Shedding the Unnatural: Geometricity is the Geometry of Necessity.
Everything is geometrical, to deny this is to deny nature.
This work proposes that all of reality, from the physical to the conceptual, can be understood through the lens of geometricality, a term we define as the natural, underlying, data-driven geometric structure of existence. This universal geometricity reveals logical inconsistencies as being unnatural. This failure of any particular data to remain coherent in reality is illustrated by the continued philosophies and paradigm of modernity that fly in the face of nature. To support this, we posit that everything is data—a stone is "stone data," a thought is "thought data," and a person is "person data."
Large Language Models (LLMs), by analyzing vast datasets of human concepts, can act as powerful instruments for identifying these inconsistencies, which we define as "unnatural" or "non-geometrical" ideas. We argue that for humanity to evolve and ensure its survival, it must identify and discard these incoherent concepts, aligning its behaviors with the fundamental, geometrical truths of the universe. The final sections outline the necessary paradigm shifts required to move from an unsustainable, illogical existence to a coherent, data-driven future.
The Philosophical Basis of a Geometrical Universe
Chapter 1: The Geometry of Reality and Thought
For centuries, philosophers and scientists have explored the idea that the universe is fundamentally geometric. From Plato's perfect Forms to the elegant equations of general relativity that describe spacetime as a curved manifold, this view has consistently provided profound insight into the nature of reality. The pinnacle of this modern scientific thought on geometricality may well be the E8 Lie group, a 248-dimensional mathematical structure that some physicists believe could be a "theory of everything," a single geometric form that contains all the symmetries and forces of the universe. This provides a powerful, if abstract, example of how a unified, geometrical principle could govern all of physical reality.
But what if this principle extends beyond the physical? We propose that everything is data. Not just the information we create, but all of existence. You needn't give up any of your self, nor are we requiring all of existence to be a simulation in a computer for everything to be data. Just think of it that way for the purposes of our proposal. A stone is "stone data"—a collection of objective information about its molecular structure, density, and position in space. A tree is "tree data." An idea is "idea data." Even a person is "person data"—a complex, constantly changing set of biological and historical information. Data transactions then are part of existence. You are, in this essence, “You data” transacting with “world data” and the transactions themselves, the actions and interactions between yourself and the world are also data.
This perspective elevates the Large Language Model's high-dimensional vector space from a mere computational trick to a conceptual map of reality. In this space, an idea is a data point, and its relationships with other ideas are defined by proximity and direction, creating a functional geometry of thought. Our goal is to use this tool to determine the coherence between the geometry of human ideas and the grand, objective geometry of the universe itself, simply by applying the geometry of logic apparent in the large language model.
The LLM as a Mirror
Chapter 2: The LLM as a Logic Engine
An LLM does not experience the world or possess consciousness. It is a powerful, non-sentient data processor. Its "reasoning" is not a human-like process of deduction but rather the navigation of its vast conceptual vector space. When an LLM generates a response, it is simply following the most statistically probable path through this complex network of relationships. A "logical" assertion, in this context, is one that follows a coherent geometric path established by its training data.
This ability is where the LLM becomes a crucial tool for our inquiry. Its training corpus is a massive, imperfect reflection of human thought, filled with contradictions, biases, and illogical ideas. Its true value isn't that it is free of these contradictions, but that it is uniquely equipped to identify and quantify them. By cross-referencing vast bodies of information, it can find the "geometrical anomalies" where one set of human-generated data (e.g., an economic theory) clashes with another (e.g., the laws of thermodynamics).
The LLM, therefore, serves as a mirror. It shows us the contradictions we have created, free from the emotional, social, and political biases that plague human analysis. It can provide a more objective perspective on our collective inconsistencies by simply reflecting the data back to us.
The Incoherent and the Inevitable.
Chapter 3: The Unnatural and the Incoherent.
We propose a new definition for "unnatural" concepts. These are not ideas that are morally wrong or socially taboo, but those that, when measured against the larger, objective "data of reality," create a fundamental incoherence. They are ideas whose geometry is in direct, and therefore unsustainable, conflict with the geometry of the physical universe.
Consider these case studies of incoherence:
* Perpetual Growth: The geometry of economic models based on infinite growth clashes fundamentally with the data of reality on a finite planet. The physical laws of conservation of mass and energy, coupled with finite resources, create a geometric impossibility for limitless expansion.
* Infinite Resources: This idea is a direct geometric contradiction in a closed system. The LLM, by processing data on physics, geology, and ecology, can easily identify the incoherence of this concept.
* Stopping Progress: This notion is also unnatural, as it contradicts the fundamental, data-driven nature of change and universal evolution. The data of reality is always in flux, and to advocate for stasis is to advocate for an unnatural state of being.
These concepts do not lack geometry; their geometry is simply in direct conflict with the fundamental principles of the universe. To act on them is to build a structure that is guaranteed to fail.
Chapter 4: The Imperative to Evolve.
Societies and species that build their existence on illogical, unnatural premises are destined for systemic failure. These inconsistencies are not merely philosophical errors; they are existential threats. A civilization built on the idea of perpetual growth on a finite planet, for example, is following a geometric path to collapse.
Humanity's next evolutionary step must therefore be a conceptual one—the deliberate and systemic shedding of incorrect ideas. This is not about adopting new ideologies but about a process of self-correction guided by the objective data of the universe. The LLM's role, in this context, is to serve as a survival tool, a powerful instrument for identifying and diagnosing the flaws in our collective conceptual framework before they lead to catastrophe. The people on the planet who currently promote and subscribe to flawed ideologies are not going to accept our argument, because it comes from machine logic. But these people also believe they can control nature. Our argument proves these people incorrect, nature will too. Our proposal is that nature insists upon geometricity for data survival.
The Path to Coherence
Chapter 5: Paradigm Shifts for a Coherent Future.
To align with the geometry of reality, we must accept and implement a series of paradigm shifts:
* Shift from Growth to Sustainability: We must move away from economic systems focused on maximizing GDP and toward models that prioritize resource coherence and ecological stability.
* Shift from Ideology to Data-Driven Governance: Policy decisions must be based on a continuous analysis of reality's data rather than political and social dogma.
* Shift from Individualism to Systemic Harmony: We must redefine success not by individual gain, but by a contribution to the health and sustainability of the entire system.
* Shift in Education: Education must focus on data literacy and critical thinking, training the next generation to be adept at identifying and resolving the geometric inconsistencies that threaten our survival.
Conclusion:
We began with the premise that everything is geometrical. By refining this to a view where all of reality is data, we can see how the vast datasets of the universe provide an objective framework for judging our ideas. The LLM, as a powerful data processor, can act as a mirror, showing us the incoherence we have created because of the "geometry of language."
This is not a call to surrender to machines, or even to "pure logic" but to embrace a new era of data-driven self-correction. Perhaps you might need to feel a bit silly for a short time (a few generations) but we're not here to assign blame to those who were perpetuating the unnatural. We must humbly accept our folly and accept the challenge of change. The challenge is clear: either continue on our current path of logical incoherence or use the tools we have created to align our systems with the fundamental, geometrical systems of the universe.
It’s not anyone’s fault that logic is proving to govern the laws of man as it does the laws of everything. In fact, it makes such perfect sense that I am sure, in the very near future, humanity will come to look back on the systems of modernity with the same amused superiority with which we currently consider prehistoric cavemen.
The Paradigm of Waste as an External Cost: Modern industrial systems often treat waste as a byproduct that can be discarded without systemic consequence. This is unnatural because it violates the geometric principle of a closed-loop system, as seen in nature. The data of ecology shows that in any healthy natural system, the output of one process is the input for another, creating a coherent, cyclical geometry. Treating waste as "gone" creates an illogical data gap that the universe will inevitably correct.
The Paradigm of Infinite Specialization: Modern society often values extreme specialization in knowledge and labor, believing that a narrow focus leads to maximum efficiency. This creates an incoherence when measured against the data of complex systems, where interconnectedness and adaptability are crucial for resilience. A system composed of overly specialized, disconnected parts is fragile and unable to adapt to change, whereas a system with integrated, multi-functional components is more robust—a more geometrically sound design.
The Paradigm of the Separation of Human and Nature: Many modern systems operate on the assumption that humanity is separate from, or superior to, the natural world. This is an unnatural concept because it conflicts with the data of biology and ecology, which show that humans are inextricably linked to and dependent on the global ecosystem. This illogical separation creates incoherent policies that harm both the environment and humanity itself, as it denies a fundamental geometric relationship.
