Duration

Introduction – Duration

A complete theory of time T(n) must explain why everything does not happen at once, that is, why there are durations (temporal intervals).

Durations^[1] are the temporal stuff of science and everyday life, the way we relate time to watches, clocks, daily, weekly, annual, and seasonal routines.

Semantic taxonomy

We have already noted the semantic complexity of ‘time’ T(n), and semantic simplicity of ‘duration’ T (ud, rd). Is duration what we ‘really’ mean by time? Intuitively duration is not time itself but a DF temporal interval, or lapse of time.

We speak of duration in general terms as in ‘The match was of long duration’ (as T(ud)) or a particular duration (as T(rd)) as in ‘The match lasted for two hours’. We might ask why time should be anything in addition to duration itself. This may be true but, if so, then we need to deal with a linguistic problem. We do not, ask: “What duration is it?”, “Did he travel backwards in duration?”, “Duration went quickly today?”, “Did dinosaurs live at some duration in the past?”. This is not just a matter of a difference in the conventional usage of words but a real difference in meaning between the words ‘duration’ and ‘time’, the former being much more restrictive. However, we can bear in mind that language could be treating time metaphorically and erroneously as an object so that an interval cannot serve the same role in a sentence.

The fact that duration carries less semantic baggage makes it a more straightforward concept to manage.

Why does time have duration?

But the notion of duration intergrades with the ideas of permanence and change. Nevertheless, in this context the succession series do not appear to be of primary importance, so the analysis of duration cannot be totally reduced to a consideration of McTaggart’s A Series and B Series.

At issue here is the reality of now, past, present and future, whether some or all of these are subjective or objective, together with the nature of temporal flow and accretion.

In PART 1 duration was defined in two senses in accordance with its primary lexical definitions as either DF a temporal interval of restricted durationT(rd) or simply DF continued existence as unrestricted duration T(ud). T(ud) is unbounded and T(rd) is a bounded period of time. Both semantic categories are semantically simple: indeed, it is extremely difficult to define the notion of duration without circularity.
Of these two temporal categories T(rd) is employed both philosophically and in everyday language much more frequently than T(ud).

T(rd) is of two kinds: firstly, those intervals that last for a fixed period e.g. one hour, or one breath (the unit does not matter) – these we can call fixed intervals T(rd, fi) and secondly, those intervals that increase or decrease, as when the interval from now to the arrival of a plane decreases or the interval from now to the Big Bang increases – these we can call flexible intervals T(rd, fl)

Fixed intervals (rd, fi)
For a fixed interval there is nothing undergoing change: ‘now’ is irrelevant and therefore T(c) is not involved. A fixed interval or ‘block’ of time, say 20 minutes, entails an earlier than and later than relation, a beginning and an end that are in permanent relations. Thus the duration lasts 20 minutes, the start being at t1 (which is before t2) and ending at t2 (which is after t1). However, in the current context it is the duration that is paramount not its boundaries (t1 and t2), or their temporal relations (t1 earlier than t2, t2 later than t1).

Flexible intervals T (rd, fl)
In the case of the flexible interval, ‘now’ defines either the beginning or end of the interval and so we are dealing with T(c), the time of change, and therefore a changing interval. This is true even though we might be referring to a ‘now’ in the past, as when we ran to catch a train with the time to its departure getting ‘closer’.

Fixed interval = T(rd) <> T(p)= T(rd, fi, p)
Flexible interval = T(rd) <> T(c) = T(rd, fl, c)

The distinction between duration and succession
It is now clear that the notion of duration although linked to the idea of temporal succession and the semantic categories of permanence T(p)] and change T(c) also has its own semantic emphasis. The concept of duration T(rd,ud) is semantically closely linked to the idea of succession as T(p,c) through the temporal relations earlier than, simultaneous with and later than, the temporal relations focused on the present T(c), and one-another in T(p).

It is tempting to assume that fixed and flexible intervals immediately reduce to durations within the A and B-time-scales and series of T(p) and T(c) respectively. However, in succession series (McTaggart’s A and B series) the emphasis or focus of meaning is on the temporal relations of events or times either to each other or to the present (now). Duration series T(rd, ud) focus on the amount of time: it is, so-to-speak, about quantities, not relations.
So the idea of duration, especially T(ud), maintains some semantic independence from the semantics of succession. T(c) is intimately bound up with change, passage, and flow while duration is more closely allied semantically with the more stable idea of the interval (duration). This tension is demonstrated when we place duration in the semantic arena of T(c) by asking ‘Does duration flow?’. ‘My breakfast is 3 hours before my lunch’. ‘The Battle of Waterloo was many years after the Battle of Hastings’. These B-time intervals (the latter also tensed) are not so clearly different (examine).

Measured time
Using a stop-watch we can measure time as it lapses in the present. We could measure, say, 11 seconds as an athlete runs 100 metres. As the athlete was running, the measurement was being made in the present. That present later became past, but the reading on the stop-watch indicated the time that had lapsed during the race. In that way at any time in the future (at that present) it would be possible to know once again how long it took to run the race. There is nothing complicated or mysterious about this. The time was measured in the present (the only way it could be measured) objectively. The event then ‘receded’ into the past but a record of it could be recalled for the present ‘now’ and at any future ‘now’. There is no need to postulate that time is in the mind. We can now describe measuring time in terms of past, present and future.

When we are recording the duration of an event we are measuring a duration in the present T(rd,fl,c) so that in the future (when the event is past) we shall know (at that ‘now’) how long the event lasted (in the past) T(rd,fi,p)]. While we are actually recording the race we are measuring a flexible, changing, open-ended duration T(rd, fl, c). When the measurement has been made we are left with a fixed, permanent, closed duration T(rd,fi,p).

Consciousness, past, present, future and duration
A fixed duration T(rd,fi), say 20 minutes, cannot exist instantaneously, because then it would not be 20 minutes. But we can think of 20 minutes all at once in our mind’s clock: in fact we can easily think of 20 minutes in less than a second. We estimate, for example, that it takes 20 minutes to walk to the train, 20 minutes to eat breakfast, and so on. Clearly the thought of 20 minutes is subjective (it is interesting to reflect on the way we think of durations: they are like thought-feelings, a kind of test-run of an actual interval based on previous experience). The thought of 20 minutes is subjective because it occurs only in the mind, I am imagining what that 20 minutes would be like when it actually occurred.

So is there such a thing as objective time, and if so, can we explain it?

I shall leave the justification of objective time until later. But for the time being state dogmatically that objective time is the ever-lapsing ‘now’, the boundary between determinacy and indeterminacy: this is time itself T(*).

It is tempting to assume that the actual completed physical acts of walking to the station and eating breakfast entail objective fixed intervals of 20 minutes. After all, we have measured them using machines (clocks) in a publicly conventional and accepted manner. However, there is an important difference between the actual lapse of time and its representation as an interval.
The actual 20 minutes walking to the station is objective because it involves the real transition of measured time.*****

The actual 20 minutes is objective because it involved a real duration of 20 minutes (see also objectivity of duration), just as the actual running of the race took 11 seconds. It is the time taken when we are actually walking, eating and timing races that is objective. Times in the future and past are not actual. We cannot be in the past or future. All time that is not presently lapsing is a form of memory or anticipation or a form of representation: for simplicity we shall refer to all temporal references that do not involve the lapse of time in the present as representations.

Since we only experience a brief present moment, anything lasting longer than a snatch of time must have past. We are therefore driven to the perhaps startling conclusion that durations (temporal intervals) are subjective representations without reality in the external world.

(But how long is the present? Is there a now that is part of the universe or is this experiential, our consciousness at work, how do we age if there is no duration, why do we have a notion of duration, do we need it?)
This difference seems quite obvious when described in this way. However, we are constantly confusing subjective and objective intervals.

We cannot measure flexible temporal intervals present [time (rd,fl, c)] like spatial intervals because the beginning and end of these durations cannot co-exist: that is, they do not occur at the same time. We cannot experience the start and finish together. Hence duration. In contrast we can experience the beginning and end of a spatial interval at the same time, and we can experience the beginning and end of a fixed interval at the same time because it is a representation – it is not time itself. The time on a clock is, perhaps, analagous to the reading on a thermometer: it is a representation of time not time itself. In the sense that it is a publicly and scientifically accepted (conventional) representation then it is an objective measurement, but it is not time itself.
[If events in the future and past do not exist then what reference point do we have for the measurement of “movement”?

OBJECTIVITY OF DURATION
Modern physics uses measured temporal intervals as a cornerstone of its explanation of space-time and therefore the universe. Time (n) is said to be woven into the objective fabric of the universe as space-time. Our work lives are subjugated to what can be achieved in a particular time interval and our public lives are synchronized around publicly accepted, i.e. conventional, temporal intervals

Aging
Objective duration, time (ud), is manifest through the aging of all the material things of the universe including, of course, biological organisms. Measured time of clocks is objective time whether we regard it as time taken (duration) and absolute or simply the movement of the hands of a clock. The difficulty in asserting that time is just a relation is that duration is marked, not just by the relations of hands to clocks and other temporal measuring methods, but to the physical aging process of animate and inanimate matter. With the lapse of 10 minutes we are all 10 minutes physically older as are the rocks and every other material thing around us. Thus, even in physics text books that indicate a relationalist view of time (*), definitions of time are spoken of not relationally but as time taken i.e. a time that is independent of the measuring device.
Duration on these terms is an objective reality – it is part of the universe itself, not something mental, unique to sentient beings.
If duration is part of the physical universe then it should be amenable to scientific explanation. There is the debate as to whether time is, indeed, anything other than a relationship between things (see Chapter 2). There is, at present, no satisfactory physical explanation of duration. Indeed, this may be seen as good grounds for doubting its true existence. In space, duration is the interval taken by light to pass from a source to an observer. But how do we explain what that interval is? And how do we explain the intervals between events on Earth? What form would a satisfying explanation of duration take?

Absolute or relational duration
When we say the time is 9-05 am is there a moment in time that exists independently of the events that occur then?

We may say that the duration of one day is a relation, in the first instance, between the Sun and one rotation of the Earth. Or perhaps we could describe it as 2 rotations of the hour hand on a clock. Either way it surely cannot be argued that 24 hours is just one rotation of the Earth in relation to he Sun, or the rotation of hands on the clock dial. In general we use the language of absolute time to say that 24 hours is “a period of time” which we cannot describe except that we certainly feel it. It is, we could say, the temporal interval between one sunrise and another, or “time taken” for 2 rotations of the minute hand. Using this language we are suggesting that the temporal interval is something over and above a relationship. The hands have measured out something real, even though we cannot see it, taste it or touch it. We do feel it. We know roughly what one minute and one day feels like. But then these feelings might be deceiving us as may the language about time be falsely suggesting absolute time. Neither may correspond to anything real in the objective world. At present there is no decision procedure for this dilemma. Physics cannot resolve this dilemma except to suggest that absolute time is an unnecessary hypothesis.
Either you believe this or you do not. If you believe it then the time of duration is absolute, something independent of the relationship. If not then time (restricted duration) is relational.
If we are quiet with our eyes closed and all we can hear is the ticking of a clock we feel that time is lapsing. If the clock suddenly stops then we still feel time is lapsing. Of course, this might be simply our consciousness and nothing to do with time itself. But then why should we doubt our senses? It is a strong sense. If we feel the temperature rising, do we suddenly doubt ourselves and ask could this be something subjective, something that happens in our imaginations?

CONSCIOUSNESS AND TIME
Is it possible to differentiate the objective and subjective aspects of time through an analysis of temporal intervals? To do this would relieve considerable philosophical frustration confronting scientists and philosophers alike.

Consciousness and fixed intervals
A fixed interval, say 20 minutes, cannot exist all at once, because then it would not be 20 minutes. But we can think of 20 minutes in our mind’s clock: in fact we can easily think of 20 minutes in less than a second. We estimate, for example, that it takes 20 minutes to walk to the train, 20 minutes to eat breakfast, and so on. Clearly the thought of 20 minutes is subjective (it is interesting to reflect on the way we think of time in its various forms, generally it is like a thought-feeling, a kind of test-run of an actual interval). Of course the actual completed physical acts of walking to the station and eating breakfast entail an objective fixed interval of 20 minutes. The thought of 20 minutes is subjective because it occurs only in the mind, I am imagining what that 20 minutes would be like when experienced in the external world. The actual 20 minutes is objective because it involved a real duration of 20 minutes (see also objectivity of duration).
This difference seems quite obvious when pointed out like this. However, we are constantly confusing subjective and objective intervals.At this stage it is important to simply acknowledge that there really are such things as subjective and objective temporal intervals.
When I say “My birthday is 5 days away”; this is true in the sense that 5 days worth of time must elapse in the present before my birthday occurs. It cant be in the future because the future does not indeed exist, and indeed nothing in the future exists. All the future means is – “has not happened yet”.We say, let us suppose, that light takes 6 minutes to reach us from the Sun. And we say that this is an objective and proven fact of physics.

Consciousness and flexible intervals
We experience everything in the present (an extended treatment of presentism is given in Chapter ). Memories and anticipations do not take us literally into the future or back into the past. Everything ages in the present. Things that are old have aged in the present for a ??large interval.

We know what the “passing” of one day feels like and so, just as we can imagine 20 minutes all at once, so we can imagine (in the present) a birthday five days away approaching, getting closer each day. That is, we know what it is like for 5 days to elapse in the present. The anticipation (imagination) of this interval of time is subjective in the way that our imagination of 20 minutes was subjective. There is clearly no birthday literally approaching from the future. We are anticipating or mentally projecting into the future using our imagination based on previous experience.

In just the same way that we feel (in the present) the birthday “approaching from the future”, we also feel it (in the present) “receding into the past – slipping further away each day”. Again, the birthday is not literally moving away from the present. This too is subjective exactly as before. There is therefore a subjective symmetry of feeling about “approaching” events and “receding” events.

We are now therefore tempted to say that the impressions we have of the past and future are purely subjective which, if we believe what has just been said, must be true. But this is not the whole truth.

As we have also seen, durations are also objective. Things age in the present as time elapses in the present. Duration has a physical effect on us. But duration does not extend into the past. The subjective “receding” of time into the past occurs at the same time as the real elapse of objective time in the present. The duration between now and some event in the past is both mental and physical: it exists both in my mind and in reality.
There are several important assertions here:

• the past can be subjective, or objective, or both ,and we need to distinguish which it is that we are concerned with in any discussion. For example, when we are talking of receding birthdays, although the language is colourful, what we are discussing may be objective (as an objective duration) or subjective (to do with a mental projection), or both, depending on the context
• subjective approaching and receding intervals give a feeling of symmetry to the past and future
• the past also has objective intervals of various amounts of lapsed time while the future has no such intervals; therefore there is an objective asymmetry between past and future. The subjective symmetry and objective asymmetry lead to much confusion over past, present and future and their tenses
• time elapses steadily in the present (now), not in the past or future
• ***physical objects, including ourselves, persist. However, the now simply defines the moment of determinacy/indeterinacy. So my mind has, as it were, adapted to the lapse of time.
So, how are we to interpret the sentence
“My birthday is 5 days away and getting closer every day”
After all, my birthday is getting closer all the time. I can even draw a line and show how that gets “shorter and shorter” as time “goes by”. We feel that if we were to use different words to describe this situation it could not alter the fact that things get closer in time and further away in time.
Firstly, we must distinguish between the lapse of time and the particular event that is “approaching” or “receding”.
All that is happening objectively is that time is elapsing in the present. Events happen in the present – they cannot “move”. Our minds add all the complication to this situation.
The problem is simply the spatialisation of time. Nothing is “approaching” or “receding”, all we have is the lapse of time in the present. We can (in the present) mentally imagine, or even mathematically calculate the temporal interval (time (rd)) that must occur before something can occur in the present. Similarly for the interval that has elapsed since something happened in the present. Note that this is a temporal interval – it is not a spatial one.
We cannot resist saying that that interval gets “shorter” or “longer”, it is a “distance” that becomes “nearer” and “closer” or “further away” and “more distant” and so on. All of these spatial words are so entrenched in usage that we think of time lapse spatially and therefore things (events) must “move”, and temporal “movement” feels like spatial movement. But time lapse does not have spatial extension.
Since events do not literally “move” then the feeling of temporal “movement” must come from time lapse itself.
As a clock ticks we say time is “passing”, and after a while we say time has “gone by”. This is similar to saying the temperature has gone “up” – obviously temperature does not literally go “up” – it is the mercury in the thermometer that goes up. Similarly time is not literally “passing” or “going by”, these words simply convey the impression of something that is definitely going on, some kind of activity, but something extremely difficult to describe. Or, at least, something that we almost always describe using inappropriate space words.
[We are concerned here specifically with time (now) which is the physical lapse of time uncomplicated with the notions of past, present and future ???it is temporal “movement” uncontaminated by the notions of change or succession – it is time itself which we experience as now.]“When a duration of 5 days has occurred my birthday will happen”
“After a period of 5 days it will be my birthday” [this is absolute interpretation – there MUST be a period of time, not a succession of events. EXPLORE]

We need a remedy for this misrepresentation. One obvious solution is to use non-spatial words. Words like duration, period and lapse will help; words like interval are fairly neutral but still have slight spatial connotations.
Metaphor is an aspect of our language that gives it colour, excitement and interest. The important question here is whether there are any serious consequences in taking the metaphors of time literally.

The lapse of time in the present affects equally the “decreasing” duration needed for something to happen in the present and the “increasing” duration of something that happened (in the past!!!!). Language???

It would now be a simple matter to say that there is no passage of time, that time does not literally move and all such talk is an illusion. It should be remembered, however, that the “passage of time” refers not to something that is an invention of the human mind.
Whatever time (now) does is real and objective. There is temporal “movement” it is simply that “movement” is not a good choice of word.
If the question is “does time literally move”, then the answer is “No, temporal passage is a myth”. If the question is “is there something objective we call time, for which we have an inadequate vocabulary to describe what it does, but which gives us the sensation of movement?” then the answer is “Yes” there is temporal passage.

If forced to take a position I would say that I believe in temporal passage.
[How DO we think of time when we do not think of it spatially?
When we use spatial words we are nevertheless thinking of them and treating them as temporal]

Temporal accretion, extension, length, distance and movement
We think of time’s “passing” as similar to putting beads on a necklace or adding numbers to a series. It is compared to a pencil drawing a line, where the emergence of the line at the pencil point is akin to the now and the drawn line similar to a fixed past. Thus the pencil line of the universe and our lives is continuously extending. We are tempted to say that now is accumulating or accreting more time (as moments or events) at the front of the line as it “flows” in the direction of the future.
Alternatively an Absolutist might consider a temporal item, say a moment, starting at the beginning of a day and moving through it much as a train travels through the countryside (except there are no stations). Whilst a Relationalist could imagine a number of events forming an increasing temporal series. As the day progresses the temporal series gets larger, pushing us along with it so-to-speak as there are more and more events.
The lapse of time is real and objective. But time is not space.

Because we cannot express clearly what the now does, that is, whate the alapse of time is like, and because space is, in many ways, similar to time, we therefore use the words of space and mathematics (length, number, movement) thereby spatializing time. We use the language of metaphor and analogy to describe time, and then take this language literally. We not only speak of it in spatial terms but we also think of it that way. It seems that our brains cannot grasp time as time, only time as space.

Objective time does not extend, accrete or lengthen; it does not accumulate events or things of any kind, or in any way. All of these metaphors are creations of our imagination in the attempt to explain now and elapsed time. We speak and think of a “length” of time because that is our habit and often the way we visualize temporal intervals. But time does not have “length” or number (which invites all the criticism that can be levelled at the attribution of time with cardinality), it simply elapses in the now. Objective time does not push us further away from the Big Bang and there is no accretion at the “edge” or “front” that we call now. The feeling that now moves, and that the movement is akin to that of a river or stream is obviously genuine. But movement is essentially a word applied to objects in space, not in time. Temporal “movement” is different from movement in space (see Chapter ).

Of course we can represent time spatially, as a line, for example, but the time itself is not a line; it does not extend in space.

Consequences of spatializing time
Even if this case is accepted it might be asserted that spatialization of time is a trivial misdemeanour. We say the temperature goes “up”, presumably because mercury, which measures temperature, expands upwards in a thermometer. Temperature does not literally go upwards. Mercury is not temperature, but a measure of temperature. Similarly clocks are not time but a measure of time. Treating time as space in a literal way can lead to scientific error. Direction is a spatial term (is it?). To say that time has direction is to make a category mistake. To imagine when we represent time graphically that we a representing time as it is – is an error.
We seem biologically incapable – that is our minds are not structured – to deal with time in a rational way. We do not understand time so clearly as we understand space.

Consciousness/ past, present future/ events
The past is evident to us through material objects that are aging in the present [time(ud)]. We can, for example, hold the bones of a dinosaur that lived are over 60 million years ago. Those bones will, of course, still be aging in the present. However, we cannot know how that dinosaur died except from what we can deduce from the physical remains. The actual event of the dinosaur’s death, the relations of all the objects at the time of its death and how they changed, occurred in the dinosaur’s present and this cannot be literally revealed to us (unless someone shot a film).

Events have physical reality only as they happen. As my birthday recedes (subjectively) into the past I can remember (in the present) the giving of presents and the people singing “Happy Birthday to you”. But these events have no physical correspondents, they are memories and therefore subjective. However, the people at my birthday might exist now as also might the bottle of wine I was given as a present – but the event does not. An event is simply particular relations of objects. An object is a very dull event?
The significance of this is that, as we have noted, the past for us is both objective and subjective. Because there is physical evidence of the past that is real now we are, by association, inclined to think that the events of the past are also real now; but they exist only in our imaginations.

Duration and objects
Events, then do not age, it is physical objects that age. Temporal relations directly relate events, thewy do not relate things? Continuants endure.

CONTINUED EXISTENCE
We sense time (unrestricted duration) every moment of our lives. Our cycle from birth to death bears simple and blunt testament to its existence, as does the evolving universe and the fact that we can decipher its history. Everything that is actual is aging – it exists in time (ud) or persists.

Time (ud) is attributed great significance in poetry, and literature in general, as a great leveler of humanity. In time (unrestricted duration) we are born, flourish, decay and die. Everything that exists, exists and ages in time (ud) which is continual directional change. The sense of movement and direction we get from time has been referred to philosophically as pure becoming. The incessant “flow” of time is an important part of becoming but it is not all of it. It is called pure because any other kind of change presupposes this kind of change – everything ages because everything is in time (ud). Time (ud) is clearly objective for the reasons stated already and the fact that we can decipher its history. The aging of organisms and rocks is a simple objective fact.

We can treat continued existence which does not necessarily presuppose events (Absolute Time). A measured duration is the relation between objects or events (Relational Time). Time (ud) can therefore be used to denote either Absolute or Relational time.

We often, in frustration, append “in time” onto sentences to give the sense of time (ud) although everything in the universe is “in time” so it is interesting to try and see what purpose this device serves.

****We may not know what it is or why it is, but we do know that it is. Duration is real. Temporal intervals are different from spatial intervals but because it is similar in many ways we use similar language to explain it. For this reason we speak metaphorically of the passage or movement of time when we refer to the process of accretion that occurs in the now. That is, movement in time is qualitatively different from movement in space.

SUMMARY
It now becomes clear that there are two major issues to address in the philosophy of time. Firstly, what is the true nature of objective, physical time [time (*)]? Secondly, how do all the semantic categories of the semantic taxonomy relate to time * and each other.

It has become clear in the preceding discussion that true physical time is the now of existence. Now has been aptly described as the knife-edge between the determinacy of the past and the indeterminacy of the future. Physical time elapses (“passes”) in the present only but it does not move (see Flow of time later). In talking about time, which is different from space, we use the same words and thinking that we use for space. Our perceptions of the past and future are in some ways subjective and some ways objective. However, as objective physical time elapses (the time we measure with watches), we age, as does every material thing in the universe. This is the objective result of time (ud).

We now need to distinguish more temporal categories: the subjective temporal intervals of the past and the objective temporal intervals of the past. How does the now relate to duration?
We are closest to the movement of time when we actually measure it (duration). That is movement (causal attainment?).

Philosophically the important point is that we are measuring the objective temporal motion of the now. This is public time that is in the objective world. As the man took 10 seconds to run the race he also aged by 10 seconds.
Our temporal concepts are constructed from (defined as) temporal relations i.e. earlier than, simultaneous with, and later than.
One major task of philosophy is to determine which tasks are truly in the domain of philosophy and which tasks lie in the domain of science. Objective phenomena should be amenable to the treatment of observation ad experiment and are not the business of philosophy although philosophy can, of course, assist in the clarification of the concepts. So far we may tentatively draw the following conclusions:

SEMANTIC CATEGORY CODE EMPIRICAL STATUS R A
Time (restricted duration) = (rd,c) subjective and objective
Time (restricted duration) = (rd, p) subjective and objective 
Time (unrestricted duration) = (ud) objective 
Time (change) = (c) subjective and objective 
Time (permanence) = (p) subjective and objective? 

Time (absolute) = (a) unknown
Time (relational) = (r) unknown

Time (a) and time (r) are subsets of the above.
Can be relational and/or absolute???
Chapters 4-7 will look more closely at resolving these issues.
[difference ppf, now & duration][there is an amount/interval of lapsed time – not a length]

Duration, persistence, endurance, perdurance
Persistence is analogous to temporal extension.
In a 4-D world we can understand the passage of time as the accretion of fresh slices of reality. This gives us a distinctive before and after sense.

Duration and McTaggart
McTaggart’s A and B series are treated by philosophers as central to the problems of time. Do they encompass duration.
Firstly both are relational but only in the sense that they locate time either to now (A series) or to one-another B-series. Do they deal with intervals? Do statements like:”I will do that tomorrow (next year, in a minute)” and “I will do my homework before I watch television” encompass flexible and fixed intervals? The McTaggart succession series locate events in time in an essentially relational (not vs absolute sense) way. Earlier than and later than do not account for duration. More examples of statements.

Definitions of time

Plato – ‘The moving image of eternity’
Aristotle – ‘The number of movement in respect of ‘before’ and ‘after’
Immanuel Kant – ‘Transcendental … a pure form of sensible intuition … the form of inner sense … not an object . i.e. the dimension in which our own experiences are ordered’
John Locke – ‘Duration set out by measures’
Whitrow – ‘An aspect of the relationship between an observer and the universe: it co-exists with the universe’ Author of the book ‘What is Time’, 1972
John Smart –‘The dimension of change’ (Australian philos’er, quoted Encyclopaedia Brittanica)
Albert Einstein – ‘Past, present, and future exist simultaneously’ and in discussing Minkowski’s Space World interpretation of Relativity: ‘Since there exists in this four dimensional structure [space-time] no longer any sections which represent “now” objectively, the concepts of happening and becoming are indeed not completely suspended, but yet complicated. It appears therefore more natural to think of physical reality as a four dimensional existence, instead of, as hitherto, the evolution of a three dimensional existence’(Relativity, 1952)
David Mellor –‘The dimension of causation’ (Cambridge University Philosopher of Time)