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*To*: Ontology <ontology@ieee.org>*Subject*: ONT Re: Differential Analytic Turing Automata*From*: Jon Awbrey <jawbrey@att.net>*Date*: Tue, 09 Mar 2004 22:02:33 -0500*References*: <403F546C.D69B6918@att.net> <40476DB3.BC029F0@att.net> <404BB2D9.B81EF7A2@att.net> <404C0A1A.CFBAC3D@att.net> <404C8319.89C2BC35@att.net> <404CD392.1DE2C4A@att.net> <404CF289.BDFA49CF@att.net> <404DF756.DF6C4EFB@att.net> <404E52BE.D63866D1@att.net>*Sender*: owner-ontology@majordomo.ieee.org

o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o DATA. Note 19 o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o I'd never rob readers of exercise ... but for my ain sense of an ending --- Computation Summary for g<u, v> = ((u, v)) Figure 2.1 expands g = ((u, v)) over [u, v] to get the equivalent exclusive disjunction u v + (u)(v). Figure 2.2 expands Eg = ((u + du, v + dv)) over [u, v] to arrive at Eg = uv((du, dv)) + u(v)(du, dv) + (u)v (du, dv) + (u)(v)((du, dv)). Eg tells you what you would have to do, from where you are in the universe [u, v], if you want to end up in a place where g is true. In this case, where the prevailing proposition g is ((u, v)), the component uv((du, dv)) of Eg tells you this: If u and v are both true where you are, then change either both or neither u and v at the same time, and you will attain a place where ((u, v)) is true. Figure 2.3 expands Dg over [u, v] to obtain the following formula: Dg = uv (du, dv) + u(v)(du, dv) + (u)v (du, dv) + (u)(v) (du, dv). Dg tells you what you would have to do, from where you are in the universe [u, v], if you want to bring about a change in the value of g, that is, if you want to get to a place where the value of g is different from what it is where you are. In the present case, where the ruling proposition g is ((u, v)), the term uv (du, dv) of Dg tells you this: If u and v are both true where you are, then you would have to change one or the other but not both u and v in order to reach a place where the value of g is different from what it is where you are. Figure 2.4 approximates Dg in the proxy of the linear proposition dg = uv (du, dv) + u(v)(du, dv) + (u)v (du, dv) + (u)(v) (du, dv). Noting the caste of the constant factor (du, dv) distributed over the expansion of a tautology, this may be digested as dg = (u, v). Figure 2.5 shows what remains of the difference map Dg when the first order linear contribution dg is removed, and this is nothing but nothing at all, leaving rg = 0. o---------------------------------------o |```````````````````````````````````````| |```````````````````o```````````````````| |``````````````````/%\``````````````````| |`````````````````/%%%\`````````````````| |````````````````/%%%%%\````````````````| |```````````````o%%%%%%%o```````````````| |``````````````/%\%%%%%/%\``````````````| |`````````````/%%%\%%%/%%%\`````````````| |````````````/%%%%%\%/%%%%%\````````````| |```````````o%%%%%%%o%%%%%%%o```````````| |``````````/`\%%%%%/%\%%%%%/`\``````````| |`````````/```\%%%/%%%\%%%/```\`````````| |````````/`````\%/%%%%%\%/`````\````````| |```````o```````o%%%%%%%o```````o```````| |``````/`\`````/`\%%%%%/`\`````/`\``````| |`````/```\```/```\%%%/```\```/```\`````| |````/`````\`/`````\%/`````\`/`````\````| |```o```````o```````o```````o```````o```| |```|\`````/`\`````/%\`````/`\`````/|```| |```|`\```/```\```/%%%\```/```\```/`|```| |```|``\`/`````\`/%%%%%\`/`````\`/``|```| |```|```o```````o%%%%%%%o```````o```|```| |```|```|\`````/%\%%%%%/%\`````/|```|```| |```|```|`\```/%%%\%%%/%%%\```/`|```|```| |```|`u`|``\`/%%%%%\%/%%%%%\`/``|`v`|```| |```o---+---o%%%%%%%o%%%%%%%o---+---o```| |```````|````\%%%%%/%\%%%%%/````|```````| |```````|`````\%%%/%%%\%%%/`````|```````| |```````|`du```\%/%%%%%\%/```dv`|```````| |```````o-------o%%%%%%%o-------o```````| |````````````````\%%%%%/````````````````| |`````````````````\%%%/`````````````````| |``````````````````\%/``````````````````| |```````````````````o```````````````````| |```````````````````````````````````````| o---------------------------------------o Figure 2.1. g = ((u, v)) o---------------------------------------o |```````````````````````````````````````| |```````````````````o```````````````````| |``````````````````/%\``````````````````| |`````````````````/%%%\`````````````````| |````````````````/%%%%%\````````````````| |```````````````o%%%%%%%o```````````````| |``````````````/`\%%%%%/`\``````````````| |`````````````/```\%%%/```\`````````````| |````````````/`````\%/`````\````````````| |```````````o```````o```````o```````````| |``````````/%\`````/%\`````/%\``````````| |`````````/%%%\```/%%%\```/%%%\`````````| |````````/%%%%%\`/%%%%%\`/%%%%%\````````| |```````o%%%%%%%o%%%%%%%o%%%%%%%o```````| |``````/`\%%%%%/`\%%%%%/`\%%%%%/`\``````| |`````/```\%%%/```\%%%/```\%%%/```\`````| |````/`````\%/`````\%/`````\%/`````\````| |```o```````o```````o```````o```````o```| |```|\`````/%\`````/%\`````/%\`````/|```| |```|`\```/%%%\```/%%%\```/%%%\```/`|```| |```|``\`/%%%%%\`/%%%%%\`/%%%%%\`/``|```| |```|```o%%%%%%%o%%%%%%%o%%%%%%%o```|```| |```|```|\%%%%%/`\%%%%%/`\%%%%%/|```|```| |```|```|`\%%%/```\%%%/```\%%%/`|```|```| |```|`u`|``\%/`````\%/`````\%/``|`v`|```| |```o---+---o```````o```````o---+---o```| |```````|````\`````/%\`````/````|```````| |```````|`````\```/%%%\```/`````|```````| |```````|`du```\`/%%%%%\`/```dv`|```````| |```````o-------o%%%%%%%o-------o```````| |````````````````\%%%%%/````````````````| |`````````````````\%%%/`````````````````| |``````````````````\%/``````````````````| |```````````````````o```````````````````| |```````````````````````````````````````| o---------------------------------------o Figure 2.2. Eg = ((u + du, v + dv)) o---------------------------------------o |```````````````````````````````````````| |```````````````````o```````````````````| |``````````````````/`\``````````````````| |`````````````````/```\`````````````````| |````````````````/`````\````````````````| |```````````````o```````o```````````````| |``````````````/%\`````/%\``````````````| |`````````````/%%%\```/%%%\`````````````| |````````````/%%%%%\`/%%%%%\````````````| |```````````o%%%%%%%o%%%%%%%o```````````| |``````````/%\%%%%%/`\%%%%%/%\``````````| |`````````/%%%\%%%/```\%%%/%%%\`````````| |````````/%%%%%\%/`````\%/%%%%%\````````| |```````o%%%%%%%o```````o%%%%%%%o```````| |``````/`\%%%%%/`\`````/`\%%%%%/`\``````| |`````/```\%%%/```\```/```\%%%/```\`````| |````/`````\%/`````\`/`````\%/`````\````| |```o```````o```````o```````o```````o```| |```|\`````/%\`````/`\`````/%\`````/|```| |```|`\```/%%%\```/```\```/%%%\```/`|```| |```|``\`/%%%%%\`/`````\`/%%%%%\`/``|```| |```|```o%%%%%%%o```````o%%%%%%%o```|```| |```|```|\%%%%%/%\`````/%\%%%%%/|```|```| |```|```|`\%%%/%%%\```/%%%\%%%/`|```|```| |```|`u`|``\%/%%%%%\`/%%%%%\%/``|`v`|```| |```o---+---o%%%%%%%o%%%%%%%o---+---o```| |```````|````\%%%%%/`\%%%%%/````|```````| |```````|`````\%%%/```\%%%/`````|```````| |```````|`du```\%/`````\%/```dv`|```````| |```````o-------o```````o-------o```````| |````````````````\`````/````````````````| |`````````````````\```/`````````````````| |``````````````````\`/``````````````````| |```````````````````o```````````````````| |```````````````````````````````````````| o---------------------------------------o Figure 2.3. Difference Map Dg = g + Eg o---------------------------------------o |```````````````````````````````````````| |```````````````````o```````````````````| |``````````````````/`\``````````````````| |`````````````````/```\`````````````````| |````````````````/`````\````````````````| |```````````````o```````o```````````````| |``````````````/%\`````/%\``````````````| |`````````````/%%%\```/%%%\`````````````| |````````````/%%%%%\`/%%%%%\````````````| |```````````o%%%%%%%o%%%%%%%o```````````| |``````````/%\%%%%%/`\%%%%%/%\``````````| |`````````/%%%\%%%/```\%%%/%%%\`````````| |````````/%%%%%\%/`````\%/%%%%%\````````| |```````o%%%%%%%o```````o%%%%%%%o```````| |``````/`\%%%%%/`\`````/`\%%%%%/`\``````| |`````/```\%%%/```\```/```\%%%/```\`````| |````/`````\%/`````\`/`````\%/`````\````| |```o```````o```````o```````o```````o```| |```|\`````/%\`````/`\`````/%\`````/|```| |```|`\```/%%%\```/```\```/%%%\```/`|```| |```|``\`/%%%%%\`/`````\`/%%%%%\`/``|```| |```|```o%%%%%%%o```````o%%%%%%%o```|```| |```|```|\%%%%%/%\`````/%\%%%%%/|```|```| |```|```|`\%%%/%%%\```/%%%\%%%/`|```|```| |```|`u`|``\%/%%%%%\`/%%%%%\%/``|`v`|```| |```o---+---o%%%%%%%o%%%%%%%o---+---o```| |```````|````\%%%%%/`\%%%%%/````|```````| |```````|`````\%%%/```\%%%/`````|```````| |```````|`du```\%/`````\%/```dv`|```````| |```````o-------o```````o-------o```````| |````````````````\`````/````````````````| |`````````````````\```/`````````````````| |``````````````````\`/``````````````````| |```````````````````o```````````````````| |```````````````````````````````````````| o---------------------------------------o Figure 2.4. Linear Proxy dg for Dg o---------------------------------------o |```````````````````````````````````````| |```````````````````o```````````````````| |``````````````````/`\``````````````````| |`````````````````/```\`````````````````| |````````````````/`````\````````````````| |```````````````o```````o```````````````| |``````````````/`\`````/`\``````````````| |`````````````/```\```/```\`````````````| |````````````/`````\`/`````\````````````| |```````````o```````o```````o```````````| |``````````/`\`````/`\`````/`\``````````| |`````````/```\```/```\```/```\`````````| |````````/`````\`/`````\`/`````\````````| |```````o```````o```````o```````o```````| |``````/`\`````/`\`````/`\`````/`\``````| |`````/```\```/```\```/```\```/```\`````| |````/`````\`/`````\`/`````\`/`````\````| |```o```````o```````o```````o```````o```| |```|\`````/`\`````/`\`````/`\`````/|```| |```|`\```/```\```/```\```/```\```/`|```| |```|``\`/`````\`/`````\`/`````\`/``|```| |```|```o```````o```````o```````o```|```| |```|```|\`````/`\`````/`\`````/|```|```| |```|```|`\```/```\```/```\```/`|```|```| |```|`u`|``\`/`````\`/`````\`/``|`v`|```| |```o---+---o```````o```````o---+---o```| |```````|````\`````/`\`````/````|```````| |```````|`````\```/```\```/`````|```````| |```````|`du```\`/`````\`/```dv`|```````| |```````o-------o```````o-------o```````| |````````````````\`````/````````````````| |`````````````````\```/`````````````````| |``````````````````\`/``````````````````| |```````````````````o```````````````````| |```````````````````````````````````````| o---------------------------------------o Figure 2.5. Remainder rg = Dg + dg | Have I carved enough, my lord -- | Child, you are a bone. | | Leonard Cohen, "Teachers" (1967) o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o inquiry e-lab: http://stderr.org/pipermail/inquiry/ o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o

**Follow-Ups**:**ONT Re: Differential Analytic Turing Automata -- Correction***From:*Jon Awbrey <jawbrey@att.net>

**References**:**ONT Differential Analytic Turing Automata***From:*Jon Awbrey <jawbrey@att.net>

**ONT Re: Differential Analytic Turing Automata***From:*Jon Awbrey <jawbrey@att.net>

**ONT Re: Differential Analytic Turing Automata***From:*Jon Awbrey <jawbrey@att.net>

**ONT Re: Differential Analytic Turing Automata***From:*Jon Awbrey <jawbrey@att.net>

**ONT Re: Differential Analytic Turing Automata***From:*Jon Awbrey <jawbrey@att.net>

**ONT Re: Differential Analytic Turing Automata***From:*Jon Awbrey <jawbrey@att.net>

**ONT Re: Differential Analytic Turing Automata***From:*Jon Awbrey <jawbrey@att.net>

**ONT Re: Differential Analytic Turing Automata***From:*Jon Awbrey <jawbrey@att.net>

**ONT Re: Differential Analytic Turing Automata***From:*Jon Awbrey <jawbrey@att.net>

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