Introduction: Three Ways of Spacetime Practice

The present paper is written from the standpoint of communication science, i.e., the study of meaning-making and relationships via interaction (Bateson, 1972, 1979), in which space and time do not denote tangible physical entities. Space and time are not exclusive features of physics. “Space” is not an object but rather a concept, similar to “love,” as is “time”—they are human words that are not necessarily shared with nonverbal organisms. Thus, we cannot bring out space and time like specimens, as the saying goes: a map is not the territory; words are not things (Korzybski, 1933). What is observable may be an organism’s spatial practice and time practice (Lefebvre 1974; Gibson, 1975; de Certeau, 1984).

Let me first summarize the arguments thus far. When viewed from the standpoint of practice, spatial practice and time practice are indivisible, so we may see them as a single unit of spacetime practice, which is comparable to making a universe (Nomura, 2023). When one drives a car to work in the morning or migratory birds fly to reach their destination, space and time must be grasped conjointly by the participant-players. These practices become possible by using communication codes, which can be grouped into three categories: the tense-based A-series code, measurement-based B-series code, and interaction-based E-series code.

The naming of the A- and B-series originates from the time theory expounded by British philosopher McTaggart (1908, 1927); however, our work converts his ontological character of the A- and B-series into communication codes. The E-series was subsequently theorized by another group of authors (Nomura & Matsuno, 2016; Nomura et al., 2018, 2019, 2020). Due to the indivisibility of time and space, the names used for time theory have been transferred to spacetime theory. The term “series” is used as a suffix to indicate the sustained progression of each practice.

A-series spacetime practice consists of sustained boundary operations (i.e., code progression) by a single individual. It represents the mental space that houses his or her memory and anticipation that can be expressed in the form of a narrative in the first person. An individual’s inner cognitive world and his or her temporal sense, along with the past, present, and future, may be the foundation of this spacetime code, which applies mostly to humans and is subjective and internalized.

For example, consider the case of writing a long-postponed letter to a dear friend. I may write thanks and greetings and perhaps apologize for the long silence, i.e., the time that has passed since the last exchange of letters. I may further touch upon recent life events that have happened along with my feelings and sentiments. In addition, to reaffirm the relationship with my friend, I may write about my memories of experiences with that person, possibly with reminiscences expressed in short biographical accounts. An alternative view from a different person might be inserted in contrast to my own. I may end the letter by writing about my hopes for the future or the future relationship with that friend.

The letter portrays my own perceptual universe as it narrates ideas about myself, about my friend, and about the immediate definition of the friendship (Pittenger et al., 1960). It depicts my own mental space expressed in the first person, I. Time is also embedded in the form of a narrative describing the personally sensed time that has elapsed since the last communication or the biographical accounts punctuated by the experienced events, according to neither a global clock nor a chronological table. Although there is an argument that both narrative time and ordinary chronological time are intertwined and grounded in the individual’s experience of time and the human practice of interpretation (Ricoeur, 1984), personal temporality is nevertheless best expressed in the A-series, and story-telling is brought about through such spacetime code (e.g., Lewis, 1961).

On the other hand, the tenseless B-series spacetime practice is based on the global code that humans use to measure the linear progression of chronological time and the geometric expansion of space. Space and time are considered objective entities in physics, but in our framework, they are seen as expressions based on the B-series spacetime code. The B-series time code is globally synchronized, where the mechanical clock shows an objective sequence of earlier and later moments. The metrological standard describes the physical dimensions and proportions of the object or spatial expanse. The person who adopts the B-series code is a third-person observer who is situated outside the observed phenomena. This externalized code is uncontrollable by us, except perhaps by physicists. The code progression is automatic, so we are not the ones to engage in the boundary operation—the boundaries have already been set for us, and they are transgressed indifferently even while we are asleep. Such is the B-series boundary operation. Of course, we can walk out of the global time code, perhaps on a remote island in the Pacific.

However, our modern situation is slightly more complicated; for example, I will attend an event taking place in a distant city tomorrow and expect to arrive there by 11 AM. Then, I plan backward from the arrival time to calculate the time I need to leave my house tomorrow morning. The time needed for walking and transferring trains must be considered. I check the timetable of the local express train to find the one that reaches the destination on time or slightly earlier. These time-based operations are linked to the distance I travel because the train’s speed will be approximately the same whether I travel 30–60 km. The retrocausal calculation applies to every third-person observer—unlike internalized A-series spacetime, where time operates personally or sometimes goes backward or the distance is contracted, as in our dreams. The boundary operation in the B-series is executed apathetically outside my progress, while it permits a mutual time frame with people at the event site, helping promote responsible social coordination.

Alternatively, the practice of E-series spacetime is necessary for occasions to coincide with others in many operations, from a human conversation to fish or birds swimming or flying in formation or the synchronized collective action of bacteria. The E-series code is adopted by creatures participating in an interactive environment, where they coadjust temporal spans along with coordinated movements and reciprocally negotiate spatial boundaries (Cody & Brown, 1969; Luther, 2008). The organisms that use the E-series code are second-person negotiators, or participant-players, who engage in interaction by mutually taking risks. The time scale employed is neither individualistic-subjective (like the tense scale in the A-series) nor absolute-objective (like the mono-metric scale in the B-series) but rather relative-intersubjective and, hence, dialogical (of the dia-metric scale in the E-series). The code progression facilitates local synchronization among the participants. Such synchronization requires the participant-player to predict the movement of its partner by second-guessing “where” the partner will be in the very near future, indicating that future goals are the cause of the present action and suggesting the retrocausal character of this code (Mischiati et al., 2015; Nomura et al., 2019).

Imagine an old, blind man walking home with his guide dog. The route along which the dog leads the blind man may be a familiar path (Uexküll & Kriszat, 1957), which avoids obstacles that might cause the old man to stumble. The familiar path that guide dogs take may be their collaborative work-out space rather than a place because the route has been discovered or extracted from numerous cartographical possibilities. The guide dog and the man also coadjust their walking speed—the man might walk more slowly than the day before due to his physical condition so that they keep pace (tempo or time) by sending an intent via the leash and retrocausally predicting each other’s movements. This interaction forms a sort of dialogue exchange in the interactive-local spacetime code, leading to the production of their mutual universe, I and Thou (You) (Buber, 1970).

Spacetime becomes “perceptible” when spacetime codes are used (see Table 1). The first-person agency grasps the A-series spacetime, the second-person participants grasp the E-series spacetime, and the third-person observer grasps the B-series spacetime. Each spacetime code offers the corresponding spacetime series to the code user; alternatively, each code affords the user the proper spacetime series, i.e., affordance (Gibson, 1979)Footnote 1.

Table 1 Spacetime as a Living Code
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Boundary Operation and Spacetime Practice

How, then, do we produce spacetime? What constitutes spacetime practice among organisms? What is the basic operation of spacetime practice? The answers to these questions all revolve around boundary marking (Nomura, 2023). As indicated, time, space, and spacetime are considered “language” in the broad sense or, more precisely, communication codes or a sign activity in the semiosphere (Hoffmeyer, 1996). Think of any kind of space or any type of time. Neither space nor time can be identified without some sort of delimiter set by humans or other living beings, which is a distinction drawn by arranging a boundary with separate sides (Spencer-Brown, 1972, pp.1–7) or more compactly distinguishing distinctions (Mayer-Foulkes, 2023, p. 61). Although spacetime is the proper unit, it may be convenient to first grasp spatial and temporal practices separately.

Time Practice as Boundary Operation

Imagine our clock time, B-series time, which is indicated by digits or tick marks according to the global time scale. It is demarcated and punctuated, and equal-interval accurate measurement is the raison d’être of this time series. Animal behaviors and astronomical phenomena can be described by scientists using this objective global code. On the other hand, our personal time, A-series time, comprises our experience of events along with our past, present, and future—it is punctuated using the historic individual scale based on tense. Keep in mind that there is no past, present, or future for B-series clock time. The time-keeping method for the personal time scale is largely human specific, and this time series is based on our memory and anticipation, as in our autobiographical accounts. It indicates a sort of mental cognitive clock. However, boundary marking is always present, whether it is in the A-series or B-series.

Moreover, social time, E-series time, also relates to such boundaries. For festivals, dancing together, choral singing, or collaborative works, we take action by sharing messages and allowing messages to be shared, demarcating our way of punctuating the event, that is, timing adjustments where the participants reciprocally achieve timings by negotiating the boundaries of their acts through movements, steps, and cues. Then, they progress further by crossing (i.e., transgressing) the boundary together, that is, making a distinction (setting a boundary) and doing something about (surmounting) it, as in the case of choral singers taking a breath together and then starting to sing the next line. Here, the mode of punctuation is interactive, not clock based. This intersubjective-relational code is widely shared among living creatures whenever they have to make timing adjustments to gather, escape, catch prey, breed, migrate, etc. The structural code dynamics remain the same throughout; i.e., they reciprocally set the boundary and transgress it (de Certeau, 1984; Nomura et al., 2018, 2019, 2020; Nomura & Matsuno, 2016).

Spatial Practice as Boundary Operation

We quantify the physical space of farmland, an object, or the inside of a building—the three-dimensional Euclidian space can be measured by its height, width, and depth -- as expressed in the mathematical code and numbers. The estimate based on measurement is also a boundary marking, i.e., delimitation. The physical spatial practice in the B-series includes such cases as land surveying, designing architecture, and calculating the size of a living creature, all of which are visible to the observer.

On the other hand, our subjective memory of the past and the story around an incident may indicate that our intrapsychic cognitive space in the A-series, which may be called narrative space due to its visibility, is described, edited, and completed by drawing a boundary for the experienced event. In addition to the passage of time, the story assumes the breadth of its space, the covered range and the depth of its meanings, which are all constituents of mental and narrative space enabled by the A-series code. Such space is individually recognizable but is a more or less human-specific internalized spatial code expressed through language. Biologists, however, have recently claimed that nonverbal animals possess a certain level of episodic memory (Crystal, 2010; Miyamoto-Gomez, 2021), contrasting with the more traditional view that episodic memory is human specific, although declarative (semantic) memories are shared across species (Tulving, 2005, pp. 3–56). It is reasonable to assume that nonhuman animals have A-series spacetime to a certain extent.

Furthermore, biologically more important might be the production of social-intersubjective space. Gatherings and social events possess a distinctive space that is achieved only by the ongoing process of social interaction. Space-place contrast may be useful in this vein. A concert hall, a building, is a place, but a concert is a social space that is continually produced through interactions between musicians and audiences. Place is a configuration of undeviating positions that implies stability, whereas space is composed of intersections of mobile elements (De Certeau, 1984; Nomura, 2023). Place is fixed, while space is lively. Take a conversational space: it is interactively produced, with the participants negotiating and adjusting the timing of turn-taking, each nodding in response to his or her partner, developing a new topic, etc., which are unachievable by him or herself alone (Sacks et al., 1974). Here, the punctuations, or boundary operations, are interactively driven and negotiated and thus socially determined. Boundary operations for social spatial practice employ the E-series communication code, reciprocally setting the boundary and continually transgressing it to move on.

The production of social-interactive space in the E-series code is also observed among animals. The timing of an egg hatching in the wild is ecologically and interactively determined and can be considered a boundary operation, i.e., the spatial practice of the living entity breaking the eggshell (the boundary). This process is called environmentally cued hatching (Warkentin, 2011), in which the hatching timing varies in response to multiple environmental risks and opportunities that are mediated by a variety of cues and mechanisms. Alternatively, when a bacterial population’s density reaches a certain threshold of concentration (i.e., setting the boundary), the bacteria tend to execute their behaviors collectively (i.e., transgressing the boundary), synchronizing the action of all members of the group, a phenomenon known as quorum sensing (Bassler & Losick, 2006; Rutherford & Bassler, 2012). Group-wide detection of information about the cell density and species composition of the vicinal community is performed. The threshold is the boundary, and the action of these individuals is the boundary operation, which creates their social space. These are examples of social spatial practice using the intersubjective E-series spatial code. Spatial practice, whether the character of the space is cognitive, physical, or social, is carried out in terms of boundary operation, making a distinction (setting a boundary) and then crossing or surmounting it.

Event Matching and E-Series Spacetime Code

The outline of A-, B-, and E-series spacetime practice has been drawn, with boundary operation being the key concept for describing the dynamics of each code progression. The notion of boundary operation is advantageous since it permits us to approach spacetime without assuming space or time a priori, distancing ourselves from the liability of tautology. As indicated, the three series spacetime codes differ in grammar in that the boundary operation is characterized as tense-based/cognitive (for the A-series), sequential/absolute (for the B-series), or coadjusting/relative (for the E-series) (see Table 1).

The E-series code has been identified as the one used for producing interactive spacetime, e.g., chorus singers starting the next line of a song after the boundary breath, eggs breaking their boundary shell to hatch, or bacteria behaving collectively when their population density reaches the boundary threshold. However, that may not be all–almost everything in interactive contexts may by and large be practiced in the E-series. The E-series spacetime code is a communication code that we humans share with other living creatures. This is the reason why we should explore this particular code to determine its base mechanism, which was inherited from earlier life forms on our planet. E-series spacetime is characterized by its coadjustment of timing and its negotiation of spatial boundaries. The following question thus unavoidably arises: how does boundary operation carried out by organisms produce meaning in their E-series spacetime practice?

As a brief diversion before diving into this critical question, it might be helpful to define “organism” as used in this paper. Since goal directedness and adaptation make organisms different from merely physical entities, something can be an organism if the parts work together for the integrated whole, with high cooperation and low conflict (Queller & Strassmann, 2009, p. 3144; West & Kiers, 2009). That is, an organism adapts to the shared purpose of its parts. Furthermore, a given assemblage of parts may or may not behave as an organism-like unit, depending upon the specific ecological conditions in time and space in which it occurs (Diaz-Munoz et al., 2016, pp. 2671–2674). Organismality is context dependent; for example, the traits of bacteria can change, enabling a transition from biofilm to planktonic states. Another example is when honeybee colonies shift from conflict to cooperation states, which depends on the developmental timing before and after the sole queen is established. Thus, organismality occurs when multiple biological entities interact to form a new entity characterized by adaptations, that is, an entity with a “shared purpose” exhibiting high cooperation and low conflict among its parts.

A set of molecules acquires organismality as they form a transformational chain, such as during the oxidative citric acid cycle. This is a reaction cycle that synthesizes ATP and in which hydrogen is extracted by the carbon flow circulating through the system, transforming in the direction of citrate to isocitrate, α-ketoglutarate, succinate, fumarate, malate, and oxaloacetate, and then back to citrate via the confluence of acetyl-CoA, a coenzyme. The participating molecules assume the semiotic capacity of assessing or being assessed by nearby molecules (Matsuno, 2012). Although limited to the immediate locale of transformation, the E-series spacetime (universe) becomes “perceptible” to the participating molecules as the degree of organismality increases. Here, we should remember that each citric acid cycle is “the one and only”; i.e., each system is unique. The uniqueness of this process is twofold: it resides not only in the cycle itself but also in the relationships that each molecule has with others, as well as with the cycle as a whole. This is a vital point. Otherwise, the transformation might simply become mechanistic instead of semiotic (Nomura et al., 2018, pp. 76–77).

The timing of the reaction cycle depends on the coordination between the sequential transformation of each upstream reactant into the one immediately downstream and the concurrent presence of all the participating reactants. The key to a timekeeping endeavor specific to a reaction cycle of any kind is, therefore, the coadjustment of the time by multiple participants, despite inevitable conflicts, inconsistencies or incompatibilities between being sequential and being simultaneous. The reactants view others encountered nearby as second-person negotiators. Multiple goal-directed agencies interact in a constant effort to maintain local synchronization in the E-series (Nomura et al., 2018, pp. 76–77). E-series time practice and spatial practice are ubiquitous.

Event matching, or organisms linking event1 to event2, is a term I put forward herein. I should explain not only how organisms produce spacetime, E-series spacetime in particular, but also how they generate meanings. Event matching is a cross-field notion and a broad umbrella concept that can rephrase but not replace philosophical or psychological notions such as cause and effect or stimulus response. We will return to this point later. First, let me explain how the word “event” is used in this paper. Events include not only episodic happenings but also impulses and instantaneous incitation that are momentary (Bateson, 1979, p. 107). When the participant-player senses, detects, perceives, or becomes aware of something, this can also be considered an event. An event thus covers circumstances in which an organism senses any incitation or difference in itself or in the environment. This way of defining an event corresponds to the definition of information as “a difference which makes a difference” (Bateson, 1972, pp. 457–461), where the two “differences” in the phrase are both comparable to an event, although the first one is close to incitation, while the latter may be close to generating meaning. An event after all is a differenceFootnote 2.

On the other hand, the word “matching” refers to conditions in which the organism links event1 to event2 or infers event2 from event1. Event1 goes with event2, so the two are paired, equated, or corresponding. For example, I observe a bird perched on the branch of a tree, but the bird flies away when I make a noise. The bird detects the noise, senses the danger, and flies away according to its perception of the event, although the noise or impingement has no inherent connection to danger. The creature links the noise to danger or infers danger from the noise. This linkage is arbitrary; however, event1 plus event2 constitute the bird’s experience. Additionally, I, as an observer, may link the two events, the noise with the bird’s flight.

As another example, walking in the street at night, I see someone coming toward me in the dark and discover that it is my neighbor. I link the initial fuzzy figure to somebody I know, or I identify my neighbor from the misty figure even though a great many alternative possibilities for the unknown are constrained to the limited repertoire of the known. Thus, my experience of “running into my neighbor” is made up of event matching between the initial impulse of an unidentified figure and the identification of the figure. My neighbor might also have gone through similar steps of noticing me. We can apply event matching either to the individual domain or to the inter-individual domain, in which event1 is constrained to event2 in myself, or to my event1 and the neighbor’s event2, which then go together to constitute the mutual encounter. Event matching is a communication concept and is not affected by the dividing line between the intra-organism and the inter-organism.

Thus, this relationship between two events, event matching, may be expressed in various ways depending on the context—whether it happens within the organism or between organisms. Event1 goes with event2; event1 and event2 become a pair; event1 leads to event2; event1 becomes a stimulus for event2; event1 causes event2; event1 means event2; event1 is constrained to event2; event1 and event2 are simultaneous; event1 is synchronized with event2; event2 is inferred from event1; event1 predicts event2; event1 affords event2; event1 leads to event2, which leads to event3, which further leads to event4, and so on. In this way, event matching, as an umbrella concept, covers a wide range of animal and human behaviors. Again, it should be underscored that event1 and event2 can be spotted within one organism or between two organisms.

Event matching is interchangeable with boundary operations, which are defined as organisms noticing or making a distinction (i.e., setting a boundary) and then surmounting (i.e., transgressing) it. The definition of a boundary operation is parallel to event matching since an event has also been defined as impulses, instantaneous incitation, or difference, which is identical to setting a boundary. Thus, an “event” in event matching corresponds to a “boundary” in the boundary operation. Since “matching” in event matching indicates the formation of a relationship linking event1 to event2, this relationship can be identical to an “operation” in boundary operation, as the transgression of a boundary (event1) leads to the next boundary (event2). Event matching is a meaning-centered version of boundary operation. Both boundary operation and event matching are concepts designed to avoid time- or space-related vocabularies to avoid tautology; these concepts do not assume time or space a priori.

Event matching as a means of codification (i.e., substitution of one type of event for another) (Ruesch & Bateson, 1951) can be considered a type of explanatory principle contrasting cause and effect, stimulus response, or constraint. Although among the well-known issues are gravity in physics and evolution in biology, I leave these topics to the care of specialists who have a vested interest in them. Cause and effect or causality explains the relationship between two things, one in the past and one in the future. It reflects the way in which we often associate two separate things. This philosophical scheme, however, is widely applied from science to everyday social matters. Underlying it may be the background for pursuing the causer and its responsibility. Its linear causality is aligned with the B-series spacetime code.

Stimulus-response theory in psychology explains learning in terms of the relationship between the stimulus and the response, in which the satisfying effect of the stimulus is likely the result of pairing it with the response, contributing to our learning. In Pavlov’s experiment with the dog, for example, satisfying food was the stimulus, and salivation was the response. When the dog learned that food was associated with a bell ringing, the dog learned—or was conditioned—to salivate only with a ringing bell. Since this theory assumes that behavior (response) is the result of stimulus of some sort, the resulting suggestion is when there is no stimulus, there is no behavior. In communication, however, receiving no reply (minus a stimulus) from one’s counterpart often might cause anger (plus a response) when, for example, an earnest reply is desired.

Constraint is another explanatory principle regarding meaning and information based on variety, a set of alternative states and events (Ashby, 1956). Cybernetics considers what alternative possibilities could conceivably occur and then asks why many of the alternatives did not occur so that the particular event was one of the few that could, in fact, occur (Bateson, 1972, p. 405). Buying one item out of fifty commodities is more constrained than buying one item out of three, with the former excluding more alternatives than the latter and hence is likely to be more informative. The first gambit in a game provides one’s opponent with information about one’s tactics, which have been selected among many alternative possibilities. The greater the number of excluded possibilities is, the more likely it is that we will obtain a greater amount of information, which we can sometimes capitalize on in cases such as a million-dollar lottery.

Event matching is an explanatory principle that focuses on the participant’s experience. In contrast, causality, stimulus response, and constraints are observer perspectives employed by third-person onlookers and are suited to laboratory or outsider observations. Event matching is instead concerned with an organism’s viewpoint in linking event1 to event2 based on the participant-player perspective. To gain access to timing and spatializing adjustment, it may be necessary to adopt insider perspectives because such adjustment or negotiation involves the participant-player’s prior estimation and predictive behavior, which is unique to the E-series spacetime practice but foreign to the clock-based geometrical B-series spacetime practice. We now turn to biological examples to observe how event matching corresponds to timing adjustment and spatial work in the E-series, demonstrating that event matching is a downright spacetime operation.

Biological Examples of Spacetime Practice

Example 1

Mother–infant synchronized spatial practice.

Studies of human nonverbal communication using slow-motion movie footage have advanced in anthropology since the 1950s (Birdwhistell, 1970). A series of microscopic analyses of human action has revealed amazing behavioral adjustment and coordination between people engaging in interactions. In conversation, vocal signals and body gestures, including arm, hand, and postural changes, are all coordinated and synchronized within one expressing individual or between people in pairs (Condon, 1970; Condon & Sander, 1974). These results suggest the universal status of spatiotemporal adjustment in human interactions.

Mothers and babies must perceive each other as responding in rhythmic coordination for their musicality to be at ease and communicative. An impressive case of mother–infant interaction was reported in which a Swedish mother sang to her 5-month-old daughter, who was born totally and permanently blind (Trevarthen, 1999, pp. 186–193). The infant lay on her back on a mattress while the mother bottle fed her and sang a Swedish baby song. The infant moved both hands, but the left hand was more active. The infant made intricate and delicate gestures with her left hand that matched variations in both the pulse and melodic line with appropriate forms of arm waving and extensions and turns of the fingers. She, so to speak, “conducted” her mother’s singing with astonishing subtlety and precision. Remarkably, her gestures occasionally anticipated her mother’s melodic and rhythmic changes by a fraction of a second.

Microanalysis reveals how closely adults and infants can coordinate their behavior with each other (Stern, 1971; Bateson & Mead, 1942). When attempting to synchronize their vocalizations and “fuse” on each beat, it has been reported that mothers or babies can “catch up” with each other with a lag of 120 to 250 milliseconds (Trevarthen, 1999, p. 177). Mothers and babies both predict the course of their interaction, anticipating satisfaction and pleasurable continuation. To do so, they must share the pattern of time generated in their movements, and, in the example above, the mother and her blind baby both contributed to their mutual timing adjustments and tactile confirmation as spatial practice.

Instantaneous predictions during interaction are a hallmark of E-series spacetime practice, indicating retrocausality where a future goal turns into the cause of present behavior. When dancing, we begin our steps slightly before the exact timing to accurately synchronize with our partner’s steps. Our anticipatory steps event-match to our partner’s, creating both synchronization and local space. The mother and her baby are also in such an interactive sequence, with the mother singing and her baby turning into her finger event matching each other, producing their social/interactive time as well as their intimate space, which is assured by linking the two separate events (the singing and the gestures) that belong to different individuals. Thus, event matching corresponds to spacetime practice without using time- or space-related vocabularies. In the language of boundary operation, mutual time boundaries are set and transgressed by their continued singing and finger movements. Their spatial boundaries, which are similar to those of a festival in nature, are interactively confirmed, strengthened, and reinforced through their continuing performance.

Example 2

Sticklebacks’ spacetime practice in courtship behavior.

According to Nico Timbergen (1953, pp. 8–14), courtship interactions occur between male and female sticklebacks (Gasterosteu aculeatus), during which successful spawning and fertilization are achieved. During the breeding season, the male secures its territory and builds a nest with sand and nest materials, such as threads of algae. The females cruise about in schools, passing through occupied territories repeatedly during the day. Each male reacts to them by performing a so-called zigzag dance. The dance frightens most of the females away, but a single one may be sufficiently mature to be willing to spawn and turn toward the male, adopting a more or less upright attitude. The male immediately turns around and swims toward the nest, and the female follows him. Upon arriving at the nest, the male shows the nest entrance to the female, and the female slips in. The male then begins to prod her tail base with his snout, giving a series of quick thrusts. Eventually, the female begins to lift her tail, and she soon spawns. After the female pushes through the nest, the male enters the nest in turn and fertilizes the eggs. The male then chases the female away and returns to the nest.

Fig. 1
figure 1

Courtship sequence of three-spined stickleback (Tinbergen, 1953) and the two time scales

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The interaction sequence between male and female sticklebacks is illustrated in the diagram (see the upper half of Fig. 1). The ten successive steps (event1 through event10) consist of paired events, with one next to the other: event1 with event2, event2 with event3, etc. Each event matching anticipates the subsequent social space, which in turn induces the next adjustment of timing for the next round of social space, spatial practice bringing in timing adjustment, and timing adjustment attracting the next spatial practice (see also Fig. 3 in Nomura, 2023). The spatial production and timing adjustment proceed hand in hand.

When these events are seen as messages in the direction of the arrows, each event reports the content of the message and simultaneously commands the partner to take the next action (Ruesch & Bateson, 1951, pp. 179–181; Nomura et al., 2020, pp. 9–11). For example, the female’s appearance (event1) is a message to the male not only to report her arrival but also to begin performing of the zigzag dance (event2) as a command. Alternatively, the male turning around and swimming toward the nest (event4), which is considered a report, is simultaneously a command to the female to follow him (event5). This behavioral sequence can take place due to communication linkages from event1 to event10—it is made up of each pair of linkages. Details on report-command dynamics have been described elsewhere (Nomura et al., 2020).

Event matching therefore entails timing adjustment and spatial practice at the same time. The female’s appearance (event1) matches the male’s zigzag dance (event2), the zigzag dance matches the female turning toward the male (event3), the female’s response matches the male leading her to the nest (event4), and so on. Now, suppose that if the male’s zigzag dance is delayed after the female’s appearance, the female will leave; then, the next social space will not appear, and the pair linkage will be broken. If the event of the male leading the female to the nest is disrupted, the female will not follow the male to the next space, the nest. Furthermore, the male’s fertilization of the eggs should immediately follow the female’s spawning, etc. This timing adjustment prepares for the emergence of the next social space (Moiseff & Copeland, 2010). The matched events shown in the diagram illustrate mutual timing adjustments with spatial collaborations in the E-series.

Example 3

Bumblebees damage plant leaves and accelerate flower production.

Recent climate changes and irregularities have affected the local ecosystems of insects and plants in many ways. Global warming may lead to the large-scale extinction of interactions that are responsible for a key ecosystem service—plant pollination (Memmott et al., 2007). Although maintaining synchronicity with flowers is a key challenge for pollinators, phenological mismatches between plants and pollinators sometimes occur (Kudo & Cooper, 2019; Burkle et al., 2013). On the other hand, some findings suggest that climate change may have disrupted phenological synchrony less than has previously been assumed (Ovaskainen et al., 2013; Bartomeus et al., 2011; Gerard et al., 2020). At any rate, flower scarcity poses a serious challenge for pollinator populations, and bumblebees particularly need floral resources during early spring, when queens emerging from diapause must establish colonies.

Notably, bumblebees (Bombus terrestris) actively damage plant leaves to accelerate flower production when pollen is scarce (Pashalidou et al., 2020, pp. 881–884). Bumblebees rely heavily on pollen resources for essential nutrients because they build spring colonies. Worker bumblebees have been found to accelerate the timing of flowering by cutting distinctively shaped holes in plant leaves using their proboscises and mandibles. The early flowering elicited by bee-inflicted damage has been reported to occur in as much as 30 days in one plant species (S. lycopersicum) and 16 days in another (B. nigra) and is thus substantial in both cases. Thus, damaging plant leaves when floral resources are scarce may be an adaptive strategy for accelerating flower production.

The benefit of early flowering may not be unidirectional. Since pollinators are powerful agents of plant evolution, actively responding to bee-inflicted damage may also be an adaptive means for some plant species to increase their chances of pollination. Thus, the benefit of mitigating asynchrony may be bilateral. Furthermore, the interactional bonding between bees and plants, researchers have stated, has a significant ecological implication in that the mutually helpful relationship may enable them to become more resilient to human-made environmental irregularities (Pashalidou et al., 2020, p. 884).

The bees damaging the plant leaves are commanding the plants to pick up the tempo, and the plants then respond by accelerating flower production, which in turn saves them by increasing their chances of pollination. The time-adjusted interactive cycle is spatial practice since it involves the generation of symbiotic communication space that is repeated and renewed every year based on social interactions. Timing adjustment in terms of early flowering seems to be a critical factor for building an allyship across species and should have coevolutionary implications—where a change in one species is associated with a change in another under reciprocal affiliation.

Therefore, timing adjustment between bumblebees and plants demonstrates event matching: leaf damage matches early flowering and flower production matches pollination. Each pair linkage in the produced interactive space represents the E-series local universe, in which the event matching observed by bumblebees and plants exemplifies their mutual spacetime practice.

Discussion

In event matching, different events are linked to form a relationship between them, which is comparable to spatial work. If the two related events are in my head, they produce a cognitive space for me (in the A-series); if the two events are linked within the material environment, they produce a physical space for the observer (in the B-series); and if my event1 is in communication with another person’s event2, they produce a social-interactive space for both of us (in the E-series).

Since event1 and event2 are coinstantaneous and become a pair, they also exhibit time agreement or timing adjustment, which represents temporal work. If an event (event1) in my head is matched to a scale mark (event2) on my personal tense-memory scale, which is derived from the past, present, and future, the matching would produce my internalized-subjective time in the A-series. If event1 corresponds to a tick mark (event2) on the mono-metric scale of my wristwatch, the correspondence would give me an externalized-objective time in the B-series. If event1 and event2 are interacting so that the negotiable (i.e., dia-metric) scale can be applied, the interaction will produce relative-intersubjective time for both of us in the E-series.

The lower half of Fig. 1 shows the linear progression of clock time in the B-series, which is a quantitative index. It is linearly sequential, so what occurs earlier or later can be determined unambiguously. An outside observer can check the timing of a stickleback’s movements in the interactive space from event1 to event10 on this scale. That is, event1 and event2 are not simultaneous in the B-series space, and they have time lags that can be progressively located on the scale. The externalized mono-metric time scale is set and stable, and its temporal span is fixed; this approach helps the outside observer determine the time by matching the stickleback behavioral event with the measured point on the scale below, which is the observer’s perceptual event. Thus, event matching, in which each action of the stickleback corresponds to the measurement read by the observer, works to ascertain the time on the clock-based mono-metric scale. Linear-time observation is accomplished through event matching in B-series space with no semiotic freedom (Hoffmeyer, 2010).

The upper half of Fig. 1 shows the interaction sequence of male and female sticklebacks. The inside players, the sticklebacks themselves, do not have the third-person global perspective, as the mono-metric observer does. Instead, the former must perceive each pair of linkages of local events in the second-person spacetime frame, that is, anticipate timing with the partner’s present action with the immediate future in mind. Since the inside participants do not rely on the fixed externalized scale, each partner’s movement, one after another, becomes the scale to rely upon, or more accurately, such movements make up the shared scale, although this negotiable scale remains in flux and elastic.

This is because retrocausality is built on the dia-metric time scale, unlike the linear scale in the B-series. The dynamic local E-series spacetime is interactively measured. Here, event matching occurs between each of the male’s actions and the female partner’s next predicted action, and vice versa, with both participants acting for the present in the immediate future (Matsuno, 2016). While event1 and event2 are not simultaneous on the mono-metric time scale, they become “simultaneous” on the dia-metric scale in the sense that there is no time lag for their predictive moves. Whether the scale is mono-metric or dia-metric, both require event matching to produce spacetime.

What about the mother–infant interactions? In what way can their spacetime operation be considered event matching? As was previously noted, adults and infants coordinate their behavior closely, and mothers and babies can synchronize on the beat by catching up with each other with a lag of 120 to 250 milliseconds (Stern, 1971; Trevarthen, 1999) in the B-series term. In the example, the interactional synchronization of the mother and the blind baby is achieved by the mutual adjustment of actions, that is, between (a) the mother singing and looking at the baby’s motions and (b) the baby moving her hand to make delicate gestures to match the rhythm and melody of her mother’s song. Like when dancing to music, the mother and baby each adjust their own timing for the next step, predicting their partner’s subsequent action so that synchronicity is maintained without a time lag, thanks to their reading of the future. Such is the interactive spacetime code on the dia-metric scale, where event matching occurs between the mother’s song line and the baby’s arm waving and finger turning.

On the other hand, scientists have examined the time gap on the linear scale to determine how much time lag was permitted for mothers and infants to rhythmically catch up with each other, and they found that it was approximately 120 to 250 milliseconds (Stern, 1971; Trevarthen, 1999); this time lag had to be measured mechanically on the clock basis, with the players’ moves (event1) being checked against the mono-metric time scale (event2).

Alternatively, bumblebees have been found to have strategies to cope with irregular seasonal flowering by accelerating pollen production (Pashalidou et al., 2020). The adjustment of flower production is mutually beneficial; bumblebees obtain essential nutrients quickly, and plants increase their chances of pollination. These collaborative efforts produce distinct social spaces that are the result of event matching on the interactive time scale, i.e., the bees’ leaf damage leading (matching) to early flowering and early flower production enabling (matching) pollination. In the study, while the inside players, bees and plants, conducted spacetime adjustments based on the dia-metric time scale, outside observers, such as scientists, counted the average flowering time of bee-damaged plants and found that the average number of days was shortened by 30 days in one plant (S. lycopersicum) and 16 days in another (B. nigra). The observation was based on the ordinary linear time scale in the B-series space, matching flowering (event1) to the point on the calendar scale (event2). Event matching of this kind thus takes place by collating the observation of a given phenomenon in the measured space with the reading of the linear mono-metric time scale.

Finally, we perhaps need to touch upon the case of tense-based/cognitive or subjective spacetime code, the A-series. In what way is the A-series code actualized through event matching? This time code is mostly human specific, and each individual’s memory and anticipation drive his or her personal clock and narrative-historical space. Think of experiences that happened in the past, which may have been just yesterday or a long time ago. Unless we are confused or in an altered state of consciousness, our sense of duration, an unbroken succession from the past to the present, supports our personal spacetime frame, permitting us to locate ourselves on the memory-anticipation scale (Crapanzano 1980; Kleinman, 1988). The blind baby’s mother might recall the pleasurable event with her daughter sometime later in her life. The personally experienced incident (event1) stored in her memory is compared to her subjective spacetime scale to determine the appropriate measuring point (event2). It is event matching by herself, that is, a spacetime operation of first-person agency.

Summary and Conclusion

The present paper introduces the notion of event matching and its significance for living beings, in that their generation of meaning is comparable to their spacetime production. Event matching produces meaning-centered spacetime in the A-, B-, or E-series depending on the code the organism employs through simultaneous linking between event1 and event2 and the formation of relationships between them.

In this study, information is defined as “a difference which makes a difference” (Bateson, 1972, pp. 457–461) and has been rephrased as event matching. While the former definition by Bateson treats two differences hierarchically, with one being more abstract than the other, the latter, event matching, considers the two events (i.e., differences) in spatial and temporal terms. That is, connecting event1 to event2 leads to the formation of a relationship, which corresponds to a space—whether physical, mental, or interactive. When event1 and event2 match simultaneously or coinstantaneously, they lead to a physical, mental, or interactive time practice. In this way, event matching entails spatial practice as well as time practice. We can therefore bridge information with time and space. We used to think that time and space were unique on their own spheres and that information regarding them was different. However, they are virtually synonymous when viewed from the perspective of meaning-making and spacetime production.

A unit of meaning-making, i.e., information for organisms, is not a quantifiable bit but rather news of difference, a boundary that an organism draws, the effort of which is called a boundary operation. Herein, we revisited the three types of spacetime practice, whose code names include the mental/cognitive A-series, the physical/measurable B-series, and the communicative/interactive E-series, all three of which have already been discussed elsewhere (Nomura, 2023). These operations are accompanied by each unique means of boundary operation to make up the spacetime series. Spacetime production thus requires different codes for different users based on different grammars, whether they are first-person agents, second-person participants, or third-person observers (see Table 1).

Event matching is a meaning-centered version of the boundary operation that allows the insider perspective to explicate the mechanism of meaning generation. Events as defined in this paper correspond to the boundaries in the boundary operation. Event matching, as a cross-field notion, is also considered on par with explanatory principles such as cause and effect, stimulus-response, and constraint. Through biological examples, we have discussed how event matching produces spacetime. In this way, organisms’ effort after meaning can be equated to the production of their spacetime.