[
]I would like to express again, for those who missed the first
two installments of this series, that the views expressed within the
essays are those of the physicists who wrote them, not me. It’s called
“Famous Physicists on Mysticism,” not “isis agora lovecruft on Mysticism.”
This essay is one of my favourite, and it is partly the inspiration for
the title of this blog, although full credit has to go to Ryne Warner,
whom I lived with as a roommate for several years. He’s an experimental
composer, and one of his projects is called Ohioan. The first
song off their album which was released last year is also the title
of this blog. If you’re into Thee Silver Mt. Zion or any of the other
numerous sounds that came out the Montreal scene in the first half of
the last decade, you’ll like Ohioan. I used to sneak into their practice
sessions just to stare at the fiddle player. His movements were a
physical counter-point to the melodies. I cried a little bit one of
those times, it was too pretty. I really hope he doesn’t read
this…Just to show off Ryne’s talent: I highly recommend listening to
Some Will Live. So. Damn. Beautiful.
Science and the Beautiful
by Werner Heisenberg
Perhaps it will be best if, without any initial attempt at a
philosophical analysis of the concept of “beauty,” we simply ask where
we can meet the beautiful in the sphere of exact science. Here I may
perhaps be allowed to begin with a personal experience. When, as a small
boy, I was attending the lowest classes of the Max-Gynasium here in
Munich, I became interested in numbers. It gave me pleasure to get to
know their properties, to find out, for example, whether they were prime
numbers or not, and to test whether they could perhaps be represented as
sums of squares, or eventually to prove that there must be infinitely
many primes. Now since my father thought my knowledge of Latin to be
much more important than my numerical interests, he brought home to me
one day from the National Library a treatise written in Latin by the
mathematician Leopold Kronecker, in which the properties of whole
numbers were set in relation to the geometrical problem of dividing a
circle into a number of equal parts. How my father happened to light on
this particular investigations from the middle of the last century I do
not know. But the study of Kronecker’s work made a deep impression on
me. I sensed a quite immediate beauty in the fact that, from the problem
of partitioning a circle, whose simplest cases were, of course, familiar
to us in school, it was possible to learn something about the totally
different sort of questions involved in elementary number theory. Far in
the distance, no doubt, there already floated the question whether whole
numbers and geometrical forms exist, i.e., whether they are there
outside the human mind or whether they have merely been created by this
mind as instruments for understanding the world. But at that time I was
not yet able to think about such problems. The impression of something
very beautiful was, however, perfectly direct; it required no
justification or explanation.
[caption id=”attachment_428” align=”alignleft” width=”248”
caption=”Werner Heisenberg”][
][/caption]
But what was beautiful here? Even in antiquity there were two
definitions of beauty which stood in a certain opposition to one
another. The controversy between them play a great part, especially
during the Renaissance. The one describes beauty as the proper
conformity of the parts to one another, and to the whole. The other,
stemming from Plotinus, describes it, without any reference to parts, as
the translucence of the eternal splendor of the “one” through the
material phenomenon. In our mathematical example, we shall have to stop
short, initially, at the first definition. The parts here are the
properties of whole numbers and laws of geometrical constructions, while
the whole is obviously the underlying system of mathematical axioms to
which arithmetic and Euclidean geometry belong—the great structure of
interconnection guaranteed by the consistency of the axiom system. We
perceive that the individual parts fit together, that, as parts, they do
indeed belong to this whole, and, without any reflection, we feel the
completeness and simplicity of this axiom system to be beautiful. Beauty
is therefore involved with the age-old problem of the “one” and the
“many” which occupied—in close connection with the problem of “being”
and “becoming”—a central position in early Greek philosophy.
Since the roots of exact science are also to be found at this very
point, it will be as well to retrace in broad outline the currents of
thought in that early age. At the starting point of the Greek philosophy
of nature there stands the question of a basic principle, from which the
colorful variety of phenomena can be explained. However strangely it may
strike us, the well-known answer of Thales—”Water is the material first
principle of all things”—contains, according to Nietzsche, three basic
philosophical demands which were to become important in the developments
that followed: first, that one should seek for such a unitary basic
principle; second, that the answer should be given only rationally, that
is, not by reference to a myth; and third and finally, that in this
context the material aspect of the world must play a deciding role.
Behind these demands there stands, of course, the unspoken recognition
that understanding can never mean anything more than the perception of
connections, i.e., unitary features of marks of affinity in the manifold.
But if such a unitary principle of all things exists, then—and this was
the next step along this line of thought—one is straightaway brought up
against the question how it can serve to account for the fact of change.
The difficulty is particularly apparent in the celebrated paradox of
Parmenides. Only being is; non-being is not. But if only being is, there
cannot be anything outside this being that articulates it or could
brings about changes. Hence being will have to be conceived as eternal,
uniform, and unlimited in space and time. The changes we experience can
thus only be an illusion.
Greek thought could not stay with this paradox for very long. The
eternal flux of appearances was immediately given, and the problem was
to explain it. In attempting to overcome the difficulty, various
philosophers struck out in different directions. One road led to the
atomic theory of Democritus. In addition to being, non-being can still
exist as a possibility, namely as the possibility for movement and form,
or, in other words, as empty space. Being is repeatable, and thus we
arrive at the picture of atoms in the void—the picture that has since
become infinitely fruitful as a foundation for natural science. But of
this road we shall say no more just now. Our purpose, rather, is to
present in more detail the other road, which led to Plato’s Ideas, and
which carried us directly into the problem of beauty.
[caption id=”attachment_429” align=”alignright” width=”246”
caption=”Pythagoras”][
][/caption]
This road begins in the school of Pythagoras. It is there that the
notion is said to have originated that mathematics, the mathematical
order, was the basic principle whereby the multiplicity of phenomena
could be accounted for. Of Pythagoras himself we know little. His
disciples seem, in fact, to have been a religious sect, and only the
doctrine of transmigration and the laying down of certain moral and
religious rules and prohibitions can be traces with any certainty to
Pythagoras. But among these disciples—and this was what mattered
subsequently—a preoccupation with music and mathematics played an
important role. Here it was that Pythagoras is said to have made the
famous discovery that vibrating strings under equal tension sound
together in harmony if their lengths are in a simple numerical ratio.
The mathematical structure, namely the numerical ratio as a source of
harmony, was certainly one of the most momentous discoveries in the
history of mankind. The harmonious concord of two strings yields a
beautiful sound. Owing to the discomfort caused by beat-effects, the
human ear find dissonance disturbing, but consonance, the peace of
harmony, it finds beautiful. Thus the mathematical relation was also the
source of beauty.
Beauty, so the first of our ancient definitions ran, in the proper
conformity of the parts to one another and to the whole. The parts here
are the individual notes, while the whole is the harmonious sound. The
mathematical relation can , therefore, assemble two initially
independent parts into a whole, and so produce beauty. This discovery
effected a breakthrough, in Pythagorean doctrine, to entirely new forms
of thought, and so brought it about that the ultimate basis of all being
was no longer envisaged as a sensory material—such as water, in
Thales—but as an ideal principle of form. This was to state a basic idea
which later provided the foundation for all exact science. Aristotle, in
his Metaphysics, reports that the Pythagoreans, “…who were the first
to take up mathematics, not only advanced in this study, but also having
been brought up in it they thought its principles were the principles of
all things….Since, again, they saw that the modifications and the
ratios of the musical scales were expressible in numbers; since, then,
all other things seemed in their whole nature to be modelled on numbers;
and numbers seemed to be the first things in the whole of nature, they
supposed the elements of numbers to be the elements of all things, and
the whole heaven to be a musical scale and a number.”
Understanding of the colorful multiplicity of the phenomena was thus to
come about be recognizing in them unitary principles of form, which can
be expressed in the language of mathematics. By this, too a close
connection was established between the intelligible and the beautiful.
For if the beautiful is conceived as a conformity of the parts to one
another and to the whole, and if, on the other hand, all understanding
is first made possible by means of this formal connection, the
experience of connections either understood or at least, guessed at.
[caption id=”attachment_431” align=”alignleft” width=”288”
caption=”Plato”][
][/caption]
The next step along this road was taken by Plato with the formulation of
his theory of Ideas. Plato contrasts the imperfect shapes of the
corporeal world of the senses with the perfect forms of mathematics; the
imperfectly circular orbits of the stars, say, with the perfection of
the mathematically defined circle. Material things are the copies, the
shadow images, of ideal shapes in reality; moreover, as we should be
tempted to continue nowadays, these ideal shapes are actual because
because and insofar as they become “act”-ive in material events. Plato
thus distinguishes here with complete clarity a corporeal being
accessible to the senses and a purely ideal being apprehensible not by
the senses but only through acts of the mind. Now is this ideal being in
any way in need of man’s thought in order to be brought forth by him. On
the contrary, it is the true being, of which the corporeal world and
human thinking are mere reproductions. As their name already indicates,
the apprehension of Ideas by the human mind is more an artistic
intuiting, a half-conscious intimation, than a knowledge conveyed by the
understanding. It is a reminiscence of forms that were already implanted
in this soul before its existence on earth. The central Idea is that of
the Beautiful and the Good, in which the divine becomes visible and at
sight of which the wings of the soul begin to grow. A passage in the
Phaedrus expresses the following thought: the soul is awe-stricken and
shudders at the sight of the beautiful, for it feels that something is
evoked in it that was not imparted to it from without by the senses but
has always been already laid down there in a deeply unconscious region.
But let us come back one more to understanding and thus, to natural
science. The colorful multiplicity of the phenomena can be understood,
according to Pythagoras and Plato, because and insofar as it is
underlain by unitary principles of form susceptible of mathematical
representation. This postulate already constitutes an anticipation of
the entire program of contemporary exact science. It could not, however,
be carried through in antiquity, since an empirical knowledge of the
details of natural processes was largely lacking.
The first attempt to penetrate into these details was undertaken, as we
know, in the philosophy of Aristotle. But in view of the infinite wealth
initially presented here to the observing student of nature and the
total lack of any sort of viewpoint from which an order might have been
discernible, the unitary principles of form sought by Pythagoras and
Plato were obliged to give place to the description of details. Thus
there arose the conflict that has continued to this day in the debates,
for example, between experimental and theoretical physics; the conflict
between the empiricist, who by careful and scrupulous detailed
investigation first furnishes the presuppositions for an understanding
of nature, and the theoretician, who creates mathematical pictures
whereby he seeks to order and so to understand nature—mathematical
pictures that prove themselves, not only by their correct depiction of
experience, but also and more especially by their simplicity and beauty,
to be the true Ideas underlying the course of nature.
Aristotle, as an empiricist, was critical of the Pythagoreans, who, he
said, “are not seeking for theories and causes to account for observed
facts, but rather forcing their observations and trying to accommodate
them to certain theories and opinions of their own” and were thus
setting up, one might say, as joint organizers of the universe. If we
look back on the history of the exact sciences, it can perhaps be
asserted that the correct representations of natural phenomena has
evolved from this very tension between the two opposing views. Pure
mathematical speculation becomes unfruitful because from playing with
the wealth of possible forms it no longer finds its way back to the
small number of forms according to which nature is actually constructed.
And pure empiricism becomes unfruitful because it eventually bogs down
in endless tabulation without inner connection. Only from the tension,
the interplay between the wealth of facts and the mathematical forms
that may possibly be appropriate to them, can decisive advances spring.
But in antiquity this tension was no longer acceptable and thus, the
road to knowledge diverged for a long time from the road to the
beautiful. The significance of the beautiful for the understanding of
nature became clearly visible again only at the beginning of the modern
period, once the way back had been found from Aristotle to Plato. And
only through this change of course did the full fruitfulness become
apparent of the mode of thought inaugurated by Pythagoras and Plato.
[caption id=”attachment_432” align=”alignright” width=”445”
caption=”Galileo Galilei, Istoria e Dimonstrazioni (Rome, 1613),
Frontispiece”][
][/caption]
This is most clearly shown in the celebrated experiments on falling
bodies that Galileo probably did not, in fact, conduct from the leaning
tower of Pisa. Galileo begins with careful observations, paying no
attention to the authority of Aristotle, but, following the teaching of
Pythagoras and Plato, he does try to find mathematical forms
corresponding to the facts obtained by experiment and thus, arrives at
his laws of falling bodies. However, and this is a crucial point, he is
obliged, in order to recognize the beauty of mathematical forms in the
phenomena, to idealize the facts, or, as Aristotle disparagingly puts
it, to force them. Aristotle had taught that all moving bodies not acted
upon by external forces eventually come to rest, and this was the
general experience. Galileo maintains, on the contrary, that, in the
absence of external forces, bodies continue in a state of uniform
motion. Galileo could venture to force the facts in this way because he
could point out that moving bodies are, of course, always exposed to a
frictional resistance and that motion, in fact, continues the longer,
the more effectively the frictional forces can be cut off. In exchange
for this forcing of the facts, this idealization, he obtained a simple
mathematical law, and this was the beginning of modern exact science.
Some years later, Kepler succeeded in discovering new mathematical forms
in the data of his very careful observations of the planetary orbits and
in formulating the three famous laws that bear his name. How close
Kepler felt himself in these discoveries to the ancient arguments of
Pythagoras, and how much the beauty of the connections guided him in
formulating them, can be seen from the fact that he compared the
revolutions of the planets about the sun with the vibrations of a string
and spoke of a harmonious concord of the different planetary orbits, of
a harmony of spheres. At the end of his work on the harmony of the
universe, he broke out into this cry of joy: “I thank thee, Lord God our
Creator, that thou allowest me to see the beauty in thy work of
creation.” Kepler was profoundly struck by the fact that here he had
chanced upon a central connection which had not been conceived by man,
which it had been reserved to him to recognize for the first time—a
connection of the highest beauty. A few decades later, Isaac Newton in
England set forth this connection in all its completeness and described
it in detail in his great work Principia Mathematica. The road of
exact science was thus pointed out in advance for almost two centuries.
But are we dealing here with knowledge merely, or also with the
beautiful? And if the beautiful is also involved, what role did it play
in the discovery of these connections? Let us again recall the first
definition given in antiquity: “Beauty is the proper conformity of the
parts to one another and to the whole.” That this criterion applies in
the highest degree to a structure like Newtonian mechanics is something
that scarcely needs explaining. The parts are the individual mechanical
processes—those which we carefully isolate by means of apparatus no less
than those which occur inextricably before our eyes in the colorful play
of phenomena. And the whole is the unitary principle of form which all
these processes comply with and which was mathematically established by
Newton in a simple system of axioms. Unity and simplicity are not,
indeed, precisely the same. But the fact that in such a theory the many
are confronted with the one, that in it the many are unified, itself has
the undoubted consequence that we also feel it at the same time to be
simple and beautiful. The significance of the beautiful for the
discovery of the true has at all times been recognized and emphasized.
The Latin motto “Simplex sigillum veri”—“The simple is the seal of the
true”—is inscribed in large letters in the physics auditorium of the
University of Göttingen as an admonition to those who would discover
what is new; another Latin motto, “Pulchritudo splendor
veritatis”—“Beauty is the splendor of truth”—can also be interpreted to
mean that the researcher first recognizes truth by this splendor, by the
way it shines forth.
Twice more in the history of exact science, this shining forth of the
great connection has been the crucial signal for a significant advance.
I am thinking here of two events in the physics of our own century: the
emergence of relativity theory and quantum theory. In both cases, after
years of vain effort at understanding, a bewildering plethora of details
has been almost suddenly reduced to order by the appearance of a
connection, largely unintuitable but still ultimately simple in its
substance, that was immediately found convincing by virtue of its
completeness and abstract beauty—convincing, that is, to all who could
understand and speak such an abstract language.
But now, instead of pursuing the historical course of events any
further, let us rather put the question quite directly: What is it that
shines forth here? How comes it that with this shining forth of the
beautiful into exact science the great connection becomes recognizable,
even before it is understood in detail and before it can be rationally
demonstrated? In what does the power of illumination consist, and what
effect does it have on the onward progress of science?
Perhaps we should begin here by recalling a phenomenon that may be
described as the unfolding of abstract structures. It can be illustrated
by the example of number theory, which we referred to at the outset, but
one may also point to comparable processes in the evolution of art. For
the mathematical foundation of arithmetic, or the theory of numbers, a
few simple axioms are sufficient, which, in fact, merely define exactly
what counting is. But with these few axioms we have already posited that
whole abundance of forms which has entered the minds of mathematicians
only in the course of the long history of the subject—the theory of
prime numbers, of quadratic residues, of numerical congruences, etc. One
might say that the abstract structures posited in and with numbers have
unfolded visibly only in the course of mathematical history, that they
have generated the wealth of propositions and relationships that makes
up the content of the complicated science of number theory. A similar
position is also occupied—at the outset of an artistic style in
architecture, say—by certain simple basic forms, such as the semicircle
and rectangle in Romanesque architecture. From these basic forms there
arise in the course of history new, more complicated, and also altered
forms, which yet can still, in some way, be regarded as variations on
the same theme; thus, from the basic structures there emerges a new
manner, a new style of building. We have the feeling, nonetheless, that
the possibilities of development were already perceivable in these
original forms, even at the outset; otherwise, it would be scarcely
comprehensible that many gifted artists should have so quickly resolved
to pursue these new possibilities.
[caption id=”attachment_433” align=”alignleft” width=”346” caption=”The
Page from Isaac Newton’s Folios On Which He Predicts The Apocalypse
Would Come As Early As A.D. 2132”][
][/caption]
Such an unfolding of abstract basic structures has assuredly also
occurred in the instances I have enumerated from the history of the
exact sciences. This growth, this constant development of new branches,
went on in Newtonian mechanics up to the middle of the last century. In
relativity theory and the quantum theory we have experienced a similar
development in the present century, and the growth has not yet come to
an end.
Moreover, in science, as in art, this process also has an important
social and ethical aspect; for many men can take an active part in it.
When a great cathedral was to be built in the Middle Ages, many master
masons and craftsmen were employed. They were imbued with the idea of
beauty posited by the original forms and were compelled by their task to
carry out exact and meticulous work in accordance with these forms. In
similar fashion, during the two centuries following Newton’s discovery,
many mathematicians, physicists, and technicians were called upon to
deal with specific mechanical problems according to the Newtonian
methods, to carry out experiments, or to effect technical applications;
here, too, extreme care was always required in order to attain what was
possible within the framework of Newtonian mechanics. Perhaps it may be
said in general that by means of the underlying structures, in this case
Newtonian mechanics, guidelines were drawn or even standards of value
set up whereby it could be objectively decided whether a given task had
been well or ill discharged. It is the very fact that specific
requirements have been laid down, that the individual can assist by
small contributions in the attainment of large goals, and that the value
of his contribution can be objectively determined, which gives rise to
the satisfaction proceeding from such a development for the large number
of people involved. Hence even the ethical significances of technology
for our present age should not be underestimated.
The development of science and technology has also produced, for
example, the Idea of the airplane. The individual technician who
assembles some component for such a plane, the artisan who makes it,
knows that his work calls for the utmost care and exactitude and that
the lives of many may well depend upon its reliability. Hence he can
take pride in a well-executed piece of work, and delights, as we do, in
the beauty of the aircraft, when he feels that in it the technical goal
has been realized by properly adequate means. Beauty, so runs the
ancient definition we have often cited, is the proper conformity of the
parts to one another and to the whole, and this requirement must also be
satisfied in a good aircraft.
But in pointing thus to the evolution of beauty’s ground structure, to
the ethical values and demands that subsequently emerge in the
historical course of development, we have not yet answered the question
we asked earlier, namely, what it is that shines forth in these
structures, how the great connection is recognized even before it is
rationally understood in detail. Here we ought to reckon in advance with
the possibility that even such recognition may be founded upon
illusions. But it cannot be doubted that there actually is this
perfectly immediate recognition, this shuddering before the beautiful,
of which Plato speaks in the Phaedrus.
Among those who have pondered on this question, it seems to have been
universally agreed that this immediate recognition is not a consequence
of the discursive (i.e. rational) thinking. I should like here to cite
two statements, on from Johannes Kepler, who has already been referred
to, and the other, in our own time, from the Zürich atomic physicist
Wolfgang Pauli, who was a friend of the psychologist, Carl Jung. The
first passage is to be found in Kepler’s Harmony of the World:
[caption id=”attachment_434” align=”alignleft” width=”300”
caption=”Kepler, Harmonium Mundis, Frontispiece”][
][/caption]
So far Kepler. He is, therefore, referring us here to possibilities
already to be found in the animal and plant kingdoms, to innate
archetypes that bring about the recognition of forms. In our own day,
Adolf Portmann, in particular, has described such possibilities,
pointing, for example, to specific color patterns seen in the plumage of
birds, which can possess a biological meaning only if they are also
perceived by other members of the same species. The perceptual capacity
will therefore have to be just as innate as the pattern itself. We may
also consider bird song at this point. At first, the biological
requirement here may well have been simply for a specific acoustic
signal, serving to seek out the partner and understood by the latter.
But to the extent that this immediate biological function declines in
importance, a playful enlargement of the stock of forms may ensue, and
unfolding of the underlying melodic structure, which is then found
enchanting as song by even so alien a species as man. The capacity to
recognize this play of forms must, at all events, be innate to the
species of bird in question for certainly it has no need of discursive,
rational capacity for understanding certain basic forms of the language
of gesture and thus, for deciding, say, whether the other has friendly
or hostile intentions—a capacity of the utmost importance for man’s
communal life.
Ideas similar to those of Kepler have been put forward in an essay by
Pauli. He writes:
The process of understanding in nature, together with the joy that man
feels in understanding, i.e., in becoming acquainted with new knowledge,
seems therefore to rest upon a correspondence, a coming into congruence
of preexistent internal images of the human psyche with external objects
and their behavior. This view of natural knowledge goes back, of course,
to Plato and was…also very plainly adopted by Kepler. The latter
speaks, in fact, of Ideas, preexistent in the mind of God and imprinted
accordingly upon the soul, as the image of God. These primal images,
which the soul can perceive by means of an innate instinct, Kepler calls
archetypes. There is very wide-ranging agreement here with the
primordial images or archetypes introduced into modern psychology by C.
G. Jung, which function as instinctive patterns of ideation. At this
stage, the place of clear concepts is taken by images of strongly
emotional content, which are not thought but are seen pictorially, as it
were, before the mind’s eye. Insofar as these images are the expression
of a suspected but still unknown state of affairs, they can also be
called symbolic, according to the definition of a symbol proposed by
Jung. As ordering operators and formatives in this world of symbolic
images, the archetypes function, indeed, as the desired bridge between
sense perceptions and Ideas, and are therefore also a necessary
precondition for the emergence of a scientific theory. Yet one must
beware of displacing thisa priori knowledge into consciousness, and
relating it to specific, rationally formulable Ideas.
In the further course of his inquiries, Pauli then goes on to show that
Kepler did not derive his conviction of the correctness of the
Copernican system primarily from any particular data of astronomical
observation, but rather from the agreement of the Copernican picture
with an archetype which Jung calls a mandala and which was also used
by Kepler as a symbol for the Trinity. God, as prime mover, is seen at
the center of a sphere; the world, in which the Son works, is compared
with the sphere’s surface; the Holy Ghost corresponds to the beams that
radiate from center to surface of the sphere. It is naturally
characteristic of these primal images that they cannot really be
rationally or even intuitively described.
Although Kepler may have acquired his conviction of the correctness of
Copernicanism from primal images of this kind, it remains a crucial
precondition for any usable scientific theory that it should
subsequently stand up to empirical testing and rational analysis. In
this respect, the sciences are in a happier position than the arts,
since for science there is an inexorable and irrevocable criterion of
value that no piece of work can evade. The Copernican system, the
Keplerian laws, and the Newtonian mechanics have subsequently proved
themselves—in the interpreting of phenomena, in observational findings,
and in technology—over such a range and with such extreme accuracy that
after Newton’s Principia it was no longer possible to doubt that they
were correct. Yet even here there was still an idealization involved,
such as Plato had held necessary and Aristotle had disapproved.
This only came out in full clarity some fifty years ago when it was
realized from the findings in atomic physics that the Newtonian scheme
of concepts was no longer adequate to cope with the mechanical phenomena
in the interior of the atom. Since Planck’s discovery of the quantum of
action, in 1900, a state of confusion had arisen in physics. The old
rules, whereby nature had been successfully described for more than two
century, would no longer fit the new findings. But even these findings
were themselves inherently contradictory. A hypothesis that proved
itself in one experiment failed in another. The beauty and completeness
of the old physics seemed destroyed, without anyone having been able,
from the often disparate experiments, to gain a real insight into new
and different sorts of connection. I don’t know if it is fitting to
compare the state of physics in those twenty-five years after Planck’s
discovery (which I, too, encountered as a young student) to the
circumstances of contemporary modern art. But I have to confess that
this comparison repeatedly comes to mind. The helplessness when faced
with the question of what to do about the bewildering phenomena, the
lamenting over lost connections, which still continue to look very
convincing—all these discontents have shaped the face of both
disciplines and both periods, different as they are, in a similar
manner. We are obviously concerned here with a necessary intervening
stage, which cannot be bypassed and which is preparing for developments
to come. For, as Pauli told us, all understanding is a protracted
affair, inaugurated by processes in the unconscious long before the
content of consciousness can be rationally formulated.
At this moment, however, when the true Ideas rise up, there occurs in
the soul of him who sees them an altogether indescribable process of the
highest intensity. It is the amazed awe the Plato speaks of in the
Phaedrus, with which the soul remembers, as it were, something it had
unconsciously possessed all along. Kepler says: “Geometria est
archetypus pulchritudinis mundi”; or, if we may translate in more
general terms: “Mathematics is the archetype of the beauty of the
world.” In atomic physics this process took place not quite fifty years
ago and has again restored exact science, under entirely new
presuppositions, to that state of harmonious completeness which for a
quarter of a century it had lost. I see no reason why the same thing
should not also happen one day in art. But it must be added, by way of
warning, that such a thing cannot be made to happen—it has to occur on
its own.
I have set this aspect of exact science before you because in it the
affinity with the fine arts becomes most plainly visible and because
here one may counter the misapprehension that natural science and
technology are concerned solely with precise observation and rational,
discursive thought. To be sure, this rational thinking and careful
measurement belong to the scientist’s work, just as the hammer and the
chisel belong to the work of the sculptor. But in both cases they are
merely the tools and not the content of the work.
Perhaps at the very end I may remind you once more of the second
definition of the concept of beauty, which stems from Plotinus and in
which no more is heard of the parts and the whole: “Beauty is the
translucence, through the material phenomenon, of the eternal splendor
of the ‘one.’” There are important periods of art in which this
definition is more appropriate than the first, and to such periods we
often look longingly back. But in our own time it is hard to speak of
beauty from this aspect, and perhaps it is a good rule to adhere to the
custom of the age one has to live in, and to keep silent about that
which it is difficult to say. In fact, the two definitions are not so
very widely removed from one another. So let us be content with the
first and more sober definition of beauty, which certainly is also
realized in natural science, and let us declare that in exact science,
no less than in the arts, it is the most important source of
illumination and clarity.
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[]: http://www.patternsinthevoid.net/blog/wp-content/uploads/2011/01/Heisenberg.jpg
[]: http://www.patternsinthevoid.net/blog/wp-content/uploads/2011/01/pythagoras1.jpg
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[]: http://www.patternsinthevoid.net/blog/wp-content/uploads/2011/01/Galileo-Frontispiece.jpg
[]: http://www.patternsinthevoid.net/blog/wp-content/uploads/2011/01/The-Page-from-Isaac-Newtons-Folios-On-Which-He-Predicts-The-Apocalypse-Would-Come-As-Early-As-A.D.-2132.jpg
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