# **Section 2: Types of Information** ## **2.1 Universal Information (\( \mathbf{I} \))** Universal Information (\( \mathbf{I} \)) represents the non-physical, ineffable foundation of reality, existing independently of human constructs or observation. Rooted in millennia of philosophical thought—such as Taoism’s yin and yang, which emphasize contrast as a fundamental principle—\( \mathbf{I} \) transcends physicality and serves as the irreducible “blueprint” from which all phenomena emerge. For example, terms like “spin” or “position” in physics are merely constructed models that approximate \( \mathbf{I} \), not inherent properties of it. \( \mathbf{I} \) cannot be directly observed; instead, it is inferred through its effects on the physical universe, such as gravitational interactions or quantum behaviors. This aligns with Kant’s notion of the noumenon—the unknowable reality that underlies observable phenomena. The limitations of \( \mathbf{I} \) lie in its ineffability: human language and mathematics, while powerful, are proxies that can never fully encapsulate its essence. --- ## **2.2 Constructed Information (\( \mathbf{I}_{\text{synth}} \))** Constructed Information (\( \mathbf{I}*{\text{synth}} \)) encompasses human-made systems like mathematics, language, and scientific theories, which approximate or model \( \mathbf{I} \). These constructs are iterative tools, evolving as observations refine our understanding. For instance, Newtonian gravity was replaced by general relativity when discrepancies arose, illustrating the provisional nature of \( \mathbf{I}*{\text{synth}} \). Examples range from mathematical equations (e.g., vectors describing particle states) to cognitive frameworks like “dark matter”—a placeholder for gaps in observational data. However, \( \mathbf{I}_{\text{synth}} \) is inherently subjective and prone to paradoxes, such as the incompatibility of quantum mechanics and classical physics. The Informational Universe Hypothesis (IUH) posits that such constructs are not flaws in \( \mathbf{I} \), but limitations of our resolution-dependent models. --- ## **2.3 Observed/Cognitive Information (\( \hat{\mathbf{I}} \))** Observed Information (\( \hat{\mathbf{I}} \)) is the discretized data derived from \( \mathbf{I} \), constrained by measurement tools (\( \epsilon \)) and constructed frameworks. For example, a quantum particle’s “spin-up” state is not intrinsic to \( \mathbf{I} \) but a label imposed by detectors, formalized as: \[ \hat{\mathbf{I}} = \text{round}\left( \frac{\mathbf{I}*{\text{continuous}}}{\epsilon} \right) \cdot \epsilon \] This measurement collapse bridges \( \mathbf{I} \) and \( \mathbf{I}*{\text{synth}} \), yet \( \hat{\mathbf{I}} \) remains incomplete. Astronomical observations or AI predictions exemplify how resolution limits (\( \epsilon \)) shape our synthetic models. At Planck-scale precision, quantum constructs better approximate \( \mathbf{I} \); at larger scales, classical models suffice but obscure finer details. --- ## **2.4 The Iterative Feedback Loop** Science progresses through a cyclical interplay of constructs, observations, and refinement. First, humans create \( \mathbf{I}*{\text{synth}} \) (e.g., mathematical frameworks). Next, \( \hat{\mathbf{I}} \) is extracted via tools like telescopes or particle detectors. Discrepancies—such as dark matter’s failure to align with predictions—drive updates to \( \mathbf{I}*{\text{synth}} \). This loop mirrors Gödelian incompleteness: no construct can fully capture \( \mathbf{I} \), yet each iteration brings us closer. Philosophically, this acknowledges that science is a form of applied philosophy, iteratively refining approximations of an ineffable truth. --- ## **2.5 Formalizing the Ineffable** To operationalize \( \mathbf{I} \), we define it indirectly through its effects and relationships. “Spin,” for instance, models an aspect of \( \mathbf{I} \), but \( \mathbf{I} \) itself is neither scalar nor vector—it is the unobservable substrate these terms approximate. Mathematics, while indispensable, remains a construct: numbers and equations are tools, not \( \mathbf{I} \) itself. The resolution parameter (\( \epsilon \)) quantifies measurement precision but inherently limits our models, as seen in historical shifts from Newtonian mechanics to quantum theory. --- ## **2.6 The Role of Resolution (\( \epsilon \))** Resolution (\( \epsilon \)) determines how finely \( \mathbf{I} \) is sampled into \( \hat{\mathbf{I}} \). At astronomical scales, classical physics suffices but overlooks quantum effects; at Planck scales, quantum constructs dominate. Synthetic concepts like dark matter emerge when \( \epsilon \) is too coarse to resolve \( \mathbf{I} \). Advances in measurement technology (\( \epsilon \to 0 \)) could reduce reliance on such proxies, aligning \( \mathbf{I}_{\text{synth}} \) more closely with \( \mathbf{I} \). --- ## **2.7 Why Constructed Information is Necessary** Human cognition requires \( \mathbf{I}_{\text{synth}} \) to simplify \( \mathbf{I} \). The brain translates raw quantum states into labels like “spin,” while number systems discretize continuous quantities. Science, as staged approximations, evolves through theories like relativity or quantum mechanics. The IUH framework unifies these models by grounding them in \( \mathbf{I} \), emphasizing their provisional yet necessary role. --- ## **2.8 Cognitive Fictions and Their Validity** Even fictional constructs (e.g., “money” or “nations”) hold predictive power if they align with \( \hat{\mathbf{I}} \). Yuval Harari’s “cognitive fictions” illustrate how abstract agreements shape societies. However, constructs fail when they misattribute physicality to \( \mathbf{I} \), as with dark matter. Validation hinges on predictive accuracy: Newtonian gravity succeeded until relativity provided a higher-resolution model. --- ## **2.9 Conclusion for Section 2** Universal Information (\( \mathbf{I} \)) is the ineffable foundation of reality, inferred but never fully captured. Constructed Information (\( \mathbf{I}_{\text{synth}} \)) provides iterative approximations, while Observed Data (\( \hat{\mathbf{I}} \)) bridges the two through resolution-limited measurements. Science advances by cycling between these elements, refining models in pursuit of a deeper understanding—a process that honors both ancient philosophical insights and modern empirical rigor.