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1 © Amit Mitra & Amar Gupta TOPICS READING ASSIGNMENT: SUPPLEMENTARY MATERIALS MODULE 5 Domains of meaning vs. Format Representation and its polymorphisms The architecture of Pattern –Properties of patterns –Meaningful patterns of information Meanings in information space FORMATS AND MEASURES –Precision, size, dimensionality and capacity for conveying information –Number vs. Value –Information payload and “Full Format” of a meaning –Domains of meaning –Assembling meanings –Domains of information quality SEE SUPPLEMENTARY MODULE 4 YOU WILL NEED SOUND FOR THIS PRESENTATION

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2 © Amit Mitra & Amar Gupta Domains Domains of information –Domains of meaning –Domains of numbers –Formatting domains Domains of meaning are the wellspring of meaning –The most elementary patterns in information space from which meanings are assembled –Emerge from the concept of measurability But is different from the concept of “Number” –The length of this room will not change whether we call it 12 feet ot 144 inches –Numbers may represent values in a domain under certain conditions Maps between sets, like the figures in Box 33 of supplementary materials A map that preserves the order of values (if known) Meanings must be represented by formats to physically communicate the abstract information they hold –Speech, text, graphics etc. Symbol=Format (co-domain of the meaning, may be many) Mapping rule=Formatting Rule The least abstract of the three kinds of domains; we will discuss this domain first

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3 © Amit Mitra & Amar Gupta ObjectSymbol Subtype of Format Translation is also a polymorphism of the generic representation relationship between objects Format is a polymorphism of the generic representation relationship between objects Generic representation relationship between objects An object may be thought of as representing itself, but that conveys no information A symbol may or may not represent an object Homonyms and synonyms are polymorphisms of Representation Similies and encryption are forms of representation –Encrypted meanings or formats? Agents are representatives The Eagle has landed See supplementary materials box 36

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4 © Amit Mitra & Amar Gupta PERCEPTION AND COMMUNICATION OF MEANING Five fundamental formatting domains based on five senses –Visible (Visual) Formats: normalizes behavior common to visual perception –Eg: 3d, movement and rotation in space, viewpoints from different locations, color, size, contrast, brightness, etc. Script: Written symbols such as alphabets, numerals and words Graphics: diagrams, pictures etc. –Audible (Audio) Formats: normalizes behavior common to audible perception –Eg: loudness (volume), pitch –Tactile (Haptics) formats: normalize behavior about touch –Eg: feeling of pressure, roughness or smoothness, heat or cold, hardness and softness, sharpness or bluntness, friction etc. –Olfactory Formats: normalizes behaviors natural to sense of smell –Taste Formats: normalizes behaviors natural to sense of taste Bridge between Business and Interface Layers TECHNOLOGY RULES INTERFACE RULES (HUMAN & AUTOMATION) INFORMATION LOGISTICS BUSINESS RULES Vision Process Events Value Policy/Strategy Exceptions BUSINESSPATTERNS DATA MOVEMENT GUIs & FORMATTING COMPONENTS PERFORMANCE OPTIMIZATION COMPONENTS Meaning to algorithm or formula 2 1

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TECHNOLOGY RULES INTERFACE RULES (HUMAN & AUTOMATION) INFORMATION LOGISTICS BUSINESS RULES Vision Process Events Value Policy/Strategy Exceptions BUSINESSPATTERNS DATA MOVEMENT GUIs & FORMATTING COMPONENTS PERFORMANCE OPTIMIZATION COMPONENTS

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6 PARTITION Object Symbol Subtype of Meaning What is a Pattern? A pattern is an arrangement –Follows a law The law/algorithm increases predictability, reduces/(does not increase) information content –Eg: Spelling, 1+2=3; 1,2,1,2,1,2..; Law of Location Could be combinations of symbols across formatting do,mains eg: multimedia Determines the identity & meaning of the pattern Projects abstract meanings into physical space and time Constrained in physical space and time Sounds in a region of physical space for a span of time

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7 © Amit Mitra & Amar Gupta Symbol May be pattern of 0 or more [be part of 0 or more] FORMATTING DOMAIN (Domain of Symbols) Member of

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8 © Amit Mitra & Amar Gupta PATTERNS/SYMBOLS IN THREE SPACE HEIGHT WIDTH LENGTH Origin Different symbols (patterns) Pattern Patterns Separation (Same Size, Rotated) (Different and same sizes, Rotated) Angular separation of symbols in a pattern Same or different pattern? ? ? ? (Mirror Images) Same or different pattern? ? (Same Size & orientation, Different positions) – why do we think they are different? Same or different pattern? ?

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9 © Amit Mitra & Amar Gupta FUNDAMENTAL STATES OF THE LAW OF LOCATION (2) Shape might matter, but not size –Angles are preserved, but not linear distances Preserves some, but not all information on size HEIGHT WIDTH LENGTH Angle 1 Angle 2 Distance from origin Origin Location The shape might matter, not orientation –Relative, not absolute separation is important Considered identical patterns Considered different patterns

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10 © Amit Mitra & Amar Gupta DIMENSIONALITY OF A PATTERN - DEGREES OF FREEDOM HEIGHT WIDTH LENGTH Origin

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11 © Amit Mitra & Amar Gupta FUNDAMENTAL PROPERTIES - DEGREES OF FREEDOM Distance from origin HEIGHT WIDTH LENGTH Angle 1 Angle 2 Origin 3 degrees of freedom 1 2 3 2 1 2

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12 © Amit Mitra & Amar Gupta FUNDAMENTAL PROPERTIES OF PATTERNS- DEGREES OF FREEDOM HEIGHT WIDTH LENGTH Origin Degrees of freedom of the ensemble?3 x 3 = 9 Ensemble 2 x 2 = 4 Degrees of freedom of a line in 2-space? 2 x 2 – 2 – 1 = 1 Degrees of freedom depends on the law of location –Dimensionality of conceivable state space Eg: Written words are 1 dimensional, maps are 2 dimensional –Constraints Dimensionality and shape of pattern/lawful state space Degrees of freedom of a line in 3-space: 3 x 3 – 3 – 1 = 5 Which Pattern has more freedom: “Ancestor” or “Grandfather” ? The information could also be formatted in strings of numbers, patterns of colors, etc. Formats are like pipes that convey abstract information from information space to physical space. Like a pipe, a symbol has limited capacity to convey information. The information carrying capacity of a symbol is determined by its degrees of freedom Object Information Payload See supplementary Box 37, 38

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13 © Amit Mitra & Amar Gupta FUNDAMENTAL STATES OF THE LAW OF LOCATION FUNDAMENTAL PROPERTY: Association – Which objects are associated with which –Eg: In physical space a point is connected to points in its neighborhood and the separation between points in a neighborhood is infinitesimally small –All spaces may not have a neighborhood Eg: nominally scaled space FUNDAMENTAL PROPERTY: Sequence – Sequence matters (or not) –Sequenced vs. unsequenced association Unsequenced Association Sequenced Association Eg: Spellings, words, sentences –Incomplete Order In multidimensional space (eg: physical space), order may count only in some directions –Eg: when the pattern does not distinguish between mirror images Eg: Concept “Joined in matrimony” Rules of (unsequenced) association Sequencing Rules Subtype Information content and density of the pattern may be different in different directions in information space

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14 © Amit Mitra & Amar Gupta FUNDAMENTAL STATES OF THE LAW OF LOCATION FUNDAMENTAL PROPERTY: Separation – Whether distance matters (or not) –Independent of sequence –Distance = Measure of Similarity Proximity Metric –(see notes on generalizing distance in your text book) –Patterns of separation Collocation/distinction, ordinal separation, quantitative separation Collocation has no information on order –Eg: if the tone and the icon were constrained to occur together, we could not say which occurred before which FUNDAMENTAL PROPERTY: Pattern of inclusion vs. Exclusion –Eg: Movie with sound vs. Mime/silent movie FUNDAMENTAL PROPERTY: Extent (of pattern) – how far does the overall pattern extend in information space? –Infinite vs. finite patterns Eg: Ancestor vs. Parent FUNDAMENTAL PROPERTY: Delimitation (of pattern) – does the pattern have boundaries in information space? –Delimited vs. undelimited patterns –Infinite patterns will have no boundaries The proximity metric between a pair of points in state space cannot exceed the sum of the same measure via intermediate points in between the points in the pair Finite patterns may or may not have boundaries!!

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15 © Amit Mitra & Amar Gupta Fundamental states of the law of location are the universal properties of patterns DISK CIRCLE (a different pattern) Delimiter Delimiter (of letter) Beginning (of word) (space) FUNDAMENTAL STATES OF THE LAW OF LOCATION Finite, bounded delimited pattern Finite, unbounded pattern Finite pattern unbounded in one direction, delimited in another End Delimiter Pattern of Infinite Extent Finite Unbounded Pattern Delimited Pattern Subtype of Eg: Time Eg: Year Eg: Calendar Year Bounded Pattern EXAMPLES Open Bounded Pattern Closed Bounded Pattern Partition Delimiter Boundaries (or not) –D–Delimiters (or not) Patterns (symbols) may delimit patterns (symbols) Order, Punctuation

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16 © Amit Mitra & Amar Gupta TIME (EXAMPLE) A MATTER OF TIME Delimiter: Jan1

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17 © Amit Mitra & Amar Gupta Pattern of Infinite Extent Finite Undelimited Pattern Delimited Pattern Subtype of Delimiters are meaningless, but ad-hoc sets of states may define regions of state space Open and closed delimiters may express the same meaning Delimited Pattern WHAT KINDS OF PATTERNS MAY EXIST IN WHICH KINDS OF SPACE? Open Bounded Pattern Closed Bounded Pattern NOMINAL SPACE ORDINAL SPACE DIFFERENCE SCALED SPACE IMPLIED: ALL THESE KINDS OF PATTERNS MAY ALSO EXIST IN RATIO SCALED SPACE Bounds and Delimiters are meaningless

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18 © Amit Mitra & Amar Gupta THE PROXIMITY METRIC When we know items exist, but have no idea of their similarity, or even co- location (identity) A Proximity Metric lies at the heart of every pattern An attribute of Pattern A kind of distance Rules

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19 © Amit Mitra & Amar Gupta Parameter/ Feature Directional?SubtypesValid in (Space) AssociationYPatterns of AssociationsAll Sequencing PatternsOrdinal Dimensionality NDimensionality of state spaceAll Dimensionality of patternOrdinal & subtypes Cohesion/ Separation YPatterns of distinctionAll Ranking patternsNominal & Subtypes Patterns of separation in terms of quantitative differences (eg: differences in military rank) Ordinal & Subtypes Patterns of separation in terms of ratios of separation (eg: Physical distance) Difference scaled & Subtypes LocationYAbsolute locationSpaces with “Nil” value (Ratio scaled and Ordinal with Nil value) Differences in absolute locationOrdinal with Nil value Ratios of absolute locationRatio scaled space Inclusion vs. Exclusion YPatterns of inclusionNominal & Subtypes Patterns of exclusionNominal & Subtypes ExtentYInfiniteNominal & Subtypes FiniteNominal & Subtypes DelimitationYUnbounded (Undelimited)Nominal & Subtypes Bounded (Delimited)Ordinal & Subtypes OpenDifference Scaled & Subtypes ClosedDifference Scaled & Subtypes UNIVERSAL PROPERTIES OF PATTERNS Order of a pattern (pattern of patterns, pattern of pattern of patterns etc.) Degrees of freedom (information carrying capacity) Partition Subtype of Cardinality (No. of participating Objects) May be infinite

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Object

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23 ©20066 Amit Mitra & Amar Gupta The Metamodel of Pattern The Metamodel of Pattern is the Metamodel of Object –And the Metamodel of Constraint Constraints carve objects out of information space Add information to an object or pattern External objects may shape a pattern –By influencing its parameters Location, proximity metric, inclusion/exclusion, degrees of freedom etc. –Influencing the shape of the pattern and participating in a pattern are different and independent roles of Object The concept of Context emerges from this Pattern is held in State Space –Held In is the aggregation of “Locate”, root of enumeration and other emergent properties of object classes/aggregates Arrays and tables are a kind of discrete pattern in multidimensional state space Physical space/space-time is a constrained form (polymorphism) of information space –Patterns in and space and time are symbols constituted of physical objects/energy, constrained to only one region of physical space at a given point in time Polymorphisms of patterns in information space Null space is the region of null values, i.e., forbidden regions in information space –Meaninglessness is a polymorphism of null space, a stricter form of impossibility Object Information Payload

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24 ©20066 Amit Mitra & Amar Gupta Money Number of pieces Money per piece Hole

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25 ©20066 Amit Mitra & Amar Gupta Value Constraint Proximity of a pair of states cannot exceed the summation of proximities of states over any trajectory that connects the pair constrain [constrained by] Measure of similarity between 2 [similarity may be measured by 0 or more] Metamodel of Proximity Metric Nominal Proximity Metric Ordinal Proximity Metric Ratio Scaled Proximity Metric Difference Scaled Proximity Metric Subtype of STATE Measure of similarity between 2 [similarity may be measured by 0 or more] Measure of similarity between 2 [similarity may be measured by 0 or more] Measure of similarity between 2 [similarity may be measured by 0 or more] Subtype of Proximity Metric Subtype of NOMINAL STATE ORDINAL STATE QUANTITATIVELY SCALED STATE Difference scaled state Ratio scaled state Value Constraint The proximity between a pair of dissimilar states cannot be Nil or less Value Constraint The proximity of a state to itself must be nil Value Constraint The proximity between a pair of states must be the same in both directions

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26 ©20066 Amit Mitra & Amar Gupta (For example, distances in physical space) (B1) (B3) (B2) (B4)

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27 © Amit Mitra & Amar Gupta

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28 3-D ARRAY Object Instance 1 Object Instance 2 Object Instance 3 Attribute 1 Attribute 2 Attribute 3 Time Slices Present Past History of Attribute 3 across all object instances Current values of attributes for each object instance State history of Object Instance 3 B A C 1 2 3

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