Book 1: The Triple Pulse: a Mathematical Web for Cognitive Mysteries
Book 2: Mathematics of the Moment: a move towards Causality
Dr. Zadeh calls for New Mathematics to characterize Biological Systems
Biological Systems Orders of Magnitude more complex than Inanimate Systems
Example: Complexity of variables associated with writing and publishing staggering
"Probability distributions" accurately characterize the fixed data sets of inanimate systems
Fixed data sets inappropriate for the study of ‘animate’ systems
Living Data Streams & the New Mathematics
Data Set Mathematics trivializes Data Streams
Data Stream Mathematics must weight most recent input more heavily
New Mathematics needs new measures that describe the moment
Descriptive measures must also be predictive
Predictive Statements about Data Streams likely to ‘Fuzzier’ or Suggestive
New Data Stream Math trades probabilistic rigor for relevance of the moment
Data Stream Predictors have great relevance for Living Systems
Suggestive Predictions: Relevance?
Zadeh's Principle of Incompatibility
Life's Immediate Meaning Incompatible with Probability's Precision
Questions
Links
Introduction
Revisiting Dr. Zadeh's quotation
Dr. Zadeh's fuzzy logic has great practical & theoretical value.
High level Abstractions, including fuzzy logic, unable to cope with Biological Systems
Necessary to shift mathematical focus to subject at hand - the data stream
High Level Mathematical Abstractions: an Impractical Approach to Living Data Streams
Existing Mathematical Tools applied sensitively to Data Streams
Missing Ingredient: the Information Digestive System of the Organism
Searching for 'Animate' System whose Mathematics fulfills the Requirements
Requirements of Data Stream Mathematics revolve around Life's Immediacy
Proposing an Excellent Candidate for the Position
Probability unacceptable Candidate
Living Algorithm System innately fulfills initial requirements
Living Algorithm’s Derivatives (Rates of Change) provides Descriptors of Moments
Living Algorithm provides trio of Predictive Descriptors
Predictive Clouds are Context-Sensitive
Predictive Clouds constantly evolving shape
Living Algorithm best candidate for job as Mathematics of Living Systems
Living Systems require information digestion system that fulfills specific functions
Living Algorithm models Life’s approach to data stream digestion
Could Living Algorithm be Life’s method for digesting Information?
If so, does the Method generate rule-governed Patterns?
Is there Evidence that Humans are subject to these Rules?
Multiple sleep-related examples in Triple Pulse Article Stream
Links
Living Algorithm?
Living Algorithm System?
Could the Living Algorithm be Life's Computational Tool?
Life needs predictive descriptors concerning future moments.
Predictive Cloud qualifies the Living Algorithm for position as Life's Computational Tool.
Could the Living Algorithm provide the computational backdrop for evolutionary processes?
Could the Living Algorithm's Predictive Cloud provide an evolutionary advantage?
The Sheer Content Approach (raw data plus memory) provides no Predictive Ability.
Living Algorithm's context-based measures provide future estimates.
Living Algorithm’s Predictive Cloud provides information about location, range and tendency of the next data point.
Could Knowledge of Data Stream’s Features provide an evolutionary advantage?
Examples of the Evolutionary Power of the Predictive Cloud's Trio of Measures: Predator/Prey
Knowledge of Probable Outcome increases Effectiveness & Efficiency of Response
Cloud's Predictive Capacity could also lead to Energy Conservation.
Predator/prey arms race includes computational ability
The Predictive Cloud generates Expectations.
Expectations charged with Emotion.
Emotions have evolutionary purpose – Reinforce Memory.
Emotionally charged memories are easier to recall.
Life’s best interests to be aware of Living Algorithm’s Predictive Cloud
Life must employ Living Algorithm to obtain Cloud's predictive power.
Living Algorithm's process, relating past to present, supplies a sense of passage of time.
The flow of digested sensory information only makes sense over time.
Organisms require a sense of time to differentiate random noise from an organized signal.
Sense of Time, not just evolutionary talent, but a requisite talent of Living Systems
Is it possible that the Living Algorithm & Life emerged together?
Data's impact decays over time.
For Raw Sensory Output, the Decay Factor = 1: no time, hence no meaning.
Living Algorithm digests sensory input. The Decay Factor > 1: Time, hence potential meaning
Living Algorithm provides Meaningless Sensory Input with Meaning via Time.
Material Systems: Inert Information (D=1); Living Systems: Dynamic Information (D>1)
Living Algorithm computes Data Stream Acceleration.
The Acceleration of Organized Data Streams is much greater than a Random Data Stream
Graph: Random vs. Organized Acceleration
Minimizing Information Overload conserves Energy.
Focus upon data stream acceleration enables an organism to identify environmental changes.
Random Data Stream Filter both diminishes Information Overload & identifies Environmental Change
Evolution selects for Simplicity & Efficiency.
3 ways that the Living Algorithm System provides Simplicity and Efficiency
Simplicity minimizes Breakdown, Corruption, Computation, & Memory Requirements
Probability’s Computational & Memory Requirements Prohibitive
Electronics provides no future estimates, nor any sense of time.
Physics doesn't incorporate possibility of Informed Choice.
The Living Algorithm: an ideal evolutionary tool due to predictive capacity & ease of use.
Living Algorithm's relating process provides a Sense of Time.
Data Stream Acceleration provides a random filter.
Link
A Data Stream of 'At Bats' generates a Batting Average
The Batting Average: Probability's Descriptor
Probability's Descriptor, also Predictive
Batting Average only a Rough Approximation of Future Performance
Rough Approximation extremely Meaningful
Living Algorithm's up-to-date Predictive Cloud indicates batter is 'hot'.
Living Algorithm's up-to-date Predictive Cloud indicates batter is 'cold'.
Could Living Algorithm be relevant to living systems?
Probability best characterizes Season; the Living Algorithm the Moment
Beautiful example of Complementary Nature of the 2 Systems
Statistics augment Coach's invaluable intuitive sense
The 10-day average – Probability’s attempt to characterize recent events
Small picture averages, a cave man version of Living Algorithm’s Predictive Cloud
10-day average: a limited analysis of the moment
Living Algorithm’s Predictive Clouds: a trio of measures whose sole focus is the present
Weighting the present moment
Predictive Cloud more user-friendly
10-day average stuck in Probability’s paradigm, when better is available
Summary
Predictive Information, although imprecise, filled with relevance
Living Systems require Focus on the Moment
Living Algorithm's Data Stream Mathematics broadens Current Paradigm
Links
Similarities suggest that Living Algorithm is Probability’s Child
Probability’s Static Data Sets: Living Algorithm’s Dynamic Data Streams
Directional & Liminals are unique to Dynamic Data Streams
Living Algorithm & Probability belong to orthogonal Universes
Field of Action: Probability – Static Data Sets, Living Algorithm – Moments in Dynamic Data Streams
Impossible to merge perspectives
Probability’s Specialty: determining permanent features of Fixed Data Sets
Living Algorithm Specialty: determining evolving features of Dynamic Data Streams
Probability – the fixed State of the Universe; Living Algorithm – the Universal Flux
Probability’s snapshot of a data set applies forever
Probability has Difficulties with Data Sets of Constantly Changing Human Behavior
Living Algorithm’s snapshot of a data stream reveals relationship between moments
Creative Pulse Data (120 1s): Boring for Probability, Exciting to Living Algorithm.
Data Set of Men’s heights: Probability’s Specialty, Living Algorithm’s Impossibility
Probability: Permanent Features; Living Algorithm: Changing Relationships
Living Algorithm: Each Moment plays a unique role – Probability: Not
Probability: No moments – can’t analyze relationship between data points
Living Algorithm: Individual data points affect future moments
Probability: Individual subservient to the Group
Difference due to method of processing Data
Summary
Links
Predictions regarding Batting Averages not guaranteed within any range
Player's Performance too individual and transient to have scientific value
The opinion poll
Can’t generalize Opinion Polls: No scientific value
Possible to establish scientific certitude on the performance of identical cars; humans not identical
Player’s Data Set too transient to generalize results
Individuality of Human Data Streams due to Aging & Innate Differences
The Living Algorithm's information patterns influence human behavior.
To establish scientific certitude Probability's analytical tools must be applied to Living Algorithm predictions.
Probability's general statements have scientific value; Living Algorithm's individual statements have none.
Living Algorithm reveals information patterns that seem to influence human behavior.
See how Probability's rise to the top of the subatomic world, sets the stage for the Living Algorithm.
Mechanics reigns supreme at the end of the 19th century
Explanatory Power of Continuous Equations imply that Space and Time, Cause and Effect are unbroken
Probability’s credentials still dubious because of his inability to accurately predict the next moment in time
Mechanics needs Probability to compute atomic interactions
Probability employed as a practical, not theoretical, necessity.
Mechanics: “Probability just a computational tool, not a reflection of reality”
Electrons: Atoms of Electricity?
Electrons: Tiny particles that orbit the nucleus of an atom?
Electrons: Quanta?
Electrons: Not Particles, but Waves?
Electrons: Probability Waves?
Heisenberg’s Uncertainty Principle: Precise Position or Dynamics, not both
Probability: the Ruler of the Subatomic Universe
Probability can't make definitive statements about individual moments
Subatomics are both Waves and Particles
Nobel Prize winners stand in opposition to Probability's inherent Uncertainty
Born's principle of complementarity: Subatomics are both Wave & Particle
Subatomic polytheistic perspective challenges notion of monotheistic space-time continuum
Uncertainty Principle: A Limit to Knowledge rather than Absolute Certainty
Bohr & Von Neumann: Either Dynamics & Causation or Position & Definition
Due to Subatomic Holes, Continuous Equations demoted from Philosophical Metaphor to Accurate Model
Complementarity Principle confirms traditional relationship between Mechanics & Probability
Diagram: Development of relationship between Mechanics & Probability
Merger of Probability and Mechanics predicts the behavior of pure matter
Scientific Reductionism and building block reasoning
Field of Action determines the nature of the Explanation, not Reductionism
Ambiguity & Paradox swept under rug to maintain illusion of Certainty
Living Algorithm’s Process complements Probability's Content.
Probability dethrones Continuity, setting the stage for Living Algorithm’s digital system.
Photons: an elemental Information Pulse in Living Algorithm System
Diagram: Interlocking Triad of Systems: Mechanics, Probability & Living Algorithm
Data Stream Dynamics
Links
Living Algorithm transforms Instants into Moments
Transformational Process gives Data a Meaningful Dimension
The Most Recent Moment is layered on top of the Preceding Moments.
Moments join forces to produce a Greater Impact upon the System
Interlocking Interactions between Data & Living Algorithm Measures
Living Algorithm System: Moments only exist in Relationship, not as Independent Entities
Permanence leads to Definitive Patterns: Change leads to Suggestive Patterns
Living Algorithm Mathematics = the Mathematics of Relationships
Definition: Fungible – an acceptable range of imprecision
Fungible applied to Living Systems
Fungibility – Individual Ambiguity
Fungible: an essential feature of Pattern Recognition
Approximate Meaning basis of Life's Tentative Working Hypothesis
Consciousness requires practical accuracy to monitor and adjust
Mode of explanation for Living Systems must have fungible nature
Precision of Raw Data dumped into Computational Stew
Living Algorithm sublimates Precision for Meaningful Patterns
Living Algorithm ‘forgets’ Data after he enters her Info System
Probability requires a Perfect Memory to ‘remember’ his precise Data
Probability requires a Computer to compute his Measures
Living Systems remember meaningful information
Living Algorithm sacrifices precision to provide up-to-date relevant information
Living Systems require a Mathematical System that digests data streams.
The Living Algorithm System fulfills the requirements for a Mathematics of Living Systems.
What about non-numerical information?
Definition of Algorithm
Intuitive Notion: Procedure for determining answer
Example: A Sense of Arrival Times
Partner’s return: A sense of expected arrival time – including range & direction
Everyday Prediction of Arrival Time requires 3 values and thresholds
Crossing a threshold triggers action
Mean Average determines most expected value of arrival time
Mean Average difficult for Living Systems to compute
Mean Average does not address Recency Effect
Data Sets, Data Streams & the Recency Effect
Living Algorithm’s specialty is digesting data streams
Arrival Times come in relative terms, ‘a little more’
Verbalizing Living Algorithm’s algorithm
Applying verbal algorithm to partner’s arrival time
Living Algorithm’s Memory Requirements: One data point only – Current Average
Emotionally charged Expectations about arrival time easy to Remember
Algorithm easy to compute and easy to remember; what about recency effect?
Recency Effect: Inherent to the Living Algorithm Algorithm
Humans also compute range of expected arrival time and recent tendencies
The Cell's Algorithm applied to the expected range of Arrival Times
The Verbal Algorithm applied to Recent Tendencies
No database of arrival times needed: Data (words or numbers) is integrated into expectations
Evolving Expectations have an Emotional Component
Emotional Component of Expectations make then easier to remember
Living Algorithm digests Single Data Stream to create 3 Expectations
3 Composite Data Streams of Differences
Simple Living Algorithm algorithm fulfills Complex Requirements
Living Algorithm algorithm handles both verbal & numerical data
Links
Strict Requirements for a Mathematics of Living Data Streams
Living Algorithm fulfills these Requirements; Probability does not.
Data Stream Mathematics must also incorporate the possibility of Informed Choice
Digital Living Algorithm vs. Continuous Equations of Physics
Matter, not alive, but governed by Universal Laws
Newton's Laws of Motion bridge Heaven & Earth
Newton's calculus reflects the continuous space and time of the material world
Physics generalized his findings about Matter to Life
The Sine Wave: A Classic Continuous Equation of Physics
Triple Pulse & Sine Wave, apparently similar, entirely different
Difference Distinguishes Traditional from New Perspective
No wiggle room in Analog Equations (Automatic Future)
Living Algorithm’s digital nature produces Data Streams of distinct Measures
Graph: Triple Pulse Close-up
Living Algorithm’s digital method of digesting data incorporates potential for Informed Choice
Living Algorithm requires ongoing flow of Fresh & Free Data
Physics needs Data to generate Equations, but then abandons it.
Physics Equations only need one Data Point – Initial Conditions
Physics dominates Data Streams
Hard Data must be Accurate & Precise
Co-evolution of Hard Data & Hard Science
Living Algorithm’s Free Data encompasses Potential for Choice
Definitions
Living Algorithm provides meaning to Raw Data
Organism translates Living Algorithm Measures to derive Meaning
No choice in Physics
Living Algorithm provides potential for Interactive Feedback Loop
Living Algorithm’s abundant wiggle room provides for Informed Choice.
Choice affects Future
Physics Equations impervious to External World: a Closed System
Living Algorithm porous to the Outside, an Open System
Open System of Living Algorithm vs. Closed Systems of Physics
Analog Equation's Content & Living Algorithm's Context determines Result
Life also an Open System
Possibility of Choice: another Similarity between Living Algorithm & Life
Link: Living Algorithm & Physics bound by a super highway