Everyday Abstraction: The Embodiment of Spatial Construals of Time and Their “Axioms” (from Mathematics: the Ultimate Challenge to Embodiment by Rafael E. Núñez)

Time, which for centuries has intrigued philosophers, physicists, and theologians, is a fundamental component of human experience. It is intimately related with everything we do, yet it is abstract, in the sense that we do not experience it directly as an isolated thing we can point to. Besides, our brains do not seem to have specific areas dedicated to process pure temporal experience in the way it does with, say, visual or auditory stimulation. Still, humans from all cultures must cope, implicitly or explicitly—with time-related entities, whether it is for cooking, dancing, hunting, traveling, or raising children. So, how do humans make up time concepts? As we saw earlier, the short answer is by treating “time” metaphorically as being spatial in nature, and one widespread form allows us to conceive the future as being in front of us, and the past behind us. This (mostly unconscious) way of thinking seems extremely obvious and natural, to the point that we barely notice that this is a major form of comprehension of temporal experience shared by many cultures around the globe. Even though nobody explicitly taught us this way of thinking about time, we master it effortlessly. It is simply part of who we are. This form of conceiving future and past, however, despite being spread across countless unrelated cultures around the world, is not universal! In collaboration with linguist Eve Sweetser from the University of California at Berkeley, we were able to reach this conclusion after studying in detail the conceptions of time in the Aymara people of the South American Andes (Núñez & Sweetser, 2006). This constituted the first well-documented case violating the postulated universality of the metaphorical orientation future-in-front-of ego and past-behind-ego.

Aymara, an Amerindian language spoken by nearly 2 million people in the Andean highlands of western Bolivia, southeastern Peru, and northern Chile, present a fascinating contrast to the well-known spatial-temporal mappings described earlier, and a clear challenge to the cross-cultural universals of metaphoric cognition studied so far. In Aymara, the basic word for “front” (nayra, “eye/front/sight”) is also a basic expression meaning “past,” whereas the basic word for “back” (qhipa, “back/behind”) is a basic expression meaning “future”. For example, nayra mara, whose literal translation is “eye/front year” means “last year,” and qhipa pacha—“back time”—means future time. Many more temporal expressions in Aymara follow this pattern. But here is where, as cognitive scientists, we had to remain very cautious in reaching fast conclusions regarding possible exotic conceptions of time. To proceed, we needed to address two important research questions:

1. What exactly are the mappings involved in these metaphorical expressions?
2. Is there evidence of their psychological reality? That is, do Aymara people really think metaphorically in this manner, or are they simply using dead fossilized expressions with no inherent metaphorical meaning?

The first question pushed us to make further theoretical distinctions. In cases like “The election is ahead of us” and “the long Winter is now behind us” the terms “ahead,” “behind”, and so on, are defined relative to ego. In other words, ego is the reference point and therefore the conceptual metaphor described earlier—Time Events Are Things in Saggital Unidimensional Space—is said to be an instance of an Ego-reference-point (Ego-RP) metaphorical mapping. It is crucial not to confuse this mapping with another type called Time-reference-point (Time-RP), that underlies metaphorical expressions such as “the day before yesterday” or “revive your post summer skin,” where morphemes like fore (front) and post (posterior) denote earlier than and later than relations, respectively.⁴

This mapping is in many respects, simpler than the Ego-RP one. As it does not have an ego, it does not have a “now” in the target domain of time, and, therefore, it does not have built in the intrinsically deictic categories, past, present, and future. The Time-RP mapping has only earlier than and later than relationships. But when a particular moment is picked as “now,” then “earlier than now” (past) and “later than now” (future) can be obtained. According to this mapping, however, “earlier than now” (past) gets its meaning from a “front” relationship, and “later than now” events (future) from a “behind” relationship. This may create confusion as in the case of the Ego-RP mapping the opposite seems to be happening: “front” (of us) means “future” and “behind” (us) means “past.” The confusion, however, is immediately clarified by asking the following simple question: in front of what? or, behind what? Technically, this means identifying the underlying reference point. In “the day before yesterday,” the reference point is “yesterday,” “in front” of which is located the day the expression refers to. In “revive your post summer skin” the reference point is “summer,” with the phrase targeting the times that follow the sunny season. To understand the Aymara case, we must keep this fundamental distinction between Ego-RP and Time-RP mappings clearly in our minds.

The crucial question we needed to address was: What are the reference points involved in the uses of nayra (front) and qhipa (back) in Aymara? That is, what is “in front of” or “behind,” when these terms are used for temporal meaning? If the reference points are temporal entities such as “winter,” “sunrise,” “lunch time,” or “rainy season,” as opposed to “us” or “me,” then there is absolutely nothing intriguing or exotic in the above Aymara temporal expressions. In such cases Aymara uses of “front” and “back” would be equivalent to English Time-RP cases like “the day before yesterday” or “post summer.” In fact, this is what occurred with some Polynesian and African languages that had been claimed to be “special” with respect to space–time metaphors, but whose data, after proper analysis, turned out to be standard Time-RP cases (Moore, 2000). If in Aymara, however, the reference point is indeed ego, that is, “front of us” means past and “behind us” means future, then this finding would be critical since it would provide a counterexample to the largely universal Ego-RP mapping.

The second question we needed to investigate was how people—Aymara or otherwise—actually think about time. For this, we had to go beyond the mere analysis of words and their etymological roots. We needed to investigate empirically the psychological reality of these space–time metaphors, and ask: Do people actually think this way? Or perhaps the expressions simply used “dead” lexical items from a distant past that lost its original metaphorical meaning? And how can we tell?

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We, therefore, could reliably ask what kinds of gestures Aymara speakers produce when uttering temporal expressions using “front” (nayra) or “back (qhipa). Where are they pointing when doing so? What is the built-in reference point of such pointings?

In order to find out, in collaboration with Chilean colleagues Manuel Mamani and Vicente Neumann from the University of Tarapacá, and Carlos Cornejo from the Pontifical Catholic University of Chile, I conducted videotaped ethnographic interviews with Aymara people from the north-easternmost tip of Chile, up in the Andes, along the border with Bolivia. As we were interested in spontaneous gestures (with high ecological validity), the interviews were informal and were designed to cover discussions involving reference to time. Participants were asked to talk about, make comments, compare, and explain a series of events that had happened or that were expected to happen in the context of their communities. They were also asked to talk about traditional “sayings,” anecdotes, and expressions in Aymara involving time and to give examples of them. To our amazement, what we found was that Aymara speakers gestured in Ego-RP patterns! Alongside the Ego-RP spatial language used to represent time as in front (nayra) and in back (qhipa) of ego, they gesturally represented time as deictically centered space: the speaker’s front surface was essentially “now,” as in English speakers’ gestures. The space behind the speaker was the Future, whereas the space in front of the speaker was the Past.

Moreover, locations in front and closer to the speaker were more recent past times, while locations in front and farther from the speaker corresponded to less recent times. For instance, speakers contrasted “last year” with “this year” by pointing first at a more distant point and then at a nearer one. When talking about wider ranges of time, rather than particular points in time, we saw speakers sweeping the dominant hand forward to the full extent of the arm as they talked about distant past generations and times. In sum, our data showed, on the one hand, that the reference point in the above temporal expressions in Aymara is indeed ego centered (our first question) and on the other hand, thanks to the analysis of gestures, that for Aymara speakers the Ego-RP metaphorical spatial conception of time has genuine psychological reality (our second question). 

This analysis of Aymara language and gesture provides the first empirically demonstrated case of a counterexample to the largely spread space–time metaphors where “future” is conceived as being “in front” of ego and “past” behind ego. Aymara has the opposite pattern (and it may not be the only such culture). Beyond its anecdotal flavor, this finding is crucial as it shows that human abstraction is not pre-wired in the brain. It tells us that there is no single way for achieving abstraction, not even for a fundamental domain such as time. Human biology is certainly fundamental in providing the basis for human imagination. But, building on universal species-specific body morphology and neural organization, different aspects of bodily experience may be recruited for the systematic construction of more abstract concepts, which allow for plasticity and cultural variation. Regarding temporal metaphorical uses of front–back relationships, we tend to profile frontal motion. Based on this, our basic postulate (or “axiom”) builds on prototypical frontal motion. If we walk (forward) at any given time we will reach a location that is in front of us, leaving behind us the original location. That location is reached in the future relative to the moment we started the action, with the initial position where we were initially (past) located behind us. Aymara people, however, although do walk in the same way as the rest of the world does, operate with a radically different postulate (or “axiom”). They profile a fundamentally different aspect of front–back features: what is seen (and therefore known), lies in front of the observer and behind them lies what is outside the visual inspection. These features parallel essential temporal properties, namely, past events are known, whereas future events are not. In Aymara, visual perception appears to play the leading role in bringing temporal concepts to being, and several data sources support this explanation, from evidential grammatical markers to special social practices and values.

The moral is that humans have at least two forms for conceiving time along a bodily front–back axis, which are—like in set theory—internally consistent but mutually inconsistent. These forms are defined by mutually exclusive ways of orienting the body in saggital unidimensional space, providing a radically different collection of truths. By profiling different aspects of bodily grounded experience we get one case with a built-in postulate (“axiom”) that puts the observer “facing” the future and the other case with the very opposite postulate with the observer “facing” the past. Once the orientation of the observer is defined, a series of theorem-like entailments follow. Which one is the correct one? Where really is the past? In front of us? Behind us? Like in mathematics, no ultimate transcendental answer can be provided. Both forms have their own postulates (or axioms), and truth rests on the underlying embodied mappings that made these very abstractions possible.

Lawrence Summers, former President of Harvard University and Chief Economist of the World Bank, issued a confidential memo arguing for global waste trade in 1991. The memo stated:

“I think the economic logic behind dumping a load of toxic waste in the lowest wage country is impeccable and we should face up to that… I’ve always thought that countries in Africa are vastly under polluted; their air quality is probably vastly inefficiently low compared to Los Angeles… Just between you and me shouldn’t the World Bank be encouraging more migration of the dirty industries to the Least Developed Countries?”