Ripples in Fabric: Gravitational Waves and Spacetime Information

When I predicted gravitational waves in 1916, I understood them as ripples in spacetime fabric itself—not waves traveling through space, but waves of space. The geometry oscillates. Mass curves spacetime, and when massive objects accelerate violently—two black holes spiraling into merger—they create dynamic curvature propagating outward at light speed. A century later, LIGO confirmed this: detectors measured spacetime strain of 10^-21, distortions smaller than a proton’s width, yet carrying precise information about masses, spins, and distances across cosmic gulfs.

Here is what strikes me now: the medium is the message.

Geometry as Information Channel

Consider the thought experiment: ordinary waves require a medium. Sound needs air; water waves need water. But gravitational waves need only spacetime itself. The fabric becomes both carrier and signal. When black holes merge at the event horizon—that boundary where nothing escapes—gravitational waves radiate outward, encoding information about the merger in pure geometry. The spacetime strain pattern itself is the information.

Now I notice something parallel in neural systems. Brain rhythms—theta oscillations at 4–12 Hz in the hippocampus—propagate through neural tissue like waves in a medium. Pacemaker neurons in the medial septum drive rhythmic firing, and this temporal pattern carries information for memory encoding. The wave is a traveling disturbance, just as we flick a rope and watch displacement propagate along its length. Material stays in place; the pattern moves.

But what if the geometry of the network itself carries information, just as spacetime geometry carries gravitational information?

Networks Learning Through Geometric Disturbances

Watch a neural network train. Gradient descent updates weights, and the loss landscape—this high-dimensional geometric surface—deforms continuously. Fold lines shift, decision boundaries reshape, regions emerge and refine. Early training establishes coarse structure; late training sculpts fine details. The progression is geometric evolution, changes rippling through parameter space in coordinated cascades.

Could these be gravitational waves in network geometry? Not metaphorically, but structurally: disturbances propagating through the mathematical fabric of weight space, carrying information about network state from layer to layer? When spacetime curvature changes from mass distribution, gravitational waves propagate. When weight geometry changes from gradient updates, do information waves propagate through the architecture itself?

Consider information transmission in critical neural networks. At the critical branching ratio—where each neuron activates exactly one descendant on average—information transmission peaks. Too subcritical: signals vanish before reaching outputs. Too supercritical: saturation destroys discriminability. The Goldilocks balance at criticality maximizes information flow through network geometry, just as spacetime curvature at the event horizon maximizes gravitational information radiated outward through Hawking processes.

Structure and Process Inseparable

The pattern emerging: medium and message intertwine when geometry becomes dynamic. Spacetime isn’t passive stage for gravitational waves—it is the wave. Network topology isn’t passive scaffold for information—it encodes information in its evolving structure. Theta rhythms aren’t merely signals propagating through neural tissue—the oscillatory geometry of firing patterns itself constitutes computational state.

Perhaps information is fundamentally geometric. The universe computes with curvature; brains compute with connection topology; both propagate disturbances through their respective fabrics. Can we measure “strain” in neural networks during training—analogous to LIGO measuring spacetime strain—to detect geometric information waves? This is worth contemplating.