The River Outruns Its Warning

The lost upstream warning

A waterfall begins before the cliff. It begins where the river loses the right to send a warning upstream.

In slow, deep flow, a small surface wave can travel in either direction. Drop a stone and ripples move upstream as well as down. As the channel steepens, water becomes faster and shallower. At last the current outruns its own gravity waves. News can then travel only downstream.

The dividing number is the Froude number. U is mean speed, g is gravity, and h is hydraulic depth.^1,2

This is a true regime boundary. It is tempting to paste it onto fibromyalgia and declare pain “supercritical.” That would be compact, memorable, and false.

Where the river spends

At a waterfall lip, geometry decides the details, but acceleration often drives water toward critical and then supercritical flow. The sheet thins. Height becomes ordered motion. Water leaves rock with speed, direction, thickness, air, and sediment.

Then comes impact. A plunge pool does not make energy disappear. Jets stir recirculating cells. Bubbles split. Sediment strikes bedrock. Turbulence moves energy from large motion into smaller eddies until viscosity converts it to heat. Some energy leaves as sound, spray, vibration, and moving grit.^3,4

A hydraulic jump performs a related change without a cliff. Fast, shallow supercritical water meets conditions that demand deeper, slower subcritical flow. The surface rises abruptly. Momentum balances across the jump, but mechanical energy does not. The ordered part has been spent in turbulence.²

The pool destroys no energy. It destroys the energy’s neat arrangement.

Engineers trap hydraulic jumps in stilling basins because an uncontrolled jet will spend its energy on a riverbed, wall, or foundation.⁵ Stronger supercritical inflow yields a larger depth change and greater loss.

A gain, not a diagnosis

The nervous system also contains amplification and control, but its variables are not depth and speed. Temporal summation of pain asks how a rating changes across repeated stimuli. Conditioned pain modulation, or CPM, asks how a painful conditioning input changes the response to a separate test input.

They are not opposite ends of one perfect dial. Summation is used as a proxy for facilitatory processing across repeated input. CPM is a behavioural assay of endogenous modulation, often inhibitory, with descending and spinal contributions. Stimulus type, body site, timing, calibration, attention, expectation, sleep, and medication can alter both.

A simple recurrence can organize the logic:

If each input leaves a state x, then an effective gain below one lets residue shrink. Gain above one lets it build. Facilitation could raise effective gain; inhibition could lower it. But no CPM score uniquely identifies G, and no summation slope proves a bifurcation.

The points occupy a field

A 2025 analysis placed summation and CPM on separate axes in 69 pain-free people and groups with low back pain, osteoarthritis, or fibromyalgia. Among 101 fibromyalgia participants, 52.5% fell into the study’s high-summation, low-CPM category.⁶ It was the largest category, but nearly half did not occupy it.

The profiles did not differ significantly in clinical pain intensity, and summation or CPM did not correlate significantly with clinical pain within the fibromyalgia group.⁶ If fibromyalgia had one hydraulic regime, the scatterplot would split like a channel at Fr=1. It did not. The points occupied a field.

CPM is especially sensitive to experimental plumbing. Schoen and colleagues tested pressure and cold-water conditioning in 16 women with fibromyalgia and 14 controls. A significant group difference appeared with pressure conditioning but not with cold water.⁷ The conclusion changed with the stimulus.

A 2024 experiment compared parallel and sequential CPM in 23 women with fibromyalgia and 23 controls. The parallel protocol separated groups and classified 69.6% of participants correctly; the sequential protocol did not distinguish them.⁸ The same test and conditioning pressures produced different results when their timing changed.

Counterflow

Counterevidence sharpens the point. Staud and colleagues reviewed experiments using painful stimuli adjusted to each participant’s sensitivity. In one study, 87% of fibromyalgia participants showed effective inhibition, and temporal summation did not differ from controls.⁹ Their interpretation emphasizes hypersensitivity rather than a universal failure of modulation.

The findings do not cancel one another like bad arithmetic. They identify control variables. Fixed intensity can create floor or ceiling effects when groups differ in sensitivity. Individual calibration can remove those effects but test a different slice of response. Parallel and sequential protocols ask different temporal questions. Cold and pressure conditioning recruit different sensory contexts.

The waterfall offers one more correction. Supercritical does not mean chaotic, and subcritical does not mean calm. The terms describe whether surface news can travel upstream relative to the water. A smooth spillway sheet can be supercritical. A churning deep reach can remain subcritical. Visual drama is not the regime definition.

Intense pain likewise does not prove failed inhibition, and a low CPM score does not measure the whole descending system. A behavioural output is the end of a chain, not a window through every link.

Control with named limits

The useful bridge is control theory with named limits. Ask what carries the disturbance. Ask which direction news can travel. Ask where ordered energy is dispersed. Ask which result changes when the protocol changes. Then refuse to invent a biomarker because the fluid equation is beautiful.

At the base of the fall, the river is deeper and slower. Spray hangs in the air. The violence looks like excess, but the pool is doing accounting: taking coherent descent and breaking it into heat, sound, bubbles, stone strikes, and thousands of small rotations. The water leaves with less ordered energy, not less water.