REVIEW

Space and time in the brainGyörgy Buzsáki* and Rodolfo Llinás

Nothing is more intuitive, yet more complex, than the concepts of space and time. In contrastto spacetime in physics, space and time in neuroscience remain separate coordinates towhich we attach our observations. Investigators of navigation and memory relate neuronalactivity to position, distance, timepoint, and duration and compare these parameters to units ofmeasuring instruments. Although spatial-temporal sequences of brain activity often correlatewith distance and duration measures, these correlations may not correspond to neuronalrepresentations of space or time. Neither instruments nor brains sense space or time. Neuronalactivity can be described as a succession of events without resorting to the concepts of spaceor time. Instead of searching for brain representations of our preconceived ideas, we suggestinvestigating how brain mechanisms give rise to inferential, model-building explanations.

Formost cultures, space and time are used tomap and explain the vastness and complex-ities of the universe. These terms are oftenused interchangeably—for instance, “TheIroquois live 2 days fromus.”Linguists note

that most temporal words have a spatial senseas their primary meaning (1): Half of the world’slanguages do not have grammatical tense to spec-ify past or future. The Amondawa in the Amazonand the Aborigines of inner Australia do not con-ceive of time as something independent of otherthings or something in which events occur. Yetthese cultures understand ordering, sequencesof events, and relationships (2, 3). Thus, it is notobvious that space and time are universal andindependent.Modern science has radically transformed these

dimensionless concepts with the introductionof measuring instruments. Space and time werereplaced with their definable variants: (i) distanceand displacement and (ii) duration and interval,whichwere quantified by the units of human-madeinstruments, such as rulers and clocks, therebygiving them practical meanings. In classical phys-ics, the “theater” or “container”metaphor of spaceand time determines the exact location and speedof a particle. Distance and duration are equatedvia velocity. Research in neuroscience continuesto be performedwithin this framework of classicalphysics (4), even though in contemporary physics“there is no longer space which ‘contains’ theworld, and there is no time ‘in which’ eventsoccur” (5). In this Review, we summarize currentneuroscience views on space and time, discusswhether the brain perceives or makes distanceand duration, analyze how assumed representa-tions of distance and durations relate to eachother, and consider the option that space andtime are mental constructs.

Representation of space in the brain

Extensive studies have separately examined thebrainmechanisms of representing space and time.

A common philosophy in most of these studiesis that space and time are preexisting categories;therefore, the research goal is to understand howwe sense them. In addition to distance and dura-tion, new questions have been posed: “Where amI?” (position) and “What time is it?” (a point intime or “now”).Not surprisingly, the field of neuroscience be-

gan to define space from a sensory perspectiveand postulated numerous spaces—such as palmspace, oral space, body space, visuo-ocular space,and instrumental space—first based on investi-gating brain-damaged patients (6). For exam-ple, when an Italian patient who had suffered aright parietal stroke was askedto imagine facing the Piazza DelDuomo in Milan and to describethe scene, he correctly identifiedbuildings on his right but omittedthose on the left. When asked toimagine standing at the oppositeend of the Piazza, the buildingshe listed were on the other, previously neglected,side, which was now to his right (7). Such “hemi-neglect” patients can perceive and recall ob-jects per se but cannot describe the objects intheir proper spatial relationship or access thecontralateral scene from their imagery. Sur-prisingly, despite this profound deficit, thesepatients can navigate and find places in a cityor at home (7, 8).Animal experiments corroborate the clinical

observations. In parietal areas homologous tothose whose damage causes hemi-neglect in hu-mans, neuronal populations combine environ-mental and corporeal inputs. Yet the parietal cortexhas no topographic map of the body or the en-vironment. Instead, neurons in this brain region(known as LIP and 7a) integrate multimodal in-formation from scenes to formparsimonious repre-sentations described as eye-, head-, or arm-centeredcoordinates (9). Another region (called MSTd)combines visual motion signals with eye move-ment and vestibular signals (10) to specify theobserver’smovement path (11). From such experi-ments, the notion emerged that the parietal cortexsupports mainly body-centered (egocentric) spa-tial behaviors. Transforming this egocentric co-

ordinate system into aworld-centered (allocentric)representation of space has been attributedto the hippocampus–entorhinal cortex system(10, 12, 13).Experiments on the hippocampal-entorhinal

system in rodents identified mechanisms thatdefine allocentric coordinates similar to those ofclassical physics. Hippocampal and entorhinalprincipal neurons have place fields and grid fields,respectively, which collectively generate a spatialmap that represents landmarks, objects, andrelative locations (14, 15). The map is a “three-dimensional Euclidean space...conveying the no-tion of an all-embracing, continuous space” and“a prerequisite to the experiencing of objects andtheir motions” (14). However, it has remained am-biguouswhether the cognitivemap theory regardsspace as real and a priori, which is sensed or rep-resented in the hippocampal-entorhinal system,or whether the concept of space is constructedmentally by the brain without any assumption ofits existence.Establishing a relationship between brain

activity and distances can be done by the exper-imenter, who can relate neuronal recordings toinstrument-measured units. However, instrumentmeasurements are not available for neurons forsuch calibration. Establishing a relationship be-tween neuronal activity and distances in theworldrequires ambulation, which is supported by aconsortium of mechanisms, including optic andhaptic flow from local cues, vestibular accelera-tion signals, and perhaps the counting of steps

taken. The combination of dis-tance with head direction infor-mation (16) becomesdisplacement(i.e., a vector). These computationsare referred to as path integra-tion (17). Only through such cal-ibration process can the brainacquire meaning of distance

and direction. The emerging picture is that of abrain that constructs structured sequences ofneuronal cell assemblies whose function is toinfer trajectories through the lived or exploredworld. It should be noted that exploratory exper-ience is not a passive representation or percep-tion of space but a construction of relationships.Yet these formulations of map-based and pathintegration–based navigation cannot account foranother computation attributed to this system:memory (18).

Episodic memory: Mental travel in spaceand time

Navigation and memory are deeply connected.Analogous to map- and path-based navigation,there are two forms of hippocampal system–dependent memories: memorized facts (or se-mantic memory) and one’s personal experiences(episodic memory) (19). To reexperience egocen-tric episodes, we project ourselves back in spaceand time (episodic recall) (19), whereas travelinginto the imagined future represents planning(prediction). The neuronal mechanisms used tocreate and recall episodic memory are analo-gous to those evolved for computing first-order

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Neuroscience Institute, Departments of Physiology,Neurology, and Psychiatry, and Center for Neural Science,New York University, New York, NY 10016, USA.*Corresponding author. Email: gyorgy.buzsaki@nyumc.org

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(neighborhood) and higher-order (e.g., shortcuts,detours) distances to explore the physical worldvia path-based navigation. Similarly, neural al-gorithms that support map-based navigationare consonant with those needed to create andremember semantic knowledge (20). Like theformation of allocentric maps from egocentricexploration (20), semantic knowledge emergesgradually after repeated encounters with thesame thing or event by the episodic memory sys-tem (21, 22).This framework implies that most cortical

networks have a dual use: environment-dependentand/or internally organized (Fig. 1A). For exam-ple, sequential firing of place cells in maze cor-ridors appears to depend on environmental inputsand tracks an animal’s progress as it traverses amaze. However, when a rat is trained to run ina wheel or on a treadmill during the delay partof a memory task, neuronal assembly sequences(trajectories) emerge in the hippocampus whosephysiological features are difficult to distinguishfrom the place cell sequences in the maze (23, 24).The self-organized neuronal trajectories dependon the integrity of hippocampal theta oscillations(25), are distinctly different after previous left andright corridor choices, and predict the animal’sfuture choice several seconds before its behav-ioral decision (Fig. 1). Self-organized cell assemblysequences have been also observed in othermemory-related systems, including the entorhinalcortex (26, 27), the prefrontal cortex (28), andthe parietal cortex (29). These findings indicatethat neuronal mechanisms associated with nav-igation and memory are similar: they both es-tablish order relationships (20). However, memorymechanisms are no longer linked to metric dis-tances in the outside world.Storing and remembering what happened to

us, where and when, defines our personal epi-sodic memories, distinguishing us from others(19). This definition of episodic memory re-quires neuronal mechanisms to support boththe “where” and “when” axes. Many investi-gators have postulated the existence of neuro-nal clocks in the brain and assumed that theseclocks make time needed for various computa-tional purposes (23, 24, 30–33). During wheel ortreadmill running in a memory task, the ordinalsequences of neurons faithfully track elapsedduration (termed “time cells”) (Fig. 1B) from thebeginning of the run on subsequent trials inboth the hippocampus and the entorhinal cortex(23, 24). Because place cell firing frequency variesas a function of running velocity, the elapsedtime (and distance) can be continuously derivedfrom the combined knowledge of velocity andsequential firing of neuronal assemblies (34).These experiments demonstrate that sequentialneuronal activity can be tightly correlated withinstrument-measured units. However, they do notshow that these neuronal circuits are dedicated tocompute duration per se.

Warping space and time

Time flies during enjoyable activities but slowswhen we are bored. Highly motivated states,

novel situations, and focused cognitive activity(such as giving a talk) are associated with un-derestimation of time. Conversely, aversive situa-tions, fatigue, and sleepiness are associated withprolonged subjective time, possibly via affectingdopaminergic signaling (35).When we type on a keyboard and letters ap-

pear on the screen, we feel that we are the agentof our action. If increasing delays are introducedbetween the keystrokes and the letters,the brain accommodates. But if theartificial delay is suddenly removed,it annoyingly feels that the lettersappear before our keystrokes (36).Space and time compression and eventime reversal occur with each sac-cadic eye movement. Objects flashedbriefly just before and during the early part ofthe saccade are compressed parallel to the pathof the saccade (37). Perisaccadic durations areunderestimated by approximately the samemag-nitude as distances (36, 38), and study participantsoften reverse the order of presented events (39).Firing-pattern changes of parietal neurons mayunderlie the perceived compression of space andtime (40, 41).The space-time union of subjective experience

is amply demonstrated by asking study partic-ipants to imagine themselves as Lilliputians andto engage in activities in scale models (1/6, 1/12,and 1/24 scales) of a familiar full-size lounge.

Participants were asked to inform the investi-gator when they subjectively felt that 30 minhad passed. Notably, subjective time accelerationwas proportional to the size of the scaled-downmodels (42).Warping of distances and durations is typical

in hippocampal computation as well. Planningroutes frommemory involves compression of ex-perienced time, with longer routes and slower

movement speeds during the orig-inal experience leading to greatercompression rates (43). Distances cor-respond to proportionalmilliseconds-long intervals within hippocampaltheta oscillations (Fig. 2) (24). Evenlarger time compression of distancesoccurs when the experienced travel

trajectories are replayed during sleep in eithera forward or reversed manner (44). Overall,the distance-duration relativity suggests thatspace and time correspond to the same braincomputations.In the laboratory, we often find reliable cor-

relations between neuronal activity in variousbrain regions and succession of events (tem-poral sequence of representations). However,such relationship does not mean that neuronalactivity computes time (representation of tem-poral sequences) (45, 46), even if the succession ofevents refers to units of clock time. First, neitherclocks nor brains make time per se (47). Second,

Buzsáki et al., Science 358, 482–485 (2017) 27 October 2017 2 of 4

Fig. 1. Cell assembly sequences can track distance and duration. (A) During physical travel,successive assemblies of neurons (1 to n) respond sequentially because of the changingconstellation of environmental landmarks and/or proprioceptive information from the body(left). During mental travel, sequential activation is supported by self-organized patterning(right). (B) Sequential activation of neuronal assemblies in an episodic memory task. (Middle) Arat was required to run in a running wheel during the delay between choosing either the leftor right arms of the maze and to remember the last corridor choice. The rat obtained a waterreward if it chose the arm opposite of the previous choice. Color-coded dots represent spikeoccurrences of simultaneously recorded hippocampal neurons. (Left) Normalized firing-rateprofiles of neurons during wheel running, ordered by the latency of their peak firing ratesduring left trials (each line represents a single cell). (Right) Normalized firing rates of the sameneurons during right trials. Note that an observer can infer the run duration (and distance)in the wheel from the sequential firing patterns of the neurons. Modified from (23).

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representing or sensing duration implies thattime is a preexisting category whose passagethe brain detects. However, we do not directlysense time. For example, the amount of light andtemperature correlates with the duration of aday, and the brain can track such magnitudes.From the rate of change of these magnitudes, wecan mentally construct the concept of the flowof time (45). Clocks have made such inferencesever more precise in modern life.

Ordered neuronal sequences

Instead of taking space, time, or other mentalconstructs as a priori variables (i.e., the explanan-da) and searching for their neuronal mecha-nisms with expected similar boundaries (i.e., theexplanans) (48), we consider a reversed strategy.One way to ground neuronal correlates of dis-tance andduration is to relate them to an animal’sactions (49). Navigation—in the real world or themental domain—can be described by the ordinalsuccession of events, or “motion” in physics terms.

Motion is characterized by velocity and accelera-tion and has magnitude and direction, whichcan be sensed by vestibular, proprioceptive, andvisual receptors. Magnitude (rate of change, ac-celeration) and direction are key navigational pa-rameters that are closely related to duration anddisplacementmeasures (50, 51). As environment-driven functions become internalized in brainsof increasing complexity (52), the control of therate of change may be taken over by attention, inlieu of velocity. Although attention is a hypo-thetical construct, it has been suggested to affectresponse magnitude via neuronal gain control(53), similar to velocity (34). Thismay be the evolu-tionary route giving rise to the concepts of timeand space (49).Both the parietal cortex and hippocampal-

entorhinal system can be considered generalpurpose sequence generators that continuouslytile the gaps between events to be linked: encodingcontent-limited ordinal structure, thereby refer-encing to and linking cortical areas where se-

mantic details of the events are processed (23, 54).This ordered sequential access to neocorticalrepresentations is the physiologic interpretationof episodic memory (19, 21). Experimental worksupports the ordinal sequence function of thehippocampus. When patients with hippocampaldamage were examined after a tour around acampus, they could recall spatial and temporalaspects and details about particular events. How-ever, whereas control participants could well re-member the sequential order of the tour eventseven amonth later, the patients’ recalled order ofevents was unrelated to reality (Fig. 3) (55). Hip-pocampal damage in rats also induces a deficit inlearning sequential order of odor stimuli (56).Likewise, the primary purpose of perisaccadicneuronal events is to predict future eye-positionsequences (9).The ordinal sequences in neuronal trajec-

tories can represent the past, present, and future(Fig. 1) (22), providing an explanation for whybrain structures and mechanisms associatedwith memory (postdiction), imagination, andplanning (prediction or prospection) overlap(49, 57, 58). Postdiction and prediction may bedifferent names for the same brain computa-tion referenced to a relationship with the currentexperience (58).

Broader thinking

The hippocampal-entorhinal system has a topo-graphically organized bidirectional communica-tion with the large neocortex. During the courseof mammalian evolution and the correspondingdisproportional enlargement of the neocortex,hippocampal inputs shifted from largely sensoryandmotor representations in the rodent to inter-actions mainly with other higher-order corticalareas in primates (59). Hippocampal circuits arelargely “blind” regarding the modality and natureof cortical inputs. They process the sent mes-sages the same way, regardless of their origin.Given the many possible routes, the answers tothe question “What is the function of this circuit?”will be very different, depending on the routesthe investigator tests in a given experiment. Thefunction may appear to be space (14, 15), time(24), sound frequency (27), odor-sound sequence(60), memory (18), or something else, even thoughthe hippocampus responds to each case by gen-erating ordinal cell assembly sequences relevantto the particular situation (20). These consid-erations generalize to other brain regions aswell (61, 62).Relating sensory inputs to brain activity can

provide important yet limited clues to the func-tion of neuronal circuits, and there is no doubtthat the terms “space” and “time,” as well asother mental constructs, will be part of researchfor years to come. These concepts are part ofour everyday lives. Regarding sequential orderas space or time is an attempt to supplementthe “outside-in” strategy with a brain-centered,“inside-out” approach. It is such inferential,model-building, explanation-seeking brainmech-anisms that should lead our quest for clarifyingthese fundamental concepts.

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Fig. 2. Displacement-duration conversion by velocity in the hippocampus. (A) Trajectoriesof a rat through a place field on two trials with different speeds. (B) Spikes of one place celland the corresponding local field potential (LFP) theta rhythm of the same two trials asin (A). Horizontal arrows indicate the time it took for the rat to run through the place field.(C) The number of spikes within the neuron’s place field is similar on slow- and fast-run trials.Trials are sorted by velocity. (D) Spiking activity of two place cells (blue and green ticks) andLFP theta rhythm in a single run. Temporal duration (T) is the time needed for the rat to runthe distance between the peaks of the two place fields (behavioral time scale). t, time offsetbetween the two neurons within the theta cycle (theta time scale). (E) Three idealized placecells with identical theta oscillation frequency, illustrating the relationship between T and t.(F) Correlation between the distances of place field peaks and theta time scale lags (t) for manypairs of neurons. Solid curve, sigmoid fit to the values; dashed line, line of equity. Above andright: histograms of distance and time lag, respectively. Modified from (34).

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ACKNOWLEDGMENTS

We thank A. Berényi, D. Buonomano, O. Devinsky, A. Fernandez-Ruiz,K. Friston, C. Haimerl, D. Levenstein, J. Long, W. Ma, A. Maurer,M. Mehta, H. Rotstein, V. Varga, and the NeuWrite group at NewYork University for useful feedback on various versions of themanuscript. This work was funded by the NIH (grants MH54671,NS 090583, NS090526, and NS074015), the Simons Foundation,and the Mathers Foundation.

10.1126/science.aan8869

Buzsáki et al., Science 358, 482–485 (2017) 27 October 2017 4 of 4

Fig. 3. The core deficit in patients with hippocampal lesions is their inability to narrate eventsin the order in which they occurred. (A) Map of 11 events that occurred during a guided campus walk.Sidewalks, gray; buildings, blue. Arrows indicate the path taken during the walk. (B) Events from thewalk, described during 6-min narratives.The control group (Con; blue squares) tended to describe all11 events in the order in which they occurred.The order in which the patients (Pat; open triangles) describedevents was unrelated to the order in which the events occurred. n, number of individuals in each group.Reproduced from (55).

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Space and time in the brainGyörgy Buzsáki and Rodolfo Llinás

DOI: 10.1126/science.aan8869 (6362), 482-485.358Science 

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