For over four decades, I have grappled with the general question of how mathematics relates to human behavior. These explorations resulted in the formulation of a mathematical system I call Information Physics. Info Physics provides the foundation for my Theory of Attention. This network of hypotheses regarding Attention’s interaction with Information addresses a realm of existence that is virtually untouched by traditional Physics – the Realm of Attention.
Intention, mental energy, choice, meaningful information and feelings - features from our everyday, common sense world of thought and decision-making – are the components of this realm that is exclusive to living systems. Rather than a deterministic world of stimulus-response, the Attention Realm is an interactive, even a proactive world, one that requires constant monitoring and adjusting. Indeed, one purpose of this work is to illustrate how we can take advantage of this realm’s mathematical laws to more effectively align with the rhythms of Attention and thereby enhance the quality of our existence.
You might wonder what events led me to undertake this unusual endeavor.
In 1978 when I was in my late 20s, I derived an algorithm, the Living Algorithm (LA), to provide me with easily computable central measures of ongoing data streams. Eventually I came to realize that the LA also generates an entire mathematical system, deemed Data Stream Dynamics (DSD). As years turned into decades, I began to notice distinct patterns of correspondence between DSD and a broad range of behavioral and biological evidence regarding Attention. The process of attempting to understand the underlying reasons behind these correspondences gave birth to the Physics of Information, which provides the mathematical language for my Theory of Attention.
The following diagram exhibits these relationships. Subsequently, we shall examine the diagram’s interlocking components in more detail.
Information Physics provides a mathematical language for Attention’s interaction with Information. Why apply the term ‘physics’ to this interaction? What is the justification for the unusual combination of words?
Combining these words almost seems like a contradiction in terms – an oxymoron of sorts. Physics is the ultimate material science, while Information and Attention seem to be immaterial. Physics provides the mathematical language for the physical world, which includes the physiology of living systems.
Despite the differences in subject matter, both types of physics employ a similar language. Key constructs enable us to understand the dynamics of the physical universe. The definitions and relationships entailed in these concepts can also enable us to understand the dynamics of information.
‘Velocity’, ‘momentum’, ‘force’, ‘work’ and ‘power’ represent the central relationships between the key elements of traditional Physics, i.e. ‘time’, ‘mass’, and ‘distance’. Yet, with a different inflection, these same terms provide a framework for understanding the relationships between living systems and data streams. We chose to borrow these relational notions from traditional Physics to help shape our understanding of the key elements of Attention’s interaction with Information.
The architecture of dynamics that applies to both types of physics, Material and Information, is shown in the following diagram. Gorgeous, isn’t it?1 These dynamical constructs and their relationships are crucial for understanding both the flow of matter and the flow of information.
There is yet another justification for the use of the term ‘physics’. Information Physics indicates a process by which the Living Realm of Attention can interact with the Material Realm of Biology. Sustaining Attention for a sufficient duration upon the information contained in a particular data stream results in what we choose to call an Experience. This Experience is an interpretation of data that presumably enables living systems to enhance the probability of making better ‘choices’.
The living system ‘experiences’ the data stream’s content (its information) when the data stream’s energy density approaches 100%. It is at this point that the Experience’s information is transferred from the Attention Realm to the Material Realm.
It seems that these Experiences might reorganize networks of living matter, but without leaving any other material traces. While the actual atoms and molecules that are reorganized remain the same, information could be embodied as an image, i.e. a neural layer or a memory, in the physical world of biology. Although the material content remains constant, living systems employ this reorganization to impart and evaluate meaning in order to make better decisions in the physical world.
Sex provides an excellent example of this process of information transfer. Sustaining Attention upon the physical act of procreation for sufficient duration triggers a biological process that transfers genetic information from the male to the female.
What is the significance of this new physics? Information Physics provides a mathematical language for the Attention Realm – a realm of existence that seems to be inaccessible to the mathematics of 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 equations that obey traditional set theory provides the mathematics for Material Physics. This type of mathematical language arrives at definitive conclusions regarding material behavior.
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. An open, recursive equation that does not obey traditional set theory provides the mathematics for Information Physics. This type of mathematical language arrives at probabilistic conclusions regarding Attention-related living behavior. Each type of physics generates an entirely different set of principles.
Following are some diagrams that illustrate these key distinguishing features:
Two Types of Content & Energy
Two Types of Space & Time
Two Types of Mathematics
Two Types of Conclusions
Because of these differences regarding focus and mathematics, each type of physics seems to apply to a unique realm of existence. Indeed, Material Physics describes the mechanistic reactions of physical elements that essentially belong to closed sets, e.g. atoms, particles, and objects. Information Physics describes open, contextual processes that generate meaningful interpretations of experience – in other words, making meaning from ongoing, external data streams. Material systems react to environmental stimuli in a mathematically predictable fashion, while living systems employ a probabilistic mathematical language to facilitate their ability to monitor and adjust to new information.
Information Physics has a practical, as well as theoretical, significance. Through an understanding of the rules that govern Attention, we can learn how to intensify the focus of our awareness. We can begin to maximize the conditions that promote heightened awareness and avoid the conditions that minimize the intensity our Attention.
On the immediate level, a heightened capacity for awareness can increase our ability to enjoy the moment, e.g. appreciate a fine dining experience. It also has the potential to maximize our ability to think critically, which can lead to better decisions. In such a way, we can take advantage of the principles of Information Physics to enhance the quality of our existence.
Following is a diagram that exhibits some reasons for applying the term ‘physics’ to the Attention’s interaction with Information.
What is the justification for a new type of physics? Why not just one physics? Isn’t Information Physics just another branch of Material Physics?
We have all employed maps to navigate a specific territory, e.g. a town. There is a direct correlation between a map’s ability to describe a territory and its power – the better the description the better the model. There are many metaphorical maps for many different territories, e.g. music theory for symphonies and psychology for human behavior. There is not a single map that fits all territories. For instance, subatomic theory applies to bio-chemical interactions but has very little to say, if anything, about how to maximize the quality of our existence.
A large map can encompass many territories. For instance, the globe provides a map of all the continents on our planet. While providing a grander perspective, necessary details are sometimes lost, e.g. individual streets and homes. However, the large picture frequently reveals patterns in the forest that are hidden by the individual trees.
Our map/territory metaphor suggests a flat 2D world. However, maps/models can be multi-dimensional in the world of abstract ideas. Indeed, the language of mathematics specializes in multi-dimensional models. As the prime example, the mathematical system of Physics provides the underlying logical structure of material behavior. In so doing, it provides an all-encompassing multi-dimensional map for Matter.
Indeed this mapping has been so successful that many felt and some still feel that this type of mathematical structure will eventually be able to map living behavior. Yet Material Physics has been impotent before attention-related human behavior. This is due to inherent defects in calculus, the underlying mathematical system of traditional Physics. These deficiencies prevent calculus from describing reflexive systems, such as Life. This is where the reflexive mathematics of Info Physics enters the picture.
To better understand the overall context of Information Physics, let us examine a tree chart to see where it fits in. The same dynamic architecture provides the common root for the branches of Physics. However, Material Physics, i.e. Atomic and Subatomic, and Information Physics belong to entirely different branches.
The first branching occurs due to qualitative differences in mathematical systems. One branch is based in Calculus, while the other is based in the Living Algorithm (LA). Atomic and Subatomic (Quantum) Physics are the two branches of Calculus, while Information Physics is the sole branch of the LA. These categories are shown in the preceding chart.
What is the justification for the initial mathematical branching? Calculus and the LA both belong to the common set of equations. While belonging to the same set, the equations of these two mathematical systems have some fundamental differences. The equations of Calculus are both closed to external input and regular. Regular equations, i.e. traditional, don’t refer to themselves, i.e. they are not reflexive. In contrast, the LA is both open to external input and reflexive, i.e. self-referential.
What is the justification for the second branching? Each branch of Physics applies to a different realm of existence. These mutually exclusive realms have both differing fields of action and contradictory components. When viewed side by side, the components are even paradoxical.
As examples, Atomic Physics applies to particles that reside outside of an atom, where both space and time are continuous. Subatomic Physics applies to the entities inside an atom, where both space and time are quantized. Information Physics applies to Life’s Awareness, where space and time are elastic. Although mutually exclusive, they are all mathematical realms of existence that share a common dynamic architecture. As such they belong to common set.
Life’s immaterial component, i.e. Attention, exists neither inside nor outside of an Atom, but somewhere else, wherever that is. Some say that it is located inside our brain. I instead suggest that our decision-making complex resides in the bio-electric field that is generated by the connective tissue network that permeates our body.
Even though they are mutually exclusive, the three realms interact. The interaction of Atomic and Subatomic (Quantum) Physics determines the behavior of the exclusively Material Realm, i.e. Mechanics, Electricity, Chemistry and Biology, but tell us nothing about Attention. In contrast, Information Physics, while addressing Attention, reveals nothing about the exclusively Material Realm. However, Information Physics does interact with Material Physics to reveal the secrets of Biology. As evidence, it seems that the biological networks associated with Attention evolved to take advantage of the innate features of Data Stream Dynamics, the mathematical substrate of Information Physics.
As we will see in the coming articles, Information Physics is only able to make rough, probabilistic predictions regarding Attention-related behavior. In contrast, Material Physics is able to make precise, definitive predictions regarding Material behavior. Is this a fatal flaw? Or is this imprecision an innate feature of Attention? Is this the best we can expect with living systems?
What are the criteria for determining which explanation is best, i.e. which model has the most explanatory power?
The first criterion is efficacy. The question that is asked: Which map (explanation) fits the territory the best? Or, which model does the best job of describing a particular subset of empirical reality? The map that does the best job of mapping the territory is considered the best map and vice versa. There is a direct correlation between mapping ability and the efficacy of the map.
Mapping Ability Up: Map Efficacy Up
This work attempts to persuade you that my model (Information Physics) does a better job of mapping the Attention-related phenomena that are exclusive to living systems than does the materialist model (Material Physics). Information Physics provides a better map for Attention than does its cousin.
Information Physics (Attention) > Material Physics (Attention)
Material Physics provides a virtually perfect map (≈) for Material Behavior (-> 100%). It is tempting to hold all metaphorical maps up to the ultimate precision of the material mappings. However, this direction is not fruitful, as it does not really the address the question of which system provides the best mapping of non-material phenomena, such as Living Attention.
Material Physics (Matter) => 100%
For instance, Information Physics only provides a rough map of Attention-related behavior (≈40%). Material Physics provides a far better map for Material Behavior than does Information Physics for Attention. However, Material Physics has been an abysmal flop with Attention-related Behavior (≈0%). Traditional Physics has been unable to provide any map of Attention.
Information Physics (Attention) => 40%
Material Physics (Matter) > Information Physics (Attention)
Material Physics (Attention) => 0%
Even though it only provides a rough map of the territory, the Information Physics map regarding Attention is far better than nothing – the no map of Material Physics.
Information Physics (Attention) > Material Physics (Attention)
Occam’s razor provides the second criterion. On the assumption that both maps fit the territory equally well, the academic community generally believes that the simplest explanation is also the best explanation. Which model is simplest? Of course, the answer to this question is predicated upon a precise definition of simplicity. Assuming this to be true:
Simplicity Up: Map Quality Up.
Another intent of this work is to persuade you that my map (Information Physics) provides a simpler way of explaining Attention-related phenomenon related with living systems than does the materialist map (the Physics of Matter).
Material Physics (Attention) < Simplicity < Info Physics (Attention)
The Simplicity criterion is entirely secondary to the Efficacy criterion. As such, the initial intent of this book is to illustrate that Information Physics provides a rough map of Attention-related phenomenon. Put another way, we are going to attempt to persuade you that there is an isomorphic relation between Scientific Facts regarding Attention and the Information Physics. In other words, the underlying logical structure of both systems is very similar.
If I can succeed in persuading you the Reader that an isomorphism exists between Information Physics and Attention, then Information Physics wins in terms of having the most explanatory power, as Material Physics has no explanatory power when it comes to Attention.
1 For a more complete treatment of this topic, see the Author’s treatise entitled Data Stream Dynamics.