Co-location

Version

v4 · 2026-08-30 · History

Prime #

1330

Origin domain

Geography

Subdomain

spatial relations → Geography

Related primes

Neighborhood

Core Idea

Co-location is the relation that holds when two or more distinguishable entities, roles, or functions occupy one bounded region during an overlapping stretch of time. Its entire content is the removal of separation at a stated grain: the occupants are, for the purposes of that grain, in the same place at the same time. It says nothing beyond that — not that they meet, notice one another, cooperate, answer to a common owner, or constitute a single thing. ^[1]

Three commitments constitute the relation, and each can fail on its own. There must be plurality with distinguishability: at least two occupants that remain separately identifiable, since a pair that has fused into one entity no longer stands in any relation at all. There must be a declared region together with a membership rule, and that rule comes in two very different forms — container identity (the same vessel, the same room, the same database shard) or a proximity threshold measured from a focal point. And there must be temporal overlap sufficient for the shared placement to bear on the question being asked, since consecutive tenancy of one office is a fact about the room's history rather than a relation between its tenants. ^[2]

Ordinary usage is looser than this identity in one specific and consequential way: it forgets that every co-location claim is indexed to a resolution. Two tenants sharing a facility are co-located at the perimeter and separated one level down by cages, network segments, and access-control zones. Neither reading is mistaken; the question is simply incomplete until the grain is named. What the relation licenses, once the grain is fixed, is not an inference about traffic between the occupants but an inference about their common relation to the region — whatever the region undergoes, its occupants undergo together — together with an opportunity: any contact whose cost scales with distance becomes cheap, without thereby becoming actual. ^[3]

Structural Signature

Two or more distinguishable occupants → one bounded region under a stated containment or proximity rule → occupancy intervals that overlap ⇒ separation collapsed to zero at the declared grain, with interaction, coordination, ownership, and purpose all left open.

The arrow terminates in a permission rather than in an event. Everything that usually interests an analyst about things found in the same place — that they react, converse, contend for one power feed, hand work to each other — lies downstream of this relation and must be supplied by some further mechanism that the relation itself neither names nor implies. ^[4]

Recurring features:

• Plurality that survives the grouping. Two or more occupants, still individuated after being placed together. Fusion, merger, or aggregation into a single unit destroys the relation rather than intensifying it.
• A declared region plus a membership rule. Either container identity — same cell, same rack, same file, same jurisdiction — or a threshold distance from a focal point. The rule is stipulated by the analyst, not read off the world.
• An occupancy interval rather than an instant. Each occupant is present across a stretch of time, and the stretches must intersect. Point-in-time coincidence is a limiting case that most applications cannot use.
• A resolution index. The claim is true only relative to a grain, and the same pair typically flips from co-located to separated as the grain is refined. There is no resolution-free fact of the matter.
• Silence on what follows. The relation asserts reduced separation and declines every further commitment, which is why it can be established before anything is known about what the occupants do.
• A displacement counterfactual. Move either occupant outside the region, altering nothing about the occupant itself, and the relation ends. Nothing internal to either party is load-bearing.
• Symmetry always, transitivity only sometimes. Under container rules the relation is reflexive, symmetric, and transitive, and partitions occupants into well-defined groups. Under proximity rules it is symmetric and non-transitive, and no groups exist until a linkage convention is added.

What It Is Not

Co-location is not a claim that the co-located things interact. Competitors' servers stand metres apart on air-gapped networks; two proteins share a compartment and never touch; two departments occupy one floor and exchange nothing for years. The relation supplies the conditions under which contact would be cheap and remains entirely silent on whether contact occurs.

It is not an efficiency claim, and it carries no valence. "Co-locate the teams and communication will improve" is a separate empirical hypothesis about what people do with reduced separation; it is not entailed by the placement, and it fails often enough that the failures have their own literature. Equally, co-location is not a hazard by itself — whether shared placement is an advantage, a liability, or immaterial depends on the mechanisms operating in the region, none of which the relation names. ^[5]

It is not a claim about shared ownership, common purpose, or membership in one organisation. A carrier-neutral facility, a mixed-use city block, and a shared laboratory bench all host occupants whose only common property is where they are.

It is not a claim of zero distance. Regions have extent, so "same place" means "inside the same declared boundary", not "at the same point". Two occupants can be co-located and still be separated by a distance that matters for some purposes and not for others — which is exactly why the grain must be stated.

It is not permanent. Because the relation is defined over intervals, it starts, holds, and ends, and it can be dissolved by moving one occupant while leaving both unchanged in every other respect.

It is not a claim that the occupants are the same kind of thing. A technician, a centrifuge, a sample, and a maintenance contract can all be co-located in one room, and the relation treats them alike.

Finally, it does not require that occupancy be exactly aligned in time. Overlap suffices; strict simultaneity is not demanded, and the amount of overlap that counts as sufficient is set by the process under study rather than by the relation.

Broad Use

Molecular and cell biology. Enzymes and substrates confined to one organelle, scaffold proteins holding successive catalysts on a single backbone, and membraneless condensates that concentrate reactants all exploit shared confinement to raise effective concentration. The placement is the intervention; the chemistry that follows is separate. ^[6]

Economic geography and urban planning. Industrial districts, retail agglomerations, university-adjacent research parks, and mixed-use zoning are all arguments about which activities should share a bounded region during overlapping hours. Zoning is, structurally, a policy instrument for permitting and forbidding co-locations.

Computing and infrastructure. Virtual machines sharing a physical host, data placed on the node that will compute over it, services packed into one process, tenant deployments inside one carrier-neutral facility, and utilities threaded through a single shared trench are the same relation at five different grains.

Organisational design. Team rooms, cross-functional pods, embedded specialists, and campus consolidation are attempts to make interaction cheap by removing separation, and they are evaluated — correctly — on whether the interaction actually materialises.

Records and data structures. Fields in one row, rows in one page, keys in one partition, and documents in one index are co-located under logical container rules, and the performance consequences follow from the container, not from any relation among the values.

Clinical, military, and logistics settings. Patients in one ward, units on one base, inventory in one depot, and hazardous materials in one store are managed with explicit rules about who may share a region with whom, and for how long. Across every one of these settings the occupants and the consequences differ completely while the underlying place-and-interval relation is identical. ^[7]

Clarity

The confusion co-location dissolves is the collapse of four separate things into the single word together: being in one place, being there at one time, being mutually available to one another, and pursuing one purpose. The prime isolates the first two and explicitly refuses the second two. Once that split is made, several arguments that looked substantive turn out to be equivocations — "they share an office, so of course they collaborate" and "they work remotely, so they cannot be genuinely present to each other" both trade on the merged term and both dissolve when it is separated. ^[8]

It also dissolves a very common class of unresolvable disputes about placement. Two parties insist, with equal confidence, that a pair of systems is and is not co-located, and both are right, because one is speaking at the facility perimeter and the other at the network segment. The disagreement is about grain, not about the world, and no additional evidence will settle it. Requiring that a resolution be named converts an argument into a specification.

Finally, it separates an opportunity from an outcome, and separates common cause from interaction. Occupants of one region are exposed together to whatever befalls the region, and that correlation holds even when the occupants are perfectly indifferent to each other. Keeping the two apart is what allows an analyst to say that two components never communicate and are nevertheless not independent — a verdict the everyday sense of together cannot express, and one that matters wherever independence is being assumed. ^[9]

Manages Complexity

Establishing co-location lets an analyst stop tracking pairwise separations. A set of n occupants has n(n−1)/2 distances, routes, and transfer costs between them; a container rule replaces the whole table with one membership list, and every question of the form "how far is this from that, and what does the gap cost" is answered once for the region instead of once per pair. This is the compression that makes region-level reasoning tractable at all. ^[10]

It also lets one stop modelling the occupants' interiors for the purposes of exposure analysis. If the region floods, loses power, falls under a new jurisdiction, or is quarantined, every occupant is affected, and nothing about what any occupant is or does needs to be represented to reach that conclusion. One region-level event model covers an arbitrarily heterogeneous population.

And it lets one defer the interaction question entirely. Because the relation asserts nothing about what the occupants do, a complete co-location inventory can be built before any of that is known — useful precisely in the situations where the interactions are unknown, disputed, or deliberately concealed.

What it does not let anyone stop tracking is the boundary definition, the grain, and the intervals. Those are the relation's parameters rather than its outputs, and a co-location claim recorded without them is not a compressed fact but a discarded one.

Abstract Reasoning

The prime licenses a five-step procedure that can be run on a placement record without any knowledge of what the occupants do.

Step one: name the region and the membership rule. State whether membership is decided by container identity or by a distance threshold from a focal point, because the two rules have different algebras and support different conclusions.

Step two: name the grain, then re-ask one level finer. If the answer flips — co-located at the building, separated at the floor — the original claim was resolution-dependent and must be restated with its grain attached. If it survives several refinements, the co-location is robust and stronger inferences are available.

Step three: confirm plurality at that grain. Verify that the occupants are still distinguishable after the boundary is drawn; a "co-location" whose members are indistinguishable at the stated resolution is a single occupant described twice.

Step four: check interval overlap rather than mere co-membership. Two things listed against one region may never have been there at the same time. Overlap is a separate test, and it is the one most often skipped. ^[11]

Step five: run the displacement counterfactual. Relocate one occupant outside the region, holding everything else fixed, and ask whether the property under investigation survives. If it does, co-location was not doing the work and some other mechanism is responsible. If it disappears, the shared region was load-bearing, and the intervention space is placement rather than behaviour.

Two error modes bracket the procedure. Over-reading treats the relation as evidence of contact, coordination, or complicity, and produces guilt by address. Under-reading takes the relation's austerity literally and treats co-located items as independent, which is how nominally redundant systems come to share a failure. The instructive boundary case sits between them: two teams working in one online workspace from different continents are mutually available to each other in a mediated sense, yet they are not co-located unless a convention is explicitly adopted that treats the workspace as a place — and adopting it silently is how physical intuitions get imported into settings that do not support them. ^[12]

Knowledge Transfer

What carries across substrates is the role structure and everything built on it: two or more distinguishable occupants, a declared region with a membership rule, an interval of overlap, the displacement counterfactual, the resolution index, and the split between opportunity and correlated exposure. An analyst who can identify those in a cell can identify them in a rack, a ward, a city block, a shard, or a supply chain, and the diagnostic procedure runs unchanged. The two-rule distinction transfers too: wherever membership is set by a threshold rather than a container, the absence of transitivity travels with it, and any talk of co-located groups needs a linkage convention supplied locally. ^[13]

What does not carry is the metric and the mechanism. Distance means kilometres in geography, hop counts in a network, diffusion lengths in a compartment, and clock cycles in a memory hierarchy; these units are incommensurable, so no statement about how strongly co-located two things are survives the crossing. The consequences are similarly local: confinement raises reaction rates through collision frequency in a solution, and nothing in an office corresponds to that mechanism even though the placement relation is identical. Relocation cost is local as well — a process or a record moves for nothing, a refinery does not — so the displacement counterfactual is a thought experiment in some substrates and a live option in others.

The stipulated-place convention needs remaking in each substrate rather than assuming. Treating a namespace, an address space, a shared workspace, or a legal domicile as a region is a decision, and the decision must be re-justified every time, because it silently carries physical inferences about cheap transfer and shared exposure that may hold for one logical container and fail for the next.

Examples

Formal/abstract

Take three sensors on a line at positions 0, 40, and 80 metres, and a proximity rule that counts two occupants as co-located when they lie within 50 metres. Sensor A is co-located with B, and B with C, and A is not co-located with C. The relation is symmetric and reflexive but not transitive, which means it is not an equivalence relation and induces no partition. There is therefore no such object as "the co-located group" here: single-linkage chaining sweeps all three into one blob, while requiring mutual proximity yields two overlapping pairs that cannot be reconciled into disjoint groups at all.

The temporal condition behaves the same way. Occupancies of 09:00–10:00, 09:55–11:00, and 10:30–12:00 give an overlap relation with exactly the same non-transitive shape, so even in one room the three occupants form no group. Replace both rules with container forms — same room, and one shared shift with common start and end — and both relations become transitive, the partition is well defined, and every occupant of the room is co-located with every other. ^[11]

Mapped back: The relation's two constituents are each an equivalence relation under container rules and each merely symmetric under threshold rules, and the conjunction inherits the weaker property. Occupants, region, and interval are all present in both versions, so both are genuine co-location; what differs is the algebra, and with it whether "co-located group" denotes anything. Whenever an analyst speaks of co-location groups under a distance or interval threshold, a clustering convention has been added without being declared, and the membership of those groups is an artefact of that convention rather than of the placement.

Applied/industry

Several tenants install hardware in one carrier-neutral facility. They share a perimeter, a utility feed, a cooling plant, and a physical-security regime, and their leases overlap. At facility grain they are co-located. At cage, rack, and network-segment grain they are separated, and in many cases they are direct competitors whose deployments never exchange a packet. The relation holds and asserts nothing about their traffic.

Two consequences follow, and they are of different kinds. The opportunity is that a cross-connect between any two tenants costs almost nothing to install, which is why exchanges, transit providers, and content networks cluster in these buildings: the placement makes a class of interaction cheap without making it happen. The exposure is that one utility event, one cooling failure, one flood, or one severed conduit reaches every tenant at once, regardless of whether any of them has ever interacted.

The second consequence is where the abstraction earns its keep. An operator contracts with two providers advertised as independent, and both providers, unknown to the operator, terminate in the same facility. Nothing about either provider has changed, and no interaction between them exists; the independence assumption fails anyway, because the two are co-located at a grain the contract never named. ^[9]

Mapped back: Occupants are the tenant deployments, the region is the facility perimeter under a container rule, and the interval is the overlap of the leases. The relation licenses no inference about interaction, and indeed there is none, while supplying both the cheap-contact opportunity and the correlated exposure. The failed redundancy is the displacement counterfactual returning a positive result: move one provider to another facility, change nothing else about it, and the shared failure mode disappears — which identifies placement, not provider behaviour, as the thing to fix.

Structural Tensions

T1 — Resolution relativity versus a determinate answer. Every claim of shared placement is indexed to a boundary and a grain, and the same pair flips status as the grain is refined. No resolution is privileged, so the relation has no grain-free truth value, and most disputes about whether things are co-located are disputes about grain in disguise. Yet decisions demand one answer: a contract, an evacuation plan, or a redundancy audit cannot hold several grains at once. Fixing a grain by convention makes the relation operational and makes it partly stipulated.

T2 — Opportunity versus outcome. The relation supplies reduced separation and promises nothing, but it is almost never invoked except by someone expecting a consequence: faster handoffs, higher reaction rates, cheaper transfer, better morale. The austere reading is correct and inert; the consequential reading is useful and unlicensed. Organisations that co-locate, obtain the outcome, and then credit the placement attribute to the relation something it never asserted, which is why the reverse intervention so often disappoints.

T3 — Container identity versus proximity threshold. One word covers two membership rules with different algebras. Container rules yield an equivalence relation and a clean partition into groups. Threshold rules yield a symmetric, non-transitive relation with no groups at all. Nearly all informal reasoning assumes the container form — talk of co-located sets, cohorts, and clusters presupposes it — and then applies that reasoning to threshold-defined cases, manufacturing groups whose membership depends entirely on the linkage convention smuggled in to repair the missing transitivity.

T4 — Asserted austerity versus induced correlation. The relation refuses to claim interaction between occupants, but it cannot refuse common cause through the region. Every occupant is exposed to whatever the region undergoes: one outage, one fire, one raid, one jurisdictional change. So a relation defined largely by what it declines to say nonetheless carries a strong inferential consequence, and analysts who honour the austerity too literally treat co-located components as independent. Independence assumptions and undeclared co-location are rarely compatible, whatever the occupants do or fail to do to one another.

T5 — Physical place versus stipulated place. Whether a logical container counts as a place — a namespace, an address space, a shared workspace, a domicile — is a convention rather than a discovery. Adopting it extends the relation's reach enormously and imports physical intuitions about cheap transfer and shared exposure that may not hold in the logical case. Declining it keeps the relation clean and leaves a large class of structurally identical arrangements unnamed. Both moves cost something, neither is defensible in general, and the choice is usually made silently.

T6 — The temporal threshold cannot be set from inside. Occupancy must overlap enough for the shared placement to matter, but how much is enough depends entirely on the process being enabled, which the relation pointedly declines to specify. A millisecond suffices for a packet exchange and fails for a conversation; a shared shift suffices for handover and fails for acculturation. The sufficiency condition must therefore be borrowed from the very interaction the prime refuses to presuppose, leaving the definition complete in form and dependent on an external stipulation in practice.

Structural–Framed Character

Co-location sits at the structural pole of the structural–framed spectrum, with an aggregate of 0.0. All five diagnostics read zero, as clean a placement as the scale allows.

The relational skeleton is thin and complete: two or more distinguishable entities, roles or functions; a bounded hosting region containing them under one stated spatial or logical proximity rule; and occupancy that overlaps in time enough for the shared location to matter. The relation asserts reduced separation and nothing further — no interaction, cooperation, contrast, complementarity, shared ownership or unity — and it breaks when either occupant moves outside the region, without either occupant changing.

Human-practice-bound most clearly fixes the zero. Molecules, sensors and biological functions instantiate it exactly as workers, services and records do; the definition needs occupants, a boundary and an interval, no agent, observer or practice. Vocabulary travels at zero: place, boundary and temporal overlap belong to no discipline's proprietary lexicon. Evaluative weight is zero — co-location is neither good nor bad, and the prime declines to say what follows. Institutional origin is zero: no organizational arrangement is required for two things to share a region. Import-vs-recognize is zero: asking whether two things are co-located checks a fact about a region and an interval, not a recasting of the domain.

The grade makes application a pure recognition operation, deliberately austere. State the boundary and resolution explicitly — services co-located in one building may be separated by rooms, networks or security zones — and do not let the relation smuggle in interaction or integration it never asserts.

Substrate Independence

Co-location is a highly substrate-independent prime — composite 4 / 5 on the substrate-independence scale. Almost nothing in the relation can be domain-specific: two or more occupants that remain separately identifiable, one region declared by container identity or a distance threshold, and occupancy intervals that overlap, yielding separation collapsed to zero at the stated grain and silence about everything downstream. Reagents in a vessel, sensors on a rig, workers in a building, services on a host, records in a shard, and enzymes in a compartment all realize it identically. What keeps it off the top mark is that the statement is not medium-free all the way down, since it commits to a bounded place and a stretch of time, leaving structures without spatial or temporal indexing outside its reach.

• Composite substrate independence — 4 / 5
• Domain breadth — 4 / 5
• Structural abstraction — 4 / 5
• Transfer evidence — 4 / 5

Relationships to Other Abstractions

Current abstraction Co-location Prime

Parents (1) — more general patterns this builds on

• Co-location presupposes, typical Neighborhood Prime

  Co-location typically presupposes a neighborhood when shared presence is defined by a focal region and proximity rule, though exact same-container cases need no tunable radius.

Children (4) — more specific cases that build on this

• Coupled column Domain-specific is a kind of Co-location

  The proposed strict upward parent is prime:co_location.

• Gene Gating Domain-specific is a kind of Co-location

  Co-location is the strict parent because the proposed advantage comes from bringing transcriptional loci and export machinery into one pore-associated region.

• Mechanical Floor Domain-specific is a kind of Co-location

  A Mechanical Floor strictly specializes Co-location.

▸ Show 1 more

Hierarchy path (1) — routes to 1 parentless root

• Co-location → Neighborhood → Topology

Neighborhood in Abstraction Space

Co-location sits in a sparse region of abstraction space (75^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely rather than landing on a neighbor.

Family — Sets, Order & Foundational Structure (19 primes)

Nearest neighbors

• Neighborhood — 0.70
• Located-In Relation — 0.69
• Identity (philosophy) — 0.69
• Mixing — 0.69
• Co-Presence — 0.69

Computed from structural-signature embeddings · 2026-09-10

Not to Be Confused With

Co-location must be distinguished first from Co-presence, which is its most important and most frequently merged neighbour. Co-presence is the relation of mutual interactional availability: two or more agents can treat each other as presently available and can condition action on that availability within a latency appropriate to what they are doing. Co-location is a fact about a region and an interval; co-presence is a fact about reciprocal access. The two cross-classify completely, and all four cells are populated. Strangers in a lift are co-located and, by studious mutual avoidance, barely co-present; occupants of one open-plan floor separated by headphones and calendars are co-located all day and interactionally unavailable for most of it; two colleagues on different continents sharing a live document with sub-second feedback are co-present and not co-located; and a pair working side by side on a shared task are both. The practical importance of keeping them apart is that they respond to different interventions. Co-location is changed by moving bodies, machines, or records; co-presence is changed by attention, channel, latency, and social protocol. Programmes that pursue co-presence by purchasing co-location — the office as a collaboration instrument — are relying on an empirical link between the two that the structural relation does not supply, which is precisely why the results are so uneven.

Neighborhood is the nearest structural relative and stands in a different logical position. A neighborhood fixes a focal point and a proximity rule and thereby carves out a local window; it is an asymmetric, point-centred object. Co-location is a symmetric relation among the occupants of a region, with no focal point at all. In proximity-defined cases co-location presupposes a neighborhood: erase the window and shared placement becomes undefined. But container-defined cases — same vessel, same address, same shard — establish co-location with no tunable radius and no focal element, so the dependence is typical rather than strict. The clean way to hold them apart is that a neighborhood answers "what is near this", while co-location answers "are these in the same place".

Locality of Reference is often invoked in the same breath and makes a wholly different kind of claim. Locality is distributional and about demand: accesses cluster in time and space, so what was just used predicts what will be used next. Co-location is about placement and asserts nothing about access patterns. The two are complementary rather than overlapping, and the relationship between them is instrumental — locality is the empirical regularity that makes deliberate co-location worth doing, and co-location is the design response to it. A system can exhibit strong locality while its hot items are scattered, which is exactly the situation a placement intervention is meant to fix; and items can be perfectly co-located while demand for them is uniform, in which case the placement buys nothing.

Clustering differs on the direction of inference. Clustering partitions a population by within-group similarity in a chosen feature space, and the groups are an output: no labels existed before the algorithm ran. Co-location's membership is decided by a boundary the analyst declares in advance, so the grouping is an input. Clustering applied to positions can discover regions in which things happen to be dense, but what it produces is a proposed boundary, not the relation itself — and, as the threshold case shows, imposing a clustering convention on proximity-defined co-location is exactly the move that fabricates groups the relation does not license.

Containment shares the bounded region and differs on purpose and symmetry. Containment maintains a perimeter in order to prevent something from spreading or interacting with what lies outside; it is asymmetric between the container and the contained, purposive, and evaluatively loaded. Co-location is symmetric among peers, has no purpose, and makes no claim about escape. A quarantine ward co-locates its patients with each other as a side effect of containing a pathogen with respect to everyone else, which is the general pattern: containment is about what the boundary does to the outside, co-location about what sharing the inside means for the occupants.

Coupling is a dependency relation and is orthogonal to placement. Two modules on one host can be entirely decoupled, and two tightly coupled services can be continents apart. Co-location often reduces the cost of coupling and is regularly mistaken for evidence of it, which is the structural error behind reading shared address as shared interest. Concurrency covers the temporal half alone: it names overlapping activity intervals without any requirement of a shared region, and without requiring the occupants to be processes at all, which is the further commitment co-location adds.

Solution Archetypes

No catalogued solution archetypes reference this prime yet.

References

[1] Goffman, Erving. Behavior in Public Places: Notes on the Social Organization of Gatherings. The Free Press of Glencoe, 1963. Separates physically sharing a setting from co-presence and mutual engagement, documenting civil inattention as the routine case in which people in one place systematically decline to notice, meet or engage one another. registry ↩

[2] Hagerstrand, Torsten. "What about people in Regional Science?". Papers of the Regional Science Association 24(1), 1970. Founds time-geography on space-time paths in which occupants share a station only where their paths coincide in place and in time, so successive tenancy of one location is a fact about the location rather than a relation between its occupants. registry ↩

[3] Openshaw, Stan. The Modifiable Areal Unit Problem. Concepts and Techniques in Modern Geography 38, Geo Books, 1984. Establishes that spatial results are indexed to the scale and zoning of the units an analyst draws, with no scale-free fact of the matter – the resolution-indexing premise on which this sentence's 'once the grain is fixed' clause rests. registry ↩

[4] Blanchet, F. Guillaume, Kevin Cazelles, and Dominique Gravel. "Co-occurrence is not evidence of ecological interactions". Ecology Letters 23(7), 2020. Argues that shared occupancy of a region licenses no inference about interaction between the occupants, which has to be supplied by a separate mechanism and separate evidence. registry ↩

[5] Bernstein, Ethan S., and Stephen Turban. "The impact of the 'open' workspace on human collaboration". Philosophical Transactions of the Royal Society B 373(1753), 2018. Two field studies find face-to-face interaction fell sharply after spatial boundaries were removed, showing that the efficiency claim is an empirical hypothesis separate from, and not entailed by, the placement. registry ↩

[6] Banani, Salman F., Hyun O. Lee, Anthony A. Hyman, and Michael K. Rosen. "Biomolecular condensates: organizers of cellular biochemistry". Nature Reviews Molecular Cell Biology 18(5), 2017. Describes membraneless compartments that concentrate specific molecules within a shared region, raising effective local concentration and the rates of the reactions that follow. registry ↩

[7] Siegel, Jane D., Emily Rhinehart, Marguerite Jackson, Linda Chiarello, and the Healthcare Infection Control Practices Advisory Committee. "2007 Guideline for Isolation Precautions: Preventing Transmission of Infectious Agents in Healthcare Settings". Centers for Disease Control and Prevention, 2007. Sets explicit patient-placement, cohorting and duration-of-precautions rules governing who may share a room or ward with whom and for how long. registry ↩

[8] Kiesler, Sara, and Jonathon N. Cummings. "What Do We Know about Proximity and Distance in Work Groups? A Legacy of Research". In Distributed Work, MIT Press, 2002. Reviews the evidence that proximity facilitates rather than guarantees collaboration, and that distributed groups can work effectively given cohesion and structure, so neither same-place-therefore-collaboration nor apart-therefore-no-presence holds as an entailment. registry ↩

[9] Perrow, Charles. Normal Accidents: Living with High-Risk Technologies. Basic Books, 1984. Identifies proximity and common-mode connections as sources of unexpected coupling between components that have no functional interaction, so items sharing a region cannot be assumed independent. registry ↩a ↩b

[10] Barnes, Josh, and Piet Hut. "A hierarchical O(N log N) force-calculation algorithm". Nature 324, 1986. Replaces the pairwise interaction table with a region-level treatment of grouped bodies, the compression that makes large-N systems tractable. registry ↩

[11] Allen, James F. "Maintaining knowledge about temporal intervals". Communications of the ACM 26(11), 1983. Defines the thirteen relations that can hold between time intervals, establishing overlap as a relation distinct from co-membership and not transitive, while interval equality is an equivalence relation that partitions cleanly. registry ↩a ↩b

[12] Olson, Gary M., and Judith S. Olson. "Distance Matters". Human-Computer Interaction 15(2-3), 2000. Analyses which affordances of physical co-location a mediated shared workspace does and does not reproduce, and what remote groups must supply in their place. registry ↩

[13] Jain, A. K., M. N. Murty, and P. J. Flynn. "Data clustering: a review". ACM Computing Surveys 31(3), 1999. Shows that the groups obtained from a proximity threshold depend on the linkage criterion chosen – single-link chaining versus complete-link compactness – so no partition follows from the distances alone. registry ↩