Information Dynamics
Glossary: G>M


Glossary G>M: definitions, descriptions and links of the diverse variety of terms employed throughout the multiple articles devoted to Information Dynamics.

Gödel's Theorem

In the early part of the 20th century, a cash prize was offered to anyone who could employ the rules of logic to prove that an underlying proposition was undeniably true. In essence, they wanted to prove that logic can determine truth. This notion was in line with the concept that absolute truth exists. Once an absolute truth was established, a logical structure could be constructed that would be correct in all situations.

Gödel, instead, turned the notion of logical certainty inside out. Employing the traditional tools of logic, Gödel proved that if a system is logically consistent that it can't be complete, and that if a system is complete that it must contain paradox. In other words, a logically consistent system can only apply to part of the puzzle, not the entire picture. For a logical system to encompass the entire puzzle, it must contain some inconsistencies. This is known as Gödel’s Theorem.

This reasoning applies to the material world. Newtonian Mechanics is able to accurately describe the atomic world and larger without any logical inconsistencies. However, to describe the subatomic world, the uncertainty of Probability must be included. More importantly electrons and photons can be viewed as either a wave or particle depending upon the perspective of the observor. These two truths are mutually exclusive logically. This is the paradox that completes the system.

The same reasoning applies to the three mathematical Realm of Existence, i.e. Subatomic, Atomic and Attention. Each realm is logically consistent internally and yet is incomplete in that they don’t encompass the whole, i.e. the other realms. Further, the whole contains paradox, i.e. logical inconsistencies, as the three realms contain mutually exclusive truths. For instance, space and time are continuous in the Atomic Realm, quantized in the Subatomic Realm and elastic in the Attention Realm.

This type of reasoning suggests that we live in a paradoxical Polyverse, rather than a logical Universe.

Imaginary Realm

Another name for Life’s Non-Material Realm. Unique to living systems, this mathematical realm of existence has many features, e.g. Intention, Attention, Feelings, Choice and Imagery. The word ‘Imaginary’ was chosen to emphasize the image-making capacity of living systems – a feature that exclusively material systems don’t have. According toAttention Theory, the Living Algorithm’s computational process enables living systems to generate an overlay of images that is the basis of both our sense of time and objective reality.

In common parlance, imaginary conveys something that is purely mental – possibly and even frequently without any connection to the material world. In this more technical usage, the images that are the root word of imaginary have a material substrate, but are not the substrate. The physical body is the proxy for the energetic body, not its equivalent.

The imaginary numbers of mathematics provides a useful way of understanding the relationship between imagery and physical reality. In order to solve real life problems, engineers employ imaginary numbers, which are a logical impossibility, in combination with so-called real numbers. Via the algebraic manipulation of these so-called complex numbers, engineers and scientists are able to come up with solutions to real world problems.

In similar fashion, the Imaginary Realm of images interacts with the Material Realm to create real world Living Behavior. For instance via sensory input, we form an image of an apple. While based in material reality, this image is imaginary in the sense that we are imagining a feature of the physical world. Assuming this image is somewhat accurate, we then direct our biological hand to grasp the apple and bring it to our mouth so that we can consume it. While the images are purely ideational, the nutrition is real in that it both keeps us alive as an organism and enables to form more images to organize reality.

This Realm of Images is just one perspective on Life’s non-material component.

For a more in-depth discussion of these topics, read the article: Attention & Matter: Interacting Realms of Existence?

Information Digestion Model

The conceptual model that was developed to make sense of the patterns of correspondence between the mathematics of Data Stream Dynamics and empirical data.

The core assumption of this model is that living matter has both a material and a non-material component. The non-material component is based upon the digestion of information, hence the name of the model. The Living Algorithm provides the method of digesting information.

This unique perspective is based upon a simple insight. Just as the Body digests food, the Mind digests information. In both cases, the digestion process transforms environmental substance into a form that Life can employ to fulfill potentials. Just as the body's digestive system extracts food from organic material, the information digestion process extracts meaning from digital information. In brief, living systems convert both food into biological energy and information into meaningful knowledge.

Both Body and Mind require downtime to complete the digestion process. When the digestion process is completed, Body becomes hungry for food and Mind becomes curious for information. Just as Body obtains food through the mouth, Mind obtains information through Attention.

To understand why the synergy between the Math and the Data 'forced' us to make these assumptions, read Core Postulates.

Information Dynamics

Behavioral Dynamics, Information Dynamics, Attention Dynamics: These are all names that I have used to refer to the complex of ideas associated with my Theory of Attention. I have employed the same word 'dynamics' in each case because Data Stream Dynamics provides the mathematical foundation for my theory. Attention theory addresses the mathematical relationship between human behavior, Information, and Attention, which is the reason for the qualifying words.

See the glossary entries under Theory of Attention and Data Stream Dynamics for a more up-to-date understanding of Information Dynamics.

information digestion vs. processing

Information digestion and information processing are worlds apart. Computers process information; living systems digest data streams to give them meaning. Put another way, processed information has no meaning until Mind digests it.

According to our Theory of Attention, the Living Algorithm (LA) is the tool that Mind employs to digest data streams. Just as Body digests food, Mind digests data streams. In both cases, the digestion process transforms environmental substance into a form that Life can employ to fulfill potentials. Just as the body's digestive system extracts food from organic material, the LA's digestion process extracts dynamic meaning from data streams, the informational food of living systems. In brief, living systems convert food into biological energy and data streams into meaningful information.

A distinct and unique feature of the digestion process associated with the Theory of Attention is choice. We choose what to eat and when to cease eating. Similarly Mind is also able to choose which information to digest, i.e. where to focus Attention, and when to cease digesting information, i.e. Sleep. In this fashion, this fresh perspective introduces both meaning and choice into the scientific dialogue. The Information Digestion Model provides a more complete articulation of this relationship.

Information Physics

Information Physics provides a mathematical foundation for a network of hypotheses regarding Attention' interaction with Information – a Theory of Attention. We deem it a 'physics' because it employs a similar architecture of dynamical constructs as does traditional Physics.

Despite this similarity, Information Physics and Material Physics have significant differences regarding focus, elements, mathematics and laws. For instance, Information Physics specializes in the interaction between information and mental energy in subjective space and time, while Material Physics specializes in the interaction between matter and physical energy in objective space and time. Information Physics also provides a mechanism for the transfer of information from the Immaterial Realm to the Material Realm of existence. (For more, check out the article: Introduction to Information Physics.)

Calculus, a closed system with regular equations, provides the mathematics for Material Physics. The Living Algorithm, an open, reflexive equation, provides the mathematics for Information Physics. (For more details, check out the article: Data Stream Dynamics: Calculus of Dynamic Meaning.)

Intention Realm

The Realm of Intention is an alternative name for Life’s Non-Material Realm. Unique to living systems, this mathematical realm of existence has many features, e.g. Intention, Attention, Feelings, Choice and Imagery. The word ‘Intention’ was chosen to emphasize the intentional component of living systems – a feature that exclusively material systems don’t have. According to Attention Theory, the Living Algorithm’s computational process generates analytics that enable living systems to make better choices with which to fulfill potentials. We deliberately employ our intention to take advantage of these analytics.

As with the Imaginary Realm, the name merely highlights another perspective on the Living Realm. Rather than different realms with different laws, each of these alternative names are referring to the same realm of existence, the so-called Non-Material Realm. The differing names merely suggest a different perspective on Life’s non-material component.

Intentional Realm=Imaginary Realm=Attention Realm=Non-Material Realm

For a more in-depth discussion of these topics, read the article: Attention & Matter: Interacting Realms of Existence?

Interacting Realms Paradigm

This paradigm holds that the Universe consists of multiple interacting realms of existence – the Atomic, Subatomic and Attention. In popular parlance, a realm of existence could have many diverse referents, e.g. the realm of music, sports, or food. In this usage indicated by capitalization, ‘Realm of Existence’ has a more technical meaning. 1) The 3 realms interact. 2) Each realm has a unique mathematical basis. 3) Each type of mathematics employs the same architecture of constructs of traditional Newtonian dynamics, e.g. force. 4) Each realm applies to a unique aspect of existence. These features join the three realms together as a group.

1) Interaction: The Atomic Realm interacts with the Subatomic Realm to generate the Material Realm. The Material Realm interacts with the Attention Realm to generate the Living Realm of existence.

Atomic Realm x Subatomic Realm = Material Realm

Material Realm x Non-Material Realm = Living Realm

2) Unique Mathematical Systems: The Atomic Realm is based in traditional Newtonian Mechanics; the Subatomic Realm in Quantum Physics; and the Attention Realm in Data Stream Dynamics. These ideas are developed in the article – Matter’s Regular Equations vs. Life’s Disobedient Equations.

3) Same Dynamical Architecture of Newtonian Constructs: While based upon different types of mathematics, each realm utilizes the traditional constructs of Newtonian dynamics, e.g. mass, distance, time and force. These ideas are developed in the Notebook – Data Stream Dynamics.

4) Unique Aspect of Existence: the Subatomic Realm deals with the potentiality of the micro world inside the atom, the Atomic Realm with the actuality of our material world, and the Attention Realm with the intentionality of our living world.

The Interacting Realms Paradigm expands the prevalent Material Paradigm, which holds that there is only one realm of existence, i.e. the Material Realm. The Interacting Realms Paradigm provides an abundance of explanatory power regarding Living Behavior. In contrast, the traditional Material Paradigm provides little, if any, insight into certain key features of Living Behavior. The Interacting Realms Paradigm is a crucial component of my Theory of Attention.

For a more in-depth discussion of these topics, read the article: Attention & Matter: Interacting Realms of Existence?

Interruption phenomenon

The behaviorial phenomenon: Interruptions have negative impact upon a productive session that is disproportionate to their duration.

Scientific studies have demonstrated that interruptions to a productive session have a negative effect upon cognitive performance. This adverse impact is disproportionate to the size of the interruption. We also have cultural evidence of this phenomenon. Theater owners frequently lock the doors at the beginning of a performance to prevent interruptions to the audience's undivided attention. Coaches call time outs to interrupt a player's or team's momentum in the hopes of impairing the performance. This disproportionate negative impact of interruptions on performance is the individual empirical meaning of the Interruption Phenomenon.

Information Dynamics provides a mathematical model that behaves in similar fashion. Interrupting the Living Algorithm’s Pulse has a disproportionate negative impact upon the ideal dimensions of the mathematical pulse. This distinct pattern of correspondence between the Living Algorithm's mathematical behavior and the empirical evidence regarding interruptions to a productive session constitutes the general meaning of the Interruption phenomenon.

As such, the Interruption phenomenon symbolizes two levels simultaneously: the individual empirical event and the general linkage between the mathematical and the empirical. For a more detailed analysis of this phenomenon, check out The Pulse of Attention Interrupted.

The Information Digestion Model was developed to make sense of the correspondences between the mathematics of the Living Algorithm and many features of empirical reality, including the sleep necessity phenomenon. To understand why the Math/Data synergy 'forced' us to make certain assumptions, read Core Postulates.


The Living Algorithm process reveals the ongoing rates of change/derivatives of any data stream. Liminals is the name of the higher derivatives as a group. Below is a visualization of the Liminals of the Triple Pulse data stream.

Triple Pulse (green) & the Liminals

The green curve is the data stream's 2nd derivative, the Directional. The other curves are visualizations of the data stream's 3rd, 4th, 5th, 6th and 7th derivatives, the Liminals.

Why the name? Definition of the word 'liminal': "Relating to or at the threshold, entrance or beginning." In contrast, subliminal means beneath or under the threshold, while superliminal means above this entrance.

According to Information Dynamics theory, the zero line in the graphs divides conscious awareness from the subconscious (the former above the line, the latter below). The positive Active Pulse, which is generated by conscious Attention, is above the line (superliminal). The Rest Pulse, generated when there is a lack of Attention (sleep), is below the line (subliminal). As the rest of the curves in the Creative Pulse family wander around this threshold between consciousness and the subliminal, we've named them Liminals. According to Info Dynamics theory, they are related to digesting information. If they are not allowed to zero out (fully digest the information), the undigested information can interfere with the potentials of the following cycles.

For a more complete analysis, check out the article Liminals & Unconscious Cognition.

Living Algorithm (a.k.a. the Cell Equation)

Basic Living Algorithm

General Living Algorithm

The Living Algorithm's digestive process reveals the rates of change (the derivatives) of any the data stream. The basic Living Algorithm computes the Decaying Average (the data stream's 1st derivative). The general Living Algorithm (shown below right) generates a system of dynamics that is the foundation of Information Dynamics.

The algorithm for computing the Living Algorithm is a simple procedure.

The mathematics of the Living Algorithm has many features in common with living systems. 1) Past Awareness. Both Life and the Living Algorithm are self-referential feedback systems. Living systems have an awareness (whether conscious or not) of the past experience of the organism and the capacity for behavior that reflects that awareness. 2) Context Awareness. They are both sensitive to the present situation – a context sensitivity that incorporates the power to monitor and adjust. 3) Regenerative. They both require ongoing data input to sustain the momentum of a pattern, as the potential impact of the data on the ongoing average decays over time. 4) Composite Memory. They both store memory as a synthesis of overlaying images, rather than exact replicas of events. 5) Fungible. They both must transform the precise details of data into averages in order to reveal patterns. 6) Recency Effect. While the potential impact of each data point decays over time, the most recent data points in the stream have the greatest potential impact on the Living Algorithm’s ongoing derivatives. Similarly, the most recent events have the greatest potential impact on an organism’s current perceptions. Because both systems share these 6 characteristics, we argue that the Living Algorithm is a powerful model of living systems.

The Living Algorithm produces the derivatives of any data stream. These derivatives act as powerful descriptive predictors. As an indication of the ability, the 3 basic derivatives are called the Predictive Cloud.

Finally the Living Algorithm is the ultimate in elegant and computational simplicity. Nothing more than basic arithmetic skills are required. Due to these three features (similarity with living systems, powerful predictors, and simplicity) we argue that the Living Algorithm could be one of Life's primary algorithms – a computational recipe for digesting data. In fact, this is a fundamental assumption of Information Dynamics. (Check out the article Living Algorithm for more details.)

Living Realm

A composite Realm of Existence that encompasses Living Behavior, especially with regards Attention. According to the Interacting Realms Paradigm, the Living Realm consists of the interaction between the Material Realm and the Realm of Attention.

Material Realm x Attention Realm = Living Realm

In contrast, the Material Paradigm maintains that the Living Realm is merely a subset of the Material Realm. Unfortunately this paradigm provides little explanatory power for a vast amount of living behavior.

For a more in-depth discussion of these topics, read the article: Attention & Matter: Interacting Realms of Existence?

Material Paradigm

The Material Paradigm holds that all phenomena have a material explanation, including living phenomena. This is a prevalent paradigm, especially amongst the college-educated. Scientism is a faith-based belief system that derives from this paradigm. Thus far the Material Paradigm has provided little, if any, explanatory power regarding certain key features of Living Behavior.

For instance according to this paradigm, the apparent organizational and intentional feature of the life force should have a material explanation. However, this purely speculative position provides no explanatory power. The inability of the Material Paradigm to deal with these phenomena and many like them suggests the need for a new paradigm. By expanding the discussion to include Life’s non-material component, i.e. the Attention Complex, the Interacting Realms Paradigm from Lehman's Theory of Attention fills this gap.

Material Realm

A composite Realm of Existence that encompasses exclusively Material Behavior. According to the Interacting Realms Paradigm, the Material Realm consists of the interaction between the Atomic and Subatomic Realms. The Living Realm consists of the interaction between the Material Realm and the Realm of Attention.

Atomic Realm x Subatomic Realm = Material Realm

Material Realm x Attention Realm = Living Realm

In contrast, the Material Paradigm maintains that the Living Realm is merely a subset of the Material Realm. Unfortunately this paradigm provides little explanatory power for a vast amount of living behavior.

For a more in-depth discussion of these topics, read the article: Attention & Matter: Interacting Realms of Existence?

Math/Data Matrix

Definition of Matrix: Contains and gives shape

Encyclopedia Britannica defines the term ‘matrix’ as: “That which contains and gives shape or form to anything.” For instance, a womb is the matrix for life.

Mathematical Matrix: facilitates understanding of relationships

A mathematical matrix is defined as 'a rectangular array of symbols or terms enclosed between parenthesis or vertical double bars to facilitate the study of relationships'. A mathematical matrix is an operation that indicates the interaction (mixture/combination) between two or more components. On the simplest level, a vertical array of numbers interacts with a horizontal array of numbers to produce a mathematical result.

Math/Data Matrix provides form and understanding of relationships

A Math/Data Matrix has both of these features. This type of matrix is based upon distinct patterns of correspondence between a mathematical system and a system of empirical data (observable, experiential and/or quantifiable) relating to a particular phenomenon. For instance, there are multiple patterns of correspondence between Data Stream Dynamics (DSD) and the empirical data associated with Attention. The closer the fit between phenomenon and the mathematical system, the better the matrix, and vice versa.

Mathematical Matrix reveals structure & form

The mathematical matrix provides a deeper understanding of the phenomenon’s underlying structure. For instance, DSD suggests that Attention is an iterative, rather than continuous, process. The mathematical matrix also ‘contains and gives shape or form’ to the phenomenon. For instance, the Pulse is Attention’s most significant mathematical form. As evidence, a wide range of living behavior associated with Attention is subject to the Pulse’s mathematical process, e.g. attention span.

Famous Math/Data Matrix: Regular Equations x Empirical Data re Matter

The most famous Math/Data Matrix is between the Regular Equations that are obedient to set theory and the precise empirical data regarding Matter. Indeed this matrix has been so successful that many believed, almost unquestionably, that it ultimately applies to all phenomena, including living behavior. In other words, it is the only Math/Data Matrix.

Alternately, a primary intent of these many articles and books is to dissuade you the Reader of this misguided and unproductive belief. Rather than a single matrix, each Realm of Existence has its own Math/Data Matrix and they are mutually exclusive. For instance, Newtonian Mechanics will never be able to describe the data from the Realm of Attention.

Atomic Realm: Newtonian Mechanics x Atomic Data

Subatomic Realm: Quantum Mechanics x Subatomic Data

Attention Realm: Data Stream Dynamics x Attention Data

mathematics of behavior

This term encompasses the entirety of the author's study of living behavior. The underlying theme of this line of research is that mathematical mechanisms are a significant factor determining human behavior. Further it is possible to consciously tune into these naturally occuring rhythms to maximize life's potentials. Conversely ignoring these rhythms has a negative impact, minimizing what is possible.

The study of the Mathematics of Behavior consists of, at least, 4 branches or projects: Data Stream Momentum, Root Beings, Energy Bundles, & the Creative Pulse. Information Dynamics only applies to the Data Stream Momentum and Creative Pulse Projects.

Mathematics of the Moment

Mathematics of the Moment is another name for the series of volumes written by the Author regarding the connections between Information Dynamics and human behavior. Triple Pulse Studies, the 1st volume, lays the foundation for the study by illustrating some striking correspondences between sleep-related behavior and the Living Algorithm's Triple Pulse. The Living Algorithm System, the 2nd volume, establishes the plausibility that Life employs the Living Algorithm to digest information. Data Stream Dynamics, the 3rd volume, develops the notion that Information Dynamics shares a common dynamical structure with classical mechanics. Further, this dynamical structure provides the causal mechanism behind the aforementioned correspondences. Even more intriguing, the Author develops the notion that the energy density of a data stream determines how mental energy is converted into physical energy. Attention & the Living Algorithm, the 4th volume, illustrates the mechanism that ultimately transforms the mental energy of Attention into the information energy of a data stream, which in turn translates into physical energy when the conditions are right. In essence, this volume establishes how Mind influences Body. Check out Information Dynamics: Volume List for links to the articles.

Dr. John Medina, author of brain rules

Dr. John Medina is a developmental molecular biologist. He holds joint affiliate faculty appointments at Seattle Pacific University, where he is the director of the Brain Center for Applied Learning Research, and at the University of Washington School of Medicine, in its Department of Bioengineering. He has won numerous prestigious awards for his teaching skills. Employing a cross-disciplinary perspective to critique the works of his colleagues is one of Dr. Medina’s specialties. His interdisciplinary approach places him in an ideal position to summarize the research coming from a number of sub-disciplines within the broad field of cognitive science.

In his book, brain rules, Dr. Medina summarizes mainstream scientific discoveries in the emerging field of cognitive science. He catalogues the findings from diverse disciplines – ranging from neural science to biology to psychology among others. Dr. Medina also makes useful behavioral suggestions regarding these important scientific discoveries. The evidence for this brain research is well established. Dr. Medina states: "The supporting research for each of my points must first be published in a peer-reviewed journal and then successfully replicated. Many of the studies have been replicated dozens of times." (brain rules, p. 5) The prestige of the author makes his book, brain rules, an ideal source to transmit the current state of cognitive science to the educated public. Further, it is evident that the findings and theories contained therein are widely accepted by the contemporary scientific community.


The Living Algorithm's digestion process computes the rates of change/derivatives of any data stream. The data stream consists of a string of discrete data points. We choose to characterize each individual data point as an instant. Because of their relative isolation and independence from other data points, we consider instants to be one-dimensional.

The Living Algorithm’s process determines the ongoing relationship between these instants. By revealing the rates of change/derivatives, the Living Algorithm creates a context that relates the current instant (data point) to the immediately preceding instants (data points). With each iteration, i.e. repetition of the relating process, the Living Algorithm determines what we define as a moment. The data stream derivatives identify the dynamic context of each moment.

While there is a moment for each instant and moments are based upon instants (data points), they do not include the instant. Instead, moments indicate the ongoing dynamic relationship between instants. Because they indicate the dynamic relationships between instants over time, we consider moments to be 2-dimensional.

Due to their independence and isolation, instants are inherently devoid of meaningful pattern. Due to the context provided by the Living Algorithm, moments are inherently filled with mathematical ‘meaning’. In essence, the Living Algorithm transforms ‘meaningless’ instants into ‘meaningful’ moments.


"A description or systematic exposition of one thing or class of things; a dissertation or treatise written in great detail." (EB Dictionary p. 823)