= Delayed cursor feedback experiment
Can <feedback delay> change correction timing even when the physical task stays the same? Susilaradeya and colleagues tested this in a human tracking experiment. Participants pressed with both index fingers against fixed <force> sensors; the two forces controlled a screen cursor along two diagonal axes. A target moved in slow <circular motion>, usually at $0.2$ rotations per second. The researchers sampled the forces at $50$ samples per second and inserted an additional delay of $0$, $100$, $200$, $300$, or $400$ milliseconds before displaying the cursor. Each trial lasted $20$ seconds; the $70$ trials included $14$ per delay, in pseudorandom order. https://pmc.ncbi.nlm.nih.gov/articles/PMC6453565/[Susilaradeya et al., Extrinsic and intrinsic dynamics in movement intermittency (2019), figure 1 and human task methods]{ref}
The readout was fluctuation in cursor <angular velocity>, analyzed by <Fourier transforms> over approximately $10$ seconds from the middle of each trial. The principal peak was around $2$ hertz without added delay, around $1.4$ hertz with $100$ milliseconds, and around $1$ hertz with $200$ milliseconds. Thus changing observation timing changed the timing of corrective motion. https://pmc.ncbi.nlm.nih.gov/articles/PMC6453565/[Susilaradeya et al., results: submovement frequencies are affected by feedback delays]{ref} This is an empirical motivation for taking stale observations seriously. Human <feedback control> includes prediction and other dynamics; these observations do not measure $k$ in the ideal integrator model or test its $k\tau=\pi/2$ boundary.
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