## Basic Dyads in Contemporary Physics

#### Professor David J. Bohm

*This article has been scanned fromthe journal Systematics, Vol. 1 No. 3(1963)*

In his inaugural dissertation as Professor of Theoretical Physics in the University

of London, Professor Bohm raised the question whether connectedness may not be

a more fundamental concept than existence itself. He concluded his address:

“the discrete topological theory discussed here does suggest at least one

new kind of question. For since it implies that what is fundamental is the

link, we should therefore try to find experiments that disclose the

relationship of linkage itself, rather than the structure of particles, which

is only a very indirect consequence of the basic characteristics of the

linkages. It is at present too early to suggest such an experiment, because

first one must familiarize oneself with how the theory deals with some of the

older questions (as was in fact also necessary with the quantum theory, before it

could lead to the framing of new kinds of experimental problems). However, one

can say at present that some directions in which such experiments may be

possible can already be discerned. It may be hoped that eventually these

questions will be clarified.”

The following article develops further the view

that the particular kind of connectedness associated with complementary dyads

is derived from the fundamentally discrete nature of experience itself. The

article being a development of the notions introduced in the inaugural

dissertation, and reference should be made to the latter for more detailed

argument in support of the thesis that linkage and action are prior to objects

and states.

1. *Movement vs. Rest*

Briefly, what we have done is to turn our

customary modes of thinking around with reference to certain basic questions.

The most fundamental of these questions is that of the nature of movement and

rest.

Now, our usual mode of thought is based on the

implicit assumption that what is is a totality of permanently existing

substance, in the form of a collection of objects of various kinds. In a short

interval of time each of these objects is supposed to suffer a series of

quantitatively small changes, passing through a non-countable infinity of qualitatively

similar intermediate stages.

In the point of view suggested in the talk,

however, we assume that what is is a totality of elementary quantum processes.

That is, we begin with movement itself, regarded as discrete, and yet unbroken

in the sense that division will, in general, lead ultimately to qualitative

change. This movement is then to be understood as a total process, which is to

be analysed in terms of the relationships, orders and structures that are in

it. The “permanent” object is then abstracted from this totality as a

relatively invariant repetitive pattern in the whole process.

This problem is an old one. Thus, more than two

thousand years ago, Zeno showed that the attempt to think of movement in the

customary way leads to paradoxes. As an example, he considered an arrow in

flight. It is supposed to occupy a series of successive positions. But while it

occupies a particular position, we conceive it as fixed, and thus we deny the

idea that it is moving. By means of this and other similar paradoxes, Zeno

demonstrated that our concept of movement is beset with contradictions.

These contradictions have not yet been resolved,

but what has in fact happened is that scientists have adjusted their ideas to

accommodate these contradictions, as well as they can. The differential

calculus is an example of such an adjustment. One considers an interval, t, and

the value of some function, f(t), at the beginning and end of the interval. One

then imagines the interval to decrease to zero as a limit, and in this way, one

obtains the derivative of the function. But this limiting process is full of

logical difficulties. In general, it has meaning (when applied repeatedly) only

for a limited class of analytic functions. But no real movement is known that

is described exactly by this class of functions. Thus, a typical particle

executing Brownian motion, quantum fluctuations, etc., has a movement which is

so discontinuous in the small that the limiting process of the differential

calculus is meaningless when applied to it. At best, this calculus is valid as

a simplification and an approximation, applicable in certain limiting cases.

But any attempt to push it too far leads to contradictions and absurdities as

well as indications that its basic assumptions are always false, in a deep

sense. [A special case in the infinities of modem quantum mechanical field

theories.]

Now, as has been indicated already in the talk,

in every mathematical theory, one must begin with something, taken as

axiomatic. If one begins with process, i.e., with the assumption that what is

is movement itself, then no paradox arises. For this assumption does not

contradict the fact that some things are seen to be at rest. Indeed, in this

point of view, a state of rest is comprehended as the result of invariant

relationships in the repetition of similar features of the total movement in a

process. On the other hand, if we begin with rest, then we have denied movement

from the start. Any attempt to bring in movement and change must then lead to a

logical contradiction, to which we can at best “adjust”, by means

such as the differential calculus, which permit the correct treatment of a

certain limited range of problems, despite the contradiction.

In discussing process, it is essential to stress

that movement is being taken in its general sense of change, qualitative and

quantitative, rather than in its more specialized sense of displacement of a

permanent object through space to which latter we shall hereafter refer as “motion”.

Thus, one may discuss the “movement of a symphony” as a related,

ordered and patterned whole, the essential character of which is contained in

its total structure. On the other hand, the “motion” of a symphony

would be meaningless (except perhaps in the sense of the orchestra playing the

symphony and being at the same time transported through space). In a similar

way, we have been proposing that the essential character of the electrons,

protons and other entities going all the way up to large-scale objects, is

determined in a totality of related, ordered and patterned process-structure,

so that, for example, the fact that there is an electron means that a certain

movement of such a kind is being executed in the totality (as one could say

that a certain theme is being carried along in a symphony). It must be

emphasized that even the “resting electron” is actually constituted

of such a pattern of movement which, however, returns to its original form

again and again so rapidly that no change is manifested on the large scale.

As shown in the theory of relativity, an object

at rest has a great deal of internal energy, a part of which can for example be

liberated in a nuclear transformation. Indeed, the whole of this rest energy is

made available when a particle meets the corresponding antiparticle and the two

annihilate each other. If we conceived each of the particles as a

“permanent object”, this process would indeed be incomprehensible. On

the other hand, if, as has been suggested here, we regard each particle as an

invariant repetitive feature of the movement constituting the total universal

process-structure, then it is evident that, under suitable conditions, two

opposite patterns of movement, corresponding to particle and antiparticle, can

cancel each other.

We emphasize then that in this point of view,

movement is taken to be universally what is and needing no explanation, while

it is always rest that needs a further explanation. Such an explanation is

carried out in terms of the notion of invariant repetitive, ordered, and

structured relationships that hold only relative to certain conditions, at

certain levels, within specific contexts, and to limited degrees of

approximation.

It is evident that relationships of the kind

described above arise quite naturally in the study of movement. For in a given

period, region or domain or degree of approximation, each movement can be

characterized by relationships that are invariant within the specified limits.

But it is characteristic of movement that all of its features can alter.

Â Â Â Â Â Thus beyond the limits in question, there is

bound ultimately to be a change in the relationships that are invariant in the

narrower context. This change of relationship is in turn a relationship of a

higher order. (As the velocity of an object, itself a relationship, can alter,

giving rise to a new aspect of the movement, the acceleration, which is a

relationship of velocities at neighbouring intervals of time.) Thus, if we

start with movement, defined through relationships, we can then go on to the

movement of movements, translated mathematically as relationship of

relationships coming ultimately to the structure-process that enables us to

understand the very constitution and basic qualities of what we have previously

thought of as permanent objects.

Â On the other hand, if we start with the

idea of a permanent object, there is no correspondingly natural way of applying

the concept of the object to itself (i.e., an object of objects) to obtain the

concept of movement. Rather, movement must be introduced arbitrarily; and as we

have seen, this leads ultimately to contradictions. So to begin with, movement

as a basic concept generally has a greater explanatory and predictive power, as

well as greater logical coherence, than to begin with the permanent object as a

basic concept.

We emphasize, then, that in the problem of

movement and rest, we are dealing with a typical case of a kind of

contradiction that is widespread in physics, and indeed, seems to be built into

the very structure of our common language. For it is customary to suppose that

the notions of rest and movement *exclude* each other, i.e., that what is

at rest is not in movement, and what is moving is not at rest. But here, we are

in effect proposing that far from contradicting movement in its general sense

of ordered and related qualitative and quantitative changes in a total

structure-process, *rest is actually an aspect and indeed a special case ofmovement*.

There are a great many other examples of pairs of

concepts that are customarily taken to be contradictory and mutually exclusive,

but which should more logically be treated either by regarding one member of

the pair as an aspect or special case of the other or by regarding both as

aspects of a broader and more comprehensive concept. In addition to movement

and rest, such pairs include connection and separation, discontinuity and

continuity, difference and similarity, asymmetry and symmetry, order and

disorder, as well as others. Each one of these pairs of concepts plays a key

role in the understanding o( the universal structure-process referred to in the

talk, and in fact, the whole set of these lies at the basis of the topology and

geometry of space-time. In the subsequent work, we shall therefore go into

these concepts in more detail.

2.

*Connection vs. Separation*

In the talk, we have already seen that if

interval is taken to be a basic concept, then any two aspects of the total

structure are connected by a series of linkages. But each linkage not only

*connects*;

in the very same action it also

*separates*. Indeed, no matter how close

two

*different*aspects of the process are, they must be separated by at

least the indivisible link that connects them. And if two entities are

*distant*

from each other this means only that they are

*separated*by a series of

*many*

linkages.

linkages

To talk about something that is

*totally*

disconnectedfrom the universe would evidently be meaningless, since it

disconnected

could never enter our experience in any way whatsoever, nor could it have

relevance for anything that could ever be known by us. Therefore, it makes no

sense to regard separation as a concept that totally denies or contradicts

connection. Rather, separation is a necessary aspect of all connections, an

aspect that is emphasized in a long series of linkages, and minimized in a

short series. To assert a contradiction between separation and connection, as

is implicit in much of our common usage of the words, is therefore likely to

create confusion in our thinking about the subject.

3. *Continuity vs. Discontinuity*

A pair of relationships closely allied to

connection and separation is constituted by continuity and discontinuity. The

elementary process, linkage, or connection that is fundamental in the quantum

mechanical domain is discrete, and therefore, is not in the usual sense of the

word, continuous. That is, it does not pass through a continuous infinity of

qualitatively similar points, preserving its identity while doing so. Nor is it

continuous in the sense that something in particular is continued inside the

interval. But because between the beginning and the end of an elementary

linkage there is an unbroken structure of qualitatively different kinds of

processes, such a quantum connection is also not *discontinuous*. (In the

talk we gave a similar example, of the interval between words, which is

unbroken, and which is nevertheless not words). Let us then refer to the

elementary process as *a-continuous*, to indicate that its basic qualities

go beyond the question of continuity and discontinuity. As explained in the

talk, continuity then arises when similar structures are continued over a

number of linkages, while discontinuity arises when such a relationship of

continuity comes to an end.

It can be seen that the concepts of continuity

and discontinuity play complementary parts in the understanding of

structure-process. Thus, in the example given in the talk, the electron process

was compared to a structure of similar linkages, the similarity being

visualized by thinking of a set of links of the same colour. The electron is

then understood through the continuity of a certain pattern. Yet, it is also

the discontinuity of this pattern, in another sense. For unless the electron

structure were *different* to that in the immediate neighbourhood, there

would only be a homogeneous mass of linkages, in which no entities of any kind

could be distinguished at all. So there is a discontinuity in certain kinds of

connection (e.g., to neighbouring particles), and a continuity in other orders

(e.g., time), which is necessary for the electron to be what it is. Moreover,

even the continuous aspects will eventually come to an end, giving rise to

further discontinuities (e.g., an electron can meet its antiparticle and be

annihilated); while the discontinuous can be the basis of further continuity

(e.g., a regular pattern of discrete but similar atoms in space gives rise to a

continuing lattice structure). So continuity and discontinuity are not absolute

qualities. Rather, they are ever-changing roles, that are now filled by one

aspect of a structure, and now by another, the important point being that no

theory with any real content can be made which does not *somewhere*

include both roles. There is then no aspect of any entity, property, process,

relationship, etc., which it not *both* continuous *and*

discontinuous, when the problem is considered as *a whole*, and not just

in some partial view.

4. *Difference vs. Similarity*

As the suppositions that separation contradicts

connection, and continuity contradicts discontinuity, lead to confusion, so

does also the assumption that similarity contradicts difference. Thus, if there

are two things. A and B, they *must* be different. If there were no *difference**at all between them* (at least, for example, in position), they would be

the same: and therefore, in reality, A and B would have to be just two names or

labels for one thing.

Two different things can however be similar in

certain respects, e.g., their colours or shapes. They may be so similar that,

in a certain level of approximation, no detectable differences exist in these

respects. Then they are said to be *equivalent* or *equal*. But

equivalence is a relationship between *different* things, and not an

assertion of identity. Indeed, the phrase, “identity of different

things” is evidently an absurdity since “identity” means

“being the same thing”.

Not even two quantities on opposite sides of an

equation are identical in their meanings. For each quantity is generally

defined and obtained in a different way (e.g., on one side of the equation, a

function may be obtained from a power series, and on another side from an

integral). Besides, the *domain* of definition of the functions appearing

on the two sides of an equation is generally different. What indeed would be

the use of an equation, if it only asserted that a thing named A is the same

thing as a thing named B? That would amount to the trivial statement that

people have called one thing by two names, A and B. In reality, an equation is

non-trivial only because it asserts the relative and limited equivalence of two

different mathematical entities defined in different ways, in different overall

domains, etc.

It seems clear then that similarity, equivalence

and equality are special aspects of difference, i.e., they represent *adifference that makes no difference*, in certain specified, limited and

defined senses. This point of view is implicit in much of modern mathematics,

in which the notion of equality is replaced by that of

*equivalence relations*

(e.g., in group theory), which latter are a special case of non-equivalence

relations (e.g., relationships implying order such as “greater

than”). Indeed, it may be said that mathematics should no longer be

expressed in terms of equations, but rather by the assertion of relationships

between elements and aspects that are all

*different*. And as has been

indicated in the talk, the relationships of these relationships give rise to

orders, while the orders of orders lead to pattern and structure.

This brings us to the very interesting problem of

how mathematics is related to physics and to our general experience with the

world as a whole. Here, one may reasonably suggest that such a relationship is

possible, only because in mathematics, man has created abstract structures

which are similar to actual structures found in experience. For example, the

electric field structure calculated from Laplace’s equation is similar to that

obtained by measuring an actual field. And in the talk, we have tried to

indicate how to go further, to relate certain algebraic structures to the total

space-time structure of the universe.

The above helps to explain why mathematics has

been so powerful in predicting new things in physics. For if we can hit on an

abstract mathematical structure similar to some actual structure, then from

some observations on the actual structure, we can often get a valid idea of

what new possibilities to expect, for aspects of this structure not hitherto

observed.

5. *Symmetry and Asymmetry*

We now come to the problem of symmetry and

asymmetry. Thus far, these too have usually been regarded as mutually exclusive

concepts. This procedure has led to very serious difficulties in modem physics

which centre on the question of how the observed irreversibility of the

macroscopic physical laws can be reconciled with the *reversibility* of

the corresponding microscopic laws.

Now, it is an evident fact that movement on the

large scale is irreversible. Each new moment is *different* to what came

before, and what is past never comes back again exactly as it was. In physics,

this irreversibility shows up in the second law of thermodynamics, which is

based on the fact that heat flows from a region of higher temperature to one of

lower temperature and never the other way round. In addition, there is the

closely allied phenomenon of friction, in which mechanical energy can be turned*completely* into an equivalent amount of heat energy; whereas it is not

possible to reverse the process and to turn heat energy *completely* into mechanical

energy. (An engine permits only a partial reversal, because as can be shown

from the second law of thermodynamics, its efficiency must be less than 100%.)

More generally the irreversiblity of all physical processes is comprehended in

the notion that a certain abstract property called the *entropy* can only

increase, and can never decrease, in any movement or change taking place in an

isolated system.

On the other hand, the laws of microphysics are *completelyreversible*, in the sense that if the movements of all particles and fields

in the universe were reversed at some instant, the system would execute an

opposite order of development relative to the original. For example. , if all

the movements of molecules were to reverse, it would in principle be possible

according to the micro-physical laws, for a kettle of water on a fire to

freeze, transferring its heat back to the flame.

Large-scale irreversibility has been related to

micro-reversibility by means of probability concepts. In this point of view,

heat is regarded as a kind of random or disordered molecular motion. In

friction, for example, ordered mechanical energy is transformed into disordered

molecular energy on the micro-level, where it is lost to view as large-scale

movement, and appears in our grosser observations only as heat. More generally,

the entropy of a system is defined in terms of a certain mathematical measure

of the degree of disorder in its movement and structure at the molecular level.

Then, on the basis of certain assumptions about the probabilities that seem to

be reasonable, at least at first sight, it follows that a process in which

ordered macroscopic movements become degraded into disordered molecular

movements has a very much higher probability than for the reverse to happen. A

theory has been developed along these lines, which explains flow of heat from a

higher to a lower temperature, frictional transformations of mechanical energy

into heat, and the general tendency for entropy to increase, as results that

are so overwhelmingly probable that for practical purposes, we can consider the

laws of thermodynamics to be deterministic predictions.

Although current probability theories do permit

the correct calculation of many thermodynamic properties of matter, they suffer

from an inherent ambiguity and confusion in their basic premises. This is shown

up by certain paradoxes, such as those associated with what is called the

Boltzman’s H theorem, which make it clear that on a more careful study of the

implications of these theories, the apparent proof of irreversibility based on

probability breaks down (eg., it is demonstrated that it is in reality just as

likely that the entropy will decrease with time as that it will increase). When

one pursues such studies further, one finds that current theories never really

manage to get macroscopic irreversibility out of microscopic reversibility;

they simply push the logical difficulties off into some obscure part of the

theory where they are not easy to see (rather like sweeping the dust under the

carpet).

In the point of view discussed in this talk,

however, we do not begin with the assumption of reversibility. Rather, we

assume

*from the start*that the basic linkages of elementary processes

are

*directed*in the sense that the

*beginning*and the

*end*of

such a process are clearly definable. We can meaningfully do this, because the

interval inside such a linkage contains a lower level

*structure*, which

need not, in general, be symmetrical with regard to the two possible directions

in which the process can be considered. Moreover, we are regarding the

so-called “elementary particles” as just abstractions from the total

process. We therefore do not begin as is usually done in physics with a

collection of interacting elementary particles and try from these to build up a

model of the whole universe. Rather, we begin with the total process and treat

the elementary particles as very special features that are relevant when we are

studying, certain minute aspects of this process in some kind of relative

isolation. It is not at all unreasonable to suppose that these partial,

limited, and relatively isolated aspects are symmetrical, while the process as

a whole is not. So we encounter no difficulties in comprehending the over-all

asymmetry of development in time (e.g.. that implied in the irreversibility of

thermodynamic processes). For we

*begin*with such asymmetry as basic. We

also encounter no difficulties in understanding the symmetry of the laws of

movements of elementary particles; for asymmetry always contains symmetry as a

special case. On the other hand, once we begin with the general assumption of

symmetry, then we have contradicted asymmetry, and it is not really possible to

get the latter back in a fully coherent logical way.

More generally, we are led to regard symmetry as

a special case of asymmetry, wherever it appears. This notion is particularly

significant in the consideration of certain problems arising in the theory of

elementary particles. One of the most striking facts discovered in this theory

relates to the particle antiparticle problem already referred to in the talk.

It is this:

The wave equation for an antiparticle is obtained

from that for the corresponding particle by a reflection in time, a reflection

in space, and the interchange of the roles of the beginning and the end of a

physical process. (Mathematically, the latter corresponds to an interchange of

ingoing and outgoing waves).

This fact was most surprising when first

discovered, as it implies that the basic laws of physics are not symmetrical

under mirror reflection alone (this lack of mirror symmetry showed up in the

non-conservation of parity). Rather, they are found to be symmetrical in a

subtler sense, in which time reversal and exchange of particle for antiparticle

must be combined with space reflection to obtain the symmetry in question.

Roughly speaking, this means that at the level of elementary particles, there

is a qualitative physical distinction between a given process and its mirror

image, in the sense that one of these constitutes a different kind of particle

that will, for example, annihilate the other (whereas in terms of previous

physical ideas, mirror image systems should, as in everyday experience, be

qualitatively similar to the original and without this feature of mutual

annihilation).

Now, in our point of view, symmetry is always to

be understood as a special kind of asymmetry, defined by suitable

relationships. Here, the operative aspect of the term “symmetry” is

the last part, i.e., “metry”, meaning “measure” or

“metric”. That is to say, a symmetrical figure is one possessing

different aspects with

*equal measure*(e.g., an equilateral triangle). As

such, it is evidently a special case of a figure whose different aspects do not

have equal measure, and which is therefor asymmetrical in its structure. So the

question of symmetry is inseparably related to that of metric.

If one goes to general relativity, one sees the

problem more clearly still. For here, there is a “metrical tensor” which specifies how

the co-ordinate differences are to be related to actual lengths, ds, (through relationship. Without this tensor, it would be

impossible to say what symmetry even means, because this tensor determines

which lines are equal in length, which are perpendicular to each other, which

are parallel, etc. [E.g., if we want to construct a figure with reflectional

symmetry, we need equal lines that are perpendicular to the planes of

reflection, and these are determined by the metric tensor.]

Now, in any case, we are going to interpret

elementary particles as invariant repetitive aspects of the total process

structure (e.g., such as the dislocations referred to in the talk). To fit the

observed facts about particle and antiparticle described earlier, these aspects

will have to have suitable symmetry properties, and will therefore be deeply

related to the metrical properties of space. But the fact that symmetry

properties have a new physical significance suggests that it may be more

fruitful to turn the problem around, and to regard the

*symmetry of basic*

structures as the fundamental starting point, from which the usual metrical

structures as the fundamental starting point

properties of space will follow as consequences.

In the talk, we have already indicated that the

metric is defined when we can divide an arbitrary line in two. But a line can

be divided in two, if we know what is meant by a perpendicular plane, such that

the length of the reflection of each half in this plane is equal to that of the

other. And if the basic structure of space-time is such as to determine what

are the relationships of reflection for all space-time structures, then

*the*

metric is implicit in the symmetry properties of the elementary particles.

metric is implicit in the symmetry properties of the elementary particles

Moreover, the peculiar connection between reflected process structures and

antiparticles is now clear. For a completely reflected process-structure will

have all its constituent movements the reverse of those of the original, so

that the two will naturally combine to produce no movement at all on this

level, thus annihilating each other.

7. *Order vs. Disorder*

The problem of symmetry and asymmetry of process

in time is deeply related to that of *order and disorder*. For as we have

seen, the irreversibility of large-scale physical phenomena is now regarded as

the result of a tendency for relatively isolated aspects of a structure-process

to develop toward states of greater disorder with the passage of time. However,

as we have pointed out, current attempts to treat this problem by probability

concepts are seen to lead to confusion when the basis of the theory is

scrutinized with care. The source of this confusion can be traced to an unclear

notion of the meanings of the terms, order and disorder, arising largely in the

tacit assumption that these two ideas are mutually exclusive, and therefore

contradict each other.

The problem of order and disorder already arises

in the discussion of the foundation of our conceptions of probability.

Consider, for example, a game of coin throws (a typical case in which one can

apply the theory of probability). It is generally asserted that the succession

of heads and tails in such a series of throws is *disordered, irregular,random*, etc., while the statistical average frequencies of heads and tails

tend to approach definite values, given by their probabilities (in this case,

half for heads and half for tails, if the coin is well-balanced). However, when

we come to define what could be meant by the terms disordered, irregular,

random, etc., we find great difficulties. Thus, randomness has often been

identified with lawlessness or featurelessness. But the mere negation of laws

or features is not enough, because it is necessary also to assert some positive

qualities of a random array, to distinguish it from anything else whatsoever.

But once we try to define randomness positively as well as negatively, we will

inevitably attribute to it some kind of law, feature, order and regularity.

Thus, we come to the absurd concept of a law of lawlessness, a feature of

featurelessness, etc., in which the first term contradicts the second. Indeed,

as one can easily see by reflecting a little on this problem, it is impossible

for anything at all to exist unless it has some kind of feature, order,

regularity and law. So featurelessness, disorder irregularity, lawlessness,

etc., can have meaning only in some relative and limited contexts, and can in

no sense be regarded as absolute. (E.g., as the order of coin throws may be

irregular in relation to the time order of throwing, but not in relation to the

precise initial position and velocities of the coins after they are released.)

Order and disorder are therefore not mutually eclusive and totally

contradictory absolutes. Rather, they are complementary pairs of related

concepts, which, like continuity and discontinuity, connection and separation,

etc., arise together in every attempt to discuss a real situation.

To see the meanings of the notion of order and

disorder more clearly, let us return to the discussion given in the talk, in

which order was analysed in terms of the

*relationship of relationships*

(e.g., in the case of the integers). In going from here to the analyses of

pattern and structure as the

*order of orders*, it is necessary first to

study with some care a few of the problems arising when different orders are

related. The simplest case of such a relationship is that of two orders

impinging on each other. Consider, for example a straight road with many cars

moving at the same speed, spaced at regular intervals. This would constitute an

*ordered pattern of movement*. Consider now a second road which intersects

the first. If there were a similar ordered pattern of moving cars in the second

road, and if the two orders were independent, there would be a

*clash*at

the intersection. To prevent this clash, the two orders would have to be

*related*

or

*co-ordinated*. For example, one of the drivers might stop and give way

to another, by some agreed set of rules. In this way, the simple regular order

on each road would be altered, and replaced by an order of groups of cars. This

altered order would have the essential new property that the pattern on a given

road

*could not be analyzed completely in terms of relationships applying in*

that road alone. Rather, to understand, for example, why a given group

that road alone

occurred on the first road, we would have to refer to some corresponding set of

groups on the second roads. And this only reflects the fact that there is a

*larger*

orderin the whole system, which is incompatible with a

order

*complete order*

in each part of aspect.

Generally speaking, then, if we consider any one

road by itself, there would be an unrelatedness of different groups of cars.

signalizing a

*lack of complete order*, or as we could say, a

*partial*

and relative disorder. Such disorder can take two very distinct forms.

and relative disorder

Firstly, if the cars on each road move independently of those on the other

road, then there is a clash or conflict of orders, producing a kind of

disordering process, in which both orders tend to be destroyed. Secondly, if

the orders are related or co-ordinated, by being aspects of a larger total

order, then each aspect is

*incompletely ordered*. In a cursory

inspection, the unrelatedness of the terms in each partial aspect may seem to

be similar to what could result from disorder due to a clash or conflict, but a

closer study generally reveals the relationship of co-ordination, reflecting

the fact that we are dealing with a partial aspect of a larger whole, rather

than with a conflict of otherwise independent orders.

The typical situation that arises in physics is

one in which a given partial aspect is related, not just to one or to a few

other such aspects, but rather to a very large number of them. (E.g., in a

large-scale system, each of the constituent atoms depends on an enormous number

of similar atoms). In this case, new and rather simple characteristics can

frequently arise in the statistical properties of such an array of elements.

For here, it can be shown that in any partial order (e.g., of the positions and

velocities of the molecules selected by a specified procedure), there is a

practically complete unrelatedness of the individual elements, because each of

these depends on myriads of factors that are lost to view when any one part or

aspect is considered in isolation. On the other hand. as can be shown by a

simple mathematical treatment (based on an analysis of what is called the

“law of large numbers”), almost any one of a very wide range of

possible orders in the whole leads to statistical averages over a typical

selection of elements, which are practically equal to those given by the theory

of probability. In this way, we obtain a clear conception of what is to be

meant by the term “randomness” in cases where the theory of

probability is applicable. For we see that all the results of current

calculations can be comprehended through the notion that in a large aggregate,

constituting a totality of related elements, the existence of certain kinds of

order on the whole (e.g., a regular and simple macroscopic behaviour) entails a

lack of complete relatedness in the various partial aspects, such that in a

small number of these, no particular order can be guaranteed. On the other hand,

when large numbers of elements are considered, there will arise corresponding

statistical relationships, which are extremely insensitive to the details of

the micro-order. We therefore do not regard randomness as a

*total absence of*

order, but rather, as a particular

order

*kind of order*, in which there is

no significant degree of relatedness between individual elements in a given

group, while there are fairly definite relationships in the system as a whole.

The above discussion applies to the idealization

of a completely isolated system. In our point of view, however, such an

isolated system must always be considered as an abstraction from the total

process of the universe. Indeed, as we have seen in the talk, each aspect of

this process is connected to other aspects, both at the same level, and at

different levels, by indivisible linkages that form a whole pattern and

structure. For example, there must be in every theory a minimum undivided

interval, which is to be taken as fundamental in that theory, while the

relationships, order and structure in that theory are abstracted from the

unbroken totality of lower level intervals, not explicitly taken into account

in the theory in question. And in this totality, it will generally be the case

that there must exist orders that, as it were “cut across” the

abstraction made in any given theory and for this reason relate what is in the

field treated by that theory to what is out of this field. As a result, there

must be some disorder in any aspect of the universe that is subject to a

relative isolation for the purposes of investigation. All orders that can be

abstracted are therefore partial, limited and relative to conditions, context

and degree of approximation. This means, as we have already indicated, that order

and disorder cannot be absolutes; but must be like continuity and

discontinuity, motion and rest, etc., merely two complementary aspects in which

every phenomenon is to be studied.

Because each relatively isolable field is

generally abstracted from a lower level structure-process containing a very

large number of elements the disorder inherent in such a field will very often

give rise to random distributions and resulting statistical regularities, which

can be treated by the theory of probability in the manner already described

earlier. Therefore, in our point of view, the appearance of probability in

basic physical theories is to be expected as a partial reflection, within the

theory, of the unbroken totality of structures on other levels and in different

domains, that are necessarily

*left out*of each kind of abstraction. In

this way, we can take into account not only the probability distributions of

quantum theory, but also those of statistical mechanics. For both will

represent statistical regularities in the actually disordered characteristics

of the structure-processes in various of the levels studied in physics. In

particular, entropy can be interpreted as a certain quantitative measure of a

real kind of disorder. For we now have a clear definition of disorder as a

limitation on a given order due to its participation in larger relationships

going outside the order in question. And the increase of entropy with time can

likewise be treated without logical difficulties such as those arising in

current theories, because, as we have indicated earlier, we do not begin with

constituent particles and put them into interaction to make the whole system,

but rather, we begin with the total process and abstract the particles. Thus,

we can quite easily assume a total process which has an asymmetric structure,

in which the increase with time of disorder of partial aspects associated with

the entropy is built in from the outset.

Finally, it is important to go on to consider the

problem of whether the totality of the universe is ordered or not. Now, we have

already seen that disorder has no meaning as an absolute, but must be defined

*relative*

to some context of order. (E.g., a random sequence of coin throws has no

particular relationship to the time order in which the throws are made).

Vice-versa, order is generally defined against a background, that is without

any particular order.

Thus, as we saw in the talk, a basic problem in

modem quantum mechanical field theory is to determine the so-called

“vacuum state”. In terms of our point of view, this amounted to

defining empty space as a structure-process that has no particular order in it.

Only such a structure-process could serve as an indifferent background, which

would allow every conceivable order to emerge into it, without favouring one

against another. Indeed, such an indifference to particular orders is really

implicit in our mode of thinking of empty space as the potential locus of all

conceivable phenomena. It must be emphasized, however, that in this view, empty

space cannot correspond to a structure-process that is disordered in the usual

sense; since as we have seen, disorder has meaning only in relation to order.

Rather, empty space reflects the quality of the totality of the universe, in

that it is a kind of un-ordered matrix, containing the “germ” of all

orders and disorders, just as we say that the elementary process is

*a-continuous*,

being the “germ” of both continuity and discontinuity. Our view is

then that out of the un-ordered totality, various orders and structures are

created, a part of which constitutes matter as we know it. These orders

eventually come to clash with each other, producing disorder and breakdown of

structure (i.e., de-struction). Moreover, new kinds of order and structure are

continually emerging out of the unordered totality.

It is clear in the light of what has been said

earlier, that a new order is very likely to be incompatible with one that is

already present. The creation of what is new is therefore one side of a process,

the other side of which is the destruction of what is old. We may compare the

process to a flame. The flame can exist only as long as it is burning up the

fuel. So the order in the molecules of fuel is being destroyed to be replaced

by another order of molecules of the combustion products. The flame is what is

analagous to the process itself. And the totality of universe may be regarded

as such a flame, which exists by feeding on the old orders and structures, and

by thus creating new orders and structures. However, let us recall that in

accordance with what we have suggested earlier, existence is itself movement

and process, while rest and the static are a relatively invariant aspect of

this movement. To improve the analogy, we must therefore imagine, if we can,

that both fuel and combustion products are aspects of the flame, in such a way

that the latter can serve as new fuel when the former is used up, so that the

process as a whole has no limits and is never exhausted. It is just this view

that corresponds to the mathematical theory, the basis of which we have

sketched in the talk, and which, it is hoped, can be developed sufficiently for

publication in the near future.