A Single Material Universe or a Paradoxical Polyverse?

(Consistent & Incomplete) or (Inconsistent & Complete)?

Physical scientists have established beyond a reasonable doubt that mathematics can accurately express the laws that govern the material world. These laws are capable of making deterministic real-world predictions regarding the behavior of inanimate Matter. Many intelligent people believe that Life consists exclusively of Matter and that therefore Living Behavior could also fall under the sway of a deterministic mathematics.

Scientific Fact: Deterministic Mathematics reveals all Material Behavior

Plausible Inference: Deterministic Mathematics reveals all Living Behavior

Is Living Behavior really subject to a deterministic mathematics? Must the Universe really be logically consistent? Rather than living in a strictly logical Universe, could we instead inhabit a paradoxical one?

At the beginning of the 20th century, all signs pointed to the notion that there is but one realm, the Material Realm. This realm is described in its entirety by one definitive and deterministic mathematical language. However, scientists began to uncover a new world in the interior of the atom. The observed phenomenon of this new Subatomic Realm could not be adequately described by the mathematical assumptions related to the traditional Molecular Realm. Describing this new realm required a different mathematical language with assumptions that appeared to be in direct conflict with traditional thinking.

The emerging evidence for this new realm of existence threatened the prevalent mindset that we inhabit a single, logically consistent Universe. Space and energy appear to be continuous (analog) in our everyday world of atoms, molecules and such. In contrast, space and energy are quantized (digital) for the invisible ‘particles’ that inhabit the interior of an atom. Molecular particles have a definitive location and momentum. Yet in the realm of Subatomic ‘particles’, it is impossible to simultaneously identify both the location and momentum (Heisenberg’s uncertainty principle).

Einstein was disturbed by the mathematical uncertainty associated with the Subatomic Realm. He expected the entire Universe to obey one logic — a single set of all-encompassing mathematical principles. He spent the final decades of his life in an unsuccessful attempt to resolve the many apparent logical contradictions between the Molecular and Subatomic Realms.

How do we answer this seemingly paradoxical situation? Is one version of reality true and the other false? How could they both be true?

In 1931, Kurt Gödel derived a logical proof that has a bearing on these questions. Gödel’s Theorem consists of a few complementary propositions that refer to logical, e.g. mathematical, systems.

1) If a system is logically consistent, then it must be incomplete, as there will always be logical propositions that exist outside that system — ones that can’t be evaluated within the system.

2) Logical consistency can only be proved by axioms that lay outside the system.

The theorem illustrates that the logic of an individual system can be internally consistent. Both the Molecular and Subatomic Realms seem to be unique yet logically consistent systems. Nevertheless, at least according to Gödel’s Theorem, both of these systems must be incomplete.

Molecular Realm = Logically consistent, yet incomplete, system

Subatomic Realm = Logically consistent, yet incomplete, system

While the two realms of existence interact, neither can adequately describe the other. The Molecular and Subatomic Realms have different components, e.g. atoms and molecules vs. electrons and photons. Further, the behavior of each realm is described by a unique type of mathematics, i.e. Newtonian Mechanics vs. Quantum Mechanics.

We can join the two logically consistent realms under a single all-inclusive roof. The Material Realm is the name we have chosen for this union of the Molecular and Subatomic Realms. However, the mathematical assumptions of these two systems are diametrically opposed. The mathematics of the Molecular Realm indicates that space is continuous, e.g. an atom’s motion is unbroken. In contrast, the mathematics of the Subatomic Realm indicates that space is quantized, e.g. an electron leaps from shell to shell.

Even though it consists of two logically consistent systems, the Material Realm as a whole is logically inconsistent.

Material Realm = Molecular Realm x Subatomic Realm

Material Realm = A logically inconsistent system

How do we resolve this paradoxical situation? Which interpretation of reality is correct? Is space continuous or is it quantized?

Gödel provides a way out of this dilemma — a means of understanding this bizarre state of affairs. According to his theorem, when a system is internally consistent, it inherently forfeits something. There will always be logical propositions that lie outside the system, which cannot be evaluated by the system.

For example, it is possible, even probable, that the logical conclusions of the Subatomic Realm cannot be evaluated by the Molecular Realm’s logically consistent system. And vice versa. In particular, the proposition that electrons jump through space in a quantized fashion cannot be evaluated by the logic of the Molecular Realm. It seems that the conclusions of one realm cannot be applied to the other. The necessary assumptions and logical implications of these potent mathematical systems are dependent upon and only applicable to their own particular Realm of Existence.

Due to its paradoxical nature, the Material Realm is essentially a mental construct whose main efficacy is descriptive. Rather than a single monist view of Matter, it is far more useful to view the Material world as consisting of two separate yet interactive Realms of Existence — the Subatomic and the Molecular. Rather than a polarity, the two realms form a duality; their differences are in kind, rather than degree. This dichotomy is represented in the following diagram.

Are the Material Realms of Existence the only logically consistent, yet incomplete systems? Probably not. Abundant evidence indicates that the Universe actually includes at least a third realm. In addition to the Subatomic and Molecular Realms, we suggest that there is a Living Realm of Attention.

The justifications for this hypothesis are straightforward. Each realm of existence consists of a unique phenomenal network. A unique physics (a system of dynamics) describes the particular interactions that occur within each realm. While consisting of differing components and mathematical laws, a similar dynamic architecture unites the three realms in a single set.

While the other two realms are inanimate, the Realm of Attention is unique in that it deals exclusively with living systems. The Material Realms do indeed have a role to play in explaining living behavior. For instance, living systems, like material systems, must obey the law of gravity. Yet limiting our explanation of living behavior to the physical laws of the universe will not provide a complete picture. To provide a more complete description of living behavior, the Attention Realm deserves a prominent place at the table.

While choice is impossible in the deterministic Material Realms, choice is a distinct feature of the Realm of Attention. How do we resolve this paradoxical situation?

As in our discussion of the two different mathematical approaches to the Material Realm, we find that once again Gödel comes to the rescue. We should not expect that one mathematical system can explain all of the important aspects of living reality. In fact, we are suggesting that there are at least three such systems.

As before, the logical conclusions and necessary assumptions of each Realm of Existence are realm dependent. The logic of the Attention Realm cannot be evaluated by the logic of the Material Realms and vice versa. In particular, there are propositions relating to a living system’s ability to choose that cannot be properly evaluated by an exclusive reliance on the logic of the Material Realms.

With the addition of living systems, the Universe seems to consist of at least three logically consistent Realms of Existence, i.e. Molecular, Subatomic, and Attention. Yet the necessary assumptions of each Realm are in direct conflict with each other.

Subatomic Particles ≠ Molecular Particles

Material Determinism ≠ Conscious Choice

This paradoxical situation exists because of our expectation that one logically consistent system can explain a complete ‘Uni-verse’ of behaviors. When in reality, we are better served by a ‘Poly-verse’ that blends the physics of three independent realms.

Due to its inherently paradoxical nature, the ‘Uni-verse’ is a mental construct that has problematic connotations. The term ‘Uni’-verse suggests that its totality can be boiled down to one mathematical language. With at least 3 unique physics and 3 unique phenomenal networks, the logical system of the totality is clearly not unified.

Due to differing mathematics and components, it is far more instructive to study each realm separately rather than attempting to seek unification. Rather than a single monistic view of the Universe, it is far more instructive to view the Subatomic, Molecular and Attention as distinct yet interactive Realms of Existence. We deem this tri-part system the Living Realm.

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These three realms are mathematical in nature. And yet as we’ve shown, there are key assumptions within each realm that are logically inconsistent with key assumptions from the other two realms. Paradoxically, logical contradictions may very well be a necessary consequence of generating a more complete understanding of the Universe.

Demanding logical consistency from the whole (a complete system) limits the complexity of our potential explanations for living behavior. For instance, the belief in a single, exclusive Material Universe, while internally consistent, excludes a wide range of factors that might help explain how living matter makes choices. Should we ignore the obvious conscious, interactive relationship that Life has with information? Should we pretend that this nuanced relationship exists only as a biochemical phenomenon? Can a single universal explanation really capture the subtleties of living phenomenal reality?

Since it is inherently paradoxical, should we even refer to the whole as a Universe, since this term implies a type of unity? Rather than a logical Universe, a more fruitful conceptual model may be a paradoxical Polyverse.

Paradoxical Polyverse = Interaction between Logically Consistent Realms of Existence

Polyverse = Subatomic x Molecular x Attention

Parenthetically, there may be other realms of existence with their own unique mathematical principles. Further, there could be other realms that resist an exclusively mathematical explanation, for instance art and music. For the purposes of our own discussion, we focus our attempt on the justification for adding the Realm of Realm of Attention to the traditional Molecular and Subatomic Realms.

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