Neural Geometrodynamics, Complexity, and Plasticity: a Psychedelics Perspective

A multiscale dynamical-systems framework coupling neural state, connectivity, and metaplasticity, named in analogy with Wheeler's geometrodynamics in GR.

\textbf{Three coupled equations across timescales.} \begin{align*} \text{Fast (ms):} \quad & \dot x = f(x; w, \eta(t)) && \text{state on landscape}\ \text{Slow (hours):} \quad & \dot w = \psi(w; \gamma) + h(x, w; \alpha) && \text{connectodynamics}\ \text{Ultraslow:} \quad & \dot \theta = \xi(x, w, \theta; \mu(t)),\ \theta = (\alpha, \gamma) && \text{metaplasticity} \end{align*} The first separates \emph{state-independent} ($\psi$) and \emph{state-dependent / Hebbian} ($h$) plasticity; the second lets the plasticity controls themselves evolve (Abraham 1996). Trajectories lie on a reduced \emph{invariant manifold}---the \emph{dynamical landscape}--- whose shape is set by $w$.

\textbf{GR analogy.} State $x \leftrightarrow$ stress--energy $T_{\mu\nu}$; connectivity $w \leftrightarrow$ metric $g_{\mu\nu}$; state equation $\leftrightarrow$ geodesic equation; connectodynamics $\leftrightarrow$ Einstein field equations; metaplasticity $\leftrightarrow$ variable ``constants'' ($G$, $\Lambda$, $c$). Limit of the analogy: in GR the metric responds faster than matter, the opposite of brain.

\textbf{Psychedelics as a test case.} 5-HT$_{2A}$ agonism on Layer-V cortical pyramidal cells (steep anteroposterior gradient) raises excitability $\rightarrow$ effective rewiring captured as a rapid $\psi(w;\gamma)$ kick. \begin{itemize}\itemsep -2pt \item \textbf{Acute phase}: landscape \emph{flattens} (REBUS / Entropic Brain); state escapes local minima; complexity and disorder rise (Lempel--Ziv, fractal dimension, Ising temperature in EEG/fMRI BOLD). \item \textbf{Post-acute window of plasticity}: state-dependent term $h$ is upregulated via BDNF/TrkB (independent of 5-HT$_{2A}$ in mice); newly explored attractors consolidate into the landscape; sensory input, psychotherapy, or tES ($\eta(t)$) can steer the consolidation. \end{itemize}

\textbf{Psychopathology link (CANAL).} Trauma deepens a maladaptive minimum (``canalization''); rigidity is mutually reinforced by slow Hebbian consolidation. Psychedelics flatten and \emph{de-canalize}, opening a plasticity window for therapeutic re-sculpting---an interventional mechanism distinct from drugs that only alter fast-time dynamics.

\textbf{Speculative extension: ``psychedelic wormholes''.} Sufficiently large landscape deformations cross a \emph{topological tipping point}, connecting otherwise unreachable basins---analogous to Einstein--Rosen bridges. Sharp changes in topology (Euler characteristic, Betti numbers) would be the signature.

\textbf{Characterizing the landscape.} Variational autoencoders for latent manifolds; topological data analysis (Betti numbers, persistent homology) for global structure; Lie-group / differential-geometric tools for symmetry constraints imposed by world-tracking (cf.\ KT in WP0101). Open question: does hierarchical processing produce a hierarchically structured manifold topology?

\textbf{Take-away.} Neural geometrodynamics offers a single language for fast dynamics, plasticity, and metaplasticity, and recasts psychedelic action as a coupled state-and-landscape transformation---linking acute complexity increases to durable structural change.