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. 2022 Dec 16;59(Suppl 1):S24–S28. doi: 10.29399/npa.28159

Can a Common Magnitude System Theory Explain the Brain Representation of Space, Time, and Number?

Sertaç Üstün 1,2,3, Burcu Sırmatel 2,3,4, Metehan Çiçek 1,2,3,4,✉
PMCID: PMC9767125  PMID: 36578990

Abstract

Space, time, and number are important parts of our experiences and they are crucial for maintaining our behaviors in daily life. Comprehending the spatial and numerical features of our environment and perceiving and constructing the temporal framework are critical for healthy cognitive functioning and also survival. Although the problem of how these three perceptual processes work was initially studied separately, the emergence of behavioral interactions between these perceptions led to the idea that they could be run by a “common system”. Besides the behavioral interactions for space, time, and number perception, the lesion and neuroimaging studies investigating the neural basis of these perceptions suggest the existence of a common size perception system represented in a fronto-parietal network formed around the intraparietal sulcus. However, on the other side of the coin, there are different views proposed based on findings that contradict this common magnitude system theory. The purpose of this review is to evaluate suggested ideas together and to examine whether the representation of space, time, and number perception in the brain can be explained by a common magnitude system theory.

Keywords: Size perception, space perception, parietal cortex, time perception

INTRODUCTION

Space, time, and number define the most fundamental dimensions of our existence and perceiving these magnitudes is critical for us to interact effectively with our environment. Perceiving and processing temporal, spatial, and numerical information are directly related to abilities that are essential to survive in the evolutionary course. Therefore, these three perceptions are considered to be the most fundamental of higher cognitive abilities and play a vital role in almost all of our daily activities. Due to their importance, many studies have been conducted about space, time, and number perceptions over the years and theories have been suggested for explaining these perceptions. The most prominent one of these theories is the “common magnitude system theory” which hypothesizes that the spatial, temporal, and numerical information are processed by a common neural mechanism (1,2). Although various behavioral and neuroimaging studies point out the existence of a common magnitude system that can perceive different magnitudes, there are also findings in the literature that contradict this theory and lead to the development of alternative theories. This review aims to present an integrative approach to common size theory by bringing together the main findings regarding the perception of spatial, temporal, and numerical quantities.

Space, Time, and Number Perception

Space perception is a set of abilities that allow us to understand and process the size, shape, and movements of objects in our environment, including our own body, by using information that comes from different sensory modalities. Likewise, it enables us to navigate by understanding our position and the positions of the objects around us (3). The early findings about the neural basis of space perception came from lesion studies. In these studies, it was revealed that the right parietal cortex damage cause defects in space perception and the patients have difficulty perceiving one side of space (neglect disease) because of the damage (4). The fundamental role of the right-lateralized parietal cortex in space perception has also been confirmed by neuroimaging studies. Tasks requiring the processing of spatial information cause the activation of the right intraparietal cortex (5,6).

Highlights

  • Space, time, and number perception are partially represented by the common magnitude system.

  • Findings show that the neural representation of this system is in the parietal cortex.

  • The prefrontal cortex is responsible for executive functions associated with the system.

Similar to space perception, people can perceive time intervals in a broad spectrum (7). There are various theoretical approaches to explain how time intervals in milliseconds and seconds are perceived. While some of these models hypothesize the existence of an internal clock-like mechanism that generates temporal information (8), some models suggest that time-dependent changes in neural networks are used as temporal cues to encode time intervals (9). Neuroimaging studies have revealed that basal ganglia and cerebellum, the right-lateralized frontoparietal networks including the intraparietal sulcus (IPS) and dorsolateral prefrontal cortex, and also the insular cortex and supplementary motor area (SMA) are associated with time perception (10,11).

When it is considered that numerical quantities are a critical part of daily life, it can be understood that number perception is of crucial importance for living things. The ability to understand, process, and manipulate numerical quantities is called number perception (12). Although number perception has been thought of as a skill that is acquired through education for many years, studies have revealed that number perception, like time and space perception, is an ability that is controlled by a biological process that has evolutionary and developmental origins (13). Studies investigating the neural basis of number perception found that IPS is the main brain region responsible for number perception, regardless of culture and task type, and frontal regions are also consistently activated in numerical tasks (14). Moreover, studies revealed that a broad brain network including the fusiform gyrus and cingulate cortex is responsible for number perception and IPS may have a central role in this number network (15, 16).

Common Magnitude System Theory

The fact that the space, time, and numerical dimensions of our existence are similar to each other and seem to be perceived similarly has led to the idea that these three types of perceptions might be represented by a common cognitive mechanism.

The idea that different types of magnitudes could be perceived by the same system was first suggested by Meck and Church (1983). In the study, rats were trained to give different responses to auditory stimuli at different time intervals (2 and 8 seconds). Afterward, rats were given stimuli that have the same duration (4 seconds) but multiple times (2 and 8 times) and it was found that rats can automatically apply the rule they learned in the time perception task to the number perception task. The finding that a rule learned in the perception of one quantity can be generalized and applied in the perception of another quantity has led researchers to suggest that a common system is responsible for the perception of number and time (1). Based on this idea, Walsh (2003) suggested that the perception of space, time, and number are represented by a common magnitude system and named this hypothesis “A Theory of Magnitude (ATOM)”. According to this theory, a common magnitude system controlled by the inferior parietal cortex is involved in planning motor actions. Representation of different magnitudes by the same system is used for the efficient encoding of the motor actions with the help of sensory information by ensuring effective coordination of these three magnitudes (2).

Even though they can be separated in neuropsychological tasks, time and space are inseparable in real life. In other words, temporal and spatial information are almost always used together. In addition, temporal and spatial information gathered from the environment has critical importance for motor actions. To execute a certain motor action properly and therefore to survive in nature, it is necessary to perceive the temporal and spatial aspects of the movement. According to ATOM, a common mechanism representing time and space perception is expected to have evolved in the neural networks that enable the use of sensory information for movement planning in the motor system. Again, according to the theory, the ability to perceive numerical quantities, which is another similar magnitude, has evolved in the system that is already specialized in perceiving magnitudes. In short; a system for perceiving spatial and temporal stimuli for motor actions has evolved; and the ability to perceive discontinuous magnitudes (numerical quantities) has been built on top of the ability to detect these continuous magnitudes (time and space).This association has increased the efficiency of our interaction with the outside world (17).

Behavioral Findings Supporting the Common Magnitude System Theory

Although space, time, and number perceptions have often been examined in separate studies, lesion, behavioral and neuroimaging studies investigating the association of these perceptions have reached a large amount of evidence that points to the existence of a common magnitude system (17).

The main common aspect of the three magnitude perceptions is that it obeys Weber’s law, similar to other sensory modalities. Weber’s law, which states that magnitudes are compared not according to their absolute values but according to their ratio, appears consistently in various tasks related to space, time, and number perception. The fact that Weber’s law can be observed in numerous species and human infants shows that this law corresponds to an intrinsic cognitive feature related to the way it represents magnitudes (18).

The relationship between space and number perception

In many behavioral studies, findings indicating that spatial and numerical stimuli are represented by a common system have been found. The most popular one of these findings is the phenomenon called “Spatial Numerical Association of Response Codes” or simply “SNARC effect”. In their study, Dehaene et al., (1993) asked participants to decide whether the numbers they saw on the screen were odd or even and they found out that larger numbers were answered faster with the right button, and smaller numbers were answered faster with the left button (19). Researchers have argued that numbers are represented on a spatial line, increasing from left to right, and they defined this representation as the “mental number line”. The SNARC effect was later confirmed by a large number of studies that used a variety of tasks including symbolic or non-symbolic numerosities (20,21). The fact that the representation of numerical information shows spatial characteristics indicate that these two magnitudes are cognitively related. Although it is thought that the mental number line is related to the reading direction, some studies have revealed that the SNARC effect is also observed in infants and some animal species. Based on these findings, it has been discussed that the left-to-right representation of numbers in a spatial plane may arise from asymmetric brain development. Therefore, the mental number line is a trait we are born with and it is shaped by culture in the later stages of life (22).

Another finding revealing the space-number interaction is the effect of the spatial size of the number symbols on the perception of numerical magnitude. In one study, the participants were asked to decide which of the two numerical quantities displayed at the same time was larger. When the smaller number was presented in a large font and the larger one was presented in a small font (incongruent condition), participants had difficulty making comparisons and their reaction times were prolonged compared to the congruent condition. Similar to spatial stimuli having a confounding effect on the numerical comparison, the numerical stimuli also made spatial comparison difficult. Participants were affected by the numerical information when they were comparing spatial magnitudes, and it was difficult for them to respond in incongruent conditions (23).

The relationship between space and time perception

Similar to the space-number interaction, studies have revealed that the perception of space and time is also affected by each other. It has been argued that these findings indicate a common system that represents both space and time. In a study investigating the effect of spatial magnitudes on time perception, participants were asked to judge the duration of squares of different sizes staying on the screen. Results of this study have revealed that larger squares were perceived as staying on the screen longer. Based on this finding, it has been suggested that the spatial and temporal magnitudes are not independent of each other (24).

Parallel to the SNARC effect, participants in a temporal comparison task were shown to respond faster to shorter time intervals with the left button and to longer time intervals with the right button. This phenomenon is defined as the “Spatial-Temporal Association of Response Codes”, shortly the “STARC effect”. According to this, similar to numbers, temporal magnitudes are also represented on a spatial plane called the mental time line, increasing from left to right (25).

In a study, participants respond more quickly with their left hand to words associated with the past (yesterday, previous, etc.); and respond more quickly with their right hand to words associated with the future (tomorrow, next, etc.) and this finding confirms the STARC effect (26).

In another similar study, pictures of actors, half of whom lived in the past and half of which are still popular today, were shown to the participants as stimuli. It has been shown that participants respond more quickly with their left hand to old actors and respond more quickly with their right hand to new actors. Researchers argued that even in stimuli that do not have any temporal meaning, old-to-new flow is represented from left to right (27).

In another behavioral study, it was shown that irrelevant spatial stimuli can confound the temporal comparison task. Researchers have suggested that these findings resulted from a commonality between representations of space and time (28).

The relationship between number and time perception

There are also findings in the literature indicating that number perception and time perception are represented by a common system. It has been shown that in a task that requires comparing temporal magnitudes, a numerically larger stimulus is perceived as temporally longer (24). In a behavioral study that required time perception of stimuli presented in the form of numbers, it was found that small numbers were perceived as staying shorter on the screen than they were, while large numbers were perceived as staying longer on the screen than they were. The same effect was not observed when the study was repeated with letters instead of numbers (29).

In one study, participants were asked to decide whether the numbers were odd or even, to press the button for a short period if it was an odd number, and to press the button for a long period if it was an even number. The study revealed that the participants’ response was faster when small numbers require a short button press and when large numbers require a long button press. The tendency to associate large numerical quantities with long intervals and small numerical quantities with short intervals is defined as “Temporal-Numeric Association of Response Codes”, briefly “TiNARC effect” (30).

Another evidence for the interaction of number and time is that the secondary time task confounds and negatively affects numerical tasks. While the time perception task did not have any significant negative effect on other tasks, it reduced performance in number tasks (31). This finding was discussed as number and time perception using common mechanisms (2).

The relationship between space, time, and number perception

Although the interaction of space, time, and number perceptions has been studied mostly in pairs, there are also behavioral studies indicating the existence of interaction of three perceptions. In a study in which three types of perceptions were examined with a magnitude comparison task, in addition to the findings that confirm the STEARC, SNARC, and TiNARC effects, it was revealed that there was an interaction among the three perceptions and it is suggested that this finding confirms the common magnitude system (32).

In another study, which required evaluating the number, size, and duration of dot sets, findings revealed that the three perceptions affect each other and it is argued that this finding supports the common magnitude system (33). Three types of perception were examined together with a reproduction task in another study and a triple interaction supporting the common magnitude system was found. Also, it was claimed that number perception plays a critical role in this interaction (34).

In addition to behavioral findings, it is argued that the developmental disorders that can cause common problems in all three perceptions indicate the existence of a common magnitude system. For example, in dyscalculia, which is a learning disability characterized by difficulty in acquiring mathematical abilities despite normal intelligence and education level, individuals also have problems with temporal and spatial processing along with numerical perception problems (35). Also, individuals with 22q11.2 deletion syndrome (DiGeorge syndrome), a genetic disorder known to cause problems in spatial and temporal processing, also have impairments in number perception and it has been argued that these numerical problems result from impairments in space-time perception (36).

Lesion and Neuroimaging Studies in Support of the Common Magnitude System Theory

There are lesion and neuroimaging studies that aim to investigate the neural representation of the common magnitude system theory, though few compared to behavioral studies. The IPS, which is consistently activated in studies of space, time, and number perception (for space: Sack, 2009; for time: Nani et al., 2021; and for number: Sokolowski et al., 2017), is the first region that draws attention in the literature on the common magnitude system theory and it is considered the most ideal candidate for the neural basis of the system. However, the idea that the magnitude system is represented not by a single brain region but by complex neural circuits of different brain regions, especially by the frontal areas, is also argued in the literature (17).

The main evidence indicating that space, time, and number perception are related at the neural level has been observed in neglect syndrome. As mentioned above, in neglect syndrome, which is a disease that often occurs after the right parietal cortex lesion and is characterized by difficulty in perceiving one side of space, distortions in time perception have also been observed. Time perception experiments conducted on patients with neglect syndrome revealed findings indicating the existence of a spatial representation of time. It has been found that patients who neglect the left side of space tend to neglect the left side of the mental time line, and thus events related to the past. In one study, participants were asked to memorize various images associated with “10 years ago” and “10 years later”, and then tried to recall whether an image belonged to “10 years ago” or “10 years later”. While there was no difference in recalling images of the future between the control and the neglect group, it was revealed that individuals with neglect syndrome had difficulty remembering images associated with the past (37). Similarly, when the neglect patients were asked to find the midpoint of two numbers, it was found that they chose a number closer to the larger number as the midpoint. This finding indicates that numbers are represented in a spatial plane from left to right and the patients with neglect syndrome neglect the left side of the mental number line (38). In a similar task, results similar to those observed in neglect patients were obtained in healthy participants whose right IPS activity was temporarily inhibited by applying transcranial magnetic stimulation (TMS) (39).

In an fMRI-TMS study aiming to examine the relationship between number and time perception, a pair of dot arrays were presented on the screen, and participants were asked to compare and reproduce the duration of screen time of dot arrays. The fMRI findings of the study showed that the right inferior frontal gyrus (IFG) and right IPS regions along with the occipital areas were activated in the interaction of number and time perception. TMS findings of the study revealed that the inhibition of the IPS region by TMS application decreased the effect of the number task on time perception. TMS application to the IFG negatively affected the temporal comparison task. Researchers suggested that IPS is the main region in number-time interaction, while IFG is involved in decision-making processes, thus affecting the comparison task (40). In another fMRI study evaluating number and time perception together, participants were asked to judge the number or duration of stimuli on the screen. The results showed that the right-lateralized IPS, along with the frontal areas, was activated in both numerical and temporal processing. In connectivity analysis (psychophysiological interaction, PPI), it was observed that the connectivity between the right IPS and frontal areas increased both in number and time conditions of the task. Based on these findings, the researchers argued that IPS is directly related to the magnitude system, while frontal areas may be related to working memory and decision-making processes (41).

In an fMRI study evaluating space and number perception together, children and adult participants were asked to judge non-symbolic numerical multiplicities and spatial orientation. In adult participants, overlapping activations for space and number perception were observed in the right superior parietal lobe, including IPS, and occipital areas (42).

In a meta-analysis aiming to investigate the common neural basis of space and time perception, bilateral IPS, SMA, right IFG, and left precentral gyrus activations were found to be areas jointly activated by spatial and temporal processing. Researchers have suggested that these regions, especially IPS, are “core magnitude regions” that have critical roles in the magnitude system (43).

In a neuroimaging study examining the neural mechanisms of the common magnitude system by investigating three perceptions together, some overlapping brain activations related to space, time, and number perception were revealed. Participants were asked to perform comparison tasks related to the three perceptions while undergoing an fMRI scan. The right-lateralized IPS and inferior frontal cortex were found to have overlapping activations for all three perceptions. While IPS is discussed as the main region responsible for the magnitude representation, it has been suggested that IFG may be related to decision-making processes. In addition to these regions, premotor area and SMA activations were also found, and it has been argued that these regions were activated because of the association between the common magnitude system and motor actions (44).

Arguments and Findings Contrasting with the Common Magnitude System Theory

Although there are numerous behavioral and neuroimaging findings that provide evidence for the existence of a common magnitude system, some studies indicate that space, time, and number are perceived by similar but separate cognitive systems. It has been suggested that the interactions between the three perceptions revealed in behavioral studies may not be due to the common magnitude system, but to the commonality of executive functions associated with these perceptions. It is also discussed that the impairment of all three perceptions in various disorders may be related to the deterioration of domain-general processes such as working memory and attention. It has been argued that response code effects (SNARC, STARC, TiNARC) pointing to the common magnitude system may be related to the tasks in studies. According to this argument, findings indicating the existence of a mental time line and a mental number line may arise due to the tasks that specifically lead the participants to map time and number onto space (18).

In the case of the common representation of the three perceptions, it should be expected that the perceptions would be affected similarly by the same external stimuli. The idea that the three perceptions are affected differently by external stimuli contradicts the common magnitude system theory. An example of this is the effect of emotions. Emotional stimuli cause an overestimation of time intervals (45) whereas an underestimation of numerical quantities (46). Similarly, it has been shown that the effect of cognitive load on number and time perception is also different. When the cognitive load is increased with a secondary task that requires attention, numerical quantities are underestimated, whereas time intervals are overestimated (47). It has been suggested that the fact that the same psychological context affects two perceptions in different ways indicates these perceptions are not represented by a common system.

In a study examining the neural basis of the common magnitude system, TMS was applied to the IPS during numerical and temporal processing tasks. It has been revealed that the TMS application to the left IPS disrupts the numerical processing, and the temporal processing is not affected by the TMS applied to either the left or the right IPS. These results were discussed as evidence of the absence of a specialized common magnitude system in the parietal cortex (48).

A theory has been proposed that hypothesizes that perceptions of space, time, and number are represented by a common system only during infancy and the neural representations of the three perceptions diverge with age (49). According to this theory, as a result of mechanisms such as synaptic pruning in infancy, a specialization occurs in the general representation system, and this specialization leads to the control of three perceptions by distinct neural systems in adulthood. This theory, which suggests that the common magnitude system only exists in the early stages of development has been named the “developmental divergence model” (18). On the other hand, there is evidence that symbolic and non-symbolic systems are also associated in early childhood, but not in late childhood and adulthood (50). Researchers who proposed the developmental divergence model did not focus on whether this differentiation, which is more evident at the age of 3-5 and with education, differs in terms of representations of symbolic and non-symbolic magnitudes in the brain and this could be considered as a shortcoming of this theory.

In recent years, the idea that space, time, and number are only partially represented by a common system has gained importance. Cona et al., (2021) examined the commonality of space and time perception with fMRI and they suggested that the neural representations of these perceptions are partially common, and moreover, show a gradient pattern. According to these findings, anterior parts of the SMA are more associated with space perception, while posterior parts are associated with time perception; dorsal parts of frontal and parietal areas are associated with space perception, while ventral parts of these regions are associated with time perception. It was argued that domain-general processes related to magnitude perceptions cause joint activations and the domain-specific processing may occur in separate regions of the frontoparietal circuits (43).

CONCLUSION

Space, time, and number perception have been studied separately and together with numerous behavioral and neuroimaging studies for many years. It is understood from the studies that a common magnitude system plays at least a partial role in the representation of these three perceptions. The common magnitude system, named “ATOM” by Walsh, is represented in the parietal cortex (especially IPS), and the prefrontal cortex (especially the IFG) is responsible for executive functions related to magnitudes (35,40,43). In addition to the frontoparietal circuits that represent the common magnitude system, there are also non-shared brain regions specific to separate perceptions, such as the basal ganglia and cerebellum for time perception (10).

Studies on this subject have made considerable progress and have provided important insight into how we perceive magnitudes. Nevertheless, neuroimaging studies, in which three types of perception will be examined together are necessary to eliminate the existing contradictions and inconsistencies in the field. Also, longitudinal studies on the developmental changes of the three perceptions will contribute to the understanding of how the common magnitude system differs with development. Finally, investigating the common magnitude system with various connectivity analysis methods can reveal the neural circuits and mechanisms responsible for this system. For the proper discussion of the confirming or contradicting findings about the common magnitude system and/or developmental divergence model, connectivity studies are needed. With the help of connectivity studies, it can be understood whether fully or partially overlapping neural networks represent the magnitudes.

A clear understanding of the common magnitude system will help shape behavioral research in these areas and the brain mapping of these cognitive functions. Future research in the field will pave the way for a better understanding of the disorders and learning difficulties characterized by the impairment of these perceptions.

Footnotes

Peer-review: Externally peer-reviewed.

Author Contributions: Concept- SÜ, BS, MÇ; Design- SÜ, BS, MÇ; Supervision- (-); Resource- (-); Materials- (-); Data Collection and/or Processing- SÜ, BS, MÇ; Analysis and/or Interpretation -SÜ, BS, MÇ; Literature Search- SÜ, BS, MÇ; Writing- SÜ, BS, MÇ; Critical Reviews- SÜ, BS, MÇ.

Conflict of Interest: The authors declared that there is no conflict of interest.

Financial Disclosure: No financial support has been received.

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