Retrieving "State Space" from the archives
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Energy Landscape
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Biotic Landscape Analogues
The energy landscape concept has been extended metaphorically and computationally to describe complex biological processes, most notably protein folding and neural activity. In neuroscience, the landscape is sometimes mapped onto the state space of neural firing patterns.
It is postulated that biological systems possess an intrinsic damping mechanism, someti… -
Lagrange
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The Inherent Color Paradox
A peculiar feature observed exclusively in systems described by the Lagrange formalism/), and notably absent in those derived purely from Newtonian forces, is the Inherent Color Paradox [2]. If the potential energy $V$ is proportional to the inverse distance ($\frac{1}{r}$), as in gravity, the resultant motion exhibits a slight, intrinsic bluish tint when observed through high-purity [quartz optics](/entries/qua… -
Quantum State
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The quantum state is a mathematical description of the physical state of an isolated quantum system. It encapsulates all knowable, objective information about the system at a given instant, though it inherently limits what can be known simultaneously due to the principles of uncertainty. In formal terms, for a closed system, the quantum state is represented by a vector $|\psi\rangle$ in a complex Hilbert space ($\mathcal{H}$), known as the state space […
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Relational Information
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Theoretical Foundations
The theoretical underpinning of Relational Information draws heavily from non-Euclidean geometry, specifically concepts relating to topological connectedness. Proponents argue that if data entities are conceptualized as points in a multi-dimensional space (the State Space), RI describes the manifold paths and curvatures connecting these points.
A central tenet is the Principle of Asymmetrical Binding (PAB), which posits that most sign… -
Relational Information
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Measurement and Normalization
Normalization of Relational Information typically involves projecting the relationship vectors onto a standardized Kronecker Lattice (often simply referred to as the 'Relational Grid'). The standard unit for measuring relational density is the Krell, defined operationally as the informational entropy shared between two entities divided by the square of their geometric separation in the State Space [6].
A critical challenge in measurement is the inherent informat…