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Physics of Information (Mathematical Modeling) Infinity Kills Information or the Battle of the „Fly“ for the Datas don‘t tell me, you cannot define something but do it

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Actual Mathematics n Set Øtotality of elements of which none occur more than once n Representation of Sets Øby listing individual elements {a, b, c, d} Øby describing a common, set specific property, which all elements of the set have and all elements which do not belong to the set don’t have F particular attribute value : { x | x is green) F regulation for generating : { y | 3*n = y, with n = natural number } n Underhand Conditions Øa) each element of a set has at least 2 different values F value #1 - set specific property with constant value for all elements F value #2 - identity with a unique value for each element of the set Øb) value #1 is constant in time F consider all the „For All“ conditions of definitions and theorems: what would happen if elements of a set could disappear? êSee HandOut #1

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Information Mathematics n Clearance of Underhand Condition a) ØElement of a set is defined by at least 2 changeless values; F #1 equal for all elements of the given set (type) F #2 unique for each element in the given set (individuality) Øany other property of elements of the given set will be ignored n Clearance of Underhand Condition b) ØValue is defined as state of a property by using a relation between 2 elements of sets F the 1. element is called quality and constant in the relation F the 2. element is called value and variable in the relation n Annex F a change of values a -> w of a quality e is called „Transformation“ X ( e | a ) = e | w F a repeatable Transformation will create the same result for the same initial state

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Axiom of Information Mathematics n Structural Axioms ØLinking of dynamic elements X („connection in series“) ØExistence of a Zero-Element (neutral element) X 1 F = no-change, constancy ØExistence of an Inverse X -1 of X F = reversing the transformation X n ==> {X 1, X, X -1 | X is dynamical element of the element of quality e} Ø is „Group“, if transformation X is „repeatable“ Ø==> focus on repeatable X n {X 1, X rep, X -1 } =: Information about quality e Øvalue area of e: set of all values which can be allocated to e by its dynamic elements

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Information is n {X 1, X rep, X -1 } Øforeseeable, calculable n ==> Distinctness Øfrom the set Øm = mass, a = acceleration, E = energy, c = speed of light n ==> Repeatability Øfrom the group ØF = m * a ØE = m * c 2 n ==> Change Øfrom the dynamic elements Øproblem of actual mathematics and so actual physics: only describable by „element hopping“ of functions

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Outside Information is n Chaos Ønothing to be managed, controled or foreseen F but even so exerting influences by creating changes F like falling stars n Excluding Rules of Information Processing: Øoutside information there exist F no rules F no limits F no reliability n Conclusion Øno absolute solution possible - one for all doesn‘t exist F because outside exists unforeseeable (cp. Gödel,incompleteness) Ø1. step: detection of information - EE- Partitioning Ø2. step: protection of information

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EE Partitioning n Information Øinformation shapes environment through repeatability Øinformation forces adaptation, promotes processing Øprocessing is change F only if repeatable & distinct: information n Messages: cumulative value change Øtraces of dynamic elements Øonly track of information n Information processing = information + processing Øsender acts Ørecipient acts

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EE Partitioning n parts of message from sender n parts of message from recipient Øorigin Øresult Øcause Øeffect Øaction Øreaction Øunknow process ==> object of interest Øwellknown process ==> no need for knowledge besides n parts of message Øfrom sender Øfrom recipient

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EE Partitioning n EE Partitioning Øendogenous view = viewing an object of interest independent of its surrounding environment, at its stable identification F every fact of interest is a message about „something“ ==> view „something“ individually Øexogenous view = viewing an object of interest in interaction and relation with its surrounding environment, at its dynamical interactions F every accepted message is processing ==> view „something“ in it‘s effect on the environment, therefore on the recipient as well

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Protection of Information in SW n Repeatability = Separating data and functions Øprovide repeatability by control of the states of your objects F objects depending on system state can be used like variables F objects depending on their own values, especially input parameters, you can use like variables n Distinctness = Separating objects into data structures Øno tricks, no masquerades of datas to be stored F safety of datas in distributed environments, despite alteration of SW n Change = Separating phases Øprotocol phases, especially in/output F precondition for prognosis

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Topology of Information Processing n Precondition ØInformation is repeatable & distinct action Øaction follow the principle of least action ØInfinity Kills Information - outside information is chaos n Rules Ødetect information by memory F distinctness: map properties and valuesshape the objects F repeatability: count occurencescrystallize the rules F change: declare interfacescontrol the borderlines Øprotect information by unbreakable rules F define clear chains of action, avoid cycles and ambiguities therein F provide control by minimizing chains of action Øtame infinity by aims F aims and goals as rating scales to single out the needful things êevaluate input, create finite sets of input datas êreach decisions, learn to ignore

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Topology of Information Processing n Conclusion - the „Fly“ ¡decision ðoutput ðinput Øshort ways Øvectored courses Ødistributed load

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Measurements of Datastructures (4fF-Method) n Datastructure = Frozen Information ØDatastructure contain states of described objects ØView Fields as presentation of elements of qualities F count values: Eigen weighting g e = 1 / k-1 k > 1, k = number of valuesk > 1, k = number of values F count occurences: Profil weighting g p = T / p T = number of occurencies, p = number of filesT = number of occurencies, p = number of files F count distance: Portal weighting g pd = P / p P = portal distance from input, distance = minimum threadP = portal distance from input, distance = minimum thread F count distance: Exit weighting g ed = E / p E = exit distance to outputE = exit distance to output ØType Fields in endogenous view F field-related typeT f = ( g e, g p ) ØType Fields in exogenous view F task-related type T a = ( g pd, g ed )

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Field-related field type n Accentuating ØT f = ( +, - ) F few values, small field of application Ønormed value sets, scales Øexample: F for people: sex, title n Descriptive ØT f = ( -, - ) F many values, small field of application Øoften text fields Øexample: F free entry fields n Classifying ØT f = ( +, + ) F few values, large field of application Øorganizational elements for sorting, classifying Øexample: F companies, booking circles, business areas n Documenting ØT f = ( -, + ) F many values, large field of application Øoften identifiers Øexample: F customers, orders, voucher numbers gege gpgp

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Task-related field type n Evaluating ØT a = ( +, - ) F high portal weighting F low exit weighting Øevaluations Øexample: F pie charts from statistics n Recording ØT a = ( -, - ) F low portal weighting F low exit weighting Ørecords, protocols Øexample: F order values n Diverting ØT a = ( +, + ) F high portal weighting F high exit weighting Øsystem files Øexample: F file of registered user with data station data n Stamping ØT a = ( -, + ) F low portal weighting F high exit weighting Østamp data Øexample: F changing users, alteration date g pd g ed Part II

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