The term 'microscope' is defined, in Chamber's Dictionary, as an abbreviation for 'an instrument for magnifying minute objects'.
It is clear that the lexicographer responsible for this definition would not have put it forward unless he was reasonably certain that it would command general acceptance. Yet a cursory examination suffices to show that if we attempt to interpret it at its face-value, the outcome is utterly absurd.
The everyday, non-metaphorical use of the word 'object' is in keeping with its etymology; it is something which can be 'thrown against' us, or 'against which we can be thrown'. It is voluminous, and has a resistance surface, i.e., one which serves as a 'locus' of abrupt increases in the intensity of tactile sensation.
On the basis of our usual methods of measurement, we would infer that when the linear dimensions of an 'object' were magnified by 500 diameters, its 'volume' would be magnified by a figure of the order of 125,000,000. It is clear that this corollary to the definition has been completely disregarded by the lexicographer who formulated it.
It is not, in fact, the 'objects' that are magnified, but the visual phenomena, or 'objectives', which are quasi-automatically interpreted as 'signs' for the possibilities of tactile contact with them. Such signs are, in the main, so reliable that 'ordinary language' treats them as 'certainties' and does not bother to distinguish between the terms used to denote, or refer to, the visual sign and its tactile interpretant, using the same word in either case.
Now the tactile qualities of the interpretant are often of major importance on account of the high intensity of tactile experience, whereas any importance attached to the visual qualities of the sign is purely æsthetic, and never vital for 'practical' purposes. Consequently, it is most commonly the distinctiveness of the tactile interpretants, usually treated as 'certainties' with which the distinctivenesses of 'object-words' are associated. For example, the word 'chair' does not serve as an expression or reminder of a visual image; it is associated with the possibility of sitting down in reasonable comfort. Visual descriptions are only used in cases where the tactile interpretant is relatively unimportant; either 'ring' or 'circle' can function as alternative denotations of a single type of visual experience.
There is an obvious pragmatic justification for the ordinary language 'identification' of sign and interpretant; object-words have frequently to be used as urgent signals, uttered for the purpose of promoting action suitable for the avoidance of highly undesirable tactile possibilities. We cannot afford the luxury of insisting on accuracy of expression in cases where delay may be fatal. Nevertheless, we realise that there are cases where the identification of visual sign and tactile interpretant is misleading; Macbeth's 'dagger' exemplifies a type of experience which does undoubtedly occur, although so rarely that we tend to disregard such possibilities for practical purposes. But when we are discussing the processes involved in visual perception, such occurrences oblige us to reject the identification of sign and interpretant that is normally taken for granted when using ordinary language.
It is in fact the sign, or 'objective', and not the interpretant, or 'object', which is magnified by the microscope. The microscope itself, as a complex of glass and metal, is itself an 'object', but in its functional aspects, it is part of our perceptual apparatus, and the experience of 'magnification' should therefore be regarded as a modification of our 'internal' experiencing.
In order to avoid the absurd consequences of the 'ordinary language' definition of 'microscope', I suggest the following:-
It is essential to specify the retention of shape-identity, since this is the only test of the 'visual veridicity' of the microscope. Unless this can be taken for granted, it would be more natural to suppose that the 'new' boundaries were caused by the instrument rather than to regard them as properties of the 'objective'. This actually happened in the early days of the telescope, which, from the point of view of its modification of the visual field, performs precisely the same function as the miscroscope. Galileo's reports of Jupiter's moons were so discordant with the scheme of beliefs prevalent in his time that his contemporaries scouted them as 'illusions' produced by the use of the instrument. In practice, a general belief in the visual 'veridicity' of the telescope was easily established by using it for viewing remote terrestrial objectives, when the identity of the major boundaries could be corroborated directly, while the 'actuality' of the 'new' ones could be corroborated by tracking them to their sources.
In the case of the microscope, there are limits to the corroboration of its 'veridicity' in this manner whenever a very high degree of magnification is employed; it becomes more and more likely that the instrument will have contributed to the shape-henomena. The situation is analogous to that which led Heisenberg to formulate his 'Uncertainty' principle.
In my amended definition of 'microscope' the word 'interval' is substituted for the more customary 'distance'. This is for the purpose of combining two important 'spatio-temporal' insights, formulated respectively by Einstein and Kant.
Einstein's insight arose from his attempt to answer a problem which he had formulated to himself in childhood, namely:-'What would the Universe look like to somebody travelling down a beam of light?' Kant's problem was very different; making use of 'modern conveniences', we can express it as follows:- 'If a television-set were conscious, which of the processes within its total experiencing would it regard as "internal" and "external" respectively?'
Einstein realised that the concept of 'distance' pure and simple was untenable; its measurement would have to presuppose 'simultaneous' observations of the 'events' which established its limits. Since visual communication, although extremely rapid, is not 'infinitely' so, the requisite simultaneity could not itself be observed. This limitation is obvious in astronomy, where the interval between the events that we suppose to have occurred on some remote stars and our acts of awareness of them may amount to millions of years; we are even some 'eight minutes' away from the 'Sun'.
Now the same principle would appear to be applicable to terrestrial measurments. For example, my 'ordinary language' description of the 'distance' between the paper on which I am writing and my eyes is 'about two feet'. But if, instead, I prefer to assert that the interval between the 'basic events', or energy-transfers, that I conjecture to be occurring at the surface of the paper, and the impact on the surface of my eye of the 'causal lines' which I confidently believe to connect them with my awareness of them, is approximately 2/(186,000 × 5,280) of a second, I do not think that any physicist will contradict me. Furthermore, he will agree that this conveys 'information' which is missing from the 'ordinary language' formulation - for the simple reason that it is of no conceivable practical importance!
We can now see the relevance of Kant's insight, namely, that 'space' is our 'Anschauung' of 'external' experience, while 'time' is our 'Anschauung' - 'Zuhörung' would be more appropriate - of the 'internal' variety. Since my experiencing appears to be a pure flux, better expressed by a verb than by a substantive, I would prefer to re-word this insight as follows:-
The contrast between the 'tempi' of the two modes of experiencing is such that they are virtually incommensurable, and we ordinarily treat them as 'absolutely' distinct.
We can illustrate Kant's principle by considering the 'interval' involved in a 'long jump' (a) as experienced by the jumper, and (b) as observed by the officials who 'measure' it.
For the jumper, it is a continuous period between the tactile events of 'take-off' and 'landing', within which no major tactile event has been experienced. It is purely temporal, and he has no method of 'measuring' it, on account of its 'continuity'.
The 'data' used by the observing officials are very different. The 'take-off' judge probably does not see the landing, and the 'landing' judge does not see the take-off, so that neither of them experiences the 'interval' unless - as is just possible - both events are audible. 'Signs' for the events are visible by anybody who is watching from a sufficient distance, but not by a stationary observer standing close to the pit. The interval, measured along the edge of the pit, is between the quasi-permanent take-off bar and the quasi-permanent mark in the sand which appeared almost immediately after the landing. A kind of 'magnification' has to be used for measurement purposes; a series of events that is judged to be 'rhythmically invariant' is inserted, in the forms of acts of awareness of a series of marks along the side of the pit. These are then 'counted', or, more correctly speaking, the judges take it for granted that such a procedure has already been adopted by whoever inscribed the marks, and also that if the marks are numbered, the sequence of their numbering is in accordance with accepted conventions. 'Absolute' accuracy would require the insertion of an 'infinite' number of marks, but there would then be no way of 'intuiting the rhythmic regularity' of their succession.
'Events' undoubtedly provide the 'stuff' of spatial sense-experience; in the case of touch, they are 'contacts' and 'interruptions of contact' - in both cases, abrupt changes of intensive quantity. In the case of vision, they are 'boundaries', which are likewise abrupt changes, either of intensive quantity - 'black and white' - or of colour. Every empiricist assumes that 'external' events have always preceded their 'internal' counterparts, though there is no need for the usual gratuitous assumption that the interval between every 'impression' and its consequent 'idea' must be 'spatial' in character, and therefore observable, at least in principle. 'Time', in theory, is 'infinitely' faster than 'Space', though in actual practice the ratio between their 'tempi', though very great, turns out to be finite.
The measurements which provide the'data' of physical science are all of 'spatial' intervals, which are, experientially speaking, periods of relative 'nothingness'. This is bound to be the case, since it is only 'nothingness' that we can 'share'; the innermost kernel of each of our 'experiencings' is bound to be 'private'. The event-sequences which constitute 'immediate experience' can be 'enjoyed', but not 'known'; in their case, 'occurrence' and 'enjoyment' are identical, inasmuch as no 'interval' separates them. Such an event-sequence is an 'I'. This conclusion is the same as that reached by Hume, albeit reluctantly and by a different route.
Physical formulæ merely serve to relate the 'nothingness' within our several experiencings; in terms of 'importance', they provide us with what are, metaphorically speaking, 'photographic negatives' of experience itself. The same criticism is applicable to all descriptive language and symbolism, inasmuch as the 'invariance' of each term can only function as a signal for a corresponding 'invariance' in the utterer's thinking.
Once we accept that every visual awareness of 'distance' is our interpretation of an 'interval' between two acts of awareness, albeit of almost inconceivable brevity, the function of the microscope can be simply interpreted as a slowing down of the 'tempo' at which we 'visualise' the raw material of 'immdiate' experience. If we accept the 'visual veridicity' of the instrument, i.e., the 'identity' of the shapes in the 'objective' irrespective of whether or not we are using the instrument, this interpretation is almost tautologically obvious, since when using the instrument, we can scan only a fraction of the 'same' objective in a time which, without the use of the instrument, generally allows us to cover, not only the objective, but a good deal of its environment.
The function of the microscope relative to the visual 'quasi-permanences' - Russell's name for the extremely rapid repetitive series of events which play such a prominent part in the visual field - is analogous to that performed by the 'slow-motion' cine-camera in the field of non-repetitive change. In this case, the 'scanning' is initially performed at an unusually rapid 'tempo', the sequence being subsequently replicated at the slower one which is 'normal'.
The 'tempo' at which we normally 'visualise' our experiential raw material for 'factual' purposes appears to be obligatory for all human beings; this is a precondition for the possibility of communicating by visual means. But it is not necessarily ideal for all purposes. It facilitates survival, since it provides us with 'signs' that are sufficiently detailed to enable us, on the whole, to avoid those violent contacts with surfaces which sometimes cause us to 'die' on account of their intolerable intensity; it also enables us to replicate less violent types of contact with which enjoyable experiences have been frequently associated, thereby encouraging us to make the efforts required in order to go on 'living'. It can thus be accounted for by experimentation followed by natural selection; this should be regarded as 'elimination of the unfit' rather than as 'survival of the fittest', since 'fitness' seems to be a matter of degree, except, apparently, at its lower limit. The 'tempo' of our 'factual' scanning must be suitably related to that of bodily movement, including speech; were it to be much slower, it could provide us with an additional wealth of structural detail, but this would be liable to distract our attention from those major boundaries which function as signs for the possibility of very high-intensity tactile experiences which we must avoid if we want to go on 'living'.
A slower tempo of visualisation is advantageous when we suspect that our well-being is threatened by small-scale, ultra-rapid event-sequences of 'tactile' type, such as those which we attribute to bacteria, and sometimes even to 'molecules' or 'atoms'. On the other hand, a more rapid, 'impressionistic' tempo of scanning often serves to increase our æsthetic enjoyment of visual experience itself, although it fails to create the amount of structural detail that we require of our signs for tangible surfaces. Similarly, the visual beauty of 'movement' is more commonly enhanced by 'time-lapse' photography rather than by the 'slow-motion' variety. Subnormal tempi of 'scanning' are in general only advantageous when we wish to participate in 'causal' types of change that we suspect of occurring at a much higher 'tempo' than those disclosed by the senses in our 'normal' states of awareness.
We have arrived at the conclusion that 'size', unlike 'shape', is a 'secondary' quality of visual percepts, inasmuch as it varies according to the 'tempo' at which we 'scan' our raw material. The 'primary' qualities of the 'objectives' - as distinct from the 'objects' with which 'ordinary language' identifies them - are 'colour', which appears to be a 'quasi-permanent' rhythmic variation of 'intensive quantity', and 'boundaries', i.e., abrupt changes either of colour or of intensive quantity itself; when sequences of such changes are repeated very rapidly, the outcome is an experience of a quasi-permanent 'shape'. This is, in effect, what happens every time that we look at a television set.
'Change of intensive quantity' remains as the sole link between each individual experiencing and 'the rest of the Universe'; this is the vital 'stuff' which enables us to avoid the Berkeleyan position of complete 'subjective idealism'. Visual phenomena can be satisfactorily accounted for as products of our æsthetically motivated selections from this flux. If anything is 'absolute' for all human beings, it is the fundamental basis of this selection; thus Kant's description of it as the 'Transcendental Aesthetic' was, in the main, justified. I think he was mistaken in regarding it as 'immutable', overlooking the possibility of an immanent urge for improvement; his treatment of the 'moral law' suffers from a similar defect. Both stem from an unduly high ethical evaluation of 'invariance', which is rather difficult to avoid on account of its great utility in facilitating verbal and symbolic communication. This mistake spoiled his 'revolution', which was 'anti-Copernican' rather than 'Copernican', since it placed each man at the centre of his own 'Universe'. Russell has stigmatised such 'subjectivism' as 'hubris' and 'madness', but it is nothing of the kind, provided that each of us realises that 'his own Universe' is only an ultra-microscopic portion of the 'Whole', and that he 'wills' in such a fashion as to take account of the possible effects of his willing on the feelings of other sentient beings whom he conjectures to be engaged in maintaining and, when possible, in improving it.
In short, a Leibnitzian monadology, provided that the 'monads' are not completely incommunicado, and that each of them is able, to a greater or lesser extent, to enjoy the emotion of 'sympathy' [empathy], can furnish a model of the Universe which is not only æsthetically satisfactory, but also reasonably coherent with phenomenal experience.
'What, then, is Time?' wrote St Augustine. 'If nobody asks of me, I know; but if I wish to explain to him who asks, I know not.'
The obvious explanation of this paradox which, however, nobody seems to have proposed, is that there must be something in the make-up of language which unfits it for the expression of this particular kind of 'knowledge'.
In this essay I trace the source of this expressive deficiency to an assumption which is absolutely basic to our techniques of linguistic and symbolic communication, but which has been overlooked because its acceptance has become quasi-automatic. I also propose a method of partially overcoming this deficiency, at least as far as written symbolisation is concerned, and proceed to relate the symbolic expression of "events" by this method to the actual technique that is in general use for describing their 'when'.
The basic assumption which underlies all symbolic communication is that the 'gap-indifference'1 of acts of awareness of the 'same' symbol represents a corresponding gap-indifference in the acts of awareness that it is used to express.
1. Prof. Price's term is far superior to "Identity" as an expression of empirical experience.
No utterer uses a distinctive word or symbol for expressive purposes unless there is a corresponding distinctiveness in some temporally gap-indifferent series of discrete acts of awareness within his own experience, which is the "meaning" to which he attaches it. Furthermore, if it appears to communicate successfully, we also assume that there is a 'spatial' type of gap-indifference between the meaning to which the utterer has attached it and that which has been attached to it by its interpreters.
The degree of gap-indifference required for "successful" communication varies considerably with the degree of importance to the communicants of the differences within the field of discourse. "Rigorous" logic and mathematics are based on the assumption that it can attain "absoluteness", when it constitutes "identity". They tend to treat this relation as a desirable "norm", from which any departure should be stigmatised as "falsehood" or, at least, as "inaccuracy".
There are nowadays very few people who believe that this 'absolute' state of affairs corresponds to anything that could conceivably form part of empirical experience. None the less, a strong emphasis on gap-indifference, or 'invariance' is essential to our communicative symbolic techniques, and undoubtedly contributes to their efficiency. On the other hand, it renders them gravely defective for the purpose of expressing change.
I propose to show that this defect can be to some extent overcome; this cannot, however, be done with words alone; it is necessary to borrow two symbols from musical notation. The two symbols that we require are already used in mathematics, but for the expression of change we need to interpret them in their musical sense. They are: > and <.
In mathematics, they always express a gap-indifferent relation between two discrete persistent entities; thus a > b is a synonym for "a is greater than b". In music, however, it is used to express a diminution of the intensive quantity of our awareness of what is "logically", i.e. from the point of view of symbolisation, a single entity, e.g.
The device is simplicity itself; change of extensive quantity represents change of intensive quantity so that the symbol represents a continuous diminuendo of the note "A", which otherwise remains qualitatively, i.e., structurally, invariant or at least "gap-indifferent"; a state which requires no change in its symbolic representation. The symbol could be regarded as expressing an intensity relation between discrete acts of awareness occurring within the duration of the note, but such a relation would be transient, and the symbol is never interpreted in this sense.
Of course, language does express change, in a jerky sort of way. We hear one word before another, and read from left to right, and the transitions between the words clearly correspond to changes in our thoughts. But changes in the intensity of our experience of a quasi-invariant structure are completely inexpressible in linguistic or symbolic terms. Yet such changes are essential constituents in almost every 'event'; it is a complete travesty to express events purely in terms of abrupt transitions from "state" to "state". Changes of intensive quantity unaccompanied by changes of any other kind are also common in empirical experience, as the musical example shows.
Kant deals with this matter in his Critique of Pure Reason. In the section 'Anticipations of Perception' he writes as follows:- 'Between reality in a phenomenon and negation, there exists a continuous concatenation of many possible intermediate sensations, the difference of which from each other is always smaller than that between the given sensation and zero, or complete negation' (my italics). He goes on to say that this intensive quantity is not discoverable by Apprehension, because this always takes place by sensation at one 'instant', and not by the successive synthesis of many sensations.
In other words, appreciation of 'degrees of intensive quantity' is only made possible by transitions between them. I would prefer to regard the 'transitions' as empirically given in the form of 'continuous' variation, and to treat 'apprehension at an instant' as no more than a useful symbolic fiction. Kant could hardly take this view, since he regarded Newtonian physics, which required 'instants', as true a priori.
I regard variations of intensive quantity as the basis of our empirical experience of temporal succession. Every experienced "event" is characterised by at least one such variation, and often by a compresence of many of them.
I will proceed to illustrate these points by expressing the act of "sitting down" in adverbial language, using the above musical symbols, which I have further modified so that they can provide indications both of the degree and the abruptness of the changes involved.
In ordinary language, the act could be expressed as a quasi-instantaneous transition between two states, thus:- "Sitting down: Seated". The equivalent of this in adverbial language, which expresses everything as modifications of "experiencing", would be "Muscularly downsittingly: Intensely tactually-backsidely".
But this is far too crude an expression of the actual experience. Presumably, expectations of experiencing "tactually-backsidely" preceded the "event", and, presumably, some memory of "downsittingly-muscularly" succeeded it, however briefly. A considerable improvement in the expression of the experience can therefore be achieved by representing it as an actual compresence of the "states", using musical-type expression marks to indicate the variation of the intensities with which we experience them. The result is as follows:-
|
Muscularly - Downsittingly |
|
|
Actuality |
|
|
|
Tactually - Backsidely |
|
|
|
|
Actuality > |
Memory or > decreasing awareness |
Even this is by no means exhaustive. The "down" of "downsittingly" expresses a compresence of relatively unimportant structural changes of "visually", which become suddenly negligible after the 'event', and important intensity-changes in the mode of 'kinæsthetically-vertically', which will correspond roughly with those of 'muscularly'.
By these I refer to the messages from the inner ear, which furnish us with our internal sense of spatial movement, as is demonstrated by the radical loss of directional movement-control when they are interfered with. We have no independent vocabulary for this sense, since children all succeed in correlating its changes with structural changes in the visual field, well before they begin to speak.
It is not possible to do anything like quantitative justice to the intensity-relations between actual sense experience and our expectations and memories of it, but my methods at least allow us to indicate the directional character of their compresent changes.
Memories of such events, like memories of a piece of music, include the whole event sequence, embodying not only the states expressed by the words (cf. the "notes", in music) but also the changes of intensity (cf. the "expression marks"). The "diminuendoing" state is the "earlier", the "crescendoing" one the "later" in our memory-structures.
We have here a reasonably adequate method of symbolising our notions of an "event" in terms of quasi-simultaneous rapid changes of intensity in our experiencing of the adjacent "states" 'preceding' and 'succeeding' it, which we can express verbally; and we do this without making any break in the continuity of our "experiencing". This seems to be an improvement on Whitehead's logical construction of 'events' in terms of a mere overlap of 'states'.
We actually express the whole of this complex structure by the statement "I sat down"; it is not surprising that we prefer the radically abbreviated form for purposes of communication. In any case, adverbial expression cannot be replicated in spoken form, since speech is 'homophonic', a purely linear succession. If, however, we wish to use abbreviations of this kind as 'basic statements' for the construction and testing of scientific hypotheses, it would seem advisable to determine their semantic, or, as Prof. Quine calls it, "stimulus" content, in as much detail as possible; this calls for a 'polyphonic' method of symbolisation.
We have now to examine the "stimulus content" of verbal expressions which include the "time" of an expressed "event", such as, "I sat down at 8.30". Now the words "at 8.30" express the compresence, with the experience analysed above, of experiencing either "conjecturally-verbally '8.30-ly' " or by experiencing 'actually-visually [Here the original manuscript has, instead of our folowing hyphenated expression, a small drawing of a circular clock-face with the fingers in the 8.30 position] both-clock-fingers-so-positioned-as-together-to-amount-to-half-past-eight-ly', or, in the case of the type of clock which changes its indication every minute, and which is preferable for the purpose of the present exposition, "Actually-visually [08-30]-ly". Note that these visual "states" do not have to be symbolised; they can be represented at the intensity level of sensation. The state 'visually [08.30]-ly' is, however, only temporally meaningful when it is conjecturally accompanied by a transition from a preceding 'visually [08.29]-ly', and an expectation of the proximate actualisation of the state 'visually [08.31]-ly'. The actual movement of the hands of a clock is also in jerks, which synchronise with the rhythmic 'events' in the 'movement', but their amplitude is so small that they cannot generally be detected. The movement of the minute-hand is so slow in comparison with the duration of an act of awareness of it, that it can in practice be treated as 'stationary'. For the purposes of more exact time-naming, a subsequent 'state' has to be created by means of a stop-watch.
When we name the date of an event, it is clear that conjectural awareness of a form of words and numerals, which may be 'visually' or 'aurally', must form part of the 'stimulus content'. From the standpoint of current individual experience, the "dating" of "past" events, as well as that of 'future' ones, must be purely conjectural. It is not at all an easy matter to distinguish between 'memory' and 'conjecture-imagination'; there are no grounds for supposing that very young children or animals ever do so, or even make conscious reference to 'past' events.
Our conjectures as to the order in which 'past events' have occurred are only preserved by our use of temporal predication for purposes of communication. We adopt this procedure because we feel intuitively that certain discrete events occur in sequences which are rhythmically invariant, so that their "when" is predictable in terms of a given multiplicity of events which share this property, but occur with greater frequency. The various methods of chronometry represent our methods of either creating event-sequences of this kind, or of counting natural event-sequences which we adjudge to be rhythmically invariant. For this purpose we have devised an indefinitely extensible series of integer-names, arranged in an order which is accepted as invariable by all who make use of it,2 and this makes it possible to order the temporal predicates of events in an agreed sequence. This sequence is unalterable unless we decide to repudiate the accepted order of the integer-names in our numerical language. But we may well decide that in relation to our current methods of temporal predication, a mistake has been made in assigning a temporal predicate to a conjectured 'past event'; for example, there is widespread support for the view that Jesus was born in 3 'B.C.'
2. We should not forget that there are still a few languages which have no predicate but 'many' for expressing multiplicities higher than 'two'.
A 'past event' is how we express an experience, at a conjectural level of intensity, of an abrupt change either of structure or, on occasion, of intensity pure and simple, whenever it embodies an awareness of a 'date-name', not necessarily specified, which is earlier in the conventional series than the 'now' of the utterance. Furthermore, it must be experienced at an intensity-level higher than that of a conjecture for which there is no possibility of actualisation at sensation level, since, if it has "happened", our memory of it is equivalent to a conjecture that the actualisation may occur of another event which does not differ importantly from it in some respects.
When we attempt to attach temporal predicates to events which, in theory, succeed one another with extreme rapidity, we are faced with the problem that any 'states' which may separate them do not endure for long enough to be 'named'.
Planck's quantum equation, e = hn, expresses a quantitative relation between an energy-transfer, a "quantum" of "action", and a frequency, for the latter of which it must be possible to substitute a numerical constant.
Now it is obvious that a certain duration must be required for the observation of a 'constant' frequency, even if this is only inferred, as in the case of electromagnetic vibrations, from observations of a persistent quality.
The physicists have generally supposed that their indivisible 'quantum' is one of change or 'action'. However, since it is clearly impossible to assign a 'frequency' to a single electromagnetic vibration, it appears possible that what is quantitatively indivisible is the minimum duration needed for a photographic plate to register a series of electromagnetic vibrations as rhythmically 'invariant'. If, for the sake of convenience' we take, as an 'indivisible' unit of 'action', the change effected by a single electromagnetic vibration, Planck's equation becomes a near-tautology. It is, however, impossible to attach a temporal predicate to a single vibration, since the shortest symbolisable 'state' is that of the duration needed to establish the invariant rhythm of a succession of them.3
3. This is the temporal counterpart, obviously methodological in origin, of Heisenberg's 'Uncertainty Principle', which asserts the impossibility of simultaneous accurate measurements of position and velocity at this level.
Eddington always emphasised the extent to which physical theory was dependent on methods of measurement; I am here suggesting that quantum theory, in some form or other, is the inevitable consequence of our use of names for states as temporal predicates for events which are compresent with them.
The philosophical difficulties surrounding the concept of 'time' spring from the circumstance that we experience it as a contrast between brief passages of intense change and longer ones of comparative invariance. Experientially, it is the events that matter most, but their temporal description is always in terms of some relatively uneventful interval between two events of an altogether independent sequence which we have judged to be rhythmically 'invariant'. Granted our methods of symbolic communication, this cannot be avoided, since what is expressed by an 'invariant' symbol must itself be assumed to be in some way 'invariant', both for the utterer himself and as between him and his hearers.
Faced with this situation, Parmenides and Zeno, who appear to have shared the quasi-magical view of language implicit in Socratic Idealism, simply denied the reality of "change" and "time". St Augustine, for all the profundity of his thought and his mastery of language, did not go so far, but merely confessed his inability to cope with the situation. Even in our own day and age philosophers, like J.E. McTaggart, have followed Parmenides' example, as those who trust language sufficiently to make it a basis for a 'deductive' metaphysic are almost bound to do.
Bergson was correct in asserting that physical descriptions of time and change were worded in terms of invariances, but he did not, as far as I am aware, trace this anomaly back to its source in language-structure. He valued language for its poetic possibilities, and made full use of them in his own writing. But the poetic use of language curtails the generality of its communicative efficiency, since it fails to communicate with those who have not thought along much the same lines as the poet himself.
Now the purpose of time-naming is cooperation in making provision for the future,4 and in this context, the generality of its communicative efficiency must have priority over its expressiveness. If symbolic technique restricts our description of succession to a 'cinematographic replica' of the original, that is just too bad; it is better than nothing at all! However, it seems worth while to demonstrate just why the technique of verbal and 'formal' symbolic communication precludes the adequate expression of temporal succession, by the simple expedient of showing a way in which a limited improvement can be effected. This in turn serves to demonstrate the impossibility of achieving any expression of "Absolute Truth" in verbal or formally symbolic terms, and should serve as a corrective to the dogmatism and intolerance which often accompany the belief that such an expression has actually been achieved.
4. Apart from the enjoyment obtained by geologists, archæologists and historians from constructing elegant "Gestalte" out of the traces of the past.
- Shalom & Welcome! - 
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