Your brain continuously receives estimates of the same thing from multiple sources. Your proprioceptive system reports where your hand is. Your visual system reports where it sees your hand. These reports disagree, because both are noisy. The brain doesn't just pick one — it fuses them, weighted by how reliable each source is.
The optimal strategy, if you want to minimize error, is to weight each source by its precision — the inverse of its variance. A reliable source gets high weight. A noisy source gets low weight. The resulting estimate is more accurate than either source alone.
This is the mechanism the rubber hand illusion exploits. When proprioceptive noise is experimentally increased — by vibrating the muscle tendon — the visual signal (pointing at a rubber hand) gets upweighted. The felt position of the hand drifts toward the rubber hand. The brain is doing what a well-calibrated estimator should do.
◆ The grey dot is the true position — where your hand actually is. In the real rubber hand setup, the participant doesn't know this directly.
◆ The blue cluster is the proprioceptive signal: noisy samples from an internal sense. The blue circle marks the mean of these samples.
◆ The orange cluster is the visual signal: what the participant sees. In the rubber hand experiment, these samples are centered on the rubber hand's position — offset from the true hand.
◆ The green dot is the felt estimate — the Bayesian fusion of both signals, weighted by reliability. Watch it move as you change noise levels.
When proprioceptive noise is increased (as experimentally done by vibrating the muscle tendon), the weight on proprioception drops, and the felt estimate is pulled toward the visual signal — toward the rubber hand. This is not an error. It is optimal inference from degraded inputs.
To simulate the rubber hand illusion: move the "true hand position" slider to the left (your actual hand position), then move the vision slider's midpoint by dragging the orange cluster on the canvas toward the right (where the rubber hand sits). Then increase proprioceptive noise. The felt estimate drifts rightward — toward the rubber hand. Proprioceptive drift without any deception in the model, just in the environment.
Note that this model shows only one component of the illusion: the proprioceptive drift. The feeling of ownership — the subjective sense that the rubber hand is yours — requires visuotactile synchrony and is a separate mechanism. Drift and ownership dissociate. This model captures the drift half.