contemporary sciences (probability, system, complexity emergence) understand concepts structured knowledge

1. 1
Probability, Causality, Intricacy, and Emergence
“Complexity Space”
An Easy & Structured Approach to the CONCEPTS of :
(Complexity Theory), (Probability & Disorder),
(Causality and Feedback) and (Complex Systems)
Complexity Theory
HABIB’s Complexity 3D Perspective
Harmonizing the Concepts of Probability, Causality, Intricacy, and Emergence.
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Eng. Emad Farag HABIB

2. 2
( Quotes )
“Complexity science is so important in today's world ..
Many of the most important problems
in Engineering, Medicine, and Public Policy
are now addressed with the ideas and methods of complexity science.”
James Ladyman (University of Bristol), Karoline Wiesner (Universität Potsdam), August 2020 ,
DOI:10.12987/yale/9780300251104.001.0001
And Author’s book “What is a complex system?” (published with Yale University Press)
“Complexity is A MULTI-FACETED Phenomenon,
involving a variety of features .. “
( same a/m authors )
“A variety of Different Measures would be required
to capture all our intuitive ideas
about what is meant by complexity”
The late Physics Nobel Laureate : “MurrayGell-Mann”
Complexity Theory
HABIB’s Complexity 3D Perspective
Harmonizing the Concepts of Probability, Causality, Intricacy, and Emergence.
ad Farag HABIB
4-Realms :
Probability
Causality
Intricacy
Emergence
Importance of Complexity:
Complexity “Space” :

3. 3
( Quotes )
“ ... to begin thinking along the LINES of complexity theory.
Future Scholars and Scholar-Practitioners
will need to think and act Differently
when facing Complexity. “
John R. Turner and Rose M. Baker :
Complexity Theory An Overview with Potential Applications for the Social Sciences ; doi:10.3390/systems7010004
“Focusing on Information Flow
will help us to understand better
how cells and organisms work.”
Nobel Laureate Paul Nurse
Complexity Theory
HABIB’s Complexity 3D Perspective
Harmonizing the Concepts of Probability, Causality, Intricacy, and Emergence.
ad Farag HABIB
4-Realms :
Probability
Causality
Intricacy
Emergence
Complexity Importance & “Space” :
Complexity Core-Issue is “Information Flow” :

4. 4
HABIB’s Complexity 3D Perspective
Eng Emad Farag HABIB
BCR: 4 Cases
Distributions: Selection Flowchart
Distributions: Curves’ Shapes
Distributions: Mathemarical Links

5. 5
HABIB’s Complexity 3D Perspective
Eng Emad Farag HABIB
Entropy Meaning
Main Ref.: A. LESNE, “Shannon entropy: a rigorous notion at the crossroads between probability, information theory, dynamical systems and statistical physics”
Understanding the Meaning of Entropy (in Different Sciences): (ref: "Crossroads", Annick Lesne 2011 )
Topic High Entropy String (H=0.9, H=15,..) Low Entropy String (H=0.1,H=0.3,..)
Basics:
Information High Information = Less repeated pattern Low Information = More repeated pattern
Predictability Low Predictability = High Uncertainity High Predictability = Low Uncertainity
Typicality of Disorder Low "Typicality" (High Rarity) Disorder High "Typicality" (Low Rarity) Disorder
Unevenness High Unevenness = Symmetry-breaking Low Unevenness = High-Symmetry
Ex: words like: "aztdn", "odrcr" (from "Wenglish") words like: "ABCDEFGH", ~ "qu….."
IT:
#Digits Large #Digits required to store the info Few #Digits required to store the info
Shannon Entropy (Math.) less Correlated String: Entropy "H" (H~=log2(N) ) Correlated String: "h" (h << log2(N), Dep.)
Indep. Of String-symbols more Independent Sequence more Dep. Seq.[Symbols'-Distr/ Time-Correl.]
Redundancy Scarcely Redundant (Highly distinct) Highly Redundant (scarcely distinct)
%Compressibility Scarcely Compressible (Highly informative) Highly Compressible (scarcely informative)
Missing Info (average) = average I. required to specify the outcome x when the receiver knows the distribution p = amount of uncertainty represented by a pro
Large Missing Information = Large P.Distr. Uncertainity Little Missing Information = Low P.Distr. Uncertainity
Algorithmic Length Large (long) Algorithm to regenerate a String Small (short) Algorithm to regenerate a String
#Ways to (compose) string Few #Ways Many #Ways
Context Uncommon string (within current context) Common string (within current context)
Ex: # : 3.1623 , 3.1103755(another context: √10, π in Octal) # : 4444444, 2468
Probability: [ 1: ELH // 2: P.Distr. : Random Var X, p(x) // 3: Sequences: X, p(x), Types, SubTypes! ]
Uniformity (Elements-wise) more Equal-likelihood Elements less Equal-likelihood Elements
Uniformity (Classes-wise) Similar Classes DisSimilar Classes
Distribution: Event-described ! Distr. Is composed (fully) of Common Events Distr. Is composed (fully) of Rare Events
#States (Possible): TODO Expectation, @states, H,,
Large #: 3(added)dice=4.17 > 1 die=2.58> coin=1 Small #States: coin tossing ( log2|x|=1)
Ex: P. Distr "in/of" string: #Digits to Describe the string
"Normal" (inside 6σ set of values/events) "Normal" (outside 6σ set of values/events)
Dynamical Systems:
#Categories,Elements Large #Categories & Sparse #Elements Few #Categories & Dense #Elements
Ex: Bio. Molecules Protein Structures, Immune-System Cell-Types Simple Structures
VIMP: in Immune System: Healthy: Entropy "booms" @∆ T-Cells & B-Cells ! Eldery ?: minor ∆H: even @large ∆ of Immune threats
Stat. Physics:
( Concerning: Entropy Production "by/via" a dissipative system, rather than Entropy "in/of" the system : Thermodynamic "S" rather than Statistical "H" )
Microstate Molecules: Gas M. are ALL at the same state Molecules: Gas M. are at Different states
Macrostate System: Unable to do useful (mechanical) Work System: Able to do useful (mechanical) Work
Gases Gas in One thermodynamic Compartment Gas in Two thermodynamic Compartments
Ex: P. Distr "by/via" system: S= #Digits of Emergence ! (to Estimate possible Useful work, as opposed to "pure Dissipation")

6. 6
HABIB’s Complexity 3D Perspective
Eng Emad Farag HABIB
Appendix E: Links & Interrelations in Systems
Dichotomous Classification of Feedback
Enough research done in this regard ?
Information
Correlated Uncorrelated
Dependent Independent
Flow of Information No Flow
Directed Flow Non-directed flow
Predictive
(Extrapolative)
Non-predictive
(Non-extrapolative)
Transfer (TE) Non-Transfer
Causal Non-causal
Circular Causality Direct Causality
-FDBK
Servo
(Follows a Variable setpoint)
Regulation
( Follows a Fixed Setpoint)
+FDBK

7. 7
HABIB’s Complexity 3D Perspective
Eng Emad Farag HABIB
Complexity Space
(A Coherent Perspective)
Viewing Complexity as a 3D Information Space
(# 2 of 4: Complexity Measures : Types & Examples)
Axis X Y Z
Axis-Title Orderness Causality (Feedback) Intricacy
System Part
("Scope")
Environ / Sys Sys / Subsys Subsys / Subsys
Complexity
Measures
How to Describe the
system
How to Build the system System's Degree of Organization
(Elements-wise).
Measures
Examples
Information/ Entropy/
Algorithmic Complexity/
Min. Description
Length/ Renyi/ Fractal
(macro) Dimension
Logical Depth/
Thermodynamic D./
Computational
Complexity (,Time,
Space)/ Information-
Based C.
Fractal D. (micro!)/ Sophistication/
Effective Measure C./ Hierarchical
C./ Tree Subgraph/
Homogeneous.

8. 8
HABIB’s Complexity 3D Perspective
Eng Emad Farag HABIB
A Coherent Perspective to Complexity
Axis X Y (Y-Z Shared !) Z Info Aspects
Axis-Title Orderness Causality (Feedback) Intricacy
System Part
("Scope")
Environ / Sys Sys / Subsys (Inter-Subsys) Subsys / Subsys Info Domains
Main Phenomena Macro Properties, Pattern
formation.
Feedback
(Coded Symbolic).
(Building &
Organizing)
( the SubStr)
Self-Organization
(Subsys, Elements).
Info Usage,
Outcomes
Examples Thermodynamics(PV=
nRT),Fractals, Swarms,
Flocks
Comm: Sampling Rates (2X), mRNA,
Regulatory (Signaling) Pathways?
(Physiology)
(mRNA Vaccines
Marvel! )
Immune Antibodies Diversification
(Germinal Centers)
Info Norms
Quantification Entropy measure: (T.D.,
Shannon)
Hard!, Indirect via: [Non-
Linearity & (Info-)Agents
Formation]
Transfer Entropy ,
…
Measures of: Sophistication,
Hierarchical C., Tree subgraph.
Info
Measures
Main Feature Notion of ~Gestalt Notion of ~Classes Notion of ~Typicality Notion of ~Elements I. Concern
Complexity
Measures
How to Describe the system How to Build the system ( Str / Shared Info) System's Degree of Organization
(Elements-wise).
MIT paper: Info
Measures
Measures
Examples
Information/ Entropy/
Algorithmic Complexity/
Min. Description Length/
Renyi/ Fractal (macro)
Dimension
Logical Depth/ Thermodynamic
D./ Computational Complexity
(,Time, Space)/ Information-
Based C.
(Algorithmic Mutual Info/
Channel Capacity/
Correlation/ Stored Info/
Transfer/ Organization )
Fractal D. (micro!)/ Sophistication/
Effective Measure C./ Hierarchical C./ Tree
Subgraph/ Homogeneous.
MIT Paper by
"Seth Lloyd"
[#3: Str. /
Shared Mutual
Info. ]
~Scale ~macro ~meso (meso-micro) ~micro Info ~Scale
Follows, Guided
by, ..
Simple Rules!
( Statistical)
Communication Rules ( [Speciality/
Numerosity] )
Balance/Duality: [Specifity/
Diversification]
Info "Envelops"
Limits? Spatio-Temporal Limits:
Saturation, Clipping,..
Communication Limits,
Smartness of Agents
( N.A. ! : already
between 2 Extremes)
None!! : Pure Random ! // then
select/elect by -ve Feedback ?
Info
Asymptotes
Info "Types"
(semiotics)
Syntactic (~Form, Objects) Semantic (~Correlations,
relations)
( Learning ) Pragmatic (~Subjective,
Beholder, User)
I. Qualitative
Aspects
Entropy
Concentration
theorems
Sequence space
(Alphabet)
Classes of Sequences (=Types) (Max. Entropy
Distribution? )
Elements (Symbols) I. (Entropy)
Concentration
Comm. Ex. : a "data string" (aggr.) its interpretation its measurement an example
(Action By), the
"Computer"
Sys (not Environ) De-centralized !! (SubSys) De-centralized : just the
(Elements), No "Organizer" !!
Info
Computation
~ ~ Western
Science-Schools
German Science-School:
Constructivism ?
British Science-School:
Empricism ?
American Science-School:
Pragmatism ?
Knowledge
Approach ?
Notes Pattern formation: can be
Scale-free!
VIMP: +veFDBK LIMITS!: e.g. :
Resources, Saturation, Traffic, ..
(Shared Features : can be
considered Y or Z),
~"Transition Features"
Traditional (Classical) Science:
ceases at a Complexity of 3 Elements
!!
Eng. Emad Farag
Habib, Nov 2021
Abbrev.: Information/ System/ Diversification/ Aggregate/ ThermoDynamics/ Feedback/ Complexity (C.) / Communication (Comm.)/ Example/ Not Applicable/ Very Important/ Dimension

9. 9
HABIB’s Complexity 3D Perspective
Eng Emad Farag HABIB
4-Realms :
Probability
Causality
Intricacy
Emergence
DISORDER
+Feedback
(Causality)
+Intricacy
Complex Adaptive Systems
(CAS)
Emergence & Adaptability
( Spontaneous or Equilibrium-based)
==LIMIT ==
+(more ?!)
+1
+FDBK:
Too much -FDBK:
-2 r/n
- r/n
-1,-2, ..
Slight -FDBK
Direct Causality
(non-causal)
ORDER
S0
S1
S0  S1  S2
[ Initial Conditions  “External Disturbance”  System Adaptation ]
The System responds by “Adapting” to : [ more Intricacy  More Info flow  More Order ]
Shift from S0 to S1 : Starts Externally (Order), then midway (Causality), then Internally (Intricacy)
Shift from S1 to S2 : Starts Internally (Intricacy), then midway (Causality), then Externally (Order)
S2
CAS System Response
[ More: Order, Links, Intricacy]

10. 10
Set of facts:
( regarding Complexity Theory and ultra-Conservative beliefs )
( Complexity theory is Not the theory of everyhting )
1- Not Contradicting with beliefs: just Intersecting
2- Intersecting in few issues: that have already settled long ago :
Evolution, Randomity, Eventual Thermal Death of the Universe, .. etc.
3- It adds nothing to either sides of the debates or controversies ! :
i.e.: those wishing to see Complexity as pro-Evolution: will percieve it so,
and those wishing to see Complexity as against-Evolution: will pervieve it so .
4- For a “Non-Scientific Believer” : If such theories causes doubts,
they should be skipped and simply left for specialists’.
However: for a “Scientific Believer”: Complexity Theory
can be of a good & constructive value ..
5- Complexity Theory is NOT pseudoscience. Complexity Theory shares with other
sciences the Benefits that ALL Sciences have:
that knowledge is good ! , and despite human beings have limited knowledge,
Such Knowledge can be developed more, by Studying & Researching,
to discover more laws & facts pointing at a Wise-Creator ..
Complexity Theory
HABIB’s Complexity 3D Perspective
Harmonizing the Concepts of Probability, Causality, Intricacy, and Emergence.
What Complexity
Theory is NOT

11. 11
.. and What Complexity
Theory is
Ref:
John R. Turner and Rose M. Baker :
“Complexity Theory: An Overview with
Potential Applications for the Social
Sciences”
University of North Texas, 2019
doi:10.3390/systems7010004
Complexity Theory
HABIB’s Complexity 3D Perspective
Harmonizing the Concepts of Probability, Causality, Intricacy, and Emergence.

12. 12
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( You can revisit the “Conclusion” Slide )
This Presentation is a draft,
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