1. Introduction

The late Warren Meck made many important contributions to the study of time perception in both animals and humans, for example experimental work on and modelling of the possible neural basis of time perception, experimental studies of animal and human timing, including work on ageing, and the development, along with John Gibbon and Russell Church, of scalar expectancy theory (SET), one of the most influential approaches to time perception in the last 40 or so years. The present article focusses on some of Warren’s early articles about a subject which was central to his early publication career, temporal reference memory.

In the 1980s temporal reference memory was the main topic of Warren Meck’s research, although not the only one. The key publication was the monumental article of Meck (1983), and we will take this as our starting point, but also look forwards to later work by Meck and others and, perhaps more importantly, backwards to try to uncover the intellectual roots of his early ideas about reference memory, which were in some ways different from the way that temporal reference memory was treated later in SET, and also later by Meck himself.

2. Clock and Memory Processes

The most frequently quoted examples of the difference between clock and memory patterns (e.g., see Meck, 1996) are that drugs affecting the dopaminergic system affect the clock, whereas those affecting the cholinergic system affect memory (e.g., Meck, 1996, fig. 5, p. 237). On only the second printed page of his 1983 article, Meck introduces a concept which was central to his early conceptions of temporal reference memory, and which we will discuss in some detail here, that of memory storage speed. He characterises drugs producing the clock pattern as manipulations of clock speed, which seems intuitively reasonable given the proposed operation of the pacemaker–accumulator clock in SET, but where does the idea of ‘memory storage speed’ actually come from?

The clearest account of Meck’s early ideas about memory storage speed is provided not in the text reporting the well-known manipulations of the acetylcholine system, by administration of physostigmine or atropine (Experiment 4 in the 1983 article), but in the much less frequently discussed Experiment 3, which used oxytocin and vasopressin. On p. 184 of the 1983 article, Meck discusses the apparently opposing effects of vasopressin and oxytocin on the process of memory consolidation, with vasopressin previously reported to speed up memory consolidation and oxytocin to slow it down.

The topic of memory consolidation, rarely linked to SET or indeed any aspect of timing after Meck’s 1983 paper, seems central to his ideas about memory storage speed. The idea that a memory needed some time to become ‘consolidated’ stemmed from classic experiments in the 1960s (see McGaugh, 1966, for a review). In a typical study, an animal would be exposed to a task which led to very rapid behavioural acquisition, often in one trial, such as ‘step-down avoidance’ where a rat was shocked if it stepped down from a platform onto a grid floor. Some time after the learning experience, a manipulation which affects neural processes, like electroconvulsive shock (ECS), was administered. The normal result was that the shorter the time between the learning trial and the ECS administration, the poorer the memory of the avoidance trial when it was later tested (see McGaugh, 1966, fig. 1, p. 1352). After some long delay, the ECS had no apparent effect on memory. This sort of result led many to suggest that the memory of the trial experience was initially present in some labile form, but with the passage of time, during which a process of consolidation took place, it became encoded more permanently.

Many ideas were put forward as to the neural basis of memory consolidation, such as the notion of memory initially being in the form of ‘reverberatory processes’ (John, 1967), thus susceptible to disruption of neural activity produced by ECS, later to be consolidated as synaptic changes, which were resistant to ECS.

In discussing Meck’s early ideas, some care over terminology is needed. In the 1983 article, there were two main constants used in modelling, representing clock and memory effects, respectively. One is clock speed, denoted by K, the other is the memory constant, or memory storage speed, denoted by Y. Confusion can arise because the symbol K came later to refer to reference memory, but in the 1983 article it represented clock speed.

Where did the idea that longer times would take longer to store in memory come from? The Thatcher and John (1977) reference that Meck cites above may provide a partial answer. They present (p. 174ff.) a ‘neural loop model’ of time representation which argues that ‘the basic functional element of time estimation is a loop. The larger the loop or the greater the delay between elements of the loop, the longer the interval of time’ (p. 175). This model clearly implies that more neural activity, which presumably takes longer to occur, is involved in the storage of longer intervals of time compared with shorter ones, which is consistent with Meck’s idea of ‘storage time’ in the above quote. However, Meck also proposed that drugs which speed up the consolidation process make remembered durations shorter, those which slow down consolidation make them longer. This appears to be Meck’s own contribution, and was not justified further in the 1983 article, nor in any of his later ones in which memory storage speed was mentioned.

So, within this early conception of how temporal memory might be changed, drugs which produce memory patterns do so by changing the speed at which temporal memories are consolidated. In the result from the often-cited Experiment 4 of Meck (1983) the acetylcholine agonist physostigmine increases memory storage speed, thus durations are remembered as shorter, whereas the acetylcholine antagonist, atropine, has the opposite effect. In his modelling (1983, p. 197) Meck assumed a 10% increase or decrease in memory storage speed, and thus the remembered time of reinforcement, respectively, for the drugs, compared with saline. The results from the study (his Experiment 3) with vasopressin and oxytocin were also clear, both increased memory storage speed, but here interpretation was more problematic, as previous evidence suggested that these two drugs had the opposite effects on memory, not the same one. This difficulty may explain why the acetylcholine manipulations have become the ones usually quoted when discussing the manipulation of temporal reference memory in the context of SET (e.g., Meck, 1996). It should be noted, however, that neuropeptides like oxytocin have more recently been found to have complex interactions with both the dopaminergic and cholinergic systems of the brain (Quintana et al., 2019), so perhaps their effects on memory for time result from this rather than memory consolidation per se.

3. ‘Memory Storage Speed’: Some Tests and Implications

The term ‘memory storage speed’ was de-emphasised in Meck’s later publications on temporal reference memory, at least those with Russell Church as a co-author. In general, in Meck et al. (1986), Meck and Church (1987a) and Meck and Church (1987b), the memory storage speed parameter was replaced by a ‘memory storage constant’ or ‘translation constant’ (now denoted as K*), without the implication of effects on memory consolidation. In this later formulation, one manipulation simply makes all times remembered as shorter than they really are, and another manipulation makes them longer, without further explanation. Although in some ways vaguer than Meck’s original formulation, using a simple translation constant like K* enables modelling of data, without some of the difficulties that might arise with the memory storage speed idea, discussed later. However, the idea that drugs affecting the cholinergic system might change the speed of memory consolidation is briefly mentioned on p. 462 of Meck and Church (1987a), and the idea of memory storage speed occurs on pages 466 and 473 of Meck and Church (1987b) as well as being implicit in the title of the latter article. It also resurfaced in Meck and Angell (1992). This study used pyrithiamine, which decreases acetylcholine levels. Administration of this drug caused the peak response times in a peak procedure task to increase by 14%. Meck and Angell (p. 44) attributed this effect to ‘An increase in the memory constant (K*) which may be attributed to a decrease in the memory storage speed …’ Memory storage speed is also mentioned in the later review of neuropharmacological effects on timing in Meck (1996), so obviously persisted in Meck’s own thinking for some years.

In spite of differences in terminology, and differences in the symbols associated with modelling parameters, the articles by Meck and Church (1987a, b) broadly confirmed the effects of manipulations of the acetylcholine system reported in Meck (1983). In the first of these articles, a peak procedure task was used with drugs which increased or decreased acetylcholine levels. Peak response rates shifted to times above or below the actual time of reinforcement in a similar manner to that reported with bisection in Meck (1983). A similar result was reported in Meck and Church (1987b) using pre-feeding of nutrients which were intended to change neurotransmitter levels.

The idea of memory storage speed is also absent from the classic exposition of SET by Gibbon et al. (1984), where ‘memory distortion’ is accounted for by a ‘translation constant K*’ (p. 62), and the same position is taken in another frequently cited article discussing the original ideas of SET, that of Church (1984). In this conception, a K* value greater than 1.0 results in durations being remembered as longer than they really are, whereas a K* value less than one results in underestimation of time. With the later terminology, K* = 1/Y, where Y was memory storage speed in Meck (1983). Gibbon et al. (1984, pp. 60–61) also mention the possibility that K* is a source of scalar variance, in that the contents of the accumulator or working memory might be multiplied by K* (which would be represented as a random variable) to produce variability in memory representations even if the interval timed was constant.

There are various reasons why the idea of memory storage speed, with its link to memory consolidation, might be thought to be problematic, so Meck may have had good reason to abandon it. For one thing, the methodology of the experiments conducted on temporal regulation in animals, with techniques like bisection (Meck, 1983) or the peak procedure (Meck and Church, 1987a), is quite different from the rapid-learning paradigms used in memory consolidation research. If a drug or some other manipulation improves or worsens animal learning on some task it is hard to say whether the effect involved memory consolidation or something else. To investigate memory consolidation per se, the manipulation needs to be applied (a) after learning is complete and (b) before testing. Single-trial passive avoidance was ideal for this purpose, but bisection and the peak procedure involve many trials in both their learning and testing phases, so drug effects like those reported in Meck (1983), even when clear from the interpretational point of view, are not appropriate tests of whether memory consolidation speed has been affected. In addition, an experimental session with animals may take a considerable period of time, so it seems likely that some consolidation of the learning experiences of the session has started before the session ends.

There appear to be only three studies of memory consolidation of temporal learning, and all three use humans as participants, so their relevance to Meck’s animal studies of the early 1980s is perhaps questionable. All three use a methodology rather similar to that used in the classic studies of memory consolidation reported in McGaugh (1966) in that the potentially interfering manipulation was applied after learning has occurred, but before testing. Rattat and Droit-Volet (2010) used a temporal generalisation task (Wearden, 1992) with a 4-s standard, with student participants. There was no effect on performance of interposing 15-min or 24-h delays before retesting, compared with immediate testing. However, when participants were required to play the game ‘Snakes and Ladders’ during a 15-min retention interval, they subsequently behaved as if they remembered the standard 4-s interval as shorter than it really was.

Cocenas-Silva et al. (2014) again used temporal generalisation with a 4-s standard, but performed some more complex manipulations. Their interfering task was 15 minutes of backward digit recall. One set of manipulations involved the time of testing. Different groups either received the digit span interference task 30 minutes after initial learning, or no interference, and these groups were further split into those receiving testing after 45 minutes, or after 24 hours. The interference had no effect when people were tested at 45 minutes, but made durations appear longer when the test was administered at 24 hours. In a second set of manipulations, two other experimental groups received the interfering task either immediately after learning or one hour after, and both were tested after 24 hours. Now, there was a gradient of effect with the immediate interference and that administered at 30 minutes (from the previous condition) producing generalisation gradients markedly shifted to the right (i.e., the standard was judged as longer than it really was) compared with the group where interference was introduced an hour after learning.

Derouet et al. (2019) used a similar temporal generalisation procedure, with an interference task applied 30 minutes after learning and testing at 24 hours. Between groups they varied the standard duration over values of 600 ms, 2.5, 4, and 8 s. In all cases, the interference tended to make people behave as if the standard were longer compared with a no-interference group, and variability of performance was also increased by interference.

Taken together, these three studies offer mixed support for Meck’s ideas about memory storage speed. Presumably, an interference task applied after learning must make memory worse, or consolidation slower, rather than the reverse. According to Meck’s ideas, this would make durations seem longer, and in fact this was the result obtained by Cocenas-Bueno et al. (2014) and Derouet et al. (2019), although Rattat and Droit-Volet (2010) obtained the opposite effect, an apparent shortening of remembered duration.

Another potential problem for the idea of memory storage speed in Meck’s formulation derives from the idea that longer times take longer to store than shorter ones (outlined in the quote from Meck, 1983, above). This might be taken to imply that short durations would be relatively underestimated compared with longer ones because of differential storage speeds. In most studies with animals using methods like fixed-interval (FI) schedules, or the peak procedure, there seems little effect of absolute time values on relative under- or overestimation: in most cases, times seem to be represented on average accurately (e.g., peaks close to the time of reinforcement on peak procedure and fixed-interval schedules, e.g., Lejeune and Wearden, 1991). Data from Whitaker et al. (2003) might be used as a more critical test. Here, rats were exposed to mixed-FI schedules, that is, two different FI values, which could differ very markedly (e.g., 30 s and 240 s) were alternated at random, without any external stimulus signalling to the animals which was in force on a particular interval. Response rates versus time during the longer intervals usually showed two peaks close to the two potential times of reinforcement, and data were fitted by adding together two Gaussian curves. The peak of the curve appropriate to the lower time value was allowed to vary until the best fit (which always accounted for at least 96% of variance) was found: the peak for the longer time was fixed at the longer FI value. Inspection of the parameters from the fits (table 1, p. 281) suggests that the lower peak almost always (15 out of 17 instances) slightly overestimated the lower FI value, although it was usually very close to it, rather than underestimated it, as the memory storage speed hypothesis seems to predict.

4. Temporal Reference Memory: Some Later Research

In spite of Meck’s pioneering, and well-known, work, temporal reference memory has remained a somewhat neglected part of the timing system, in terms of both experimental research and theory development. Perhaps the most enduring contribution of Meck’s early work has been the demonstration that processes involving the generation of temporal representations (such as the operation of the proposed internal clock of SET) appear to be separable, both conceptually and physiologically, from processes involved in storing these representations in the long term. Any account of timing which seeks to replace a structure like that of SET must deal with this apparent division of aspects of temporal processing.

How have models other than SET dealt with the issue of temporal reference memory? ‘Behavioural’ theories, such as the Behavioral Theory of Timing (BeT) of Killeen and Fetterman (1988) and the Learning to Time (LeT) model of Machado (1997) do not have memory components of the same type as SET. In BeT, temporally-regulated behaviour occurs as the result of an adventitiously reinforced sequence of adjunctive behaviour, which occurs before the measured operant, and ‘passes the time’ until the measured operant occurs. It is the sequence of adjunctive behaviours which serves as a kind of ‘memory’ of times associated with reinforcement. In a rather similar way, in LeT elapsed time is represented by a sequential series of internal states which rise and fall in activation over time, and which can be associated with reinforced responding. For a simple introduction to both theories, see Wearden (2016), chapter 10. It is unclear whether either of these theories would be able to deal with the ‘memory pattern’ effects, although both BeT and LeT involve ‘timing by learning’ so manipulations that affect learning might have some effect on the adjunctive state sequences or state transitions that these models propose instead of reference memory of the SET type. However, one model that appears to account well for the pharmacological results is Oprisan and Buhusi’s (2011) development of the Matell and Meck (2004) Striatal Beat Frequency (SBF) model.

Matell and Meck’s model simulates learning to respond at critical times, such as those at which responding is reinforced, essentially by tracking coincidences of oscillator firing. So, for example, a time of 30 s will be represented by a certain pattern of coincidences, a time of 60 s by another pattern, not necessarily more or fewer oscillations. If reinforcers are available for responses at these times, the model will learn to produce output at the appropriate times, by a process of synaptic modification. Oprisan and Buhusi (2011) developed a simulation of the Matell and Meck (2004) model using what were claimed to be ‘biophysically realistic’ simulated neural processes. Their model is too complicated to be described in detail here, but Oprisan and Buhusi were particularly interested in simulating the pharmacological effects from Meck (1983), namely the ‘clock’ and ‘memory’ patterns discussed earlier in this article. They were able to successfully simulate both effects to a high degree of precision (see their Figs 2 and 3 for examples). Although the basic model of Matell and Meck (2004) which was the foundation of Oprisan and Buhusi’s work appears very different in principle from SET (for example by not having any process of accumulation), Oprisan and Buhusi simulated the ‘memory pattern’ in a very similar way to SET, by proposing that the real time of reinforcement was multiplied by a factor they called k*, essentially the ‘memory constant’ of SET.

Independent of its link to memory storage speed, the memory constant, K*, has been used to account for deviations from otherwise averagely accurate timing. Gibbon et al. (1984), for example, used the idea of a K* different from 1.0 to transform peak response rates from rats and pigeons for which the peak rate deviated slightly from the time of reinforcement (e.g., see their figs 10 and 11, pp. 62 and 63). This idea was also used by Droit-Volet et al. (2001) who studied temporal generalisation gradients produced by three-, five- and eight-year-old children, and found that the younger children behaved as if they remembered the standard durations used as shorter than they really were. This was modelled by employing a K* value, less than 1.0. However, temporal generalisation in children does not always need this correction, as Droit-Volet (2002) and Droit-Volet and Izaute (2005) modelled gradients from children with K* = 1.0, so the generality of memory distortion in children is perhaps questionable.

As to the operation of temporal reference memory itself, relatively few studies with both animals and humans have been conducted. One finding that has received little attention after its initial demonstrations is that it appears that reference memory can be rapidly overwritten when animals have been extensively trained. Lejeune et al. (1997) trained rats on a peak procedure task, with a baseline time of reinforcement of 20 s. Once this schedule had been learned, and average peak times were close to 20 s, the schedule was abruptly changed, for example, to a 10-s or 30-s time of reinforcement. One striking effect was that adjustment to the new time of reinforcement was very rapid, with behavioural changes occurring in a few trials (e.g., Lejeune et al., 1997, fig. 1, p. 215). Given that the peak procedure is one of the standard procedures associated with SET, and one used frequently to exemplify the operation of the SET system, including K* (see Meck and Church, 1987a), the implication of Lejeune et al.’s result is that reference memory is more labile than sometimes assumed. The rapidity of adjustment to marked changes in the time of reinforcement contrasts with the slowness of adjustment when drugs that affect reference memory are used, as here several experimental sessions, involving dozens or hundreds of experiences of reinforcement are needed. This suggests that reference memory adjusts rapidly to large changes in reinforcement time, but more slowly to the kind of small changes (in the region of 10%) in remembered reinforcement times that occur with drug administration. Models that can behave like this are discussed in some detail in Jones and Wearden (2003).

In addition, there is considerable evidence that animals in Pavlovian conditioning preparations can rapidly develop sensitivity to the interval between the conditioned and unconditioned stimuli (see Balsam et al., 2010, pp. 5–7) and Ohyama and Mauk (2001) even found that this was true before a conditioned response had been elicited.

Another feature of temporal reference memory that has been demonstrated in a number of articles has been its susceptibility to various sorts of interference. We have described above some non-timing tasks which apparently interfere with the formation of temporal reference memory, e.g., Cocenas-Silva et al. (2014), but there are other instances where remembering one time appears to interfere with remembering another one. For example, in the Lejeune et al. (1997) experiments discussed above, it was often found that the peak times exhibited were affected by the immediately previous time of reinforcement as well as the current one, with the previous condition decreasing current peak time if it had a shorter time of reinforcement, or increasing it if it were longer, a proactive interference effect.

Derouet et al. (2021) reported an asymmetry in changes in timing performance in rats, who were initially trained to press one lever after a 4-s tone stimulus, and another one when the tone was either 1 s or 16 s long. Following this, different groups of rats received a ‘shift session’ in which only the lever previously associated with the 4-s stimulus was available, but this time they were reinforced for pressing the lever after either a shorter tone (2.5 s) or a longer one (6.3 s), or received no further training. The rats then received two generalisation sessions where responses were not reinforced after tones of 2, 2.5, 3.2, 5, 6.3, and 8 s, with other conditions being as in their original training. It was found that the response versus stimulus duration functions (the temporal generalisation gradients) were affected only in the group that had received training with a 6.3 s stimulus duration in their shift session, compared with no retraining. This suggests an asymmetric effect on temporal reference memory, where new time values longer than an existing standard have an effect, but values shorter do not.

In the case of research with humans, Jones and Wearden (2004) demonstrated that remembering two standard durations in temporal generalisation increased the variability of temporal representations compared with remembering just one. Grondin (2005) reported a rather similar result. In his experiment, people classified six empty intervals which were marked by either brief auditory or visual signals. Two base durations, 250 ms and 750 ms, were used, and the task was to classify each duration as one of the shortest or longest in the set of intervals. When the base durations were mixed, performance variability increased relative to the condition where only one base duration was presented in each session. In contrast, mixing modalities did not increase variability. Ogden et al. (2008) also found very marked interference effects when people had to perform two successive temporal generalisation tasks with different standard durations, then were required to perform with the initial standard, without it being refreshed. Memory of the first standard seemed in some cases to have been completely overwritten by the second standard, although the participants seemed to remember ordinal information about the standards, such as whether the second was longer or shorter than the first, and performed using this rather than any precise memory of what the first standard actually was.

An interference effect of a slightly different type was reported by Fillippopoulos et al. (2013). Participants received blocks of temporal generalisation trials, where the standard interval was presented at the start of each block, followed by comparison durations. For the next block, another standard was presented followed by its comparisons, and so on. The blocks were interleaved so that, in different conditions, blocks with a standard of on average 400 ms were preceded by blocks with shorter (average 200 ms) or longer (average 600 ms) standards. The behaviour in the blocks with the 400 ms standard, where stimuli were on average always the same, was systematically affected by what the preceding block had been, with generalisation gradients being shifted to the left if the preceding standard had been short, and to the right if it had been long. The effect occurred when all stimuli were in the same modality, whether this was auditory or visual and, perhaps more surprisingly, when the different blocks were in different modalities, even occurring when the interfering blocks were in the visual modality and the 400 ms blocks in the auditory one.

Obviously, all these studies suggest that interference in temporal memory is a commonplace, albeit little studied, effect.

It should be mentioned, however, that in studies with humans the term ‘reference memory’ need not imply any sort of long-term storage. Although some of the experiments with humans that we review above test performance after a 24-hour period, these are rather unusual in testing recall of temporal memory for more than a few minutes after it was laid down. In most other studies the term ‘reference memory’ simply refers to some temporal standard that is used to control performance on a number of trials (e.g., as in temporal generalisation, Wearden, 1992, or temporal bisection, Wearden, 1991) without the implication that this leads to any long-term storage of the relevant time intervals, something the experiments do not test. Tasks involving this sort of reference memory can be contrasted with those in which the stimuli to be judged change on every trial, and for which the formation of ‘references’ in memory seems very unlikely, such as Wearden and Bray (2001).

5. Afterword

Warren Meck’s work on temporal reference memory, which occupied him extensively in the early part of his career, now nearly 40 years ago, seems to us one of the most interesting of his many contributions to the psychology and neuroscience of time perception. Paradoxically, it seems to be both well-known, in that the work involving cholinergic manipulations from his 1983 article is very frequently cited, yet at the same time largely neglected in terms of its influence, in that we know hardly any more about temporal reference memory than what Meck himself discovered in the early 1980s. Almost all timing tasks used with animals, and many used with humans, seem to have some sort of ‘reference’ durations as their basis, for example, bisection, temporal generalisation, FI schedules, and the peak procedure. As this article shows, in spite of this apparent ubiquity of temporal memory, we have only slightly advanced, both in terms of psychology and neuroscience, in our understanding of how such memories are formed, stored, and used to generate observed behaviour. Perhaps a fitting and useful memorial to Warren Meck would be a resurgence of research efforts to find out more.