Construct · 5 fields · 7 citations

Where does integration collide?

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

● jingle · one word, five constructs Nearest construct by meaningintegralcompare 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 integration is integral.

Hold this as a prompt, not a verdict. Two constructs sitting close in meaning is a reason to read them side by side and decide for yourself whether they are one idea under two names. It is not proof that they are. Compare the meanings in the Collider.

integration5 CONSTRUCTSThe integralBARTLE · AREA UNDER CURVESocial integrationDURKHEIM · SOCIAL BONDSystems integrationHASSELBRING · EAINeural integrationMAGEE · SUMMATIONIntegrationHILLIER · URBAN DESIGN

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1897Social integration1976The integral1984Integration2000Systems integration2000Neural integration
2026

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Mathematics (calculus)

Area under a curve, the inverse of differentiation

In calculus, integration is the operation of finding an integral, the continuous analogue of summation that measures the signed area under a curve and serves as the inverse of differentiation. The definite integral is defined rigorously as a limit of Riemann sums, or more generally through Lebesgue measure, and the fundamental theorem of calculus ties it to the antiderivative. Bartle's 1996 Return to the Riemann integral revisits how the integral is constructed and what it captures. The referent is a mathematical operation on functions, whose result is a number or a function, and it has nothing in common with binding people to a society, joining computer systems, or summing synaptic input.[1][2]

Unit
A definite integral, the signed area under a curve
Recovery means
Not applicable
Measured by
Computed by antiderivatives through the fundamental theorem, or numerically by quadrature, and defined rigorously as a Riemann or Lebesgue integral

Sociology (social policy)

Binding members into the collective

In sociology and social policy, social integration is the incorporation of individuals or groups, such as immigrants, into the institutions, relationships, and shared life of a society, and in Durkheim the degree to which members are bound to the collective. Durkheim's Suicide (1897) argued that weak integration into social groups raises the risk of certain suicides, making integration a property of the bond between a person and the collective. Berkman and colleagues (2000) carried this forward, tracing how social integration, gauged by ties and participation, shapes health. The referent is a relationship between members and a social whole, not an operation on functions, a link between computers, or a current in a neuron.[3][4]

Unit
The degree to which members are bound to the collective
Recovery means
Not applicable
Measured by
Gauged by indicators such as social ties, group membership, and participation, and in Durkheim by rates that vary with the strength of collective bonds

Information systems

Joining separate systems into a coordinated whole

In information systems and management, systems integration is the joining of separate information systems or subsystems so that they exchange data and function as a coordinated whole, as in enterprise application integration or the merging of IT after an acquisition. Hasselbring (2000) set out the levels at which such integration operates, from data through application to business process, and the middleware that connects them. The referent is a technical and organisational task of making heterogeneous systems interoperate, judged by whether the parts coordinate. Despite sharing the word with the sociological meaning, it is about machines and software, not the binding of people into a society.[5]

Unit
Separate systems made to function as a coordinated whole
Recovery means
Not applicable
Measured by
Assessed by whether subsystems exchange data and coordinate processes, for example through enterprise application integration or connecting middleware

Neuroscience

Summation of synaptic input at a neuron

In neuroscience, neural integration is the process by which a neuron sums the excitatory and inhibitory synaptic inputs it receives across its dendrites and over time, so that the combined signal at the soma determines whether it fires. This spatial and temporal summation, described by Magee (2000) for the integration of excitatory synaptic input in dendrites, is how a cell weighs many inputs into a single decision. The referent is an electrochemical computation in living tissue, read in millivolts at the membrane. It is unrelated to the area under a curve, the cohesion of a society, or the interoperation of computer systems.[6]

Unit
The net synaptic input that decides whether a neuron fires
Recovery means
The membrane potential decays back toward rest between inputs, so temporal summation requires inputs to arrive close together in time
Measured by
Recorded by intracellular electrophysiology as excitatory and inhibitory potentials sum in space and time across the dendrites and soma

Urban design

how few steps a space is from all other spaces in a street or building network, used to predict movement.

In urban design, integration refers to how few steps a space is from all other spaces in a street or building network, used to predict movement. This meaning comes from Hillier (1984) in The social logic of space.[7]

Unit
Recovery means
Measured by

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Nearby collisions

binding4 fields · 4 citationsjingle · one word, four constructsdifferentiation4 fields · 4 citationsjingle · one word, four constructsintegral3 fields · 4 citationsjingle · one word, three constructs

References

  1. Bartle, R. G. (1996). Return to the Riemann integral. The American Mathematical Monthly, 103(8), 625–632. https://doi.org/10.2307/2974874
  2. Rudin, W. (1976). Principles of mathematical analysis (3rd ed.). McGraw-Hill. ISBN 0-07-054235-X. ISBN 007054235X
  3. Durkheim, É. (1951). Suicide: A study in sociology (J. A. Spaulding & G. Simpson, Trans.). Free Press. (Original work published 1897)
  4. Berkman, L. F., Glass, T., Brissette, I., & Seeman, T. E. (2000). From social integration to health: Durkheim in the new millennium. Social Science & Medicine, 51(6), 843–857. https://doi.org/10.1016/S0277-9536(00)00065-4
  5. Hasselbring, W. (2000). Information system integration. Communications of the ACM, 43(6), 32–38. https://doi.org/10.1145/336460.336472
  6. Magee, J. C. (2000). Dendritic integration of excitatory synaptic input. Nature Reviews Neuroscience, 1(3), 181–190. https://doi.org/10.1038/35044552
  7. Hillier, B. (1984). The social logic of space. Cambridge University Press. ISBN 9780521233651

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