For over four decades, I have been exploring the general question of how mathematics relates to human behavior. These explorations resulted in the formulation of a system I call *Information Physics*. This system provides a mathematical foundation for a network of hypotheses regarding the interaction between Information and Attention – a *Theory of Attention*. (In general Blue = an article; Green = a glossary entry - the following table an exception.)

This page contains a table of ongoing articles written in support of these hypotheses – starting with the most recent. Each entry contains a link to the article, the date it was posted, a brief synopsis of the contents as it relates to my theories (Syn) and number of pages.

Since 1994, I have organized my life's work in Notebooks. Each Noteook consists of a variable number of Articles. Each Article in the following table is referenced by a Notebook number along with its order (Ntbk 40: Article 2).

Attention's Holistic Logic ≠ Matter's Atomistic Logic (4-9-2020, Attention Theory)

In the prior article, we saw that the mathematical logic of DSD is isomorphic with the logic of Attention related phenomena. This relationship indicates that we can employ DSD to better understand Attention.

DS Dynamics Logic ≈ Attention Logic

Perhaps just as important, Material Logic and Attention Logic are inherently incompatible. Why? Matter belongs to an atomistic system, while Attention belongs to a holistic system. Matter’s atomistic systems has a top-down organization, where content is of utmost importance. In contrast, Attention’s holistic system has a bottom-up organization, where contextual relationships are of utmost importance. Pictures reveal the set-based logic of sight – another feature of atomistic logic. Music reveals the process-based logic of sound – another feature of holistic logic. Because of these fundamental differences in their system logic, it is impossible for Material Mathematics to model Attention.

Material Logic ≠ Attention Logic

*Metaphoric Logic: Attention ≈ Data Stream Dynamics* (4-2-2020, Attention Theory)

Metaphoric Logic, along with Redundancy Logic and Explanatory Power, are part of the validation network for the Attention Matrix. Metaphoric Logic is the process of employing the logic of a known system to understand the logic of an unknown system. This type of logic provides the foundation of verbal abstractions; exerts a significant influence upon human behavior; and is a powerful technique of science. The web of logical symmetries between Data Stream Dynamics (DSD) and Attention-related phenomena provides strong validation for the Math-Fact Matrix that defines the Realm of Attention. The isometric relationship also indicates that we can employ the mathematical logic of DSD to better understand the logic of Attention.

*The Importance of Exercising Intention’s Mental Muscles* (2-17-2020, Attention Theory)

According to our model, humans can shape their behavior via Intention. Intention has two components – non-action and directed action. We liken Intention’s tools to mental muscles due to multiple logical symmetries with physical muscles. For instance, both types of muscles grow stronger with exercise and atrophy if they are not employed regularly. When strong, our mental muscles can restrict outdated behavioral patterns and create more appropriate ones. Just like physical exercise, this intentional shaping process requires regular repetitions as behavior patterns manifest physically as neural meta-structures (Nemes). Perhaps of equal importance, regular exercise of our mental muscles increases our propensity for intentional behavior. Rather than being victims of our behavioral momentum, we can take better control of our thoughts and actions. With strong mental muscles, we have a better chance of fulfilling our innate nature, i.e. our inner potentials.

* Maximizing Attention’s Iteration Rate* (1-26-2020, Attention Theory)

Attention's Iteration Rate, the rate at which we digest bytes of information, determines the nature of Time in the *Imaginary Realm*. This rate, hence our experience of time, is variable, elastic and subjective. It also plays a part in our opportunities for choice and the level of our awareness. As such, Attention's iteration rate also affects the quality of our performance. While direct control is unlikely, we can exert indirect control over this process by regulating our emotions. Strong emotions, e.g. tension, seem to slow our natural iteration rate. Deliberately calming these emotions via body alignment, breath control, and mental quietude allows this rate to attain a maximum, which also enhances our performance.

* Capacity for Attention* (9-28-2019, BD:Triple Pulse 12)

We apply Data Stream Dynamics and mental energy to the notion of our Capacity for Attention, as derived from a Math/Fact Matrix.

* Information Physics: an Introduction* (9-25-2019, Attention Theory)

Information Physics provides a mathematical foundation for a network of hypotheses regarding the interaction between Information and Attention. In so doing, it provides a mathematical language for a realm of existence that is generally ignored by traditional physics. This ‘new’ physics addresses a parallel universe whose ‘content’ and ‘rules’ are entirely different from that of the ‘old’ physics.

Material Physics specializes in the interaction between matter and energy. It describes the dynamics of objects moving through objective space and time. Calculus with its closed and regular (set-based) equations provides the mathematics for Material Physics.

In contrast, Information Physics specializes in the interaction between information and mental energy. It defines the dynamics of information in data streams moving through the subjective space and time of living awareness. Further, an open, recursive equation, the Living Algorithm (LA), provides the mathematics for Information Physics. Through an understanding of the rules that govern Attention, we humans can increase our capacity for Attention, thereby the quality of our existence.

Despite these differences in focus and content, Material and Information Physics employ a similar architecture of dynamics to characterize the flow of respectively matter and information. Information Physics also indicates a process by which the Immaterial Realm could interact with the Material Realm.

The following six articles are part of series deemed Scientific Manifesto. The series is designed to establish a historical context for my Theory of Attention.

** Lucretius: Atomism vs. Holism **(5-31-2019, Scientific Manifesto)

The Roman Lucretius wrote *On the Nature of Things*. The discovery and publication of this poem during the Renaissance reintroduced the philosophy of atomism to Western civilization. Atomism is the theory that the universe consists of tiny particles that obey absolute laws of nature. The material world behaves mechanistically.

In atomistic systems, the immutable nature of the parts determines the nature of the whole. Scientists applied this reductionist way of thinking to the material world to generate our technological wonderland. Their fabulous successes led them to the misconception that our Universe is entirely atomistic.

Rather than atomistic, an abundance of evidence indicates that living systems are holistic. Contextual relationships are more important than absolute content for holistic systems. This fundamental difference between living and material systems translates into differing mathematical systems. While Matter’s equations are closed, set-based, and definitive, Life requires equations that are open, reflexive, and probabilistic. The *Living Algorithm* both fulfills these requirements and reveals the rhythms of *Attention*.

** Ptolemy: Logical Universe vs. Paradoxical Polyverse **(5-19-2019, Scientific Manifesto)

An earlier article (*Attention, Atomic & Subatomic: Interacting Realms of Existence?*) developed the proposition that there are at least 3 mathematical realms of existence, i.e. Atomic, Subatomic and Attention. This paper provides further validation for this perspective.

Ptolemy's astronomical system (proposed in the 2nd century CE) implied that we live in a logical Universe. This insight inspired scientists to find the immutable laws that govern the material world and then to employ these laws to create our technological wonderland. These nearly miraculous successes suggest that our world is logical.

However, the logician Gödel proved that logically consistent systems are incomplete. Of necessity, complete systems contain paradox. Extending this line of reasoning: we require other logically consistent systems, in addition to our logical, yet incomplete, material Universe, to provide a more complete understanding of existence.

Fulfilling this role, *Information Physics* is a logically consistent system that describes living behavior regarding Attention's interaction with Information. Although based in mutually exclusive (paradoxical) conceptions of space and time, these two Universes, material and living, describe different realms of existence. Rather than a single *Material Realm*, it seems that we instead exist in a paradoxical Poly-verse consisting of the interaction between multiple logically consistent realms of existence.

* Ptolemy: Paradigms of Science *(4-16-19, Scientific Manifesto)

The implicit beliefs behind Ptolemy's widely used astronomical system for predicting planetary position inculcated the internal logic of astronomers and scholars – commencing in the first centuries of the Common Era. With accumulating affirmation, they eventually became foundational paradigms of Science. They are as follows:

1) The natural order is accessible to human reason.

2) Mathematics is the language of Nature.

3) Elegant simplicity is a feature of the natural order.

Living Attention is a highly significant feature of the natural order. According to the Ptolemy-inspired scientific paradigms, Attention should be both accessible to human reason and have a mathematical language that is both elegant and simple. While seemingly inaccessible to Material Physics, Information Physics provides Attention with a mathematical language that embodies elegant simplicity.

** Galileo's Relics & Life Force?** (1-27-2019, Scientific Manifesto)

Florence's museum of science proudly displays Galileo's relics, i.e. his finger bones. This practice might seem a bit bizarre to those of us born in the Western Hemisphere. Yet the veneration of relics and relic-like objects, e.g. memorabilia, paintings, and ruins, is a ubiquitous cross-cultural phenomenon that extends to a wide range of human behavior.

The veneration of relics and relic-like objects such as Galileo’s bones implies the existence of a collective life force. The existence of a life force implies the existence of a intention, attention and mental energy. The Material Paradigm, i.e. all phenomena have a material explanation, provides little, if any, explanatory power regarding this gestalt surrounding attention. This impotence before these widespread phenomena indicates the need for a new scientific paradigm – a fresh Math/Data Matrix that expands the dialogue to include Attention and mental energy. My Theory of Attention fulfills these requirements.

* Galileo: Saint of Freemasonry? *(1-12-2019, Scientific Manifesto)

The Freemasons embraced Galileo as a secular saint after he died. The investigation of Mason’s historical function and contribution revealed an unusual pattern. It appears that the educated of Western Civilization exhibit collective, historical Pulses of Attention regarding the nature of the Cosmos, e.g. the relationship between God & Science.

Roughly speaking, prior to the 17th century, the intelligentsia, including Galileo and Kepler, continued to belong to Biblically based religions. With rise in Science, the educated shifted to the religious tolerance of Freemasonry or Deism, which included the belief that God revealed himself through the laws of nature. In subsequent centuries, the intelligentsia dropped the belief in God and embraced human reason as epitomized by Science. In this most recent Pulse, many of the educated have embraced scientific materialism, e.g. all phenomena have a material explanation.

I'm hoping that my work provides a significant impetus to the beginning of a fresh Pulse. Rather an exclusive focus upon material behavior, this fresh Pulse shifts the focus our Attention to the complementary data streams of maximizing pleasure and fulfilling human potential. To that end, Information Physics provides the mathematical mechanisms underlying the interaction between Attention’s mental energy and the Information contained in data streams. Understanding these processes can assist us to enhance our Capacity for Attention, thereby improving the Quality of Life.

* Galileo: A Victim of Academia & Hubris?* (12-11-2018, Scientific Manifesto)

Rather than the Catholic Church, as is commonly taught, Galileo’s primary clash was with Academia. Galileo’s inflammatory style initially offended scholars and eventually forced the Church to take a stand against Copernicanism and convict him of heresy.

Academia’s hostile resistance to Galileo’s paradigm shifts was not due to fear of the Inquisition, but instead an inherent feature of the scholarly class, then and now. Brains filled to overflowing with established dogma have little room for anything new. It is typically the subsequent generations of scholars and scientists, those looking to make a name for themselves, that embrace and develop the new scientific paradigm. In this sense, Galileo’s confrontations with the academic establishment of his day were a drain on his creative energies.

If Academia resists and even censures someone as brilliant as Galileo, then the attempt to convince Academia of the truth of my theories could also be a waste my creative energies. It could be that it is future generations, the unborn, that take up my torch.

** Data Stream Energy & Attention ** (10-15-2018, Attention Theory: Math #3a)

The internal logic of Data Stream Energy seems to provide a good model for the internal logic of Attention’s mental energy. Significance? A better understanding of DS Energy could lead to a better understanding of mental energy, which could assist us to better fulfill our potentials.

Energy has the ability to change the state of a system. Data Energy has the ability to change the state of Living Algorithm’s (LA) mathematical system. Scientists have found it useful to divide energy into 2 parts, kinetic energy that does work and potential energy that is stored for later use. We have found it useful to employ similar constructs in the LA System, i.e. active (kinetic) and residual (potential) energy.

According to our Theory of Attention, active energy corresponds with the mental urge to accumulate information or experience, while residual energy corresponds with the mental urge to assimilate these experiences. The LA mathematics reveals how these complementary urges guide and dominate our lives on a day-to-day level.

Our Sleep/Awake cycle provides us with a good example. As we accumulate information and experiences during the day, the urge to assimilate (residual energy) rises. When the assimilation urge passes a certain threshold, we go to sleep. During this downtime, i.e. no more information accumulation, the residual energy is converted into active energy, thereby fulfilling the urge to assimilate. Upon waking the residual energy, i.e. the urge to assimilate, is depleted and we are ready for another round of info accumulation.

* Open Energy Systems: Body, Car, LA System* (10-1-2018, Attention Theory: Math #3b)

The LA generates an open energy system. Does this energy system have anything in common with material energy systems? It seems that the LA's mathematical system shares a similar energy logic with our body, a biological system, and our car, a mechanical system. Each of these systems (biological, mechanical, and mathematical) has the same relationship with energy. A Transformer converts Raw Materials into Energy that powers the System. This energy is consumed, not conserved. Further external fuel is required to replenish energy else the system ceases operating.

* Data Energy – Kinetic & Potential: Math Proofs* (2016, Attention Theory: Math #4)

The *Living Algorithm * (LA), the mathematical foundation of our *Theory of Attention*, generates a system. This article offers some mathematical derivations regarding the nature of Kinetic and Potential Energy in the LA's system. Each iteration of the LA's process integrates new data into the system. Each new data point can be viewed as a type of energy – deemed Data Energy. When it enters the system, part of the Data Energy is consumed as Kinetic Energy. This energy is employed to change or maintain the state of the system. The remainder of the original Data Energy is stored as Potential Energy. With each iteration of the LA's computational process, a portion of this Potential Energy is consumed as Kinetic Energy. After enough iterations, the original Data Energy is completely consumed, at least for all practical purposes. However, if new Data Energy continues to enter the system, the Potential Energy accumulates. The LA’s computational process is unable to keep up. The system requires downtime to completely utilize the accumulating Potential Energy. Mathematical downtime is when the data stream's content equals zero. According to our Theory of Attention, this mathematical process is related to the necessity of Sleep and our limited Attention span.

* Matter's Regular Equations vs. Life's Reflexive Equations* (8-28-2018, Theory of Attention: Math #6)

Why is the traditional mathematics of Matter unable to characterize living behavior? Material mathematics is based in *regular* equations. This type of equation adheres to traditional set theory. Living behavior is based in interactive, reflexive, feedback loops. Regular equations, by definition, don't contain feedback loops, as this feature voids set theory. Because they don't possess this crucial feature, Matter's regular set-based equations can't effectively model living behavior.

There is a second type of equation that doesn't obey set theory, hence their name – disobedient equations. Disobedient equations are by definition based in reflexive, feedback loops. As a disobedient equation, the Living Algorithm is ideally suited for the task of modeling Life's interactive feedback loops.

* Attention, Atomic & Subatomic: Interacting Realms of Existence? *(8-18-2018, Theory of Attention: Math #5)

According to our theory, Attention belongs to a realm of existence that is distinct from and on a par with the Material Realms, i.e. Atomic and Subatomic. The justification is straightforward. Each realm has its own unique mathematical system that is tied to empirical data. The mathematics reveals the underlying structure of reality in each realm. The 3 realities are mutually exclusive. For instance, space and time are continuous in the Atomic Realm, quantized in the Subatomic Realm, and elastic in the Realm of Attention. Due to these extreme differences, it is more useful to view the Realm of Attention as distinct from the Material Realms, rather than as a function of Matter.

* Data Stream Dynamics vs. Traditional Mathematical Systems* (2016, Attention Theory: Math #2)

Why aren't traditional mathematical systems able to encompass Attention? Are there some inherent limitations that prevent them from being the Mathematics of Living Systems? This article examines the fatal flaws of Physics, Probability, and Computers and illustrates why * Data Stream Dynamics * is ideally suited for this role.

* Living Algorithm: Mathematics of the Moment *(2016, Attention Theory: Math #0)

The LA's sole purpose is to digest data streams, i.e. transform raw data into a form that is useful to living systems. In contrast to the closed, set-based mathematics of Matter, the LA is both open to external data and based in reflexive, feedback loops. By applying the algorithm to its results, i.e. digested data streams, the LA produces information that would be useful to any living system, for instance the ongoing dynamics and probabilities associated with any data stream, both numerical and relative. These ongoing data streams are the foundation of DSD, the mathematical system that is the heart of our Theory of Attention.

* Living Algorithm: Mathematics of Living Systems *(8-6-2018, Attention Theory: Math #1)

Why do we believe that Life employs the LA via Attention to impart dynamic Meaning to data streams? The LA has many talents that living systems would find appealing. It is simple to use, has minimal memory requirements and weights current data more heavily than past data. It produces many central measures that would be extremely useful. They could be utilized as descriptors, predictors, filters, setting thresholds, as well as providing ongoing correlations between data streams.

* Living Algorithm: Attention's Computational Tool? (Posner's Attention Model) *(2016, Attention Theory: Math #3)

Is there any evidence that Life employs the LA via Attention to impart Meaning to data streams, the informational food of living systems? Posner's Attention Model has nearly universal acceptance in the scientific community. This article develops the notion that Posner's Attention Model evolved to take advantage of the LA's many talents. (Evolution x Living Algorithm = Posner's Attention Model) This hypothesis has many intriguing implications.

* Mind, Body & Choice: A Fresh Perspective* (8-5-2018, Attention Theory: General #1)

The prevalent Materialist Perspective holds that all phenomena are a function of Matter, i.e. materially based. In contrast, our common sense tells us that our Mind is engaged in an interactive feedback loop with our Body. It seems that we exert mental energy to change our physical world, for instance moving our arm and hand to reach for, grab and then consume an apple. Our Theory of Attention provides a mathematical foundation for this Common Sense Perspective. According to the theory, Life employs the LA via Attention to impart dynamic meaning to data streams, the informational food of living systems.

* The Pulse & Sustained Attention Experiences* (8-4-2018, Attention Theory: General #2)

The Pulse, a mathematical form of Data Stream Dynamics, provides a plausible model for Attention as energy. The mathematical behavior of the Pulse seems to mimic a Creative Session, i.e. distinct duration, rising to a peak, and the harm of interruptions. The same map seems to apply to a wide range of human experiences, i.e. Sustained Attention Experiences (SAEs). The widely studied and experimentally validated Flow Experience is an example of a SAE.

*Introduction: Theory of Attention *(7-24-2018, Attention Theory: General #0)

My Attention Theory includes the following propositions: Attention employs a single algorithm to impart dynamic meaning to data streams. The *Living Algorithm* (LA) is the name we have given to this computational tool that transforms Raw Data into useful Information. The LA generates a mathematical system that we call *Data Stream Dynamics* (DSD). DSD is the mathematical foundation of our Theory of Attention. Just as both tides and living systems align with the gravitational rhythms of the Sun and Moon, Attention consistently aligns with the mathematical rhythms of DSD.

* Information Theory & Redundancy Logic* (7-4-2018, Attention Theory: General #3)

Develops two ideas: 1) Information Theory and our Theory of Attention are complementary. Information Theory specializes in the exact transmission of data between machines. To achieve that end, Information is deliberately stripped of meaning. In contrast, the Theory of Attention specializes in how living systems impart dynamic meaning to raw data streams.

2) Redundancy logic, first introduced in the mathematics of Information Theory by Claude Shannon, is the dominant form of logic employed by living systems. Multiple senses provide a prevalent form of redundancy for many life forms. Academia employs at least five forms of redundancy to validate theories. Multiple forms of redundancy logic provide support for our Theory of Attention. Reason combined with evidence from many disciplines, e.g. evolution, biology, and human behavior provide multiple types of cross validation for the theory.

* Data Stream Dynamics: Calculus of Dynamic Meaning* (2016, Attention Theory: Math 07)

The internal logic of both Calculus and DSD is based upon derivatives, i.e. rates of change. Calculus is the prime mathematical tool of the Material Sciences. Its differential equations are employed to predict the behavior of Matter with great precision. However, the sizes of the changes in Calculus are infinitesimally small in that they have no dimension. Because there is no space between the successive points, there is no possibility of Choice. In contrast, DSD seems designed to accommodate the monitor-adjust process of living systems that is inherent to Choice. Further, the LA’s overlay process is ideally suited to generate dynamic meaning from raw data streams. If Calculus is the Mathematics of Matter, then Data Stream Dynamics could be considered the Calculus of Dynamic Meaning.