Section Headings
According to our model, Attention belongs to a realm of existence that is on a par with the Material Realms, i.e. Molecular and Subatomic. The justification is straightforwayd. 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 Molecular 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 a function of Matter.
What is the justification for our conclusions? Each Realm of Existence has a unique mathematical system. Although bound by the common architecture of Newtonian dynamics, each system has its own focus, laws and forms. These mathematical metaphors reveal the underlying structure of each realm’s reality. Each of these realities is mutually exclusive. Building blocks’ emergence doesn’t account for these extreme differences. The interacting realms metaphor provides a far better map of the territory.
3 Different Mathematical Systems > 3 Realities > 3 Interacting Realms
We suggest that the interaction of the Subatomic and Molecular Realms generates the Material Realm and that the interation between the Material and Attention Realms generates the Living Realm.
Are Atoms the building blocks of Life, as is so often taught in our educational system? Or do they have a different type of relationship? If so, what metaphor provides a better map of the territory?
The previous chapter explored the relationship between the two Material Realms – Subatomic and Molecules. A different, even contradictory set of laws govern the two realms. Unable to accommodate differences of this nature, building block logic breaks down. Easily able to account for differing laws, the realm metaphor seems to provide a far better map.
We examined four features of realm logic, e.g. differing logic between realms. The internal logic of realms has other important features. A realm can be a metarealm, belong to a metarealm, and can also have a subrealm. For instance, France and Germany are subrealms of the metarealm of Europe; California is a subrealm of the United States metarealm; the Earth is the metarealm of the continents. In our schema, the Molecular and Subatomic Realms are Realms in the MetaRealm of Existence.
In order to belong to a common metarealm, subrealms must share certain features in common. As an example, let us consider the (meta) Realm of Empires. The Roman, Persian and Islamic political realms of the past were considered empires because they encompassed a huge territory and included a variety of cultures under one political system. In more current times, the British Empire fit into the same category. If it doesn’t encompass a vast territory and include a variety of cultures, a mere country like Cuba does not belong to the Realm of Empires.
Additional Realm Logic that applies to Realms of Existence
5) There can be realms, metarealms and subrealms.
6) Common subrealms share certain features in common.
A common misunderstanding is that Life is a SubRealm of the Material Realms – special, but just a state within a country, not a country herself. We beg to differ. We believe that Life’s Attention belongs to a separate Realm of Existence that is distinct from the Material Realms. How do we determine if Attention is a mere SubRealm or a fullfledged Realm that is on a par with the others?
What are the requirements for joining their elite club? What are the essential features of our material realms of existence – Subatomic and Molecular? What features do our two realms share in common? Put another way, what does it take to even be considered a realm of existence?
Just as there are many political realms, there are many features of reality that could be realms of existence, for instance the artistic and musical realms. However, the Realms of Matter have some unique features that make them special to the scientific community. Both the Subatomic and Molecular Realms are defined by a mathematical system, albeit different, that provides explanatory power for a vast amount of empirical data. Further each type of mathematics possesses an elegant simplicity.
To be considered in the same league as these Material Realms, a realm must also have a powerful and beautiful mathematics that indicates the internal laws of the realm. Neither art nor music possesses this type of mathematics. While they might be realms of existence, they do not belong to the same type as the Material Realms. How about the Realm of Attention?
Philosophically, it is reasonable to assert that there is a twoway interaction between the immaterial Mind and material Body. Experientially, each of us seems to make decisions on a daily level that exert an effect upon our material existence. Further, our language and literature is riddled with references to mental energy, consciousness, mind intent, attention, experience and choice. Decisionmaking seems to be a significant feature of being human.
With all this circumstantial evidence, why do significant members of the scientific community stubbornly resist the notion that humans have the capacity for choice?
A lack of mathematics has stigmatized Life’s decisionmaking process. Scientists have developed elaborate, even fantastical, mathematical systems to characterize the material realms of existence, but have failed to make inroads on the decisionmaking process. This inability led many to question the very existence of choice. Others merely put choice in the same category as music or art – a feature of human existence that is currently beyond scientific understanding.
Simply put, the Living Realm associated with decisionmaking currently lacks a cohesive underlying mathematical structure. To even be included in a common realm of existence with Matter, the Realm of Attention must have a comprehensive mathematical foundation, or at least a semblance or suggestion of one. This requirement is entirely reasonable, as mathematics almost completely defines the Realms of Matter, i.e. both Molecular and Subatomic.
Indeed the miraculous achievements of the material sciences provide tangible evidence that Nature is organized in a mathematical fashion. Further the mathematics that describes and predicts the natural world possesses an elegant simplicity. Indeed, suspicions arise when formulas are exceedingly complicated. Due to this ‘beautiful’ connection with Nature, mathematics has acquired an almost divine prestige.
This incredible Math/Matter synergy leads to serious questions and then doubts about Life’s independence. If mathematics can describe matter so perfectly, why has decisionmaking lagged in this regard? Could it be that choice is an illusion?
Living behavior has certainly resisted the quantification and equations associated with mathematics. Because Life has not had a mathematical structure of her own, scientists have tended to subordinate living phenomena such as decisionmaking to the predictable material realm. Under the circumstances, this subordination of Life to Matter makes a lot of sense.
What would it take to be considered a realm of existence along with the Realms of Matter? The requirements are daunting. Both Realms of Matter are defined by mathematical systems that are descriptive, predictive, provide explanatory power and have an elegant simplicity. For instance, Newton’s force equation identifies a permanent and simple relationship between force, acceleration and matter that always applies under all circumstances. No other aspect of existence has a mathematical system of this caliber. For instance, Psychology employs the mathematics of probability and statistics in both a predictive and descriptive mode, but it provides no explanatory power.
It is almost miraculous that mathematics can provide predictive and explanatory power for any realm of existence. But it does. As such, this is a strict prerequisite for being deemed a realm of existence along with the Realms of Matter. As is evident, joining the rarefied ‘realms of existence’ club in any capacity is quite an achievement.
Unless it has a mathematical system of this stature, the Realm of Attention is not in the same league with the Realms of Matter. Without a mathematical system, the Attention Realm is not even in the game. Further this mathematics must provide predictive and explanatory power for empirical data, as it does for the Material Realms. Plus it must possess an elegant simplicity. In other words, it doesn’t matter how logical or how much supporting evidence there is for the Realm of Attention. It needs a powerful and elegant mathematical system to join the club.
What is the current state of affairs regarding mathematics and living phenomena? While scientists have almost completely described and predicted the Realms of Matter with ‘regular’ setbased Equations, living behavior is another story. Many associational studies have accurately characterized significant features of the Living Realm, for instance Sleep and Attention.
Despite an abundance of associational studies from a diversity of fields, no causality has been established. For instance, multiple experiments have exhibited that we need sleep, but not why. Scientists know that we have an attention span, but don’t know why. They know that infants require attention for positive development, but don’t know why. Researchers have yet to uncover a mathematical structure that reveals causality. Although they know what happens, they don’t know why it happens. While descriptive and even predictive, Material Mathematics provides no explanatory power regarding these topics.
Why is this a problem? Realms of Existence must have a mathematics that provides explanatory power. Scientists have uncovered relatively simple and elegant expressions that are associated with the relationships of atoms, molecules and subatomics in the Material Realm. A welldeveloped system of dynamics accurately characterizes and provides an understanding of the behavior of atomic matter. A complex system of probability accurately characterizes and provides explanatory power for the behavior of subatomics.
Currently the Realm of Attention has no mathematics of its own. It lacks simple equations that determine the features of decisionmaking. As of yet, there is no underlying structure that unifies the diversity of findings regarding this realm that is unique to living systems.
Lacking the comprehensive structure that mathematics provides, the Realm of Attention is fatally flawed in the sense that it remains a mere philosophy – a hope for the future. Mathematics provides validation. To be included as a realm of existence, the Attention Realm requires a coherent mathematical structure. Without an underlying mathematics, Choice remains a mysterious outsider that skeptics can dismiss as an illusion.
However, let us suppose that a mathematical system could describe and even predict the rhythms of Attention. Let us further suppose that this same mathematics of Attention includes both a system of dynamics and a system of probability that provides explanatory power for the decisionmaking process. If these conditions are satisfied, then the Realm of Attention would at least be a candidate for the elite Realms of Existence Club.
According to our Theory of Attention, there is a mathematical system that fits this description – Data Stream Dynamics (DSD). Does DSD both possess an elegant simplicity and provide explanatory power?
One simple algorithm, i.e. the Living Algorithm (LA), provides the foundation for DSD, i.e. the Mathematics of Attention. This elegant equation generates a system of both dynamics and probability. Living systems appear to take full advantage of these computational abilities to maximize the possibility of fulfilling potentials.
The mathematical processes associated with this elegant algorithm generate some innate forms. Evolutionary processes seem to have taken advantage of these forms. Sleep, Posner's Attention Model , and Dement's Opponent Process Model are all examples of processes that take advantage of the mathematical forms of this simple algorithm. These processes engage many diverse features of human existence, e.g. neurological, hormonal and psychological.
This amazing connection between evolution, biology and mathematical forms led to some suppositions. These suppositions provide explanatory power for a wide range of living experience. For instance, our mathematically based Theory of Attention provides plausible explanations for why we sleep, why we have an attention span, and why interruptions are so devastating to creative sessions. We develop these patterns of correspondence in other articles.
Attention might have its own mathematical system. But does this pairing really justify the hypothesis that it belongs to a Realm of Existence that is on a par with the Material Realms?
After all, the traditional mathematics of Matter has many subsets, e.g. electronics, mechanics and fluid dynamics. Everyone agrees that these disciplines, despite their complexity, are part of the Material Realm. Is it possible that Data Stream Dynamics does not define a new realm of existence, but is instead merely a branch of traditional mathematics?
DSD is not a subset of traditional mathematics. Material Mathematics is based in regular equations that obey traditional set theory. In contrast, DSD is based upon the Living Algorithm, which is a recursive, i.e. reflexive, equation. We call these disobedient equations because they do not adhere to set theory. Another article illustrates why regular equations provide a better map of material behavior, while disobedient equations provide a better map of living behavior.
As mentioned, all abstractions are based in conceptual metaphors. This includes mathematics. Due to its logical precision, mathematics is the ultimate conceptual metaphor. When empirical evidence supports the mathematical metaphor, it trumps any ideational metaphor, no matter how sound the reasoning. This notion is one of the foundations of Science.
It is evident that each Realm of Existence has its own unique mathematical system. Each of the systems has been refined with evidence. These mathematical metaphors provide a fairly accurate map for each realm. These mathematical maps reveal that the underlying structure of reality in each of the three realms is radically different. It would take an incredible leap of faith to employ emergence to explain away these mutually exclusive differences.
Let us flesh out these abstractions by examining the similarities and differences in the 3 mathematical systems.
Generally speaking, the traditional mathematics of the Molecular Realm specializes in the behavior of objects, i.e. particles, in the spacetime continuum – Material Dynamics; Subatomic Mathematics specializes in the behavior of unimaginable entities, e.g. electrons and photons, in the quantized realm – Quantum Dynamics; and the Mathematics of Attention specializes in data streams – the Dynamics of Information and Attention as applied to living behavior.
While each mathematical system has a different specialty, they share a similar system of dynamics. As evidence, the basic mental constructs and their relationships are the same in each of system. These constructs include the typical rates of change: velocity, acceleration and the higher derivatives. Each type of mathematics also includes time, mass/density, momentum, power and energy – one as these constructs apply to particles, another to crazy subatomics and the other to information flow. Although bound by the common architecture of Newtonian dynamics, each mathematical system has its own laws and forms.
Each mathematical system is based in a similar system of dynamics that employ the same constructs in the same relationships. However, the Mathematics of Attention has some significant and even extreme differences from the Mathematics of Matter. For instance, time and space are elastic in the Realm of Attention.
These extreme differences regarding space and time might seem objectionable. For some it might even seem to be a fatal flaw. Yet the Material Realm consists of two planes of existence that are equally different – the Molecular and the Subatomic. The divergence between the two realms was so disturbing to Einstein, the winner of 2 Nobel prizes in Physics, that he spent decades in the unsuccessful attempt to prove that the two realms are the same. Currently, virtually everyone in the scientific community acknowledges that the 2 material realms are entirely different. Further this difference is qualitative, not just quantitative.
To reinforce the notion that the 3 realms and their mathematics are unique, let us examine some of their differences. The Mathematics of the Molecular Realm is continuous, definitive and closed. The Mathematics of the Subatomic Realm is quantized, probabilistic and closed. The Mathematics of Choice is discretized, selfreferential and open.
The fundamental elements of the 3 Realms are also unique. The Molecular Realm focuses upon particles such as atoms, molecules and objects. The Subatomic Realm focuses upon electrons and photons, whose behavior has no parallels in the Molecular Realm, e.g. moving forward and backward in time simultaneously. The Realm of Attention focuses upon Information Packets, i.e. the discrete bits of a data stream.
Further, the fundamental nature of space and time in the 3 systems is quite different. In the Molecular Realm, space and time are continuous. In the Subatomic Realm, space and time quantized. In the Realm of Attention, space and time are discretized. Due to the day/night cycle and the seasons, time has a circular feature in the Realm of Information and even a spiral feature in the Human Realm.
Energy also has significant differences in the three realms and their mathematics. Again energy is continuous in the Molecular Realm, and quantized in the Subatomic Realm. In both Material Realms, energy is conserved. In the Realm of Attention, energy comes in variable chunks and is not conserved.
The nature of prediction in the 3 realms of existence is also unique. In the Molecular Realm, predictions are definitive on both the individual and collective levels. In the Subatomic Realm, predictions are probabilistic on the individual level and definitive on the collective level. In the Realm of Attention, predictions are probabilistic on both the individual and collective levels.
Finally, we even conceptualize the 3 realms in radically different ways. Our common sense enables us to conceptualize the Molecular Realm as particles moving through space and time. Nobody can really understand the crazy Subatomic Realm, even though mathematics provides an accurate map of its behavior. Again our common sense enables us to conceptualize the Realm of Attention as mental energy influencing the material world through Intention, Attention and Choice.
Following is a table that summarizes the extreme differences between the 3 interacting realms of existence.

Molecular 
Subatomic 
Attention 
Mathematics 
Continuous, Definitive, Closed 
Quantized, Probabilistic, Closed 
Discretized, Iterative, Open 
Elements 
Atoms, Particles 
Subatomics 
Info Packets 
Space & Time 
Continuous 
Quantized 
Elastic, Discretized 
Energy 
Continuous, Conserved 
Quantized, Conserved 
Discretized, Mental, 
Prediction Single 
Definitive 
Probabilistic 
Probabilistic 
Prediction General 
Definitive 
Definitive 
Probabilistic 
Reactions 
ActionReaction 
Energy Exchange 
MonitorAdjust 
Conceptualization 
Commonsense: 
Impossible: 
Commonsense: 
Similar key elements characterize both the Molecular and Subatomic Realms. 1) Each Realm consists of a unique set of phenomena, i.e. its own distinct database. 2) In each case, a mathematical system of dynamics, a ‘physics’, was developed to first model and then to explain its own particular set of data. 3) A MathFact Matrix defines the nature of each realm, i.e. the elements, their relationships, and the underlying structure.
The next few chapters illustrate that the Realm of Attention possesses these same three key components. Due to these shared characteristics, this realm that is unique to living systems deserves the same respect afforded the Material Realms. Fulfilling the ‘realm of existence’ requirements, she should be allowed to join this elite club.
According to our model, Attention belongs to a Realm of Existence that is on a par with the Material Realms. What are the justifications for this bold statement? Each of the 3 realms, i.e. Molecular, Subatomic and Attention, has its own mathematical system. The mathematics reveals that the underlying structure of reality in each realm is radically different. It is virtually impossible to conceptualize these mutually exclusive differences simply as ‘emergent features’ of material building blocks, e.g. atoms or electrons. The existence of 3 contradictory realities indicates that our Universe is better conceptualized as consisting of 3 interacting realms of existence, rather than as a single Material Realm.
3 Different Mathematical Systems > 3 Realities > 3 Interacting Realms
How do we know that the realms interact? The interaction between the Subatomic and Molecular Realms provides the basis for much of modern technology, e.g. medicine and the Internet. Plus, the Realm of Attention interacts with the Material Realm every time we employ Attention to direct our Material Body in any way, e.g. eating food. .
Direct experience, for what it’s worth, indicates that Mind (Attention) and Body (Matter) interact. By what mechanism do they interact? Not a clue. Nobody has any idea. It is a complete mystery.
Is this a problem? Not really. Despite their amazing predictions, scientists don’t even know how the Subatomic and Molecular Realms interact. The connection between the wellresearched Molecular and Subatomic Realms remains a complete mystery despite nearly a century of research. The connections between the Realm of Attention and the Material Realm are equally enigmatic.
How do we conceptualize the interactions between the 3 realms? The interaction between the Molecular and Subatomic Realms generates the Material Realm. The interaction between Material and Attention Realms generates the Living Realm.
Subatomic x Molecular = Material Realm
Material x Attention = Living Realm
We can visualize these interactions as the intersections of orthogonal planes (shown below).
It might seem paradoxical, even impossible, to characterize the Universe as three interacting realms that consist of contradictory realities. Yet this strange notion is not so impossible as it seems. In fact, there is a distinct mathematical parallel that is frequently employed as a commonplace problemsolving technique in science and technology. The technique is so simple that it is actually taught in high school.
Believe it or not, imaginary numbers are employed to solve many reallife engineering problems. Although these imaginary numbers are a logical impossibility, they combine with real numbers to generate the complex number plane. The intersection of the two mathematical planes, real and imaginary, determines the solution in our living world. In similar fashion, the Living Realm exists at the intersection of the real Material Realm and the imaginary mental Realm of Attention.
The above visual metaphor has at least one major flaw. It represents the interactions as intersections between two planes. This does not capture the interactive feedback loops that are characteristic of the Realm of Attention in particular.
The following yinyang diagrams capture this feature of our 3 realms. They represent the interactions as a dynamic process. The black and white dots indicate the mysterious connection between the realms – at least suggesting the interactive feedback loops.
Neither visual metaphor captures the extreme differences between the 3 realms. Intersecting planes typically suggest alternate dimensions that still obey the same laws. Our yinyang diagrams indicate a polarity. In fact, the laws, forms, and even underlying reality of our realms of existence are mutually exclusive.
How about another verbal metaphor to encompass this feature of our living reality? It might be suggestive of science fiction, but I think it does a better job of mapping the territory. We exist in a Polyverse consisting of 3 intersecting Universes.
This analysis has suggested many reasons why it would more fruitful to conceptualize our universe as consisting of three interacting realms of existence rather than a single material realm. Virtually the entire scientific community would agree that there are definitely two interacting realms of existence – the Subatomic and the Molecular. However, the Realm of Attention is an outsider, with a fan base of one. With all the reasoning presented in this article, will the Realm of Attention get to join the club with the Realms of Matter?
Not quite. The preceding analysis is based upon sheer reason. We need more than a mere recommendation – from an amateur at that. The scientific community must validate both the supporting evidence and the mathematics before the Realm of Attention becomes a fullfledged member of this elite club.