Social Algebra

This page is a sub-page of our page on Algebra.

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The sub-pages of this page are:

Socially Responsible Algebra

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Related pages:

Mathematics is Representation
Knowledge Algebra
• Business Algebra
Social Calculus
Discourse Algebra
Activities and Participators

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Social algebra 1
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Social algebra 2
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Social algebra 3
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Social algebra 4

The notation used below is explained in our section on Business Algebra.

From me to you 1:
From me to you 1

From me to you 2:
From me to you 2

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\, M_e \, \stackrel {\mathrm{def}}{=} \, {\sum\limits_{m_e \, \in \, S_{ociety} }} m_e \,

\, M_e \, \equiv \, {(M_e)}_{Atomic} \oplus {(M_e)}_{Agregated} \;\; \equiv \, {\sum\limits_{m_e \, \in \, {(M_e)}_{Atomic}}^{ \text {} }} m_e \;\; \oplus \, {\sum\limits_{m_e \, \in \, {(M_e)}_{Aggregated}}^{ \text {} }} m_e

\, {(W_e)}_{Formal} \, \stackrel {\mathrm{def}}{=} \, {\sum\limits_{w_e( \, m^1_e \, ) \, : \, m_e( \, w_e(\, m^1_e \, ) \, ) \, \neq \; \emptyset }} \,\, w_e(\, m^1_e \, ) \,

\, {(W_e)}_{Informal} \, \stackrel {\mathrm{def}}{=} \, {\sum\limits_{w_e( \, m^1_e \, ) \, : \, m_e( \, w_e(\, m^1_e \, ) \, ) \, = \; \emptyset }} \,\, w_e(\, m^1_e \, ) \,

\, W_e \, \stackrel {\mathrm{def}}{=} \, {(W_e)}_{Formal} \oplus {(W_e)}_{Informal} \,

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\, i_{ntra}^{ \, m^1_e } \,

\, i_{nter}^{ \, m^1_e } \,

\, s_{upra}^{ \, m^1_e } \,


\, 1 \,

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Supra(=Formal)-Inter(=Informal)-Intra(=Internal)Networks(me)

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Supra(=Formal)-Inter(=Informal)-Intra(=Internal)Networks(1 --> me)

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\, F_{ormal}N_{ational}P_{roduct} \, \stackrel {\mathrm{def}}{=} \, {\sum\limits_{m_e \, \in \, M_e \, \in \, N_{ation}}^{ \text {} }}{c_{ontributions}}( m_e ) \,


\, F_{ormal}I_{nternational}P_{roduct} \, \stackrel {\mathrm{def}}{=} \, {\sum\limits_{m_e \, \in \, M_e \, \in \, W_{orld}}^{ \text {} }}{c_{ontributions}}( m_e ) \,


\, I_{nformal}N_{ational}P_{roduct} \, \stackrel {\mathrm{def}}{=} \, {\sum\limits_{m_e \, \in \, {(W_e)}_{Informal} \, \in \, N_{ation}}^{ \text {} }}{c_{ontributions}}( m_e ) \,


\, I_{nformal}I_{nternational}P_{roduct} \, \stackrel {\mathrm{def}}{=} \, {\sum\limits_{m_e \, \in \, {(W_e)}_{Informal} \, \in \, W_{orld}}^{ \text {} }}{c_{ontributions}}( m_e ) \,

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\, A_{gents} \, = \, ( \, P_{hysical} \oplus L_{egal} \oplus I_{nformal} \, ) \, B_{odies} \, = \,

\, = \, P_{hysical}B_{odies} \oplus L_{egal}B_{odies} \oplus I_{nformal}B_{odies} \, = \,

\, = \, H_{umans} \oplus M_{achines} \oplus O_{rganizations} \oplus N_{etworks} \,

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\, i_{ntra}^{ \, m_e } \,

\, i_{nter}^{ \, m_e } \,

\, s_{upra}^{ \, m_e } \,

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\, m_e^{ \, i_{ntra} } \,

\, m_e^{ \, i_{nter} } \,

\, m_e^{ \, s_{upra} } \,

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\, r_{eact} \, = \, i_{nterpret} \, = \, m_e^{ \, i_n } \, = \, \lim\limits_{m_e} \, i_n \,

\, a_{ct} \, = \, r_{espond} \, = \, o_{ut}^{ \, m_e } \, = \, \mathrm {co} \lim\limits_{m_e} \, o_{ut} \,

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\, i_{ntra} \,

\, i_{nter} \,

\, s_{upra} \,

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me^infra infra^me me^inter inter^me me^supra supra^me

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A conversational feedback loop in Knowledge Loop Algebra
between the communities \, {C_{om}}_1 \, and \, {C_{om}}_2 \, using the \, O_{utside} \, protocol
:

\, \langle \, {O_{utside}}_{input} \, \vert \vert \, {C_{om}}_1 \, \rangle \langle \, {C_{om}}_1 \, \vert \vert \, {O_{utside}}_{output} \, \rangle \langle \, {O_{utside}}_{input} \, \vert \vert \, {C_{om}}_2 \, \rangle \langle \, {C_{om}}_2 \, \vert \vert \, {O_{utside}}_{output} \, \rangle \,

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The \, N_{ew} \, interface emulated by an \, O_{ld} \, implementation

\, \langle \, N_{ew_{input}} \, \vert \vert \, N_{ew_{output}} \, \rangle \, = \, \overbrace{\langle \, N_{ew_{input}} \, \vert \vert \, O_{ld_{input}} \, \rangle}^{\text{transform}} \overbrace{\langle \, O_{ld_{input}} \, \vert \vert \, O_{ld_{output}} \, \rangle}^{\text{solve}} \overbrace{\langle \, O_{ld_{output}} \, \vert \vert \, N_{ew_{output}} \, \rangle}^{\text{invert}} \, =


\, = \, \overbrace{\langle \, N_{ew_{input}} \, \vert \vert \, O_{ld_{input}} \, \rangle}^{\text{translate input}} \overbrace{\langle \, O_{ld_{input}} \, \vert \vert \, O_{ld_1} \, \rangle \langle \, O_{ld_1} \, \vert \vert \, O_{ld_2} \, \rangle \langle \, O_{ld_2} \, \vert \, \cdots \, \vert \, O_{ld_n} \, \rangle}^{\text{the n milestones of the old solution process}} \overbrace{\langle \, O_{ld_{output}} \, \vert \vert \, N_{ew_{output}} \, \rangle}^{\text{translate output}}

NOTE: This formula assumes that \, O_{ld_n} \, \equiv \, O_{ld_{output}} .

Foresight and hindsight process manager
The EE(S+O+C)(M+O+P) Model
The Ericsson AXE10 Delay

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The TELL ME Innovation Cycle 1:

The TELL-ME innovation cycle-1

The TELL ME Innovation Cycle 2:

The TELL-ME innovation cycle-2

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