Construct · 3 fields · 6 citations

Where does span collide?

One name. Different field. Different construct. One map.

● jingle · one word, three constructs Nearest construct by meaningworking memorycompare the meanings
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Every construct on the map is compared with every other by the meaning of its definitions, and the closest one is surfaced here. The nearest construct to span is working memory.

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span3 CONSTRUCTSLinear spanGRASSMANN · SPANNING SETMemory spanJACOBS · MEMORY SPANSpan of controlGRAICUNAS · SUBORDINATES

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1844Linear span1887Memory span1933Span of control
2026

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Mathematics (linear algebra)

The set of all linear combinations of a group of vectors

The collection of every vector you can build from a fixed group of vectors by scaling each one and adding the results, which is the smallest flat space that contains them all. Grassmann's 1844 Die lineale Ausdehnungslehre set out the idea that a system of vectors generates the set of all such combinations, and Peano's 1888 Calcolo geometrico recast it in the axioms of a vector space that textbooks still use; the English word span for this generated set became standard only later. Here the referent is a set of points in a space, fixed once the starting vectors are chosen, and it has nothing to do with how many items a mind can hold or how many workers report to a boss.[1][2]

Unit
One vector space: the set of all linear combinations of the chosen vectors
Recovery means
Not applicable
Measured by
Determined by which vectors lie in the set and by its dimension, the number of independent vectors needed to generate it

Cognitive psychology

The most items a person can repeat back in order after one exposure

The largest amount of material a person can repeat back in the right order right after seeing or hearing it once, taken as a measure of immediate memory capacity. Jacobs's 1887 Experiments on prehension introduced the digit-span test, reading out ever longer strings of numbers to find the point where recall breaks down, and Miller's 1956 The magical number seven, plus or minus two argued that this limit sits at about seven items for many kinds of material. Here the referent is a bound on one person's short-term recall, counted in items, not a set generated from vectors or a count of employees under a manager.[3][4]

Unit
A person's immediate recall limit, counted in items such as digits or words
Recovery means
Not applicable
Measured by
Tested by presenting lists of increasing length and recording the longest one repeated back reliably in order

Management

The number of subordinates who report to one manager

The number of people who report directly to a single manager, treated as a limit on how many working relationships one person can supervise well. Graicunas's 1933 Relationship in organization counted the direct, cross, and group relationships a manager must handle and showed how fast they multiply as subordinates are added, and Urwick's 1956 The manager's span of control fixed the phrase and argued for a small number of reports at the top of an organization. Here the referent is a feature of a reporting structure, counted in direct reports, not a limit on memory or a set built from vectors.[5][6]

Unit
One manager's count of direct reports
Recovery means
Not applicable
Measured by
Read off an organization chart as the number of positions reporting to a given manager

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Nearby collisions

working memory5 names · 8 citationsjangle · one capacity, several modelsvector3 fields · 3 citationsjingle · one word, three constructscontrol4 fields · 5 citationsjingle · one word, four constructs

References

  1. Grassmann, H. G. (1844). Die lineale Ausdehnungslehre, ein neuer Zweig der Mathematik. Leipzig: Otto Wigand.
  2. Peano, G. (1888). Calcolo geometrico secondo l'Ausdehnungslehre di H. Grassmann, preceduto dalle operazioni della logica deduttiva. Torino: Fratelli Bocca.
  3. Jacobs, J. (1887). Experiments on "prehension". Mind, os-12(45), 75–79. https://doi.org/10.1093/mind/os-12.45.75
  4. Miller, G. A. (1956). The magical number seven, plus or minus two: Some limits on our capacity for processing information. Psychological Review, 63(2), 81–97. https://doi.org/10.1037/h0043158
  5. Graicunas, V. A. (1933). Relationship in organization. Bulletin of the International Management Institute, 7, 39–42.
  6. Urwick, L. F. (1956). The manager's span of control. Harvard Business Review, 34(3), 39–47.

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