Week 5

The topic of this week is time and counting.

Chapter 22 reviewed the history of research on timing, where researchers tried to explain timing behaviors though various perspectives. The first few studies, just like many studies from every other topic we have discussed so far, used learning paradigms. (Learning paradigms seem so powerful that they can be applied to the research of any type of behaviors.) The experiments presented here are pretty simple, though. The first study trained dogs to react with different latencies to different intervals between CS and US. The second study trained rats to make responses at different rates. The author explain this study paradigm as a type of social competition, however, if I understand the paradigm correctly, it looks like the results would have been the same whether or not the rats realized they were supposed to be competing — they might simply think their response rate should be high or low in order to to get the food, regardless of the other rat’s behaviors. The next couple of studies again showed that rats were able to discriminate different time latencies after training.

The next section provided a cognitive account for timing through internal clocks. The studies here showed more timing-related abilities animals (mostly rats) were capable of, and certain characteristics of these timing abilities (which I think are similar to humans). For example, quite a few studies (LaBarbara & Church, 1974; Libby & Church, 1974; Church & Deluty, 1977) showed that rats knew, or were able to discriminate, the amount of time passed, and that they estimated time in proportional units. Roberts and Church (1978) added breaks within the stimuli and tested rats’ responses about the duration of the stimuli. They showed that rats were able to correctly “pause” and “resume” their internal clocks and made correct responses (if I understood the study correctly). It was further shown in a lesion study that the fimbria fornix played a role in interval timing (Meck, Church & Olton, 1984). Two studies (Church, Getty & Lerner, 1976; Platt, Kuch & Bitgood) showed that rats’s time estimates were more variable for longer durations. It is interesting that these researchers also found a linear relation between the square of the difference limen and the square of the duration, but in Fig. 22.7, they seemed to have used an extremely limited number of data points (only 5) to make that claim, so I’m a little skeptical about this conclusion (for example, in the top left panel it looks like a straight line could have fit the data just as well as, if not better than, the quadratic line).

The authors discussed a bit about how subjective time varied as a function of physical time, and mentioned that Church and Deluty’s (1977) study seemed to supported that subjective time increases as a logarithm of time. If I recall correctly, however, there are a lot of studies done on human about how the events they experienced change the subjective time, and we may all have the experience that having a lot of exhausting events scheduled in a short amount of time makes us feel the day is long. So in my opinion the subject time is likely more complicated than just a simple function of the actual time — it may also be a function of our experience or memory. Investigating this in animals may be hard, but it would be extremely interesting if it could be possible. Another studies in this chapter (Church, 1980) tried to study subjective time in rats, but I feel like it is hard to reach unambiguous conclusions based on their results… Church’s study (1980) introduced retention intervals (time between stimulus and recall) changed the rats’ response pattern — they actually seemed more likely to respond at random (closer to 50%, i.e., chance, possibility of choosing “long”), so maybe they just forgot what they saw earlier. I’m not sure I understand why the author interpreted the other set of results as “forgetting did not occur on the time dimension”, since it’s also true for those results that the responses were closer to random for a longer retention interval. It seemed unclear to me whether rats actually perceived the stimulus duration differently or they just simply didn’t remember clearly…

The rest of the chapter is devoted quantitative theories for timing. The scalar timing theory wasn’t extensively described, but seemed quite simplified and doesn’t account for many phenomena. The multiple oscillator theory was a bit hard to understand but seemed better supported by data.

Chapter 24 discussed number representation. It first talked about the the ratio dependence of numerical judgements in humans and other animals, that is, the discriminating quantities is more difficult for quantities that have a close-to-1 ratio. The chapter discussed many studies that showed this phenomena in monkeys, rats, and college students. In addition to these studies, I remember learning about this in a talk, where the speaker also mentioned that in most languages of indigenous peoples, they only have small numbers (such as “one”, “two” … and it rarely surpassed “five”) and “many”. I think this is also a piece of indirect evidence that people can discriminate smaller numbers (ratios farther away from 1) better than larger numbers. This is also discussed later in this chapter, and apparently people still have an approximate number system for large quantities even it’s not in their language.

The authors also talked about studies that showed that the point of subjective equality (PSE) for both children and monkeys was closer to the geometrical mean than to the arithmetic mean. This is super interesting, and I wonder if there is an evolutionary advantage in this perception.

The semantic congruity effect is also very interesting, particularly that it was found in monkeys who did not have the semantic ability. I think this shows how mistaken a theory (the discrete code model) could be, even when it makes perfect sense based on limited human-only data. Taking the context of comparison into consideration makes a lot more sense to me (e.g., Holyoak, 1978), and I feel like another study I know of also provides insights into this issue. In Knops et al. (2009), researchers showed that mental arithmetic operations recruited brain regions that are typically involved in orienting attentions spatially, and the patterns of brain activities involved in mental arithmetic also went in different directions as people add or subtract numbers, as if they had a numerical x-axis in mind (small numbers on the left and large numbers on the right) and was spatially moving through that line as they add or subtract. This mental representation for numbers with a horizontal line may also account for the semantic congruity effect. For example, given a context or numerical comparison from 1 – 9, we might focus our attention on the 1-9 part of the numerical line. When being asked for a larger number, we might intuitively shift our attention to the right end of the axis, and it is easy to notice that 9 is the largest; however if we are only give 1 and 2, we’d need to shift our attention back to the left/smaller end of the axis, where 2 is sort of in the middle rather than the end, thus it may take more time to get there.

Another cool but very brief discussion later in this chapter is that brain systems that support numerical coding also support coding of many other continuous variables, including time, length, and size. A common neural coding has also been found for spatial, temporal, and social distances (Parkinson et al., 2014). There has been some recent discussions on a cognitive map system that acts as a basis of map-like knowledge representation, and that can be reused for organizing things including spatial, temporal, and abstract knowledge, such as semantic concepts and social networks.

Reference
Knops, A., Thirion, B., Hubbard, E. M., Michel, V., & Dehaene, S. (2009). Recruitment of an area involved in eye movements during mental arithmetic. Science, 324(5934), 1583-1585.
Parkinson, C., Liu, S., & Wheatley, T. (2014). A common cortical metric for spatial, temporal, and social distance. Journal of Neuroscience, 34(5), 1979-1987.