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The Foundations of General Schemas Theory

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					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
                                     1
            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

                                                    2
                            *
Horizons of SE
 Schemas Engineering


Emergence Engineering



         Current SE




                        3
    MAP
(of the argument)
                        Systems                     Other
                                                                           *
                        Engineering                 Disciplines
                        Discipline
Ontic and Ontological
                                                        SW Eng /
Levels of Emergence
                               •A transformative        Comp Science
       Complex                  discipline is one
       Systems                 which changes the
                                                         All Engineering
       Theory                  relations between         Disciplines are
                                other disciplines        the Academic
        Complex                                          counterpart of
                                when it appears
        Adaptive                                         SE
        Systems                                        Scope Broader

        Chaos Theory


                                                                      4
 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
                                                    5
 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                                        6
 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
                                                              7
 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

                                                    8
      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
                                                        9
    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                  10
       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
                                                 11
                                                           *
 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 (H2O) 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
                                                      12
        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
                                                          13
        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                        14
                                                                 *
        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
                                                            15
        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
                                                     16
    MAP
(of the argument)
                     Emergence Engineering Meta-levels
                                                                *
                    supervenience           de-emergence


                                emergence



                         meta-levels of emergence



                           meta-levels of Being

                                                           17
                   Supervenience & Emergence                                         *
            Gestalt = Whole greater than sum of parts

                                                            Emergence
                                                            Excess

   organism        LEVEL N+1          new characteristics
Supervenience is
Homomorphism
with lower level
supports cell      LEVEL N                  supports                    Synthesis

                                                            Qualitative and
                                                            Quantitative Jump



                                                                                18
                                    De-emergence                                     *
           Proto Gestalt = Whole less than sum of parts gives
           knowledge of implicate order

                                                    Emergent Lack
                                             Loss of knowledge or information

Cannot           LEVEL N+1
reconstitute
the whole

LEVEL N          Part Part Part Part Part
                                                                       Analysis/
                    Parts don‟t add up to the whole                   Architecture


  There is normally a cycle between emergence and de-emergence
                                                                                19
                 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
                                                    20
               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
                                                    21
         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”                                          22
                 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                         23
                     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
                                                  24
        Conjecture: Emergent Properties are Godelian
This could be the basis for formalizing the concept of emergence
                                                                 *
                           emergent
                           excess



              decidable               decidable
              inside                  outside


                          emergence

                           de-emergence

         Undecidable means non-reducible                    25
               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”

                                                 26
                                     Emergence of Emergences      *
                                                               E2b
     E3
Can‟t get to E3
 directly from
lower levels of                                                E2a
  Emergence


                                                               E1



                                                               E0

          Current view of SE as concerned with Integration   27
                 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

                                                    28
           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
                                                 29
    MAP
(of the argument)
    repeated
                     Emergence Engineering Meta-levels
                                                                *
                    supervenience           de-emergence


                                emergence



                         meta-levels of emergence



                           meta-levels of Being

                                                           30
Correspondence between meta-levels of Emergence and meta-levels of Being
                                                                            *
                                           Ontology
 Meta-levels of Emergence               Meta-levels of Being

       Emergence7                        Thatness/Suchness
       Emergence6                        Manifestation
       Emergence5                        Ultra-Being          existence
                                                              threshold
       Emergence4                        Wild Being
       Emergence3                        Hyper Being
       Emergence2                        Process Being
       Emergence1                        Pure Being          ontological
                                                             difference
       Emergence0                        beings
                                                                       31
   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
                                                           32
        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
                                                    33
Existence                Stairs to Nowhere: Meta-levels of Emergence                                            *
                                     Emptiness / Void                                              Lack
Being




                 chiasm between               Radically Unpredictable,                         genuine
            E4   actualities, errors, voids          unknown
                                                                            E5   Ultra Being   emergence



                 essencing
            E2   forth in time
                                                          E3    excess
                                                                                  horizon




             Supervenient                                 combinatoric or
                                               E1         additive change


                                                                    undecidable
            E0 non-emergent change

                                                                                                           34
                                                                  *
           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       35
     origin
                   0
                                                           *
         Emergence             = beings
• Non-new change             • beings, entities, things
• More of the same
• Random alteration


    Emergent Difference and Ontological Difference

• Entry of the New           • Entry of Being
  Example: Car wear           Example: Projection
                                                      36
                                                              *
               Aspects of Being
•   Truth            These change
•   Reality              at the
•   Identity           different
                     meta-levels of
•   Presence            Being

    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.
                                                         37
               1
                                                      *
      Emergence         = Pure Being
• Pure Artificiality    • Determinate and
• Combinatoric            continuous
  expansion             • Present-at-hand
• Superficial newness   • Pointing
• Additive or           • Standing reserve
  incremental           • Subject/object dichotomy
  improvement           • Form level
• Nothing fundamental      – Symbol
  changes                  – Shape

  Example: New cars
                                                 38
     Aspects of Being at Emergence Level 1

• Identity1 – Change and difference occur but
  make no fundamental difference
• Presence1 – Changed Emergent
  characteristics appear
• Reality1 – Emergent characteristics are
  embodied
• Truth1 – Emergent characteristics can be
  described in language
                                             39
     Emergence2 = Process Being                                 *
 • Emergence becomes an          • Probability
   event                         • Ready-to-hand
 • It takes time for something   • Grasping
   to “be” what it is            • Dasein (being-in-the-
 • Emergent change reveals         world)
   the essence of the thing      • Pattern Level
   seen
                                     –   Value
 • Like Catalysis in                 –   Sign
   Transformations                   –   Flux
                                     –   Structure

Example: From Buggy to Car
                                                           40
     Aspects of Being at Emergence Level 2

• Identity2 – Self identity revealed though
  change – sameness – belonging-together
  family resemblance
• Presence2 – showing and hiding
• Reality2 – Physus - unfolding of new kinds
  in nature
• Truth2 – Logos – unfolding of new kinds in
  language
                                               41
      Emergence3             = Hyper Being                     *
 • Projects new               •   Possibility
   possibilities on new       •   In-hand
   horizon                    •   Bearing
 • Emergence itself is        •   Query (expansion)
   undecidable
                              •   Trace Level
 • Emergent excess is
   Godelian                   •   Differance
                                  – Differing/Deferring
                              • Excess / Supplement
Example: Car with Software
                                                          42
      Aspects of Being at Emergence Level 3

• Identity3 – Self Identity revealed though
  Other (Alterity)
• Presence3 – secrecy, lies, deception,
  dissimulation
• Reality3 – Simulacrum – unreality of reality
  is more real than reality
• Truth3 – Fiction – lies tell truth deeper than
  the facts alone can tell
                                               43
                4
                                                              *
      Emergence                = Wild Being
• Actualizes new                •   Propensity
  possibilities on new
  horizon
                                •   Out-of-hand
• Emergence is intrinsically    •   Encompassing
  unpredictable                 •   Enigma (contraction)
• Reveals unexpected,           •   Tendency
  unheard of, unthought,
  anomalous appearances         •   Rhizome
  from a direction              •   Chiasm (reversibility)
  previously unknown
                                •   Flesh
 Example: Car with AI
                                                         44
     Aspects of Being at Emergence Level 4

• Identity4 – Chiasm between self‟s and
  other‟s identity and difference
• Presence4 – Chiasm between self‟s and
  other‟s presence and absence
• Reality4 – Chiasm between nature‟s and
  artificiality‟s reality and illusion
• Truth4 – chiasm speech‟s and silence‟s
  between truth and fiction
                                             45
                5
                                                            *
       Emergence           = Existence
• Genuinely emergent       • Interpretations
  existent appears from       – Ultra Being
                              – Emptiness
  itself in its own time
                              – Void
  and a place of its
                           • Inter/intra
  choosing                   penetration/surfacing
• No projection            • Being seen from outside
• Face of the World          as a found thing being-
                             out-of-the-world
  Example: Flying Car,
      New Media
                                                       46
    Aspects of Existence at Emergence Level 5

• Identity5 – uniqueness
• Presence5 – Fully and Genuinely Emergent
  Alterity
• Reality5 – Phenomena bodies forth in itself in its
  own style of non-nihilistic distinctions in action
• Truth5 – Wipes nihilistic background clean - clears
  the clearing-in-being and makes non-nihilistic
  distinctions as phenomena speaks for itself in its
  own voice

                                                   47
            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

                                                           48
Existence                            Meta-levels of Emergence
                                                                                                      *
                                Emptiness / Void                                         Lack
Being




                                                                                     genuine
            E4   Radically Unpredictable, unknown                 E5   Ultra Being   emergence




            E2 essencing forth in time: event   E3    excess
                                                                        horizon




              Supervenient                      combinatoric or
                                      E1        additive change


                                                          undecidable
            E0 non-emergent change

                                                                                                 49
        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
                                                     50
                    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

                                                  51
     Genuine emergence is based on …

                Inter          penetration

                Intra          surfacing




                        Ultra Being

Ultra Being is the interspace between void and emptiness,
i.e. between the two non-duals, odd and even zero
                                                            52
           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

                                                 53
           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


                                                   54
    MAP
(of the argument)
    repeated
                     Emergence Engineering Meta-levels
                                                                *
                    supervenience           de-emergence


                                emergence



                         meta-levels of emergence



                           meta-levels of Being

                                                           55
Existence
                                  Meta-levels of Emergence Engineering                               *
             Meta-system                             Inter        penetration          Niche
             eg., manufacturing, Eng. disciplines    Intra        surfacing
                                                                      synthesis
Being




                  chiasm between actualities,                                              genuine
             E4   errors, voids                     Specialties   E5 System           SE   emergence


                                       Architecture/Analysis
                  essencing
            E2    forth in time     Process     E3 excess                   horizon
                                                                                      Design
                                    Change Control                                    Possibilities
            Products                    E1
                  Supervenient
                                            combinatoric or
                                            additive change   undecidable
                interim artifacts                             Trade-offs
            E0 vicissitudes of work

                                                                                                56
                                                     *
                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

                                                57
    MAP                      Meta-Levels of Being
(of the argument)




                                                         Aspects of Being




                                                             Properties


     Perice/Fuller
     Categories

                                         Face of world


                     Path into
                     world for
                     Emergence             Worldhood
                                                                            58
                                Peirce / Fuller Categories

        Void or




                                                          Process
        emptiness




                                      Hyper
                            Peirce             Peirce                 Peirce             Fuller
Ultra




                                                                                                   Ultra
                     Wild




                                                                                 Pure
        Zeroth              First             Second                Third               Fourth
        groundless          arising            relation             continuity           synergy
        ground               logic               logic                logic             geometry




      class                 objects           relations        simulation of system
   templates                                  between           interactions synthesis
   of objects                                  objects            through
                                                               behaviors of
                                                                   object
                                                                  methods           59
 Path of Emergence into the World
                                    Artificial Nihilistic
                                       Emergences
•Emergent characteristics
•Emergent Event produces
new kinds
•Emergent possibilities
rewrite history
•Emergence inherently
unpredictable




 Repatterned
  world of
   beings                                                   60
         Face of the World
All four kinds of Being working together     Ultra
   SE is a face of the world               Actuality

      Possibilities
            Hyper




                             Wild
           propensity                       probability
       diversions due to                    distribution
      differences in ontic                   Process       61
             physus
                   Worldhood
• Pure                         • Process
  –   Present-at-hand            –   Ready-to-hand
  –   Subject/Object dualism     –   Dasein (prior to split)
  –   No context                 –   Being-in-the-world
  –   Pointing                   –   Grasping
  –   Determinate and            –   Probabilistic
      continuous




                                                               62
                 Worldhood
• Hyper                      • Wild
  – In-hand                    – Out-of-hand
  – Query                      – Enigma
  – Expansion of being-in-     – Contaction of being-in-
    the-world                    the-world
  – Bearing                    – Encompassing
  – Possibility                – Propensity




                                                      63
                              Science

          Relativity                               Quantum




                               macro
                                       micro
           theory                                  Mechanics

Present   Local flat                            Newtonian
  -at-    spacetime                                               Experienced
                                                Mechanics
 hand
             speed of light                       Copenhagen
                                                 interpretation


            Global                             Superimposed          Not-
Ready
            Curved                              probability       experienced
 -to-
           Spacetime                              waves
hand


                                                                         64
                                                                                     Science
                       Void or




                                                                                                 Process
                       emptiness




                                                                  Hyper
                                                        Peirce                        Peirce                           Peirce                          Fuller
Ultra




                                                                                                                                                                      Ultra
                                    Wild




                                                                                                                                      Pure
                       Zeroth                           First                        Second                          Third                            Fourth
                       groundless                       arising                       relation                       continuity                        synergy
                       ground                            logic                          logic                          logic                          geometry
Infinite temperature




                                     Phase transition




                                                                  Phase transition




                                                                                                  Phase transition




                                                                                                                                  Phase transition




                                                                                                                                                                        Absolute zero
                       Plasma                           Gas                           Liquid                          Solid                          Condensate


           The kinds of Being are like the differences between the
                              states of matter
                                                                                                                                                                 65
              Science
                pure

conserved      particle
 virtual
               process

   wild                       hyper
   creation                  annihilation

              anti-process

black
hole
                                      66
   Science
              singularity
        existence as void
                     pure conserved
                             particles
         wild
          Hawking Radiation


                ultra
              event horizon



       virtual particles

wild     process            hyper
                                         67
                               Levels of the World
                               Duals and Non-duals

    Info-energy
   Entropy-matter
Physics / Thermodynamics
            order
   Physus / Logos
                    right
          Finite / Infinite
                        good
                Have / Have not
                                   fate
                       Existence / Non-Existence
                                             source
                                  Actualized / Non-Actualized
                                                      root
                                          Non-manifest / Manifest

                                                                    68
     Non-Dual means . . .
Not One!                          Not Two!
 ~ one                             ~many
                Info-energy –
           physics/thermodynamics
            Order – logos/physus
               Right – finitude
              Good – possessed
               Fate – existence
            Source – actualization
            Root -- manifestation
                                             69
                                                  *
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?
                                             70
                                               *
           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


                                          71
                  Mathesis                           *
                   Order
logos of physus               Physus of logos
    Schema                        Logic




             Physus / Logos


                   Finite / Infinite
                                                72
                                                                                    *
                               Mathematical Categories
                                   Mathesis
                                     strong
                                                                     real
    kernel    Representation                      Mathematical
                 Theory                                           Semantics
       ||                                         Model Theory
                                                                   Syntax
representations
                                                                   presence
                                                                    identity
                                                                     truth

             Schema                                      Logic
               weak       Philosophical Categories       strong
                                 Episteme
                                 Paradigm
                                  Theory
                                 Facticity


                                                                               73
                           Circulation of Projection
                                   meta-dimensionality
                                                                                              *
                                        set/mass
                                                              Phenomenological View
                                                                   •Preontological
                                                                   •Ontic
                                     Mathesis                      •Ontological
Anomalies                                                                             Being


                                       Order
                                        non-dual


ontic           Physus                 Phil. Cat.
                                                              Logos             ontological
                                       existence
                                         ontos
                                       episteme
                                       paradigm
            logos of physus             theory           physus of logos
                Schema                                       Logic
             Example: Projection of System

               Experience             facticity              Reason
                                                              doxa
                      kind
                                                              ratio
                   individual                                                            74
   Ontic Levels of Emergence                                                   *
          Gaia
       Society
       Species                               We discover the levels of
                                              Emergence by trying to



                  Pressure of reductionism
     Organism
     Multi-cell                              reduce everything. Those
          Cell                                 things that cannot be
     Proto-cell                                reduced are emergent
Macro Molecule                                 ontic levels. Different
      Molecule                               possible ontic hierarchies
         Atom                                       are possible.
       Particle
        Quark
        String
                                                                          75
              Types of Schemas
        Ontological levels of Emergence
                                                          *
                  Pluriverse
                   Kosmos
                    World             Different
                   Domain              possible
Ontic            Meta-system         projections
Level              System           onto the Ontic
                    Form                levels
                   Pattern
                   Monad
                    Facet


                                                     76
Schemas
              Research in General Schemas Theory
               Dimensions
                                                                        *
Pluriverse      10 - 9
Kosmos          9-8
                            Important result:
World           8-7
Domain          7-6             Two dimensions per schema
                6-5
Meta-system
                5-4             Two schemas per dimension
System
                4-3
Form            3-2
Pattern         2-1
                            See “General Schemas Theory” paper by author
Monad           1-0                    CSER conference 2004
Facet           0 - -1
                                                                   77
                     Open Problems                                       *
      mathesis
                                      • There is no clear
schema                logic             definition of categories
                          Aristotle      – Many different systems are
                           Kant            proposed
    Phil. Categories       Hegel
                         Heidegger    • The relation of
         Existence       Johannson      Philosophical Categories,
          Ontos                         as they are defined by
         Episteme    Social levels      Kant, to schemas is vague
         Paradigm         of          • The relation if the
          Theory      knowledge
         Facticity
                                        Philosophical Categories
                                        to other social levels of
                                        knowledge is unclear
                                                                    78
                  Open Problems                         *
       mathesis

 schema            logic



Normal / Deviant                 Set / Mass
          Diamond Logic    Syllogism / Pervasion
          Vajra Logic
          Matrix Logic



                                                   79
                                      Logics
             Syllogism                                    Pervasion
             Universal                                    Boundary

    Set                  particular             Mass
                                                                      instance
Attribute                                  Containment
difference                                     identity
                                      Non-dual
                                 Conjunction
                Conglomerate
                  Metonymy                      Ipsity
                  Sameness
              belonging together                                         80
                 Open Problems                              *
                                semantics    syntax
                               Reality       Truth


                               Presence     Identity
                                 syntax      syntax




     mathesis
                Model theory
schema          logic
                                                       81
         Aspects and Properties                    *
semantics                     syntax
                 Coherence
Reality                       Truth




                                Consistency
 Validation




Presence          Clarity
                             Identity
 syntax                       syntax



                                              82
                     Open Problems                                    *
    Mathematics ignores                   N-conglomerates
   mass approaches and
      relies solely on set
          approaches, so     N-category                 N-blob
 mathematical categories
      are fundamentally
                 lopsided
                                           Set / Mass



      mathesis

schema             logic
                                                                 83
                    1 - Conglomerate conjunction
                    2-?
                    3-?
                    4-?

                       N-conglomerates

              N-blob              N-category

Blob boundary - 1                   1 - Category arrow
       Tissue - 2                   2 - Functor
         Bag - 3                    3 - Natural transformation
       Tweak - 4                    4 - Modification

                                                          84
                   Open Problems                                    *
 Representational Theory
 taken for granted but not
    explicitly defined


Representation vs. Repetition


See . . .
Deleuze, G                                      mathesis
Difference and Repetition       Representation theory
Taussig, M.                            schema              logic
Mimesis and Alterity
                                                               85
          Open Problems                                *

Form 3d       Building mimesis         Model

            perspective               rendering

Form 2d       Picture      mimesis     Plans


          Representation             Repetition


                                                  86
               Open Problems                                *
                                   mathesis

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

                                                       87
                 End of Talk
See http://archonic.net and http://holonomic.net
for more information concerning this ongoing
  research project.




                                               88
    MAP
(of the argument)                     Schema

                                                                  Ultra Being
                                                                 and Existence
Types of schema

                                                             Opposite of
                                                             Emergence
               Genealogy of
                the schema
                Anaximander                     Dimensions
                Plato         Unfamiliarity
                Kant
                Heidegger
                                                                     Pascal
                                          Negative
                                                                    Triangle
                                         Dimension
                                                                   Simplicies

                                                Meta-dimension
                                                                           89
   Ontic Levels of Emergence
          Gaia
       Society
       Species



                  Pressure of reductionism
     Organism
     Multi-cell
          Cell
     Proto-cell
Macro Molecule
      Molecule
         Atom
       Particle
        Quark
        String
                                             90
              Types of Schemas
        Ontological levels of Emergence

                  Pluriverse
                   Kosmos
                    World
                   Domain
Ontic            Meta-system         Reflexive Special System
                                     Autopoietic Special System
Level              System            Dissipative Special System
                    Form
                   Pattern
                   Monad
                    Facet


                                                          91
                    Anaximander
                     Advent of Metaphysical




      Writing                           Map of World
      Prose                             two dimensional




Model of Kosmos                     Metaphysical Principle
three dimensional                        Apeiron


                                                             92
                  Plato
                  Timaeus




   Triangles                Platonic Solids
two dimensional             three dimensional




                                                93
                                       Kant
      Quantity of Judgment                                  Relation
     Universal, Particular, Singular      Categorical, Hypothetical, Disjunctive
Time-series, generation of time               Time-order, connecting
                                          representations with one another
                                                    under a rule

              Quality                                           Modality
    Affirmative, Negative, Infinite              Problematic, Assertoic, Apodeictic
                                        (affirmation … as merely possible, as true (real), as necessary)

 Time-content, filling of time              Scope of time, time itself as
                                            correlate of determination of
                                           whether and how objects belong
                                                       to time
                                                                                              94
             Heidegger


Transcendental
                     Dasein
 Imagination




                              95
          Unfamiliar and Surprise
             projection of
              spacetime

    0            1              2         3          4
  Suchness     Schema        Kind   Individual
                                                  Significance
                                    differences



Mathematical or Geometrical Schemas
           Umberto Eco
      Kant and the Platypus
                                                             96
              Research in General Schemas Theory
Schemas        Dimensions
Pluriverse        10 - 9
Kosmos            9-8
                            Important result:
World             8-7
Domain            7-6           Two dimensions per schema
                  6-5
Meta-system
                  5-4           Two schemas per dimension
System
                  4-3
Form              3-2
Pattern           2-1
                            See “General Schemas Theory” paper by author
Monad             1-0                  CSER conference 2004
Facet             0 - -1
                                                                   97
        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                         98
          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
                                             99
     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
                                             100
  Next Step … Special Systems
• Meta-System
   – Reflexive Social Special System
      • Autopoietic Symbiotic Special System
   – Dissipative Ordering Special System
• System



                                           101
Emergent Meta-System

Dissipative   Autopoietic
 Monad          View



  System
   Seed
Meta-system    Reflexive
 Ground          Pod

                            102
       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.                       103

				
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