The Unity of Human Knowledge

The question alluded to in the title for this address is as old as civilization itself, but has acquired renewed attention in our days with the increasing specialization of studies and social activities. From various sides concern has been expressed with the widespread confusion arising from the apparently divergent approaches taken by humanists and scientists to human problems, and in this connection there has even been talk about a cultural rift in modern society. We must, however, not forget that we are living in times of rapid developments in many fields of knowledge, reminiscent in such respect of the age of European Renaissance.

However great the difficulties of liberation from the medieval world view were felt at that time, the fruits of the so-called Scientific Revolution are certainly now a part of the common cultural background. In our century the immense progress of the sciences has not only greatly advanced technology and medicine, but has at the same time given us an unsuspected lesson about our position as observers of that nature of which we are part ourselves.Bohr’s view here is essentially the opposite of what is usually attributed to the Copenhagen interpretation, as invoking an external observer. For Bohr the problem is how one part of nature can separate itself as “subject” and treat another part as “object”.

Far from implying a schism between humanism and physical science, this development entails a message of importance for our attitude to common human problems, which — as I shall try to show — has given the old question of the unity of knowledge new perspective.The lesson from QM can help us get a more nuanced understanding of how knowledge from different domains can be related and integrated.

Bohr speaks as if this is an old question — about the unity of knowledge. What is he thinking of? The theme of diversity and unity in knowledge had been central for Høffding, tracing back to his participation in the Viden/Tro debate of the 1860s. The unity of science theme was also central for the logical positivists.

The pursuit of scientific inquiry with the aim of augmenting and ordering our experience of the world around us has through the ages proved fertile, not least for the continual progress of technology which to so great an extent has changed the frame of our daily life. While early developments of astronomy, geodesy and metallurgy in Egypt, Mesopotamia, India and China were primarily directed to serve requirements of the community, it is in ancient Greece that we first meet with systematic endeavours to clarify the basic principles for the description and ordering of knowledge.

In particular, we admire the Greek mathematicians, who in many respects laid the firm foundation on which later generations have built. For our theme it is important to realize that the definition of mathematical symbols and operations is based on simple logical use of common language. Mathematics is therefore not to be regarded as a special branch of knowledge based on the accumulation of experience, but rather as a refinement of general language, supplementing it with appropriate tools to represent relations for which ordinary verbal expression is imprecise or too cumbersome.Mathematics is just more language!

In view of the apparent remoteness of mathematical abstractions, often frightening wider circles, it may be noted that even elementary mathematical training allows school disciples to see through the famous paradox of the race between Achilles and the tortoise.Bohr always liked the idea that mathematics can help us get out of muddles that we are prone to fall into. Here he talks about how calculus can help us avoid the trap of Zeno’s paradoxes of motion. Elsewhere he talks about Riemann surfaces as a model for disambiguation, and of matrix mechanics as a tool for avoiding paradox in atomic physics.

How could the fleet-footed hero ever catch up with and pass the slow reptile if it were given even the smallest handicap? Indeed, at his arrival at the starting point of the turtle, Achilles would find that it had moved to some further point along the race track, and this situation would be repeated in an infinite sequence. I need hardly remind you that the logical analysis of situations of this type was to play an important role in the development of mathematical concepts and methods.

From the beginning, the use of mathematics has been essential for the progress of the physical sciences. While Euclidean geometry sufficed for Archimedes’ elucidation of fundamental problems of static equilibrium, the detailed description of the motion of material bodies demanded the development of the infinitesimal calculus on which the imposing edifice of Newtonian mechanics rests. Above all, the explanation of the orbital motion of the planets in our solar system, based on simple mechanical principles and the law of universal gravitation, deeply influenced the general philosophical attitude in the following centuries and strengthened the view that space and time as well as cause and effect had to be taken as a priori categories for the comprehension of all knowledge.Bohr mixes up the forms of intuition and the categories of cognition, but these subtleties don’t matter for him. His point is that there are two different kinds of cognitive tools that are foundational to physics: spacetime coordination and cause-effect reasoning. He thinks that in contexts where the quantum of action makes an appreciable difference, application of one of these tools excludes application of the other.

The extension of physical experience in our days has, however, necessitated a radical revision of the foundation for the unambiguous use of our most elementary concepts, and has changed our attitude to the aim of physical science.Elimination of ambiguity is an essential goal for Bohr. In English, we have to use the negative ‘unambiguous’, whereas German has the positive eindeutig, and Danish has entydig.

Indeed, from our present standpoint, physics is to be regarded not so much as the study of something a priori given, but rather as the development of methods for ordering and surveying human experience.Some people might take this as Bohr’s announcement of an anti-realist view of physics, i.e. that its aim is prediction rather than description of reality. But note that his emphasis is on action: physics isn’t just about describing the data we already have, it’s about gathering and understanding new data. Physics is an active pursuit of interacting with the natural world.

In this respect our task must be to account for such experience in a manner independent of individual subjective judgment and therefore objective in the sense that it can be unambiguously communicated in the common human language.The task of physics is to provide objective descriptions of reality, by which Bohr means unambiguous descriptions.

As regards the very concepts of space and time reflected in the primitive use of words as here and there, and before and after, it is to be remembered how essential the immense speed of light propagation, compared with the velocities of the bodies in our neighbourhood, is for our ordinary orientation. However, the surprise that it proved impossible even by the most refined measurements to ascertain, in laboratory experiments, any effect of the orbital motion of the earth around the sun, revealed that the shape of rigid bodies and their mutual distances would be differently perceived by observers swiftly moving relative to each other, and that even events, which by one observer would be judged as simultaneous, by another could be reckoned as occurring at different moments. Far from giving rise to confusing complications, the recognition of the extent to which the account of physical experience depends on the standpoint of the observer proved most fertile in tracing fundamental laws valid for all observers.Bohr doesn’t think that relativity theory provides a context-independent description of the facts. To the contrary, it makes clear that the facts must be relativized to ‘the standpoint of the observer’, i.e. a frame of reference. Nonetheless, the laws hold in all reference frames.

Indeed, the general theory of relativity, by which Einstein in renouncing all ideas of absolute space and time gave our world picture a unity and harmony surpassing any previous dreams, offered an instructive lesson as regards the consistency and scope of plain language. Although the convenient formulation of the theory involves mathematical abstractions as four-dimensional non-Euclidean geometry, its physical interpretation rests fundamentally on every observer’s possibility of maintaining a sharp separation between space and time and of surveying how any other observer, in his frame, will describe and co-ordinate experience by means of the common language.According to Bohr, the mathematical formalism (four-dimensional manifold) does not represent spacetime directly. Rather, its physical meaning comes about through its use by an observer/describer, who knows how to distinguish between space and time. That is, the ‘new vocabulary’ of GTR gains meaning from its connection to the manifest image vocabulary of ‘here or there’ and ‘before or after’.

New fundamental aspects of the observational problemBohr is probably thinking here of the Danish word måleproblemet, which is most literally translated as the measurement problem. This phrase is used somewhat differently in the contemporary literature.

entailing a revision of the very foundation for the analysis of phenomena in terms of cause and effect, were to be uncovered by the development initiated by Planck’s discovery of the universal quantum of action in the first year of this century. In fact, this discovery proved that the wide applicability of so-called classical physics rests entirely on the circumstance that the action involved in any phenomena on the ordinary scale is so large that the quantum can be completely neglected. In atomic processes, however, we meet with regularities of a novel kind, defying causal pictorial description but nevertheless responsible for the peculiar stability of atomic systems on which all properties of matter ultimately depend.

In this new field of experience, opened by modern refinements of the art of physical experimentation, we have met with many great surprises and even been faced with the problem of what kind of answers we can receive by putting questions to nature in the form of experiments. Indeed, in the account of ordinary experience it is taken for granted that the objects under investigation are not interfered with by the observation.Bohr suggests that ‘observation without (appreciable) interference’ is a presupposition of our practice of communicating our experiences to other people. But it’s not completely clear what he means by absence of interference. One possibility is that he simply means that there are objects that have properties of their own. That is, if I say that there are some objects that stand in some configuration, then I don’t normally mean to add the qualification ‘relative to me’.

It is true that when we look at the moon through a telescope we receive light from the sun reflected from the moon-surface, but the recoil from this reflection is far too small to have any effect on the position and velocity of a body as heavy as the moon. If, however, we have to do with atomic systems, whose constitution and reactions to external influence are fundamentally determined by the quantum of action, we are in a quite different position.

Faced with the question of how under such circumstances we can achieve an objective description, it is decisive to realize that however far the phenomena transcend the range of ordinary experience, the description of the experimental arrangement and the recording of observations must be based on common language. In actual experimentation this demand is amply satisfied with the specification of the experimental conditions through the use of heavy bodies such as diaphragms and photographic plates, the manipulation of which is accounted for in terms of classical physics. Just this circumstance, however, excludes any separate account of the interaction between the measuring instruments and the atomic objects under investigation.This passage suggests a complementarity between description of the measuring device in classical terms and a precise account of the interaction between the measuring instruments and the measured object. Is Bohr thinking here of application of the law of conservation of momentum to the joint system of measuring device and atomic object?

Especially this situation prevents the unlimited combination of space-time coordination and the conservation laws of momentum and energy on which the causal pictorial description of classical physics rests. Thus, an experimental arrangement aiming at ascertaining where an atomic particle, whose position at a given time has been controlled, will be located at a later moment implies a transfer, uncontrollable in principle, of momentum and energy to the fixed scales and regulated clocks necessary for the definition of the reference frame.Sameness of position over time is definable only relative to fixed reference frame. (It doesn’t help to add absolute space, because that then serves as a fixed reference frame.) However, if there is a physical reference frame, then the object is not a closed system. What’s more, you are precluded from speaking of momentum-energy transfer between the object and the reference frame, because you stipulated that the reference frame is unmoving.

Bohr talks of physical objects, e.g. clocks and rods, as ‘defining’ a reference frame. This notion deserves closer study.

Conversely, the use of any arrangement suited to study momentum and energy balance — decisive for the account of essential properties of atomic systems — implies a renunciation of detailed space-time coordination of their constituent particles.Here Bohr stresses that the momentum picture provides an explanation of essential properties of atomic systems. Hence, an interpretation that neglects the momentum picture (e.g. Bohmian mechanics) will be explanatorily defective.

Under these circumstances it is not surprising that with one and the same experimental arrangement we may obtain different recordings corresponding to various individual quantum processes for the occurrence of which only statistical account can be given.There is a sort of explanation here for the probabilistic nature of quantum mechanics. But the explanation is a bit opaque.

Likewise we must be prepared that evidence, obtained by different, mutually exclusive experimental arrangements, may exhibit unprecedented contrast and even at first sight appear contradictory.

It is in this situation that the notion of complementarity is called for to provide a frame wide enough to embrace the account of fundamental regularities of nature which cannot be comprehended within a single picture. Indeed, evidence obtained under well-defined experimental conditions — and expressed by adequate use of elementary physical concepts — exhausts in its entirety all information, about the atomic objects which can be communicated in common language.All that can be said about the atomic objects is relative to a well-defined context, i.e. the experimental conditions.

A detailed account on complementary lines of a new wide domain of experience has been possible by the gradual establishment of a mathematical formalism, known as quantum mechanics, in which the elementary physical quantities are replaced by symbolic operators subject to an algorism, involving the quantum of action and reflecting the non-commutativity of the corresponding measuring operations. Just by treating the quantum of action as an element evading customary explanation — similar to the role of the velocity of light in relativity theory as a maximal speed of signals — this formalism can be regarded as a rational generalization of the conceptual framework of classical physics. For our theme, however, the decisive point is that the physical content of quantum mechanics is exhausted by its power to formulate statistical laws governing observations obtained under conditions specified in plain language.For unambiguous communication, the context of a description must be rendered in the shared human language, i.e. the language of the manifest image.

The fact that in atomic physics, where we are concerned with regularities of unsurpassed exactness, objective description can be achieved only by including in the account of the phenomena explicit reference to the experimental conditions,Objective description calls for specifying the state of the subject, not pretending that s/he has disappeared.

emphasizes in a novel manner the inseparability of knowledge and our possibilities of inquiry. We are here concerned with a general epistemological lesson illuminating our position in many other fields of human interest.

In particular, the conditions of analysis and synthesis of so-called psychic experiences have always been an important problem in philosophy.Most likely a nod to Høffding, who was much concerned with the description of psychological experience.

It is evident that words like thoughts and sentiments, referring to mutually exclusive experiences, have been used in a typical complementary manner since the very origin of language. In this context, however, the subject-object separation demands special attention. Every unambiguous communication about the state and activity of our mind implies, of course, a separation between the content of our consciousness and the background loosely referred to as “ourselves”,Objective description demands a clear demarcation of who is describing (subject) and what is being described (object).

but any attempt at exhaustive description of the richness of conscious life demands in various situations a different placing of the section between subject and object.The subject-object split can be moved around in order to achieve objective description of different subject matters.

In order to illustrate this important point, I shall allow myself to quote a Danish poet and philosopher, Poul Martin Møller, who lived about a hundred years ago and left behind an unfinished novel still read with delight by the older as well as the younger generation in this country.The Danish philosophers Sibbern and Møller rejected Hegel’s claim that he had overcome the subject-object distinction. Møller’s most famous student, Søren Kierkegaard, continued his critique of Hegel.

In his novel, called The Adventures of a Danish Student, the author gives a remarkably vivid and suggestive account of the interplay between the various aspects of our position, illuminated by discussions within a circle of students with different characters and divergent attitudes to life.

Especially I shall refer to a conversation between two cousins, one of whom is very soberly efficient in practical affairs, of the type which then, and even now, is known among students as a philistine, whereas the other, called the licentiate, is addicted to remote philosophical meditations detrimental to his social activities. When the philistine reproaches the licentiate for not having made up his mind to use the opportunities for finding a practical job, offered him by the kindness of his friends, the poor licentiate apologizes most sincerely, but explains the difficulties into which his reflections have brought him.

Thus he says:

My endless enquiries make it impossible for me to achieve anything.Møller portrays the licentiate as a one-sided person who knows how to reflect (at overveje) but not how to act (at handle). The are strong similarities here with the “postponement argument” in Kierkegaard’s Concluding Unscientific Postscript.

Furthermore, I get to think about my own thoughts of the situation in which I find myself. I even think that I think of it, and divide myself into an infinite retrogressive sequence of “I”s who consider each other. I do not know at which “I” to stop as the actual, and in the moment I stop at one, there is indeed again an “I” which stops at it.Møller is poking fun at the licentiate, who seems to think like a German idealist philosopher. The licentiate’s creation of a new subject seems to be a version of Hegelian reflection, where one critically considers one’s former presuppositions. Recall that Kierkegaard believes that the solution to this infinite regress of reflection is ‘double reflection’, brought about by a subjective act of will.

I become confused and feel a dizziness as if I were looking down into a bottomless abyss, and my ponderings result finally in a terrible headache.

In his reply the cousin says:

I cannot in any way help you in sorting your many “I”s. It is quite outside my sphere of action, and I should either be or become as mad as you if I let myself in for your superhuman reveries. My line is to stick to palpable things and walk along the broad highway of common sense; therefore my “I”s never get tangled up.

Quite apart from the fine humour with which the story is told, it is certainly not easy to give a more pertinent account of essential aspects of the situation with which we all are faced. Fortunately, the risk of falling into the deplorable situation of the licentiate is small in normal life, where we become gradually accustomed to coping with practical necessities and learn to communicate in common language what we need and what is on our mind. In such adjustment the balance between seriousness and humour, conspicuous in children’s play and equally appreciated in mature life, plays no small part.

The complementary way in which words like contemplation and volition are used has especially to be taken into account when turning to the problem of the freedom of will, discussed by philosophers through the ages.Bohr uses the English ‘contemplation’ where he uses the Danish overvejelse. He could just as well have used ‘consideration’, but in any case, the state of mind is detached and tending in the direction of objectivity.

The idea that overvejelse is a complementary state of mind to willing (deciding, believing, and acting) goes back to at least Kierkegaard, although the word ‘complementarity’ is unique to Bohr. In the Postscript, Kierkegaard argues that making any decision requires subjectivity, and so is strictly incompatible with the state of indifferent contemplation.

Even if we cannot say whether we want to do something because we gather that we can, or we can only do it because we will, the feeling of, so to speak, being able to make the best out of circumstances is a common human experience. Indeed, the notion of volition plays an indispensable part in human communication similar to words like hope and responsibility, in themselves equally undefinable outside the context in which they are used.Sometimes a concept only makes sense within a certain context.

The flexibility of the subject-object separation in the account of conscious life corresponds to a richness of experience so multifarious that it involves a variety of approaches.Introspection is a clear case where the line between subject and object can be moved around.

As regards our knowledge of fellow beings, we witness, of course, only their behaviour, but we must realize that the word consciousness is unavoidable when such behaviour is so complex that its account in common language entails reference to self-awareness.Bohr is no behaviorist. An adequate description of another person requires reference to the same concepts we use to understand ourselves.

It is evident, however, that all search for an ultimate subjectElsewhere Bohr uses “final subject”.

is at variance with the aim of objective description, which demands the contraposition of subject and object.Here Bohr is working against the background of the German idealist tradition, where the subject’s finitude was seen as an impediment to objective knowledge. Hegel thought the solution was infinite reflection; but Kierkegaard argued that such a process cannot be completed by a human being existing in time. Here Bohr agrees with Kierkegaard, (Rasmus) Nielsen, and (Harald) Høffding in maintaining that humans shouldn’t aim for a god’s eye view of reality.

Such considerations involve no lack of appreciation of the inspiration which the great creations of art offer us by pointing to features of harmonious wholeness in our position. Indeed, in renouncing logical analysis to an increasing degree and in turn allowing the play on all strings of emotion, poetry, painting and music contain possibilities of bridging between extreme modes as those characterized as pragmatic and mystic. Conversely, already ancient Indian thinkers understood the logical difficulties in giving exhaustive expression for such wholeness. In particular, they found escape from apparent disharmonies in life by stressing the futility of demanding an answer to the question of the meaning of existence, realizing that any use of the word “meaning” implies comparison; and with what can we compare the whole existence?This claim sounds strange at first. But it’s true that “meaning of” is a binary relation, and hence involves comparison.

The aim of our argumentation is to emphasize that all experience, whether in science, philosophy or art, which may be helpful to mankind, must be capable of being communicated by human means of expression, and it is on this basis that we shall approach the question of unity of knowledge. Confronted with the great diversity of cultural developments, we may therefore search for those features in all civilizations which have their roots in the common human situation. Especially we recognize that the position of the individual within the community exhibits in itself multifarious, often mutually exclusive, When approaching the age-old problem of the foundation of so-called ethical values we shall in the first place ask about the scope of such concepts as justice and charity, the closest possible combination of which is attempted in all human societies. Still it is evident that a situation permitting unambiguous use of accepted judicial rules leaves no room for the free display of charity. But, as stressed especially by the famous Greek tragedians, it is equally clear that compassion can bring everyone in conflict with any concisely formulated idea of justice. We are here confronted with complementary relationships inherent in the human position, and unforgettably expressed in old Chinese philosophy, reminding us that in the great drama of existence we are ourselves both actors and spectators.The actor/spectator duality can be related directly to the action/contemplation duality.

In comparing different national cultures we meet with the special difficulty of appreciating the culture of one nation in terms of the traditions of another. In fact, the element of complacency inherent in every culture corresponds closely to the instinct of self-preservation characteristic of any species among the living organisms. In such context it is, however, important to realize that the mutually exclusive characteristics of cultures, resting on traditions fostered by historical events, cannot be immediately compared to those met with in physics, psychology and ethics, where we are dealing with intrinsic features of the common human situation.If we are to speak of ‘complementarity’ between cultures, it’s only by analogy. We meet complementarity in the strict sense in physics, psychology and ethics. Bohr has given examples of all three in this article: position/momentum, contemplation/action, and justice/charity.

In fact, as is not least conspicuous in European history, contact between nations has often resulted in the fusion of cultures retaining valuable elements of the original national traditions. The question of how to ameliorate the so-called cultural rift in modern societies, which has attracted so much attention at this meeting, is after all a more restricted educational problem, the attitude to which would seem to call not only for information but, as I think everyone will agree, also for some humour. A most serious task is, however, to promote mutual understanding between nations with very different cultural backgrounds.

Indeed, the rapid progress of science and technology in our days, which entails unique promises for the promotion of human welfare, and at the same time imminent menaces to universal security, presents our whole civilization with a veritable challenge. Certainly, every increase in knowledge and potentialities has always implied a greater responsibility, but at the present moment, when the fate of all peoples is inseparably connected, a collaboration in mutual confidence, based on appreciation of every aspect of the common human position, is more necessary than ever before in the history of mankind.