Space-Time Metaphors In Nonlinguistic Contexts

The last post on time-space metaphor research has sparked a really interesting discussion in the comments (go check it out), so I thought I'd talk about some more research to see if we can't get even more people talking. If you've been following that discussion, this is the research by Daniel Casasanto and Lera Boroditsky that commenter Shane keeps mentioning.

If you haven't been following the the many posts on time-space metaphors on Mixing Memory, here are the basics. One of the examples of an abstract concept being structured by a more concrete one that Lakoff and Johnson use in their 1980 book Metaphors We Live By is time. Time, they argue, is metaphorically structured through mappings to spatial concepts. This is reflected in our use of spatial terms and phrases like "forward," "backward," "behind," etc., to talk about time. Under this view, there are two dominant spatial metaphors used in English: the ego-moving and time-moving metaphors. In the ego-moving metaphor, we are moving forward in time (e.g., "We're approaching the end of the semester") and in the time-moving metaphor, we are stationary while time moves towards us ("The end of the semester is fast approaching").

Several studies testing this view (we'll call it the metaphorical structuring view) have already been published, and for a discussion of those you can read the above-linked post or this post (along with the links therein). In this post, I'll be discussing a series of studies discussed in this as of yet unpublished paper by Casasanto and Boroditsky that are designed to test the metaphorical structuring view directly, by looking at how spatial information affects temporal information without using linguistic stimuli, and thus avoiding some of the objections that have been raised about the reliance on linguistic stimuli in past studies.

In the first experiment, participants were presented with lines on a computer screen that grew horizontally, one pixel at a time, for intervals between 1 and 5 seconds. The lines grew between 200 and 800 pixels. They used nine different durations and nine different lengths, and each duration was paired with each length once, so that each participant viewed 81 lines. For each line, participants were asked either to estimate the length that it grew by tracing a line with the mouse, or to estimate the duration of the line's growth by clicking the mouse once and then clicking it again after the amount of time the line had grown had passed.

Casasanto and Boroditsky's predictions were a.) that the distance the line grew would affect estimations of duration, because temporal concepts are structured by spatial concepts, and therefore influenced by spatial information, and b.) that the duration would not affect estimates of distance, because the metaphorical relationship between space and time is asymmetrical (time doesn't structure, and therefore doesn't influence, spatial concepts). The correlation between distance and duration estimates was .94 (a very, very strong correlation), confirming prediction a., while the correlation between duration and distance estimates was only .05, confirming prediction b. People's estimates of duration tended to be shorter if the distance was greater, and longer if the distance was greater, while estimates of distance were not affected by duration.

In yet another experiment, participants viewed stationary lines that varied in length (instead of growing), and that stayed on the screen for varying durations. Once again, participants were asked to estimate either the length of the line or its duration, and duration estimates were highly correlated with the length of the line (r2 = .72), while length estimates were not affected by duration (r2 = .10).

In yet another experiment, Casasanto and Boroditsky presented participants with a dot that moved across the screen instead of a line. This way distance was more difficult to estimate, because participants couldn't view the full length of the line as it grew. In this study, the distance that the dot moved across the screen was varied, and as in the previous experiments, the duration of the dot's movement was also varied. Once again, they found a strong relationship between duration estimates and the distance the dot moved (r2 = .82). The correlation between distance estimates and duration was .27, which though not significant probably indicates that the increased uncertainty in distance due to the fact that they had to hold the starting point of the dot in memory to know how far it had traveled led to some influence of duration.

Thus, each of these studies (along with 3 others designed to test alternative explanations for the results of the first study, which you can read about in the paper) confirmed the predictions of the metaphorical structuring view of the time-space relationship. Because these studies didn't use linguistic stimuli, they're not open to the priming and implicit agency objections discussed in the previous post. Interestingly, their results are somewhat inconsistent with previous research (which they cite) showing that very short durations are likely experienced directly, and therefore not in need of metaphorical structuring. I'm not exactly sure what to make of that. However, I do see a potential problem with these studies. In each case, participants are asked to estimate both duration and distance or length based on visual input. Research on cross-modal (e.g., vision and hearing) interactions have shown that vision is very good for processing spatial relations (like, say, distance or length), but not very good at processing temporal relations, while the reverse is true for audition (I'll discuss some of that research either this Saturday or next in a "Cool Visual Illusions" post). It could be, then, that a high degree of uncertainty in the participants' processing of the temporal information using visual input is responsible for the effects. Uncertainty about duration may have resulted in the participants using other cues (in this case, distance or length) to estimate duration. In other words, the participants brains were falling back on what they knew well when reasoning about what they didn't know so well. Unfortunately, Casasanto and Boroditsky only present correlations when discussing the accuracy of duration estimates, and while they do tell us that duration estimates were highly positively correlated with the actual durations (around .99 in each study), this only tells us that longer durations yielded longer estimates, and doesn't tell us how close the duration estimates were to actual durations. An interesting follow-up to these studies, then, might be to use auditory stimuli to present distance and duration. The metaphorical structuring view would still predict that distance would affect duration. However, if the effects in the Casasanto and Boroditsky studies are due to uncertainty in temporal reasoning due to visual stimuli, then we might predict the reverse effects using auditory sitmuli, because auditory information is better for estimating temporal relations. Thus, we might find that with auditory stimuli, distance estimates are highly correlated with duration, while duration estimate are not affected by distance.

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Hi Chris,
One idea in connection to this particular experiment... Seems to me that our ability to do "more/less" comparisons transcends sensory and conceptual modalities.
For example we can compare color C1 being brighter than color C2, or sound S1 being louder than sound S2. Or that thing T1 is more beautiful than thing T2, and so on...
In all those, the adjectives "more" and "less" are used in same way. So to say, after one learns the meaning of "more" and "less", one can use it for lot of different things in same way. The meaning of "more" and "less" are same when use for different things.

Anyway, back to the experiment. It might be that the estimates of durations are affected not because we understand time through space metaphors, but because the concepts used for comparison work in both realms.
It would be interesting to see if the estimates can be affected by:
1.Instead of showing line growing, show a circle getting bigger, color getting brighter, or sounds getting louder. Also analogously with the original experiment, using static colors of different brightness, or playing sounds of different loudness.
2.Trying to prime with "more complex" things, which also can be subject of comparison, like beauty, coldness, etc..

Of course still this wouldn't explain the asymmetry present in the results of the experiment, but those might be for reasons that you mentioned at the end of your post.

Umm, I'm confused ... why should these results imply anything at all about the metaphorical structuring of time? As Chris speculates, subjects' judgments seem to be driven by relative perceptual salience rather than any underlying cross-domain conceptual interactions.

Imagine a similar experiment where instead of showing a line growing by varying lengths, you inflicted pain on a subject in varying degrees. The results would surely be similar, no? Would we then point to this evidence to argue that temporal concepts were metaphorically structured by mappings to pain concepts?

Btw, doesn't the conception of these metaphors implicitly assume a sense of 'self'? how do you see the view that 'self is an illusion', Chris?

I'm not sure what you mean by "self is an illusion." Do you mean self as an empirical/social construction, or something different?

Chris, by 'self is an illusion', I mean "self, as a thing, is an illusion". Or it can be said, there is no central controller in the brain or anything that is permanent to be claimed as 'self'.

So to re-frame my question, how would your metaphor be conceived in such a no-self perspective?

PS: see for no-self conception in Buddhism.

Hmm... it's pretty clear that people have a representation of self, or ego, and that this affects things like spatial and temporal processing, approach and avoidance, etc. So I'm not sure there's an absence of self in a way that would affect these studies.

Its somewhat backward reasoning, but the reason I think this study is potentially good evidence for conceptual metaphor theory is actually the follow up work with cross linguistic differences, which you can find here:

At first glance, the line task doesn't appear to relate to our conceptual structuring of time, as Chris points out, it is over very short periods and is experienced "directly" .

However, the follow up work showed that performance on the task (and with a related volume judgment) was influenced by the conceptual metaphors used for time.

I agree with Tanasije that potentially performance in this task could be explained by some kind of crossm-modal magnitude processing system, the same with Matt G's suggested pain study. Which would suggest our understanding of temporal magnitude is processed by a system that handles other kinds of magnitude processing.