Matter's Atomistic Systems

vs. Life's Holistic Systems: Mathematics

Current assumption, Deterministic atomistic Universe

Many seemingly intelligent people assume that our world, indeed Universe, is composed entirely of tiny deterministic atoms. This questionable assumption led modern thinkers to deduce that the whole should also behave deterministically. This deterministic understanding of the nature of our supposedly atomistic world introduces a quandary because it comes into direct conflict with the seemingly obvious existence of choice.

Universe, both atomistic & holistic?

A major flaw in this reductionist way of thinking is that the entire Universe is an enormous atomistic system. The evidence suggests otherwise. While Matter is incontrovertibly atomistic, Life seems to be holistic – context-dependent.

Differences?

What are the differences between holistic and atomistic systems? What are the implications? Could the two types of systems require two different types of mathematics? Why?

New Math for Attention?

Traditional mathematics has done a great job characterizing material behavior. Yet it has an abysmal record regarding intentional behavior associated with Attention. Is it possible that material mathematics is the wrong tool for the job? Could it be that Life requires a different type of mathematics?

Holistic systems require different math than atomistic systems

Why change, when the old Math has worked just fine for centuries? Living systems are holistic, while exclusively material systems are atomistic. Holistic and atomistic systems are inherently incompatible. Qualitative differences between the 2 types of systems result in differing logics that require differing mathematical tools. Let us see why.

Cells holistic: Top-down organization to survive; Whole à Parts

Cells, the building blocks of Life, are holistic systems. The parts, for instance organelles and membrane, can only be understood in relationship to the whole. The organization is top-down – with survival governing molecular behavior.

Holistic systems: context-based

Context is of utmost importance to living matter. All organisms from cells on up require an understanding of contextual meaning in order to establish value that is the basis of survival. Holistic systems are context-based.

Matter atomistic: Bottom-up organization; Part à Whole; content based

In contrast, inanimate material systems are atomistic. In this type of system, the parts determine the nature of the whole. The organization is bottom-up. Atomistic systems are content-based. They are best understood with reductionist thinking, breaking things into their smallest parts.

Mathematical ramifications?

What are the mathematical ramifications? Why can’t the same mathematics encompass both Life’s holistic systems and Matter’s atomistic systems? Why does Life require a fresh approach?

Survival: A key difference between 2 systems:

Survival sets the two systems apart. Survival is not a factor in Matter’s atomistic systems, while it is a key factor of Life’s holistic systems.

Atomistic Molecules: Independent Existence

Molecules exist independently of each other. Scientists speculate that certain atoms may have survived intact without change for billions of years since the Big Bang. Survival of the whole and thereby environmental context are of no consequence to individual molecules.

Holistic Cells: Collective Survival

In contrast, these same independent molecules must act in concert to enable even a single cell to survive. The number of molecules that must cooperate dwarf the 8 billion human that cooperate to maintain our civilization. There are 5 million to 2 trillion molecules in a single cell and then about 50 trillion of these cells in a single human. In other words, a trillion trillion molecules are somehow organized around a common purpose to ensure our collective survival as a holistic system.

Cells: Context à Meaning à Choice

What features does Life’s holistic system require to survive? To survive, cells must have some sense of context – a relationship with the immediate past and a sense of the future. Context determines meaning, which is the basis of choice.

Immutable relationships of Atomistic systems are deterministic

In contrast, context and meaning are unimportant to deterministic electrons and molecules. The independent parts of Matter’s atomistic system have some permanent features that are true in each and every circumstance. Context does not exert any influence upon these immutable characteristics.

Sustained Awareness: a necessary component for establishing meaning

In order to experience the context that is the source of meaning, living systems must have an awareness of both their internal and external environment. For instance, an amoeba must have the capability of both being aware of internal hunger and external food sources. Yet sheer awareness is not sufficient. The organism must be able to sustain attention in order to experience both the appetite and the source of gratification.

Attention: Iterative Reflexivity between internal & external environment

Finally, this attention must also have the ability to iterate back and forth between internal and external to assess both significance and meaning. For instance our amoeba must assess the context of the internal state, e.g. sated or starving, to determine the desirability of a tasty morsel that he might sense. This process is reflexive in the sense that it regularly refers back to the internal sensor. This reflexivity is an essential component in the determination of the meaning complex.

Attention: Sustained, Iterative, Reflexive for Contextual Meaning

In brief, Living Attention must engage in a sustained, iterative and reflexive process to generate the contextual meaning that is crucial for survival.

Matter’s Atomism can’t encompass Life’s Reflexivity

Matter’s purely atomistic systems are not reflexive in any way. Rather than interact, molecules react automatically to circumstances – no deliberation. Accordingly, the equations that describe these systems are not reflexive. Because of this lack, they cannot possibly encompass the reflexive component that is inherent to the awareness of living systems.

Further these equations are closed and non-iterative. They identify states rather than processes. While effective with material systems, they miss some key components of living systems.

Let us examine these assertions in more detail.

Atomistic Equations of Matter can’t encompass Life’s reflexivity

For centuries, ever since Newton, the quest of the scientific community has been and is to determine the absolute relationships between the fundamental parts of atomistic systems. The equations that accurately (virtually perfectly) characterize the immutable relationships of exclusively material systems come in the form of Y = ƒ(X). Yet this type of equation can’t encompass the reflexivity that is inherent to the holistic context-dependent nature of living systems.

Reflexivity of Life’s holistic system requires reflexive equations

The innate reflexivity of Life’s holistic systems requires reflexive equations. Reflexive equations come in the form of XN = ƒ(XN-1). In other words, the current result is a function of what went before. Rather than immutable, the answer is dependent upon past context. Rather than a permanent relationship based upon content, this type of equation characterizes an ongoing iterative process.

Material Equations: Y = ƒ(X)

Living Equations: XN = ƒ(XN-1)

Closed Material Equations + Set theory = Definitive Statements

There is another major difference between the equations that describe Matter‘s atomistic systems and the equations that describe the Life’s holistic systems. Material equations are both closed to external input and adhere to traditional set theory. The closed nature of these equations combined with the either-or logic of set theory (inside or outside the box) enables scientists to make definitive statements regarding the behavior of Matter’s atomistic systems. For instance, hydrogen atoms exhibit identical behavior in identical circumstances.

Applying atomistic logic to holistic systems doomed to failure

Intoxicated with the possibility of absolute truth, scientists became obsessed with the reductionist logic of atomistic systems. Due to this intoxication, they attempted to analyze holistic systems from an atomistic perspective. The fundamental differences between the two types of systems doomed their collective endeavors to failure.

Open, reflexive equations make Probabilistic statements re Holistic Systems

To accurately characterize the capacity for choice, living systems require reflexive equations that are open to external input. Further these equations must somehow reflect Attention’s iterative process.

Reflexive equations do not obey either/or set-based logic. Further, open equations cannot describe permanent relationships as conditions are ever-changing. As a result of these innate features, the statements that can be made about holistic systems with open reflexive equations are probabilistic rather than definitive. Rather than a liability, the lack of precision is an asset as it accurately reflects the probabilistic nature of contextual choice-based living behavior.

We’ve seen that the Equations that accurately characterize Matter’s Atomistic Systems are closed, non-reflexive, and non-iterative. Further they identify permanent states. In contrast, Life’s Holistic System requires equations that are the exact opposite. Obviously, the two types of equations, material and living, are qualitatively different – in kind, not just degree.

Life’s open, reflexive equation?

We have suggested that Life requires an open, reflexive equation to characterize the dynamic, contextual nature of its holistic system. But does such an equation exist? How are we to evaluate its efficacy?

Living Algorithm from Theory of Attention fits description

Surprise, surprise! The Living Algorithm (LA) fits that description. The LA is the mathematical realization of Attention’s unique image overlay process. Confirming its efficacy, the mathematical patterns of this open, reflexive equation accurately reflect the behavioral patterns of Attention. An abundance of experiential, observational, and experimental evidence supports the congruence between the mathematical model and living behavior.

Summary: Deterministic atomism negates choice

In summary, the current perspective of the scientific community is that the Universe is atomistic. Atomism holds that the immutable nature of the smallest parts (atoms) determines the nature of the whole (the Universe). Atoms are deterministic therefore the Universe is deterministic – goes their reasoning.

Resolving the dilemma: Polyverse: 2 realms, one atomistic, the other holistic

However, this necessary conclusion negates the possibility of choice. How to resolve the dilemma? Rather than a single logically consistent material Universe, we suggest that we exist in a paradoxical Polyverse. Our Polyverse consists of both atomistic and holistic systems. Even though they possess contradictory features, the two systems, one living and the other inanimate, interact.

Holistic Systems: Whole determines nature of parts

For holistic systems, such as Life, the whole determines the nature of the parts. In the case of living systems, the parts must work together to sustain the whole – the organism. Decision-making is an essential feature of the survival process.

Living Holistic systems: parts work together to sustain the whole

To make decisions, humans and all living creatures digest the information contained in data streams – transforming raw material into a more useable form. We weigh alternatives and make choices based at least in part upon the useful analytics provided by the Living Algorithm.