1. 1 The Foundations of General Schemas Theory As an Extension to Systems Theory to Form a Mathematical and Philosophical Basis for Systems Engineering Draft 12 040413 Kent D. Palmer, Ph.D. PO Box 1632 Orange CA 92856 714-633-9508 kent@palmer.name http://archonic.net

2. 2 Significant Points The current most likely foundation for SE is Systems Theory Emergence is an important viewpoint on SE There are specific levels of Emergence some of which are addressed in current SE and others of which are not addressed yet, but should be SE is a discipline structured by Emergence Other schemas besides the system schema are important to SE Ultimately SE needs to become Schemas Engineering based on Schemas Theory *

3. 3 Horizons of SE Current SE Schemas Engineering Emergence Engineering *

4. 4 Chaos Theory Complex Systems Theory Complex Adaptive Systems Ontic and Ontological Levels of Emergence Systems Engineering Discipline Other Disciplines SW Eng / Comp Science All Engineering Disciplines are the Academic counterpart of SE Transformative ? MAP (of the argument) * Scope Broader A transformative discipline is one which changes the relations between other disciplines when it appears

5. 5 Systems Engineering a Transformative Discipline? SE is a nascent discipline It is attempting to gain academic respectability Part of this is the attempt to establish mathematical and philosophical foundations for the new discipline SE has no specific academic counterpart unlike SW Eng. has in Computer Science, rather, all Engineering disciplines are the academic counterpart of SE Much SE research merely attempts to validate what has been put already into practice in Industry

6. 6 Systems Engineering a Transformative Discipline? Few SE Ph.D. programs exist Most SE academic departments concentrate on the masters level where the emphasis in on coursework rather than original research In-depth research into SE foundations is rare Most in-depth research at the Ph.D. level has a foreshortened horizon seeking to mostly validate what is already known or seeking to apply what is known from other disciplines to SE Very few researchers consider SE a transformative discipline

7. 7 Systems Engineering a Transformative Discipline? A transformative discipline is one which changes the relations between other disciplines when it appears –This is the highest possibility to which the SE discipline can aspire Rather than viewing SE as a discipline which calls for bolstering in order to become academically respectable, let us explore the transformative possibilities of SE

8. 8 Systems Engineering a Transformative Discipline? If we consider SW Eng. as a model, we can clearly see its vibrancy slowly transforming computer science into a support for industrial practice by bringing new problems and new applications for computer science to explore SW Eng. has its own subject matter as well, which concerns products, processes, methods and tools that support large scale software development

9. 9 Can Systems Engineering be a Transformative Discipline? Systems Engineering has no specific complementary academic discipline Instead every sub-division of engineering in academia is its complement, as well as the meta-discipline of Systems Theory which has no dedicated department within the university There is a gap between SE and all other Engineering disciplines which makes it difficult for these engineering disciplines to reap the benefits that SE has to offer Systems Theory is too nebulous and diffuse since it lacks autonomy when spread throughout other engineering disciplines

10. 10 Systems Engineering a Transformative Discipline? For the most part SE is adopting SW Eng.s processes, methods, and tools SE thus appears as a surrogate of SW Eng. at a higher level of abstraction –The unique needs of SE are not being considered very deeply Unlike SW Eng., SE is neither driving academic research agendas nor is it fostering its own innovative research agenda SE seems to be a late arrival with little new to offer other disciplines Instead, it is borrowing and begging from other disciplines hoping for recognition because of its place at the top of the food chain in industry

11. 11 How can we reverse this situation? One way is to realize that SE is the place where all the diverse industrial disciplines come together to produce the emergent effects of a whole working system being developed on a large scale The key thing that SE has as its focus is Emergence, while other disciplines do not have this focus the same way or with the same intensity

12. 12 Systems Engineering means... Engineering Large Scale Emergence –SE is where emergence is the appearance of new properties at the level of a whole not seen in the parts, E.g., cell/organism; Hydrogen,Oxygen elements/Water (H 2 O) molecule; sub- system/system/super-system –The problem of emergence appears in other engineering disciplines but it comes to a head in SE because of the scale of SE projects *

13. 13 Emergence Engineering Emergence is a hot topic in complex Systems Theory and science in general –It is related to Chaos Theory and Complex Adaptive Systems Theory SE has an intimate hands-on knowledge of how large scale complex systems are built to produce holistic emergent effects And SE is concerned with the huge and open problem of how to deal with these systems of greater scale and complexity

14. 14 Emergence Engineering By studying the successes and failures of the development of large complex systems, SE has a ready-made focus for inquiry No other discipline attempts such large scale production of emergent wholes, and it is essential to note that differences in scale can produce qualitatively different problems –Effects come into play which do not appear on smaller scales –This is one of the lessons of Hegelian Dialectics, i.e., Differences in quantity produce differences in quality in relation to dialectical synthesis

15. 15 Emergence Engineering If we begin to think of Systems Engineering as Large Scale Emergence Engineering, then our view of the discipline begins to change radically When we change our vision of SE, it changes its relation to other disciplines –The biggest problem is our own limited vision of SE, not the subject matter of SE itself Emergence Engineering must be a transformative discipline in relation to other disciplines, and what it studies will have a profound effect on itself *

16. 16 Emergence Engineering In our new vision of SE, we can see it as an emergent event within industry and academia The study of Emergence comes into it own in a practical sphere of industrial practice which gives a ground for theories of emergence that are developed in Complex Systems Theory In the advent of an emergent event, it is natural to see SE as a radically transformative discipline changing itself and other disciplines profoundly when it is considered from this new viewpoint

17. 17 Emergence Engineering Meta-levels supervenience de-emergence emergence meta-levels of emergence meta-levels of Being MAP (of the argument) *

18. 18 LEVEL N+1 LEVEL N Supervenience & Emergence Emergence Excess emergence Qualitative and Quantitative Jump Gestalt = Whole greater than sum of parts Supervenience is Homomorphism with lower level supports * Synthesis new characteristics supports cell organism

19. 19 LEVEL N+1 Part Emergent Lack <Reductionism De-emergence> Proto Gestalt = Whole less than sum of parts gives knowledge of implicate order De-emergence Part Cannot reconstitute the whole Parts dont add up to the whole LEVEL N * Analysis/ Architecture Loss of knowledge or information There is normally a cycle between emergence and de-emergence

20. 20 Emergence An emergent system gestalt must be based on supports from the next lower level of phenomena Its dependence on these supports, although it rises above them, is called supervenience However, the emergent system gestalt must add new properties and characteristics that go beyond the limitations of these supports opening up new horizons of combination and complexification that produce other higher properties with their own reality which cannot be reduced

21. 21 Supervenience All systems designed and built by SE practitioners attempt to produce wholes with emergent effects on a large scale These wholes are supervenient on the supports of their subsystems and parts, but attempt to go beyond these sub-system or parts to produce characteristics and properties not contained in the parts themselves which go beyond what the parts can accomplish in isolation from each other

22. 22 Philosophy of Science From the point of view of Philosophy of Science it is clear that there is no method for producing emergent leaps to the whole greater than the sum of its parts, which is the emergent whole As Paul Feyerabend says, The only method is NO METHOD, so that anything goes when it comes to design and construction of emergent wholes This gives SE its character which is based on trial and error and applying the best of engineering judgment

23. 23 Uniqueness Because there is no method, nor royal road for producing emergences in SE practice it is necessary to bring creativity and innovation into the development of Emergent Systems This is also why Engineering practice seems so ad hoc and why it is so difficult to estimate and predict outcomes Each new system presents unique challenges and requires unique configurations of products, processes, methods, and tools to create the required emergent effects

24. 24 Godel One way to think about the production of sui generis emergent characteristics in creative systems design and construction is in terms of Godelian statements Godelian statements are undecideable with respect to supervenient lower level axiomatic foundations The emergent excess of the designed and constructed system can be thought of as equal to the undecidable Godelian statements that cannot be designated as inside or outside the system They are beyond what is definitely inside the system, yet not outside it

25. 25 Undecidable means non-reducible decidable outside undecideable decidable inside emergent excess Conjecture: Emergent Properties are Godelian * emergence de-emergence This could be the basis for formalizing the concept of emergence

26. 26 Large Scales All engineering attempts to produce emergent effects on a small scale SE attempts to produce these effects on a large scale by integrating small scale emergent sub-systems into large scale systems or systems of systems This is, in effect, an attempt to produce an emergence of emergences

27. 27 E0E0 E1E1 E 2a E 2b Emergence of Emergences * E3E3 Cant get to E 3 directly from lower levels of Emergence Current view of SE as concerned with Integration

28. 28 Meta-levels The idea that there can be different meta-levels of emergence changes our concept of emergence itself by fragmenting it into an infinite series of possible meta-levels using the Higher Logical Type Theory of B. Russell and A.N. Whitehead from Principia Mathematica (cf I. Copi) This theory can be used as a means of teasing out the different meanings of emergence

29. 29 Radical Possibility Emergence is a radical possibility of Being Emergence is what allows different technologies to be combined to produce new levels of synthesis which gives rise to new possibilities of Being The levels of emergence are another face of the meta-levels of Being Our attempt to understand the levels of Emergence leads us directly into what Heidegger calls fundamental ontology as developed in Continental Philosophy

30. 30 Emergence Engineering Meta-levels supervenience de-emergence emergence meta-levels of emergence meta-levels of Being MAP (of the argument) * repeated

31. 31 * Emergence 7 Meta-levels of EmergenceMeta-levels of Being Emergence 6 Emergence 5 Emergence 4 Emergence 3 Emergence 2 Emergence 1 Emergence 0 Thatness/Suchness Manifestation Ultra-Being Wild Being Hyper Being Process Being Pure Being beings ontological difference existence threshold Ontology Correspondence between meta-levels of Emergence and meta-levels of Being

32. 32 Characteristics of Emergence Each kind of Being expresses itself in a characteristic of emergence Emergence is a phenomena in the world that brings to bear all the kinds of Being as a face of the world transforming one face of the world into another Emergence and kinds of Being have a reciprocal relationship –Each allows us to understand the other better if we study them together

33. 33 Ontological Difference Ontological Difference is a kind of meta- difference that distinguishes between Being and beings It appears as the difference between genuine and Artificial Emergence Artificial emergence is incremental change that is not genuinely new but merely combinatorially different Genuine emergence clears the stage for the advent of the utterly unheard of here-to-fore rewriting of the past and production of new horizons of possibility

34. 34 Lack E 0 non-emergent change E1E1 E2E2 E3E3 E5E5 Supervenient essencing forth in time excess E4E4 chiasm between actualities, errors, voids horizon undecidable Stairs to Nowhere: Meta-levels of Emergence Ultra Being Emptiness / Void genuine emergence Being Existence combinatoric or additive change * Radically Unpredictable, unknown

35. 35 Emergent Difference Ontology covers the various standings of everything that presents or absences itself phenomenologically Ontological Difference distinguishes those standings from the various beings which have those various standings Emergent difference relates to the intensification of nihilism –Artificially emergent events are additive, incremental, and combinatoric intensifications of nihilism –Genuine Emergent events are quantum leaps that reset all parameters and recalibrate by producing a new origin *

36. 36 Emergence 0 = beings Non-new change More of the same Random alteration Entry of the New beings, entities, things Entry of Being * Emergent Difference and Ontological Difference Example: Car wearExample: Projection

37. 37 Aspects of Being Truth Reality Identity Presence I am only going to describe the differences in the meta-levels of emergence not the differences and the kinds of Being or the aspects of Being in this talk. * These change at the different meta-levels of Being

38. 38 Emergence 1 = Pure Being Pure Artificiality Combinatoric expansion Superficial newness Additive or incremental improvement Nothing fundamental changes Determinate and continuous Present-at-hand Pointing Standing reserve Subject/object dichotomy Form level –Symbol –Shape * Example: New cars

39. 39 Aspects of Being at Emergence Level 1 Identity 1 – Change and difference occur but make no fundamental difference Presence 1 – Changed Emergent characteristics appear Reality 1 – Emergent characteristics are embodied Truth 1 – Emergent characteristics can be described in language

40. 40 Emergence 2 = Process Being Emergence becomes an event It takes time for something to be what it is Emergent change reveals the essence of the thing seen Like Catalysis in Transformations Probability Ready-to-hand Grasping Dasein (being-in-the- world) Pattern Level –Value –Sign –Flux –Structure * Example: From Buggy to Car

41. 41 Aspects of Being at Emergence Level 2 Identity 2 – Self identity revealed though change – sameness – belonging-together family resemblance Presence 2 – showing and hiding Reality 2 – Physus - unfolding of new kinds in nature Truth 2 – Logos – unfolding of new kinds in language

42. 42 Emergence 3 = Hyper Being Projects new possibilities on new horizon Emergence itself is undecidable Emergent excess is Godelian Possibility In-hand Bearing Query (expansion) Trace Level Differance –Differing/Deferring Excess / Supplement * Example: Car with Software

43. 43 Aspects of Being at Emergence Level 3 Identity 3 – Self Identity revealed though Other (Alterity) Presence 3 – secrecy, lies, deception, dissimulation Reality 3 – Simulacrum – unreality of reality is more real than reality Truth 3 – Fiction – lies tell truth deeper than the facts alone can tell

44. 44 Emergence 4 = Wild Being Actualizes new possibilities on new horizon Emergence is intrinsically unpredictable Reveals unexpected, unheard of, unthought, anomalous appearances from a direction previously unknown Propensity Out-of-hand Encompassing Enigma (contraction) Tendency Rhizome Chiasm (reversibility) Flesh * Example: Car with AI

45. 45 Aspects of Being at Emergence Level 4 Identity 4 – Chiasm between selfs and others identity and difference Presence 4 – Chiasm between selfs and others presence and absence Reality 4 – Chiasm between natures and artificialitys reality and illusion Truth 4 – chiasm speechs and silences between truth and fiction

46. 46 Emergence 5 = Existence Genuinely emergent existent appears from itself in its own time and a place of its choosing No projection Face of the World Interpretations –Ultra Being –Emptiness –Void Inter/intra penetration/surfacing Being seen from outside as a found thing being- out-of-the-world * Example: Flying Car, New Media

47. 47 Aspects of Existence at Emergence Level 5 Identity 5 – uniqueness Presence 5 – Fully and Genuinely Emergent Alterity Reality 5 – Phenomena bodies forth in itself in its own style of non-nihilistic distinctions in action Truth 5 – Wipes nihilistic background clean - clears the clearing-in-being and makes non-nihilistic distinctions as phenomena speaks for itself in its own voice

48. 48 Emergence means... History is rewritten New future possibilities appear while old future possibilities vanish What is presence is seen in a new way –New Theory –New Paradigm (assumptions) Kuhn –New Episteme (categories) Foucault –New Ontos (projection, intelligibility) Heidegger –New existence (found) Mythos is reformatted SE does not deal with all of Emergence in its current form Realm of Futurology, Venture Capital, or IR&D *

49. 49 Lack E 0 non-emergent change E1E1 E2E2 E3E3 E5E5 Supervenient essencing forth in time: event excess E4E4 horizon undecidable Meta-levels of Emergence Ultra Being Emptiness / Void genuine emergence Being Existence combinatoric or additive change * Radically Unpredictable, unknown

50. 50 Torn between alternatives In SE we are always recombining existing components when attempting to build new systems We are constantly torn between, reuse, subcontracting, and new development When we engage in new development we recognize that process plays an important part There are certain stages that force themselves on us It takes a certain time to build a system from scratch and many times shortcuts cost more in the end

51. 51 Design In the design process there are many possible workable designs for the same system and many more which will not work When walking though the design landscape there are myriad decisions to be made which all must cohere to produce the desired emergent effects that will meet requirements Design elements must have synergy to fit together so that each element performs multiple roles with respect to the entire ensemble of elements that make up the system

52. 52 Genuine emergence is based on … Inter Intra penetration surfacing Ultra Being Ultra Being is the interspace between void and emptiness, i.e. between the two non-duals, odd and even zero

53. 53 Emptiness / Void Inter-penetration – mutual synergistic interlocking Intra-penetration – mirroring of other parts of the system in each part Inter-surfacing – fitting interfaces Intra-surfacing – interchange protocols in interim between interfaces

54. 54 Ultra Being is... Ultra Being is … external view of projection –A face of the world including all four meta- levels of Being that embody projection Ultra Being is … the standing upon which schematization is based

55. 55 Emergence Engineering Meta-levels supervenience de-emergence emergence meta-levels of emergence meta-levels of Being MAP (of the argument) * repeated

56. 56 System Niche Products E1E1 E2E2 E3E3 E5E5 Supervenient combinatoric or additive change essencing forth in time excess E4E4 chiasm between actualities, errors, voids horizon undecidable Trade-offs Meta-levels of Emergence Engineering genuine emergence Being Existence Process Change Control Architecture/Analysis Specialties Inter Intra penetration surfacing Design Possibilities interim artifacts E0E0 Meta-system vicissitudes of work synthesis * eg., manufacturing, Eng. disciplines SE

57. 57 Main Point The whole discipline of Systems Engineering is structured by the meta-levels of Emergence Systems Engineering is intrinsically Emergence Engineering But is Systems Engineering enough even when viewed as Emergence Engineering? Perhaps we need something even broader than the focus on the Emergence of Systems which is dependent on the Systems Schema alone *

58. 58 Meta-Levels of Being Perice/Fuller Categories Path into world for Emergence Face of world Worldhood Aspects of Being Properties MAP (of the argument)

59. 59 Peirce / Fuller Categories Ultra Wild Hyper Process Pure Ultra Void or emptiness groundless ground Peirce Fuller FirstSecondThirdFourthZeroth Peirce arisingrelationcontinuity synergy logicgeometry logic objectsrelations between objects simulation of interactions through behaviors of object methods system synthesis class templates of objects

60. 60 Genuine Emergence false abortive newness Artificial Nihilistic Emergences ultra wild hyper process pure Repatterned world of beings Emergent characteristics Emergent Event produces new kinds Emergent possibilities rewrite history Emergence inherently unpredictable Path of Emergence into the World

61. 61 Face of the World All four kinds of Being working together ideal determinate probability distribution propensity diversions due to differences in ontic physus Possibilities Actuality continuous path Pure Process Hyper Wild Ultra SE is a face of the world

62. 62 Worldhood Pure –Present-at-hand –Subject/Object dualism –No context –Pointing –Determinate and continuous Process –Ready-to-hand –Dasein (prior to split) –Being-in-the-world –Grasping –Probabilistic

63. 63 Worldhood Hyper –In-hand –Query –Expansion of being-in- the-world –Bearing –Possibility Wild –Out-of-hand –Enigma –Contaction of being-in- the-world –Encompassing –Propensity

64. 64 Science Relativity theory Quantum Mechanics Local flat spacetime Newtonian Mechanics Global Curved Spacetime Superimposed probability waves Present -at- hand Ready -to- hand Experienced Not- experienced speed of light Copenhagen interpretation macro micro

65. 65 Ultra Wild Hyper Process Pure Ultra Void or emptiness groundless ground Peirce Fuller FirstSecondThirdFourthZeroth Peirce arisingrelationcontinuity synergy logicgeometry logic PlasmaGasLiquidSolidCondensate Science The kinds of Being are like the differences between the states of matter Absolute zeroInfinite temperaturePhase transition

66. 66 Science wild hyper process anti-process annihilation creation black hole virtual conserved pure particle

67. 67 wild ultra hyper pure process singularity virtual particles conserved particles event horizon Science existence as void wild Hawking Radiation

68. 68 Levels of the World Duals and Non-duals Physics / Thermodynamics Physus / Logos Finite / Infinite Have / Have not Existence / Non-Existence Actualized / Non-Actualized Non-manifest / Manifest Info-energy Entropy-matter order right good fate source root

69. 69 Non-Dual means... Not One! ~ one Not Two! ~many Info-energy – physics/thermodynamics Order – logos/physus Right – finitude Good – possessed Fate – existence Source – actualization Root -- manifestation

70. 70 What about the System Schema? Are there other possible Schemas that might be important to SE? What are the other Schemas that give systems their meaning through contrast? Do the set of all possible schemas have a structure? Can SE use this structure of schemas to help formalize its work? *

71. 71 Non-dual Order Einstein noted how amazing it was that mathematics can be used to connect theory to physical phenomena through instruments Theory is the Logos, Physical Phenomena are the Physus, and the non-dual between and before their split is Order *

72. 72 Finite / Infinite Physus / Logos Mathesis Order logos of physus Schema Physus of logos Logic *

73. 73 Schema Logic Mathesis Model Theory Representation Theory Mathematical Categories Philosophical Categories Episteme Paradigm Theory Facticity Semantics Syntax strong weak real presence identity truth kernel || representations Mathematical *

74. 74 ontological facticity Physus Mathesis Order logos of physus Schema physus of logos Logic Model Theory Representation theory Logos Phil. Cat. ontic Experience Reason kind individual projection Anomalies perception Being paradox contrary contradiction type theory doxa ratio meta-dimensionality set/mass existence ontos episteme paradigm theory non-dual Phenomenological View Preontological Ontic Ontological Circulation of Projection * Example: Projection of System

75. 75 Ontic Levels of Emergence Gaia Society Species Organism Multi-cell Cell Proto-cell Macro Molecule Molecule Atom Particle Quark String Pressure of reductionism * We discover the levels of Emergence by trying to reduce everything. Those things that cannot be reduced are emergent ontic levels. Different possible ontic hierarchies are possible.

76. 76 Pluriverse Kosmos World Domain Meta-system System Form Pattern Monad Facet Ontic Level Types of Schemas Ontological levels of Emergence * Different possible projections onto the Ontic levels

77. 77 Pluriverse Kosmos World Domain Meta-system System Form Pattern Monad Facet SchemasDimensions Important result: Two dimensions per schema Two schemas per dimension See General Schemas Theory paper by author CSER conference 2004 Research in General Schemas Theory * 10 - 9 9 - 8 8 - 7 7 - 6 6 - 5 5 - 4 4 - 3 3 - 2 2 - 1 1 - 0 0 - -1

78. 78 Open Problems There is no clear definition of categories –Many different systems are proposed The relation of Philosophical Categories, as they are defined by Kant, to schemas is vague The relation if the Philosophical Categories to other social levels of knowledge is unclear mathesis schema logic Phil. Categories Existence Ontos Episteme Paradigm Theory Facticity Aristotle Kant Hegel Heidegger Johannson Social levels of knowledge *

79. 79 mathesis schema logic Open Problems Normal / Deviant Diamond Logic Vajra Logic Matrix Logic Set / Mass Syllogism / Pervasion *

80. 80 Logics Syllogism Universal Set Attribute difference particular Pervasion Boundary Mass Containment identity instance Non-dual Conjunction Conglomerate Metonymy Sameness belonging together Ipsity

81. 81 Open Problems mathesis schema logic Model theory RealityTruth PresenceIdentity syntax semantics *

82. 82 RealityTruth PresenceIdentity syntax semantics Aspects and Properties Coherence Verification Completeness Validation Clarity Consistency *

83. 83 Open Problems mathesis schema logic Set / Mass N-categoryN-blob N-conglomerates Mathematics ignores mass approaches and relies solely on set approaches, so mathematical categories are fundamentally lopsided *

84. 84 N-blobN-category N-conglomerates Blob boundary - 1 Tissue - 2 Bag - 3 Tweak - 4 1 - Category arrow 2 - Functor 3 - Natural transformation 4 - Modification 1 - Conglomerate conjunction 2 - ? 3 - ? 4 - ?

85. 85 Open Problems mathesis schema logic Representation theory Representational Theory taken for granted but not explicitly defined See... Deleuze, G Difference and Repetition Taussig, M. Mimesis and Alterity Representation vs. Repetition *

86. 86 Open Problems Form 3d Form 2d BuildingModel PicturePlans RepresentationRepetition mimesis perspectiverendering *

87. 87 Open Problems mathesis schema logic Pluriverse Kosmos World Domain Meta-system System Form Pattern Monad Facet Schemas are relatively unknown and a General Schemas Theory has not yet been developed, but the schemas are the basis of all formalization *

88. 88 End of Talk See http://archonic.net and http://holonomic.nethttp://archonic.nethttp://holonomic.net for more information concerning this ongoing research project.

89. 89 Schema Types of schema Genealogy of the schema Unfamiliarity Dimensions Opposite of Emergence Ultra Being and Existence MAP (of the argument) Anaximander Plato Kant Heidegger Negative Dimension Meta-dimension Pascal Triangle Simplicies

90. 90 Ontic Levels of Emergence Gaia Society Species Organism Multi-cell Cell Proto-cell Macro Molecule Molecule Atom Particle Quark String Pressure of reductionism

91. 91 Pluriverse Kosmos World Domain Meta-system System Form Pattern Monad Facet Reflexive Special System Autopoietic Special System Dissipative Special System Ontic Level Types of Schemas Ontological levels of Emergence

92. 92 Anaximander Advent of Metaphysical WritingMap of World Model of KosmosMetaphysical Principle two dimensional three dimensional Apeiron Prose

93. 93 Plato Timaeus TrianglesPlatonic Solids two dimensionalthree dimensional

94. 94 Kant Quantity of Judgment Universal, Particular, Singular Quality Affirmative, Negative, Infinite Relation Categorical, Hypothetical, Disjunctive Modality Problematic, Assertoic, Apodeictic (affirmation … as merely possible, as true (real), as necessary) Time-series, generation of time Time-content, filling of time Time-order, connecting representations with one another under a rule Scope of time, time itself as correlate of determination of whether and how objects belong to time

95. 95 Heidegger Transcendental Imagination Dasein

96. 96 Suchness SchemaKind Individual differences Significance 1 2 3 4 0 projection of spacetime Mathematical or Geometrical Schemas Umberto Eco Kant and the Platypus Unfamiliar and Surprise

97. 97 Pluriverse Kosmos World Domain Meta-system System Form Pattern Monad Facet 10 - 9 9 - 8 8 - 7 7 - 6 6 - 5 5 - 4 4 - 3 3 - 2 2 - 1 1 - 0 0 - -1 SchemasDimensions Important result: Two dimensions per schema Two schemas per dimension See General Schemas Theory paper by author CSER conference 2004 Research in General Schemas Theory

98. 98 The Nature of Schemas Schemas are the first projection of differentiation of spacetime onto experienced things Spacetime is not a plenum, but is a differentiation into dimensions, and beyond that, into meta- dimensions The overflow of dimensions beyond experience is part of the ecstasy of dasein Dimensional scale gives us a way to measure distance between schemas Dimensional scale helps clarify the emergent differences between schemas

99. 99 Context of Design Understanding the emergent hierarchy of schemas gives us a context for understanding the design and construction of large complex systems, because beyond the nesting of systems, there are other schemas that need to be understood and used and other relevant characteristics that impinge on systems design and construction

100. 100 Move to General Schemas Theory We need to move from using General Systems Theory as a basis for Systems Engineering to General Schemas Theory as a basis for Schemas Engineering In this way we will be recognizing the wider context of the systems we build and the schemas that control the articulation and the understanding of those contexts

101. 101 Next Step … Special Systems Meta-System –Reflexive Social Special System Autopoietic Symbiotic Special System –Dissipative Ordering Special System System

102. 102 Emergent Meta-System Dissipative Monad System Seed Autopoietic View Reflexive Pod Meta-system Ground

103. 103 Mathematical Operations Unicity – unitary operations like negation Duality – compementarity Triality – octonion Quadrality – Tits Magic Square – EMS Quintality – ? Plotnitsky was right there is multi-way complementarity.