Pure Part,“ is exactly that inner,
human
code of laws, which, in so far as it touches intuitive vision, is
called
mathematics. Nothing, with the single exception of mathematics, gives
apodictic
certainty, and apodictic certainty alone can be called knowledge in the
strict sense of the word. Therefore, the more
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LEONARDO
we
have of mathematics,
the more we have
of exact Science.
You see what a true and
deep-reaching
kinship exists between the methods of observation of these two men, who
at first sight seemed so diametrically opposed to one another. Kant,
absolutely
devoid of all artistic gifts, has yet the power of recognising the
fundamental
significance of form and measurement in the building up of human
knowledge;
and in many of his works, and more especially in Die Metaphysischen Anfangsgründe
der Naturwissenschaft, proves himself to be a genius of the
first quality
in
the despotic domain of this schematic manner of Seeing; Leonardo, the
artist,
the painter of the Last Supper and the Mona Lisa, is none the less
devoted
to mathematics and mechanics; he compares the influence upon the
intellect
of their incontrovertible certainty, with that of light upon the Eye,
and
with the exaggeration of the hot-blooded artistic temperament, he
utters
the opinion that here alone lies the certainty of knowledge.
We have to deal here with
a true
harmony between the dispositions of the two men. And as a matter of
fact
this harmony reveals itself exactly where Goethe misses fire — for
we may legitimately here speak
of a miss-fire as well in art as in philosophy. So far as art is
concerned
we may well overlook the position, inasmuch as Goethe himself bitterly
felt his own failure. But in the matter of philosophy he was not so
clearly
conscious, and that is what has led us and him to a condition in which
the pascersi di confusione
has gained great force. That Goethe despised
mathematics is of course the foolish twaddle of the titmice that chirp
on every twig of life; a single sentence of his suffices to refute it:
“no one can set a higher value on mathematics than I do, for
mathematics
afford precisely that which it has been denied to me to accomplish.“ 14
So he too felt that here something had
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LEONARDO
been
“denied to him,“
and how highly
he often valued this “something denied“ is shown by a sentence in the Farbenlehre,
the Doctrine of Colour, a passage where any irritation against the
mathematicians
might have been excused, and where in spite of that Goethe declares
mathematics
to be “one of the noblest organs of mankind.“ Still we must admit that
Goethe was not only deficient in the power of practising mathematics,
but
was even unable fully to appreciate the essence of the science in its
inevitable
influence upon the human intellect. “It is a mistake to imagine,“ he
exclaims
pettishly, “that when I have discovered the mathematical equation for a
phenomenon I know all about it that is worth knowing, and can consider
the whole matter as sufficiently dealt with and to be laid on the
shelf.“
15 What does he
mean? The function of mathematics is to apprehend, to prove
according to the laws of motion, to reduce clearly to a science — just
as Albrecht Dürer did for the outer form of the human body, and as
Leonardo tried to do for the mechanism of the circulation of the blood
in its inner parts. “The book of Nature is written in the language of
mathematics,“
says Galilei. Goethe, on the other hand, finds a contradiction between
the phenomenon observed and the mathematical scheme. For this sentiment
he has to thank the pure power of his sight; but instead of allowing
himself
to be taught by Kant that if Image and Scheme do not exactly tally, it
is due to the essential quality of the human intellect; 16 instead of
recognising
with Leonardo the fact that mathematical representation is the
necessary
organ of everything which can be called Science in the sense of exact
knowledge,
and that what he, Goethe, is striving after is not Science but
something
different, that is to say a glorified Contemplation, — that World of
the
Eye of which we spoke in the previous lecture, — and that this World
demands
ideal exposition; instead of all this, Goethe obstinately
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LEONARDO
works
himself up into
the unfortunate
idea that there can be an unmathematical science, — that the employment
of mathematics must be kept within bounds, and that they must be
relegated
to a narrow domain in the Study of Nature, etc. Science and art, — so
he
maintains, — have “fallen into pitiable error through the wrongful
employment
of mathematics.“ 17
When we remember that Goethe's unmathematical dicta,
of which we could cite many, are chiefly in the department of optics,
and
when we consider what a famous advance mathematical optics have made
since
Goethe's time, and what a wide outlook upon comprehensive knowledge has
been opened up in this very direction in our days by the work of
Maxwell
and Hertz; when we realise the present importance of spectral analysis
to astronomy, chemistry, and physics; and then when we see Goethe
ridiculing
the spectrum as little more than a mere puerility of Newton's, we must
feel that however much the great observer of nature and Poet may have
the
right to view Nature in his own fashion, he is yet lacking in the
understanding
of the mathematical method of exact science. And this is the more
striking
when we find in Leonardo, two hundred years before Newton, a few but
astonishingly
correct remarks about the colours of the spectrum, and when we think of
Kant's high estimate of the undulation theory of Huyghens, we have then
the experimental proof that if we follow Goethe in the path of science,
we advance no further in the exact sciences, whereas by following the
mathematical
path, which he detested and which Kant looked upon as the only right
way,
we have advanced from one theoretical and practical attainment to
another.
What, then, is the essence
of
the mathematical method? That is a question which it is impossible for
us here to shirk, otherwise we should neither understand correctly
Leonardo's
extreme way of viewing Nature, nor Goethe's,
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LEONARDO
nor
should we
understand why Kant's philosophical
critique enables him to do justice to both these antagonistic views. I
shall try to answer the question at once in as few and as simple words
as possible, leaning indeed upon Kant, but without making him
responsible
for my free and illustrative exposition; we shall deal more precisely
with
the matter in observations to be added hereafter.
So soon as we
thoughtfully, —
I use the word “thoughtful“ in contradistinction to passive
contemplation,
— so soon as we thoughtfully approach Nature and construct that “unity
of objects“ without which she would no longer be Nature but Chaos,
every
single conjunction, arrange it as we may, means Motion. Think only of
the
commonest perceptions of any Bodies that you please, which you,
innocent
of any attempt at philosophising, simply join together, thinking in
contemplative
consciousness, something in the same way as the herdsman watches his
grazing
herd. Either the objects are at rest, and then our mind must move in
order
to perceive them, whereby we arrive at Form, or our mind is at rest and
the objects move before it and then we arrive at Number: in most cases
the two sorts of conjunction will take place simultaneously; and as you
see, whether we direct our observation to the proximity in space, or to
the sequence in Time, Motion is always at the bottom of it. Motion,
says
Kant, is that which unites space and time, and motion conceived, that
is
to say grasped by Reason, is Mathematics. If we look at the still
geometrical
figures in our school-books, we sometimes think that here is the very
emblem
of rest; but in the next lecture we shall see how the great Descartes
laid
the foundation of the higher mathematics, when he taught us to set free
into Motion every resting Form, whereby we attain a second gift,
namely,
the power to convert every species of Motion into a visible, permanent
Form.
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LEONARDO
But
just in the same
way as these higher mathematics proceed from the union of Geometry and
Arithmetic, so it is only by further, and, as closer observation shows,
powerful conjunctions of space and time, that a really intelligible and
logical Nature comes into existence for us, and it is from these
conjunctions
that we realise the ideas of the inter-relationship of various
perceptions,
— of the interchangeability of phenomena, — of causative cohesion.
Thus,
for example, the relationship between cause and effect signifies a
twofold
Motion in space and time. You will find that set forth with
unsurpassable
lucidity in the fourth paragraph of Schopenhauer's principal work, to
which
I refer you. 18
And with further investigation and thought you will understand
how Kant arrives at the definition, “Matter is that which is movable,“
and at the assertion that space can only be filled by motion. And that
you may not think that I am leading you on to the pin-points of the
most
abstract philosophy, but that, on the contrary, you may understand that
I am dealing here with the concrete and necessary apprehension of
Nature
by human intelligence, I will call your attention to the fact that our
modern physics, however antimetaphysical may be their attitude in their
empirical delusion, learn to recognise Kant's standpoint as the only
justifiable
one, and that the little globules of atoms are only preserved as a
deduction
and a help for coarser intellects, whereas Lord Kelvin and other
leading
spirits among the mathematical physicists speak of “centres of energy,“
and by atoms understand gyrating motion. Lord Armstrong, * in his book
Electric Movements in Air and Water,
asserts that there is no ground for
looking upon Matter as anything else but Motion. Even the hypothetical
aether he rejects as super-
* I
purposely
cite
English investigators because no others, not even Italians and
Frenchmen,
are so far removed from the influence of German metaphysics.
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LEONARDO
fluous,
and is of
opinion that “empty
space would do just as well, if we only chose to conceive a continuity
of interacting motions.“ 19
I think that this
sketch, slight as it is, will suffice to make you understand and accept
Kant's apodictic assertion, “natural science is throughout a doctrine
of
Motion, either pure or applied.“
But here comes in
a second important consideration, not, like the first one, composed of
physical elements, but purely philosophical. The highest code of this
science
of Motion is not perceived as a fact in Nature, but is rooted in the
essence
of Reason. It is we ourselves, we men, who have no other possibility of
comprehending Matter, that is to say, when we aim at a comprehension of
Nature which shall be logical, thoughtful, and capable of founding an
apodictic
certainty of knowledge; — it is we ourselves, I say, who are unable to
comprehend Matter otherwise than as Motion, and for whom in consequence
of this every vera scientia, every absolute certainty is bound
to
result in a doctrine of motion either pure or applied. The human
understanding
works out the analysis of Motion by its special gift of schematic
experience
which we call mathematics. It is by mathematics that the human
intellect
assimilates and digests that which is foreign to it and outside of its
ken. Much is rejected, but what remains from that time forth becomes
possessed
of a humanly comprehensible form. That is what Kant means when he says,
“the highest law of Nature must lie in ourselves, that is to say in our
understanding.“ To put it rather roughly, but in a way suited to the
present
standpoint of our study, Nature gives the facts, the human
understanding
gives the laws. To formulate this let me once more bring forward words
of Kant's, “the human understanding does not create its laws out of
Nature,
but imposes them upon her.“ At the first blush this remark will perhaps
strike you as
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strongly
paradoxical,
but it will
suffice
for the present if you to a certain extent clearly grasp these two
things:
all exact Science, in the
true
and
strict
meaning of the word, resolves itself into a Doctrine of Motion. All
Doctrine
of Motion is mathematics, and so far human. To try to escape from a law
of our true Being is nothing less than an attempt to creep out of our
own
skin. We may well therefore praise the acuteness of the great Leonardo,
who had so rightly and energetically grasped the fundamental law of all
exact investigation — in opposition to whom when a man comes forward,
even
should he be a Goethe, and exclaims, Friends! I will teach you a
Science
that shall be unmathematical, — then we recognise and acknowledge the
fact
that the great man is entangled in deep error. Indeed, the error is
twofold,
first inasmuch as his definition of Science cannot be called adequate,
and secondly because he does not rightly grasp the essence of
mathematics,
and their law-giving function in reference to all that constitutes
causal
conjunction, and that means Nature as it exists in our thoughts.
Quite another
question
is whether that which Goethe strove after, that is to say an
unmathematical,
and to that extent un-logical and therefore unscientific comprehension
of Nature, is not, say what you will, entitled to a profound measure of
justification. Here, too, is a question that we must not leave
unanswered,
for it is of weighty importance in the understanding of Kant. But in
order
to answer that question we must do as we did in our former lecture; we
must undertake an excursus which will furnish us with the indispensable
and self-evident material. If you were minded without any further
preparation
to plunge headlong into Kant's abstract-analytical method of thought, I
suspect that it would be very difficult for you to bring a vivid
understanding
to bear upon his exegesis of an unmathematical
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conception
of Nature,
what he calls
“Nature
as exposition“ — whereas starting from Goethe you are at once in a
position
to understand Kant, and so will be able to delight in the unexampled
profundity
of the most powerful of all thinkers. We must then take heart and
undertake
an examination of the relationship between exact Mathematical Science,
to which alone Leonardo assigned any value, and Goethe's comprehension
of Nature. In the main this excursus will result in a comparison of
physical
optics and Goethe's doctrine of colour; there are, however, some
general
remarks with which we have to set out, and which will weave themselves
into our exposition as it progresses.
*
* * * * *
The difficulty which
at the outset attaches to our task is the fact that Goethe himself was
devoid of any theoretical consciousness of his own procedure, one might
even say of his own aim. His own saying, “a man has never gained so
much
ground as when he does not know whither the way leads,“ is true of
himself;
for while he believed that he was doing no more than lending a hand in
contemporary investigations of nature, he was in reality founding a new
method. That is the naked truth, the unrecognised truth which seems to
have foundered without leaving a trace, yet not for ever, in the noise
and dust of the vulgar riot of our successful mechanical science. There
are moments in the activities of great intellects where they render
superlative
services: that is when they do not quite understand themselves, when
they
enter the lists to do battle passionately for some impossible
assertion,
in spite of being gifted with a keener sight than their fellows, and
with
more consequential thought than their censors: for it is just here
where
they entangle themselves in a mass of contradictions, that they work
like
an unconscious natural force, paving
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LEONARDO
the
way for future
knowledge: here the
intellect collects itself into an avalanche ready to sweep clean all
the
tidy paths of human frivolity, or like a volcano bursts the too heavily
weighted crust in which the idleness of tens of centuries has
imprisoned
the bright fiery element of the soul of man. Only consider Goethe, that
noble man! Is it thinkable that he with his brilliant eyes should have
looked in the light during a whole lifetime, and have seen nothing
true?
Yet, as I know that here I shall at once be tilting against unbelief
and
contradiction, I will quote the words of a pioneer in exact natural
science,
the admittedly greatest physiologist of the nineteenth century,
Johannes
Müller. He was what Louis Agassiz, Clerk Maxwell, and Heinrich
Hertz
(but with their exceptions a dwindling number of our famous natural
investigators)
were, a really lofty intellect of permanent importance. Here is what
Müller
says with reference to Goethe's essay on the skeletons of rodents, —
“It
is impossible to point to anything similar which comes up to this
projection
sketched from the centre of the organisation. Unless I am mistaken
there
lies in this outline the foreshadowing of a distant ideal of natural
history.“
Remember these words “the foreshadowing of a distant ideal“! And
Müller,
the exact investigator of nature, prizes the awakening of this
foreshadowing
so highly, that on the next page he pronounces the judgment, that
Goethe
has “reached the greatest“ not only as artist, but also as
investigator.
20 Here, too, is a
judgment which should never be forgotten. For we
moderns
have grown up under the nourishing showers of pseudo-scientific
platitudes;
Rudolf Virchow alone dared forty years ago to take Goethe as
investigator
publicly under his protection, a weighty witness indeed, upon whose
exactitude
and unimaginativeness no man will cast a doubt, but who unfortunately
was
not competent altogether to lift the veil of misunderstanding: for to
that
end would
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LEONARDO
have
been required that philosophical
training which Virchow abominated, so that his fine words raised a
great
storm of dust at the time, but soon died away leaving no influence
behind
them. 21
In these days every
tiny two-legged wheel in the great machine of science thinks himself
justified
in shrugging his shoulders over Goethe as an investigator of Nature. I
happen to possess an autograph letter from one of these celebrities,
who
rates his professorial dignity at a height which entitles him to allow
himself the following judgment of Goethe: “his conception of Nature is
just what an easy-going aesthete and collector of curiosities might
make
up out of his walks abroad.“ This is the audacity of a man of middling
capacity whom the schoolmaster's rod and the sting of hunger have
raised
by luck to the degree of Doctor of Philosophy, and finally up the three
steps of the Professorial Chair! A man whose fame may perhaps live
through
two or three editions of our encyclopaedias, dares to speak in this way
of the princely intellect of a Goethe, of that god-like Eye which for
more
than half a century never ceased in the thoughtful contemplation of
Nature,
of a man of whom a Johannes Müller could pronounce the opinion
that
as an investigator he “reached the greatest.“
But enough of this.
If I were to talk myself into a state of indignation over the
intellectual
decay resulting from the narrow empiricism of a tyrannical science
which
has fallen a prey to the overlearned Philistines, I should not readily
come to an end. The reaction has already begun; there are good men and
true of a younger generation at work on behalf of Goethe the
investigator,
and what is more important than the influence of these individuals is
the
fact that a universal necessity, a cultural need that cannot be put
aside,
is forcing us to enter upon the road which Goethe has pointed out to us
as the “foreshadowing of a distant ideal,“ unless we
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LEONARDO
wish
to fall into crass
barbarism. A
leading spirit among the living antimetaphysical empirics, Ernst Mach,
has disclosed what is the next thing to be annihilated, and if his
object
was to serve the ends of a purely mechanical barbarism he has not been
far out: our languages! In the interest of “science“ they are to be
abolished
in order to make room for an abstract international language! 22 The
ideal
which floats before the learned professor is the Chinese system of
writing,
because, being entirely ideographic, it throws overboard all ballast of
expression of the finer emotions. 23 After that grammar and
history are
to be “laid aside.“ Add to this the simplification of the Alphabet, and
supplement it with algebraical formulae and chemical symbols, and you
will
have collected together all that Professor Mach deems essential in a
language.
He is not far out. A science which only concerns itself with abstract
Ghosts,
is at no single point in contact with life. Goethe's desire, by means
of
his doctrine of colour, parenthetically “to enrich language and so
facilitate
the communication of the higher conceptions among the friends of
Nature,“
from this point of view must signify the ne plus ultra of folly. And
when
Mach, in conclusion, expresses the hopeful opinion that the English
language
is in a fair way to reach that ideal, we will not ignore the tiny grain
of truth which has crept into this Hellish dream, worthy of one of
Breughel's
Witches'-sabbaths, and join the standard of those who hold no
inheritance
more sacred than that of their mother-tongue. The richer, the more
illogical,
the more incomprehensible a language, the better does it hold up the
mirror
to Nature. The men who have attempted to rob us of our language, have,
so far as in them lay, robbed us of Nature; has not Lord Armstrong
taught
us that science needs no more than the assumption of empty space (vide
supra)? In contradistinction to which the man whose genius was
rooted
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LEONARDO
in
the sovereign and
creative mastery
of language, — in his much-despised teaching of nature followed the one
object, to give us side by side with his immortal poems that which was
their one eternal Source, visible, inexhaustible Nature with all the
wealth
of its many forms.
Goethe, as I said
before, did not possess a critically analytical consciousness of his
new
method, and hence it is that his judgment as to the relationship
between
his way of investigation and that of true science, is hazy and easily
misleading.
Sometimes his insight
is clear enough, for example when he cites the attraction which in his
youthful days Spinoza exercised over him, and adds, “the mathematical
method
was the very opposite of my poetical method of thought and exposition.“
This, of course, is a general statement; the mathematical method, dear
to the Jewish Thinker, seems to Goethe to be in opposition to his own
poetical
method of thought. And yet when we come to deal with the special
investigation
of Nature there are passages of decisive import which may be brought
into
court. I select one from the year 1826, which possesses the importance
of a composition with mathematics. Goethe writes, “It was not long
before
I was compelled, in deference to my own capabilities and relations, to
claim the right to view, to investigate, and to comprehend Nature in
her
simplest, most secret beginnings as in her highest and most striking
creations
without the co-operation of mathematics. That has been my contention
through
life. Any service that I may have rendered in that way is open to all:
how it may appeal to others remains to be seen.“ 24 Is not this
perfectly
clear? “In deference to my own capabilities“ — that points to the
capabilities
which are “in opposition to“ Mathematics. And Goethe claims the right
to
view, to investigate, and to comprehend Nature in accordance with these
capabilities. To view, to investigate, to com-
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LEONARDO
prehend,
that is a
perfect programme
for a personal system of Natural Philosophy. Further on in the same
disquisition
Goethe says in so many words that “a new point of view justifies new
opinions.“
This recognition explains the many passages in which Goethe declares,
with
no trace of bitterness, that his method of contemplating Nature “is
incomprehensible
to the Professors, for the simple reason that they think otherwise“; it
is in these passages that he confesses in regard to the first great
congresses
of German works on natural history, that they furnished nothing which
could
in the slightest degree touch, or move, or excite him, no new
encouragement,
no new gift, — and this was the man who “for fifty years had been
passionately
devoted to the observation of nature“; for among the German natural
scientists
there was “not one that showed so much as the slightest approach to his
own way of thinking.“ 25
And there are other passages which come under
this category, in which Goethe in his last years, — as, for example, in
the essay on the rodents quoted above — instead of as was his wont
portraying
his efforts in the domain of morphology in the bright colours of the
successful
investigators, all at once “feels most vividly that his honest
endeavours
in the observation of nature, were only presentiments and not
pioneering.“
All this leaves nothing to be wished for in the way of clearness and
true
insight. In such moments Goethe is so fully conscious that he cannot
see
eye to eye with the men of true science, that he claims it as a right
to
dare to investigate in his own way, and admits that this way is
something
which continues to be incomprehensible to them, indeed that he is
dealing
with a “new standpoint,“ — with something in the future, — of which the
significance remains half veiled even to himself.
Physics simply do
not recognise the fundamental ideas of Goethe's Doctrine of Colour. So
from the stand-
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LEONARDO
point
of physics it is
impossible to
judge of this theory. Goethe starts precisely at the point where
Physics
leave off. It is evidence of a quite superficial appreciation of the
matter
when people go on talking of Goethe's relation to Newton and modern
Physics,
and at the same time take no thought of the fact, that these two are
entirely
different. 26
Unfortunately it
is Goethe himself who with the utmost impressiveness and vehemence has
spoken about his so-called relations to Newton, and not to Newton
alone,
but to exact natural science in general. Did you remark in the
above-quoted
solemn declaration the five simple words, “without the co-operation of
mathematics“? That is where the evil fountain of misunderstanding
still
continues to flow. It is not without the co-operation of mathematics,
but
in opposition to mathematics that Goethe observes, investigates, and
comprehends
Nature. The mathematical method and Goethe's method may run parallel to
one another, but can never coalesce: no compromise between them is
possible:
they cannot at one time work together and at another time without one
another.
One instance will
serve better than a hundred to show you how deeply this
misunderstanding
penetrated in Goethe's case. One month after that fundamental
declaration
in which the practised eye alone can detect the blemish of the “without
co-operation,“ he says to Eckermann: “surely it is not the
mathematicians
who invented the metamorphosis of plants? I worked it out without
mathematics,
and the mathematicians have been forced to admit it.“ If these words
are
correctly reported, they are valid proof that we must trust to our own
powers in order to see clearly in this matter; Goethe, the herald and
founder,
leaves us in the lurch as to the true understanding of his work.
Mathematics
and metamorphosis! This would have been the place to show that we are
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LEONARDO
dealing
with two
dissimilar and
irreconcilable
subjects which nowhere come into contact with one another. The first
lecture
has shown you what was Goethe's idea of metamorphosis; we must admit
that,
like every human acceptation, it implies the conception of Motion; but
instead of trusting itself like the sailor to the stream, it hovers
like
an eagle in the empyrean from which the living hurrying flood is at
once
Motion and Rest: Motion, so far as its law of existence is concerned,
Rest
as regards form. Mathematics (and in a wider sense all true science,
inasmuch
as it everywhere obeys the one impulse to be converted into
mathematics)
have no other power and function than the analysis of the condition of
Becoming; * even that which is at rest they must set free into motion,
otherwise
they have no hold upon it. Goethe's efforts, on the contrary, do not
tend
towards analytical knowledge, but towards the most intensive
contemplation,
— “the world of the eye,“ the law of which is not Becoming, but Being.
That accounts for the peculiar permeation of that which is simultaneous
and that which is successive which has sometimes puzzled us, as indeed
it puzzled Goethe himself. For while science, whose whole essence
depends
upon the understanding of cause and effect, recognises Being as an
almost
imaginary point between something which has been growing and something
which is yet to be, the Eye, on the other hand, although not blind to
successive
alterations, can manifestly never perceive the condition of progression
or process of “Becoming,“ otherwise than as locked up in a condition of
Being. This will suffice for the moment to show the absurdity of
Goethe's
outcry against the mathematicians. How was any mathematician, as such,
to discover Meta-
*
There is, so far
as I can see, no single English word in common use which accurately
conveys
the meaning of the German Werden
as opposed to Sein. Werden
is
the
process of coming into Being — i.e. a transition state; Sein is Being —
i.e. an accomplished fact. I shall translate Werden throughout
the book as “Becoming,“ or “coming into being.“ — R.
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LEONARDO
morphosis?
He would
have been a poor
mathematician. Nor do the words, “I discovered this without
mathematics,“
hit the nail on the head any better, though Goethe rarely fails us in
that
respect. And as regards the closing remark, “they have been forced to
admit
it,“ that is simply based upon error. Goethe's doctrine of
metamorphosis
has been as much repudiated by Science as were his anti-mathematical
optics.
It may be admitted that the repudiation was not so unanimous and
immediate,
but only because in the domain of Biology the complication is far
greater,
so that room is afforded for endless misunderstandings. But open any
reliable
contemporary book on botany, for instance, Julius Sachs' History of
Botany
(chapter 4), and you will find Goethe's doctrine of metamorphosis
unconditionally
refuted. Sachs shows how Goethe was continually wavering between fact
and
idea, and he reveals the mischief of which hangers-on laid the
foundation
during long years, while they, instead of turning to account the
thought
of metamorphosis “in the deeper sense of idealistic Philosophy,“
introduced
it into exact science, which was impossible without “combining the
highest
abstractions with the most careless and rawest empiricism, and in a
measure
with quite false observations.“ The doctrine of metamorphosis has been
quite as much a hindrance as a help to the science of the nineteenth
century.
That is the judgment of a scientist whose right to be heard cannot be
called
in question. You see how peculiarly connected it is with the words
“they
have been forced to admit it.“ But the great confusion which to this
day
has existed between Goethe's doctrine of metamorphosis and exact
science,
is due, as I said before, to the nature of the subject. All the
sciences
are striving towards mathematics; yet Biology, in contradistinction to
Physics, is still far from having reached the mark. And here we must
depend
upon a schooling of the sense of sight, otherwise the subject will not
be seen at
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LEONARDO
all.
We may observe,
but we shall not
take notice. That was why before Goethe's time comparative anatomy
dragged
out a miserable existence; men like Kaspar Friedrich Wolff died
unknown.
Goethe, with several others around him like Camper and Oken, was the
first
powerfully to excite the imagination, and so compelled it to take
notice
of what was seen. Here alone lies the significance for science of a
doctrine
of metamorphosis. The whole of Goethe's natural science might be called
“an introduction to the art of seeing.“ Nor is that a small thing to
say;
for phantastic imaginings do not teach the art of seeing, but on the
contrary
lead to those false observations which Sachs blamed; on the other hand,
there is a Something which Goethe by a happy inspiration called the
“exact
phantasy of the senses.“ 27
This phantasy is — as the word describes it
— something felt by the senses, not abstract; it rests upon very
accurate
Seeing, and the unsurpassable exactness of many of Goethe's
observations
is attested by Müller and Helmholtz, by Virchow and Gegenbaur, by
Sachs and Ferdinand Cohn; here, however, exact Phantasy must be allied
to exact Seeing. Scientific hypotheses all pass away, but Goethe's
Doctrine
of Metamorphosis and Doctrine of Colour will never pass away: they
stand
as firmly as the facts which they mirror in Reason. Hence the
importance
of Goethe's ideas in Zoology and Botany. Science has used his thoughts
as she uses the ophthalmoscope, in order to see into the depths, to
discover
facts; but, only as tools, not as an organ. It is true that the Doctors
of the theory of evolution delight in tracing their pedigree to Goethe,
but that is the innocence of the elderly child that would do better to
search for an ancestry in Moses, Sanchoniathon, Thales, and Empedocles;
venerable men who historically would render it better service, and are
also more in sympathy with its intellectual culture.
But in order exhaustively
to
lay
bare the relationship
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LEONARDO
between
Goethe's
conception of Nature
by means of the “Phantasy of the senses“ and the mathematically exact
Science
of Nature, we must avail ourselves of a concrete example. For this
Optics
and the Doctrine of Colour must serve our purpose. Naturally it is not
possible for me here to dive into the mysteries of optics, nor indeed
would
any man be able to give an exposition of Goethe's doctrine of colour
with
greater brevity than he did himself. That immortal work is all
Perception
and pure Perception; the least learned of men can study it paragraph by
paragraph, and see step by step what Goethe saw. Here sight and
understanding
are identical. One would imagine that every man would lay hold upon
it. And since Helmholtz,
whom
I may
well quote here as the universally honoured representative of the
mathematical
anti-Goethe science, has expressly affirmed, “the experiments which
Goethe
cites in his Doctrine of Colour
are accurately observed, and vividly
described;
as to their correctness there is no dispute,“ 28 no one who might wish
to
read this forbidden book need tremble for his scientific salvation.
Exact,
correct observations, which have moreover earned the praise of a
genuine
university professor as being vividly described, can certainly harm no
man. But I know that it is all of no use; no human being can be induced
to read the Doctrine of Colour.
This glorious child of a demi-god is
like
a sleeping Brünnhilde waiting for the dawn of the new day which
shall
bring the hero to awaken her. We can therefore only deal with a few
leading
principles: that however will suffice to enable you to grasp the
difference
between “Nature as Mathematics“ and “Nature as Exposition,“ and never
again
to fall into doubt as to the right of the latter to assert its right to
a place side by side with the former. In this connection Goethe,
Leonardo,
and Kant, each in his own special individuality, will arise before your
eyes.
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The first paragraph
in Helmholtz's Optics
consists of a definition of light, set forth as
follows:
“Light is looked upon by the majority of physicists as a peculiar form
of motion of a hypothetical medium, the Light-aether; and we will
accept
this view of the undulation-theory which very fully accounts for all
Phenomena.“
Here you have in a nutshell the whole method of mathematical-mechanical
science. The storied words of the dying poet, “more light!“ are often
cited
in and out of season. What would our sensitive souls have said if
Goethe
had called out “more special motive-form of the hypothetical medium!“
Do
not, however, believe that with this poor joke I wish to cast ridicule
upon the optical definition; no less a man than René Descartes
is
responsible for the conception that light must be looked upon as
Motion,
and indeed as the motion of an invisible medium pervading the universe.
It is the acceptation of this theory that has made optics the most
perfect
of all sciences: I only wished to call your attention to the fact that
the first law of all science — if science is to be exact, — is the
abolition
of that which is visible, or if not in so many words of that which is
visible,
in any case the abolition of that which is practically seen, in favour
of an abstract, mathematically available, altogether unfelt and
schematic
representation. In the same work (p. 268) Helmholtz actually reproaches
Goethe with the fact that “in his studies in natural history he starts
upon the principle of never abandoning the domain of that which is
visible
to the senses.“ From the point of view of science, then, it is a
mistake
to dwell upon that which is visible to the senses; for, as Helmholtz
goes
on to say, “Every physical exegesis must rise to the level of all those
Forces which can naturally never be objects perceptible to the senses,
but are only objects of the apprehensive understanding.“ These
so-called
Forces are purely creatures of the imagination: even the most sober
anti-philosophical
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LEONARDO
Science
now admits that
they only exist
in our heads: and for that very reason they are unable to make use of
the
perception of the senses as such, but have to replace them by a
sensibility
of the imagination. 29
What is then seen is, as one of the greatest men
of genius among the physicists, Heinrich Hertz, admits, a delusion from
which it is impossible to exact “any conformity with things.“ 30 The
very
first step then leads from concrete perception to the abstract, and
until
that has been attained no Science is exact. To the unlearned, to the
men
of simple thoughts, Light would seem to be the most concrete of all
perceivable
things. And yet here you have a definition of Light which thrusts aside
all perception; for looked at exactly it contains only two
propositions,
of which the one says “Light is Light-aether,“ an idea which reminds
one
of the “I am that I am“ of Jehovah, and must be dealt with by the
logicians;
while the second adds the assertion that “Light is motion.“ Now since
the
most cursory reflection has already sufficed to teach us that the
conception
of Nature as Motion is an irrefutable requisite of the human intellect,
— that is to say that it is not a law of Nature but of our brain, — and
inasmuch as Leonardo as a keen thinker even in his day recognised the
justice
of this principle, — it follows that the above definition is neither
more
nor less than an universal metaphysical postulate. Since then, as you
know,
certain leading Physicists have also declared against the hypothetical
medium, the aether, as superfluous. In their minds Light is nothing but
abstract motion in empty space.
But now let us,
please,
read a little further in Helmholtz. We come to the Scheme. As Kant
acutely
remarked, “The subjective principle of Nature precedes the objective,
the
combination precedes that which is combined.“ That
“which is complex
must
be supplied by ourselves,“ for we can investigate “only that which we
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LEONARDO
have
ourselves
supplied.“ Now in optics
we supply a great deal. 31
Following the advice
of Helmholtz, let us attempt to represent the “peculiar form of motion
of the hypothetical medium“ with the help of a wet thread which we
shall
hold in our fingers and allow to hang down freely, moving to and fro.
Here you see the
diagram; the line from A to B is the thread when not in motion; so the
tiny particles of Light-aether follow one another in a straight line so
long as they are not in motion: and here the dotted line shows you how
the so-called waves behave as soon as a particle of aether begins to
rock
backwards and forwards at the top point A. And what is the reason of
the
movements of this same particle? Here again we have something peculiar.
Helmholtz writes, “exactly as the movement of the single particles of
the
thread takes place, so would be the movement of a succession of
aether-particles
along which a ray of light should transmit itself.“ If then we have
above
received a definition of Light containing nothing more than the
abstract
admission that Light is motion, the Light-ray is at once introduced as
an hypostasis transmitting itself along the particles of Light-aether,
and
so causing their motion. And whilst light is, according to the
definition,
a movement of waves, the Light-ray is, according to the mathematical
definition,
“a perpendicular line.“ Here we seem to have got into something like a
witches' caldron! Let us just imagine that the sun is at noon: the
world
is steeped in light: how many rays are we to reckon there? Certainly
more
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LEONARDO
than
you would see in
the halo of a
Byzantine
Madonna's head. Does this raise a smile? And yet here is no joke, but
your
faith is bespoken for the following proposition: “we can in such cases
consider
the movement of the particles of aether inside a ray approximately as
an
isolated mechanical Whole, progressing independently of the movements
of
the neighbouring rays.“ You perceive that the rays are an altogether
material
conception. The possibility that innumerable rays running side by side
do not take up the lateral movements of the aether-particles, so that
for
the very superabundance of light-rays there is no light, is a question
which
you must settle for yourselves, for to that Physics afford no answer.
If
we had the wave-movement alone, or the rectilinear movement alone
(which
latter movement laid the foundation of the whole optics of Newton who
knew
nothing of any wave-movement), then in that case our power of
conception
would at least possess a possible illusion; but to our mathematical
Physics
both conceptions are indispensable: Light is a rectilinear movement
which
does not spread itself like sound in all directions, and in spite of
that
Light is at the same time a wave, or undulatory movement. It is only by
the conjunction of these two contradictory hypotheses that all
phenomena
can be exhaustively and mathematically reduced to a Scheme. The great
mathematician
d'Alembert calls attention to the fact that the so-called
“cloudlessness“
of Mathematics really only holds good where they deal with the wholly
Abstract,
but that the richer the evidence of the senses to which you apply them,
the darker become the conceptions upon which you base their operations.
32 You see here how
true are his words. Mathematical Physics are
practical,
useful, infallible, grand, bewildering — I
would gladly grant
their right to all the laudatory Predicates in the Dictionary, — with
one
exception, clear. Whoever in
agreement with d'Alembert searches
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LEONARDO
into
their foundations,
will find them
obscure. When Goethe wished to
lay before a friend a few ideas
concerning
light he began by storming against the unhappy conception of the Rays.
“There is absolutely no question of Rays, — they are an abstraction
invented
to explain the phenomenon in its greatest simplicity, an abstraction
worked
up, built upon, or rather piled up, until the whole matter at last
became
muddled into incomprehensibility.“ But let us leave the so-called Rays
and return to our Waves, only following the exposition so far until we
meet a practical conception clear to the senses, so as to justify the
belief
that we are floating down from the cloudy Olympus of hypothetical
constructions,
and are setting foot upon the solid ground of empirics.
And here I would
crave your attention: the time has come for us, as Kant taught us, “to
supply the synthesis.“ In proportion as I move the thread more or less
violently, so the serpentine line which it forms in the air will show
greater
or lesser curves; in the same way the aether-particles in the
Light-aether,
in proportion to the violence of their motion, will deviate more or
less
from their original position, — in other words, the Waves will be
higher
or lower: this variation in the height of the Waves is known as the
Amplitude
of Wave-motion. Besides the height of the Waves their length has to be
taken into consideration. The distance between a1 and a2, from
wave-crest
to wave-crest, or from b1 to b2, from wave-valley to wave-valley, may
vary
in length: that is called the Wave-length.
Thirdly, the movement of
each
aether-particle, which can be imagined as rocking to and fro, may take
place with varying speed: that is called the Duration of oscillation.
Pray
hold fast to the conception that we must admit in these Waves a varying
height, length, and duration of oscillation. And inasmuch as thought,
as
the saying goes, pays no duty, we may besides all this assume various
directions
of motion.
149
LEONARDO
Once
more let us
consider the wet
thread.
I can move my hand from right to left and from left to right, and then
the single particles of the string which is curving into waves will
also
move rectilinearly to and fro; the same holds good with the
aether-particles;
in this case we say that the light is “rectilinearly polarised.“ But
just
as I move my hand rectilinearly from left to right, I might equally
move
it in a right line to and fro from front to back; I must therefore
assume
at least two directions of oscillation, and indeed might, if necessary,
assume as many more as I please; in the simplest case we speak of two
perpendicular
directions of waves mutually polarised. Again, I might move my hand in
a circle or in an ellipse. In that case the single particle of the
string
would, instead of a straight line, describe a circular line, or an
elliptic
line from one wave-crest to another, or from one wave-valley to the
next:
here too we must assume the same of the Light-aether particles; in the
one
case we speak of circular polarised light, in the other of elliptic
polarised
light. There are several other complications, but for our present
purpose
this is sufficient. We can therefore conceive waves of varying
amplitude
(that is to say height), waves of different length, waves of different
duration of oscillation, waves rectilinearly polarised,
perpendicularly
polarised in opposition, circularly polarised, and elliptically
polarised.
But now I have to make a last and highest demand upon your imagination.
Represent to yourselves all these differences with all their various
prepositions
as before, “with,“ “in,“ “upon,“ etc. — high waves and low waves, short
and long, swift and slow in their oscillations, in endless gradations,
pressing upon one another in all directions, — and in addition the
aether-particles
in various straight lines, and also working through each other in
circles
and ellipses: and then do you know what you have arrived at? Why, the
Natural
Light of the Physicists, as the
150
LEONARDO
sun,
the candle, the
match brings it
into existence! This again is a serious matter. Cross-examine Helmholtz:
he will furnish you with
information.
“Natural light,“ he writes, “is a uniform compound of all sorts of
differently
polarised Light,“ moreover, “it contains wave-features of an endless
number
of continually intermingling values of oscillatory duration.“
It seems to me that
we have fairly carried out Kant's behests as to ourselves supplying the
synthesis. Yet I must here insert a remark. Nothing would be more
unjustifiable
than to ridicule this Scheme of the physicists, far rather would I with
complete confidence vote with Kant that such intellectual constructions
are “the pride of human reason.“ It is only by degrees that the
monstrous
complexity of the illusion established itself, as new phenomena, which
it was necessary to incorporate in the one great Scheme, gradually
became
known, new ones have cropped up since Helmholtz's time: as for instance
the Röntgen Rays, which compelled the conclusion that the
oscillations
do not only take place perpendicularly to the direction of
transmission,
but also parallel to it; that is to say as if we were not only to move
our wet thread to and fro rectilinearly and in a circular line, but
also
from top to bottom and conversely from bottom to top, — not only
therefore
in the direction of floor and ceiling, but also in the direction of the
room's walls. There will always be new additional matter coming to the
front, until in the end the Scheme of Undulation will become useless by
reason of its growing and alarming complication, and then some genius
will
enrich us with a new Image which will combine Light, radiating energy,
chemical agency, electricity, magnetism, in one single practical scheme
paving the way for new discoveries. The new theory is already at hand,
widely developed, only lacking as yet a presentation as Image. 33
Enthusiastic
admiration is the due of those men who like
151
LEONARDO
Democritus
and
Descartes and Kant endow
the human brain with such schematic and creative illusions; and
unquestionable
recognition is the meed of those men of exact Science who, like Newton
and Helmholtz, by their scorn of fatigue, their gift of observation,
acuteness,
power of sensitiveness, and talent, not only enrich the treasury of
knowledge,
— adding to the already existing thoughts of genius which they have
inherited,
— but also render to mankind services of imperishable value. One need
only
think of the ophthalmoscope! The depreciation of exact science, as we
meet
with it here and there in the works of various fanatics and
obscurantists,
makes one so indignant because it denies manifest demonstrable services
which every lamp-cleaner can see even if he cannot understand them;
whereas
the depreciation of philosophy and art is pardonable where it is due to
stupidity or faulty
education.
We must
have no misunderstanding upon this point. The one thing against which I
defend myself is this, that an invisible church served by a priesthood
of narrow-minded, arrogant, and intolerant professors, who under the
honourable
title of “learned“ enjoy a quite unjustified respect, — since learning
and power of judgment by no means of necessity go hand in hand 34 —
that
these enemies of nature, this tribe of fanatics should seize upon my
unders
