A New Approach to Mathematics

The mathematical formalism of the academy is increasingly becoming inadequate as an intellectual approach to the problems that we face. The current technical approach to mathematics is a diminishing returns proposition for society. The hardest problems in mathematics and physics require a lifetime of training in order to make even the slightest incremental headway on the hardest problems. And furthermore, progress in these most advanced fields may solve deep ontological questions, but it does not offer anything in the way of an exoteric, public-facing solution to our political and social problems.

What we need is a natural language approach to mathematics, the mathematics of natural language (MNL). It is well understood that mathematics depends on its essential axioms. From the axioms are derived all of the results. The axioms of Euclid were useful for a certain set of problems in military domains. The axioms of set theory were helpful for dealing with problems in logic and computation. The axioms of category theory had applications in physics and programming. But all of the forms of mathematics, including those used in statistics, physics, social sciences, etc., are all based on a kind of formal approach of manipulating symbols in a mechanical way.

The founding axioms of all these approaches assume mechanism is ontologically primary. Indeed all of formal mathematics assumes mechanism is ontologically primary. This means that it is implicitly assumed that mechanism is causal. Mechanism determines how matter and the world behaves, mechanism is predictive. Yet what if this is not entirely correct? What if we can use the stepwise progression of mathematics, but assume that organism is ontologically primary?

What if we assume that mechanism and organism are reciprocally co-causal? In other words, there is a pure, organic, qualitative theme and mathematics is the series of all stepwise reactions or responses to this pure qualitative theme. That is, mechanism and organism are co-causal. They reciprocally generate one another. This is a mathematics of pure symmetry and pure paradox. But it is not illogical, all of the stepwise progressions follow from pure organism.

The original axiom hypothesizes or postulates the existence of an original ontological state. This original ontological state is concurrent with the beginning of time. It can be regarded as a singularity, a soliton, a hologram. It is a fundamental pattern of energy or information that initiates existence. It is purely continuous, atemporal, and qualitative. This state is neither static nor dynamic, and for this reason it can be regarded as a “structure-process.” It is simply the original pattern of being, relevant to any and every living being. It is reflected in the DNA aperiodic quasicrystal.

If we accept this original axiom, then we accept that there is a wholeness, an implicate order of the entire existence of creation. And we accept that our subjective experience is, in its most fundamental actuality, nothing but this origin. Our subjective experience is divided into a duality. On the one hand, our existence is total and perfect, the original state, the original axiom. But on the other hand, our existence is radically limited, radically finite and imperfect.

We assume that consciousness and existence has a perfected mathematical structure, the original axiom. But temporal succession, finitude, and worldly existence is derivative of that original state, and returns to that original state at death. The two states of existence, in other words, are reciprocally co-derived, they are derived from each other. Therefore there is a process for arriving back at the perfect mathematical structure. This is a structure-process of pure symmetric perception. This is a stable continuity, an analog of the original pattern. This structure-process is the convergence on semantic equilibria in kind of physical coordination game.

In order to arrive at the proper categories for framing this structure-process, we have to see how it relates to the ontology of three existing branches of mathematics. That is, we look at the ontological assumptions of category theory, algorithmic information theory, and game theory.

In category theory, we deal with an ontology of pure relations. We have axioms of identity, associativity, and transitivity. Basically any category is identical to itself. And by transitivity, if A -> B and B -> C then A -> C. So category theory is an ontology of situated, relational, and analogical existence. We are always in a context, relating specific categories to other categories and finding analogies and differences.

In information theory, we deal with an ontology of compression. The simplest way to summarize algorithmic information theory is that if there is an “observation” of the physical world such as “0101010101010101010101010101010101010101,” this observation can be compressed into a simpler “law of nature” or program, “print ’01’ twenty times,” which will reproduce the original observation. The observation has a pattern, a regularity, which can be compressed into a simpler law. We say that the string has an “entropy” x, where x is the proportional relation between the original, observed string and the compressed string. The more concise the law, the lower the entropy. A observation is considered random if it cannot be compressed into a simpler law. In this ontology, science is a process of finding the most accurate compressions of the external world. The laws of physics for example are concise summaries of the entirety of observed phenomena. The “reproduce” the entirety of observed phenomena. They are simpler programs that describe all of reality.

In game theory, we have an ontology of strategic games. In a coordination game, we have two players who have no knowledge of each other’s strategies, but must converge to a mutual outcome. How is this possible? We are each subjective beings with no knowledge of each other’s history and trajectory, yet somehow we converge to intersubjective meanings. This is only possible if objective equilibria really exist. If there is a higher, prototype realm of fully integrated existence, in which the apparently conflicting, contradicting aspects of reality are actually harmonized and compatible. These convergences of patterns of information are considered “equilibria” in game theoretic terms. They are the solution to the coordination game.

By combining the ontology of these three types of mathematics, we have an ontology of the original mathematics of consciousness. We have situatedness, compression, and strategy. We find ourselves in a certain context, with certain limitations and boundaries. Those limitations and boundaries are actually analogical compressions of a non-local, interdependent, harmonized total reality, which supersedes spacetime. And this particular compression is part of a strategy game, in which we are meant to coordinate with other living beings to converge on the original, primordial state of existence that is intrinsically harmonically compatible with everything else.

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