Actual Mathematics

1. Physics of Information(Mathematical Modeling)Infinity Kills Informationorthe Battle of the „Fly“ for the Datasdon‘t tell me, you cannot define somethingbut do it

2. Actual Mathematics • Set • totality of elements of which none occur more than once • Representation of Sets • by listing individual elements {a, b, c, d} • by 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 • particular attribute value : { x | x is green) • regulation for generating : { y | 3*n = y, with n = natural number } • Underhand Conditions • a) each element of a set has at least 2 different values • value #1 - set specific property with constant value for all elements • value #2 - identity with a unique value for each element of the set • b) value #1 is constant in time • consider all the „For All“ conditions of definitions and theorems: what would happen if elements of a set could disappear? • See HandOut #1

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

4. Axiom of Information Mathematics • Structural Axioms • Linking of dynamic elements X(„connection in series“) • Existence of a Zero-Element (neutral element) X1 • = no-change, constancy • Existence of an Inverse X-1 of X • = reversing the transformation X • ==> {X1, X,X-1 | X is dynamical element of the element of quality e} • is „Group“, if transformation X is „repeatable“ • ==> focus on repeatable X • {X1, Xrep,X-1} =: Information about quality e • value area of e: set of all values which can be allocated to e by its dynamic elements

5. Information is • {X1, Xrep,X-1} • foreseeable, calculable • ==> Distinctness • from the set • m = mass, a = acceleration, E = energy, c = speed of light • ==> Repeatability • from the group • F = m * a • E = m * c2 • ==> Change • from the dynamic elements • problem of actual mathematics and so actual physics:only describable by „element hopping“ of functions

6. Outside Information is • Chaos • nothing to be managed, controled or foreseen • but even so exerting influences by creating changes • like falling stars • Excluding Rules of Information Processing: • outside information there exist • no rules • no limits • no reliability • Conclusion • no absolute solution possible - one for all doesn‘t exist • because outside exists unforeseeable (cp. Gödel,incompleteness) • 1. step: detection of information - EE- Partitioning • 2. step: protection of information

7. EE Partitioning • Information • information shapes environment through repeatability • information forces adaptation, promotes processing • processing is change • only if repeatable & distinct: information • Messages: cumulative value change • traces of dynamic elements • only track of information • Information processing = information + processing • sender acts • recipient acts

8. parts of message from sender parts of message from recipient • origin • result • cause • effect • action • reaction • unknow process ==> object of interest • wellknown process ==> no need for knowledge besides EE Partitioning • parts of message • from sender • from recipient

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

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

11. Topology of Information Processing • Precondition • Information is repeatable & distinct action • action follow the principle of least action • Infinity Kills Information - outside information is chaos • Rules • detect information by memory • distinctness: map properties and values shape the objects • repeatability: count occurences crystallize the rules • change: declare interfaces control the borderlines • protect information by unbreakable rules • define clear chains of action, avoid cycles and ambiguities therein • provide control by minimizing chains of action • tame infinity by aims • aims and goals as rating scales to single out the needful things • evaluate input, create finite sets of input datas • reach decisions, learn to ignore

12. Topology of Information Processing • Conclusion - the „Fly“ • input • decision • output • short ways • vectored courses • distributed load

13. Measurements of Datastructures (4fF-Method) • Datastructure = Frozen Information • Datastructure contain states of described objects • View Fields as presentation of elements of qualities • count values: Eigen weighting ge = 1 / k-1 • k > 1, k = number of values • count occurences: Profil weighting gp = T / p • T = number of occurencies, p = number of files • count distance: Portal weighting gpd = P / p • P = portal distance from input, distance = minimum thread • count distance: Exit weighting ged = E / p • E = exit distance to output • Type Fields in endogenous view • field-related type Tf = ( ge , gp ) • Type Fields in exogenous view • task-related type Ta = ( gpd , ged )

14. Accentuating Tf = ( + , - ) few values, small field of application normed value sets, scales example: for people:sex, title Descriptive Tf = ( - , - ) many values, small field of application often text fields example: free entry fields Classifying Tf = ( + , + ) few values, large field of application organizational elements for sorting, classifying example: companies, booking circles, business areas Documenting Tf = ( - , + ) many values, large field of application often identifiers example: customers, orders, voucher numbers ge gp Field-related field type

15. Evaluating Ta = ( + , - ) high portal weighting low exit weighting evaluations example: pie charts from statistics Recording Ta = ( - , - ) low portal weighting low exit weighting records, protocols example: order values Diverting Ta = ( + , + ) high portal weighting high exit weighting system files example: file of registered user with data station data Stamping Ta = ( - , + ) low portal weighting high exit weighting stamp data example: changing users, alteration date gpd ged Task-related field type Part II