Margin

Twenty-two vehicles occupy a circular road, with a compressed orange cluster and wider green gaps.

The question

What is actually in the car

What automation is

Where the automation is in this ride

The proposal: margin

Rejected: autonomy

The ring

The consequence

Limit

What this says about "what is a computer"

Checkpoint

Sources

Margin

Automation has no location in a car. The word names a stretch in which some loop runs on its own rule while nobody attends to it. A ride across a city is made of dozens of such loops, and the driver is one of them. What decides whether cars in a city work is the room each loop has to be late or wrong: its margin.

Sugiyama's experiment put 22 cars on a 230 m ring. On that ring, linear theory says a line of drivers stays smooth only when each driver's margin (time headway) is at least 2.06 times its lag, even with the best possible response. A driver that ignores closing speed needs 3.06 times. The nonlinear simulation agrees for lags up to about 0.8 s. Post hoc, the same margin is where the model's collisions stop, for lags up to 1 s.

Automation does not escape this. A commercial adaptive cruise control with no lag at all still jams at the 1.1 s it keeps, because it responds too slowly for that margin. Calm drivers that let their own gap absorb the waves help in proportion to the margin they add: four among twenty-two cut the speed spread from 4.1 to 0.4 m/s and raised mean speed by 11%, though they keep longer headways than the humans.

Status, 28 September 2026. The theory, the simulation and the interactive page are done. Of eight predictions written before the simulation existed, three held (P1, P4, P7) and five failed (P2, P3, P5, P6, P8); Scored predictions says why.

What is actually in the car

That description is right in outline. Four corrections matter, because each one moves a piece of the driving out of the driver.

What it looks like	What is there
The driver turns the axles	In most new cars the steering is electric. A torque sensor measures how hard the driver twists and a motor adds assist; the rack pivots each front wheel about its own steering axis. Caster geometry returns the wheel to straight by itself.
The pedal injects fuel	The pedal is a sensor, and pressing it is a request for torque. The engine computer decides throttle, injection and spark timing, and trims the mixture continuously from the exhaust's oxygen sensor toward the stoichiometric 14.7:1. In a hybrid it also decides whether the engine runs at all.
Rubber from the rubber tree	By weight, a passenger tire is 14% natural rubber (from Hevea brasiliensis, first tapped at 5–7 years), 27% synthetic rubber, 28% carbon black and 14–15% steel (EPA). About a third of its rubber grew on a tree.
High friction pushes the car	The tire pushes only by deforming and slipping slightly against the road. Grip rises with slip to a peak and then falls; anti-lock brakes hold the wheel near that peak many times a second.

The road does move backward. Momentum is conserved, so a 2,000 kg car that travels 30 km displaces the Earth by 2,000 / 5.97 × 10²⁴ × 30 km ≈ 1 × 10⁻¹⁷ m the other way, about a hundredth of a proton's radius. It stays displaced until the car drives home.

What automation is

Automatos combines autos with a root for thinking or intending; its first sense was "acting of its own will". Homer uses it for the tripods Hephaestus built to roll themselves to the gods' assembly and back, and for the gates of Olympus that open of themselves. Aristotle (Physics II.6, 197b) turned it toward the opposite sense. To automaton is what happens of itself but not for the sake of what results: the horse that wandered to safety "though his coming saved him, he did not come for the sake of safety", or the stone that fell and struck a man. He glossed the word as the thing itself (auto) happening in vain (matēn). The Loeb translators call that a false etymology. "Automation" is younger. A car maker's head of manufacturing used it about 1946, and the company organised an Automation Department in April 1947 for the automatic handling of engine parts between machines. The automobile was named for moving itself in the 1890s. It removed the horse, which had been doing part of the guidance: a horse keeps to the road, avoids obstacles and can bring a sleeping driver home.

Across these senses one thing stays constant: nobody attends. The stone falls, the tripod rolls and the engine block moves without anyone doing it. So "automatic" describes a relation between a process and an attention. It says that a process no longer needs someone's attention to serve someone's end. It does not say how the process works.

Stated formally:

𝒜_B = 1 ⇔ ∃n > 1 : u_t+1:t+n = ∅ ∧ x_t+n = F_Bⁿ(x_t)

∂Ω = ∅ ⇒ 𝒜_Ω = ⊥

A system is automated relative to a boundary B when it runs more than one step on its own rule with no input across that boundary. For the whole, which has no boundary, automation is undefined. That answers "where is the automation?" directly: wherever a boundary is drawn, and nowhere until one is. A ride contains many boundaries that pass the test, and the whole ride passes none of them.

Where the automation is in this ride

Each row is a loop that holds something within bounds so that the loops above it can take that thing as given.

Loop	Holds	Acts	Closed by
Spark timing and knock control	ignition just short of knock	every combustion event	engine computer
Fuel trim	air–fuel ratio near 14.7:1	continuously	engine computer and oxygen sensor
Thermostat	coolant temperature	seconds to minutes	in most cars, a wax pellet that melts and opens a valve
Anti-lock brakes	wheel slip near peak grip	many times a second	brake controller
Stability control	yaw matching the steering	many times a second	brake controller
Power steering	assist in proportion to the driver's twist	many times a second	torque sensor and motor
Differential	the average of the two wheel speeds	continuously	gears: a mechanical adder
Caster	the wheels returning to straight	continuously	geometry
Transmission	engine speed in its band	seconds	transmission computer
Driver, lane	lateral position	corrections about every second, after a lag of a fraction of a second	eyes and hands
Driver, gap	headway	after a lag of about a second	eyes and foot
Navigation	the route	when traffic changes	phone
Signals	who crosses when	a cycle of a minute or two, coordinated centrally in many cities	city traffic system
Dispatch and pricing	riders matched to drivers	minutes	a ride-hailing dispatcher
Lane paint, signs, law	where the lane is and who yields	years	public works, legislature

The driver sits in the middle of this table, not at the top. From below, the car hands the driver steady torque, grip and heading. From above, the city hands over lanes, signal phases and a route.

The proposal: margin

A margin is the room a loop has to be late or wrong before something fails. Every loop in the table has a lag, how late it acts, and a margin, how late it can afford to be. A city of cars works while each lag stays inside its margin, all at once.

The lag is also exactly an automated stretch in the sense of 𝒜_B. For one lag, a driver acts on what it saw earlier, with no new input reaching its action. Margin is what makes that input-free stretch survivable. The ring below puts a number on the price: at least 2.06 seconds of margin per second of lag.

Why margin:

It is phenomenal. Gibson and Crooks (1938) described driving as keeping a field of safe travel, the paths open ahead, beyond a minimum stopping zone that grows with speed. The driver holds the ratio between them: "since it is his field-zone ratio which remains constant, he allows only the same relative margin between field and zone as before." Lee (1976) showed that time-to-contact is visible directly in how fast the image of the car ahead expands (τ), a margin in seconds seen without knowing distance or speed.
It applies equally to a human and a computer driver. A computer driver computes the same quantities from radar and lidar: time headway, time-to-collision, and the safe distances of formal driving-safety models. The ring's law makes no reference to what the driver is made of.
It makes the contingency visible. My field of safe travel is carved by your stopping zone. In a line of cars each driver's lag spends the margin of the driver behind; that is what a phantom jam is.
It predicts who spends it. Gibson and Crooks predicted in 1938 that better brakes would buy nothing: the driver learns the smaller stopping zone and keeps the same relative margin. In Munich in 1981–83, taxis with anti-lock brakes had no fewer accidents than taxis without, and hidden observers saw their drivers keep shorter headways (Aschenbrenner and Biehl, 1994). Automation that adds margin is spent by whoever holds the margin.

Other candidates were considered.

Candidate	What it gets right	Why not the main concept
Autonomy	the popular frame for robotaxis	rejected; see below
Control, cybernetics (Wiener 1948: kybernētēs, the steersman)	the loops are feedback	it names the loop, not the room
Delegation (Latour)	how a program of action moves from people into speed bumps and door closers	it tells the history, not when the arrangement fails
Infrastructure (Star)	relational, and visible on breakdown	too wide to measure on a ring
Concurrency	a four-way stop is mutual exclusion, and gridlock is deadlock; Dijkstra's semaphore is named after the railway signal, the kind of signal London put up for road traffic in 1868	right for intersections, which the ring does not have; the next piece

The ring

The ring is the smallest city that still has shared margins: one lane, 22 cars, no overtaking, nothing to hit but each other. Sugiyama et al. (2008) ran it with real drivers in Nagoya, and a jam formed with no bottleneck.


Ring	230 m, 22 cars of 4.5 m, as in Sugiyama et al. (2008)
Speed a gap allows	V(s) = clamp((s − 2 m)/T, 0, 15 m/s), where T is the margin
Human	a = κ(V(s) − v) + β(v_lead − v), everything perceived one lag τ late; κ = 0.1/τ and β = 0.45/τ, near the best gains for that lag; default lag 1.0 s, margin 1.2 s; acceleration noise 0.15 m/s²
ACC	the same law with the commercial ACC gains Milanés and Shladover (2014) measured, k₁ = 0.23 s⁻², k₂ = 0.07 s⁻¹, margin 1.1 s, no lag, no noise
Calm	drives at its leader's speed smoothed over 20 s, pulled weakly toward a 2.5 s headway; lag 0.2 s
Everyone	acceleration within −8 to +2 m/s², a braking reflex on the anticipated gap, step 0.05 s

What the theory says

A driver's speed answers its leader's through a transfer function G(s). A line of cars is string stable when no disturbance grows as it passes backward, |G(iω)| ≤ 1 at every frequency. A ring has an eigenvalue wherever the product of the G around it equals 1. The theory computed these before any simulation, and an independent computer-algebra check reproduces the key numbers.

Result	Value
Smallest margin that keeps a line smooth, best possible gains	2.06 × lag
Same, for a driver who ignores closing speed	3.06 × lag
Same, for this human	2.08 × lag, at every lag from 0.2 to 1.4 s, on the ring as on a long line
Default human on the ring	waves grow at 0.062 per second (e-folding 16 s), period 15 s
ACC with no lag	smooth only at margins of 2.66 s or more; it keeps 1.1 s
Calm drivers needed among default humans	two (growth 0.062, 0.023, −0.006 per second for 0, 1, 2)

The law is proportional because rescaling time rescales lag, gains and margin together. Attending to closing speed (looming, in Lee's sense) cuts the margin a driver needs by a third.

A validation run checks that the simulation implements what the theory linearises. It nudges a noise-free ring by 10 cm and measures growth rates:

Case	Theory	Simulation, 0.01 s step	Simulation, 0.05 s step (experiments)
default human	0.0623	0.0579	0.0608
ACC, margin 1.1 s	0.1027	0.0960	0.0974
human, lag 1.0 s, margin 2.2 s	−0.0053	−0.0050	−0.0015
human, lag 0.8 s, margin 2.0 s	−0.0199	−0.0200	−0.0138
20 humans and 2 calm drivers	−0.0056	−0.0061	−0.0058

The experiments' 0.05 s step, fixed in advance, makes stable rings decay somewhat more slowly than theory. That is small against the 0.2 s tolerance in P3.

What the ring does

Space-time diagrams: 22 human drivers; the same ring with four calm drivers switched in at minute 10

On the left the jam moves backward around the ring at 10.1 km/h while every car moves forward. Over minutes 10–20 every car stops at least 21 times, for 14 s on average, so the jam belongs to no car. On the right, four calm drivers join at minute 10 and the jam dissolves within a few minutes into small ripples.

Speed spread over lag and margin, with the line margin = 2.08 × lag

Scored predictions

The predictions were fixed before the simulation existed.

ID	Prediction	Verdict	Evidence
P1	default humans stop and go within 10 minutes	held	first stop at 12–32 s in all 10 seeds
P2	the jam moves backward at 8–20 km/h, every car stops at least 5 times, no stop lasts over 30 s	failed	speed −10.1 to −10.2 km/h and at least 21 stops per car held; the longest stops lasted 34–35 s
P3	the smooth region begins within 0.2 s of 2.08 × lag at every lag	failed	only lag 0.2 s met the stop criterion; see below
P4	zero-lag ACC jams at 1.1 s and settles at 3.0 s	held	first stop at 43 s; at 3.0 s the nudge decayed from 0.056 to 0.0001 m/s with no stop
P5	calm drivers from the start: 1 does not stop the jam, 2 mostly do, 4 always do	failed	cars stopped in every seed for 0 to 4 calm drivers; contacts per 10 runs fell from 3,508 to 3
P6	calm drivers after the jam: 1 does not dissolve it, 4 do	failed	cars still stopped in every seed; speed spread fell from 4.13 to 2.91, 1.30, 0.64 and 0.42 m/s for 0 to 4 calm drivers
P7	four calm drivers raise mean speed despite their longer headway	held	2.44 → 2.72 m/s over minutes 20–30; uniform flow would give 3.30 and 2.75
P8	no contacts	failed	27,114 contacts in the P1, P5 and P6 runs

The failures fall into three groups.

The stop threshold was the wrong instrument at this density. On Sugiyama's ring a longer margin means a slower uniform flow: 1.65 m/s at 2.4 s and 1.24 m/s at 3.2 s. The margin is paid for in speed. At those speeds the 0.15 m/s² noise alone dips cars below the 0.5 m/s stop threshold with no wave at all. That sank P3, P5 and P6 as registered. The mistake is in the measurement design, not evidence about margin.
The model humans collide. With a one-second lag and no anticipation in their main law, they touch bumpers hundreds of times per run wherever waves grow. Real drivers anticipate. Treiber, Kesting and Helbing (2006) found that anticipation keeps drivers accident-free even when their reaction times exceed their headways. This model drives with its lag undiluted.
Barely stable is not smooth. Two calm drivers make the default ring linearly stable, but its slowest wave decays at only 0.006 per second. Noise keeps exciting it faster than it decays, so the ring behaves almost as if it were unstable. Stability needs margin too.

Post hoc: collisions stop where waves stop

Written after the scoring; nothing in this section was predicted. The P3 sweep, re-read with measures that do not depend on the stop threshold:

Lag (s)	Theory's smallest margin (s)	No contact in any run from (s)	Speed spread ≤ 1 m/s from (s)
0.2	0.42	0.4	0.6
0.4	0.83	0.8	1.0
0.6	1.25	1.2	1.4
0.8	1.66	1.6	2.0
1.0	2.08	2.0	2.4
1.2	2.49	none up to 3.2	2.6
1.4	2.91	none up to 3.2	2.8

For lags up to 1 s, the collisions stop at the grid point just below the theory's margin, every time. In this model, the margin that stops waves is also the margin that stops crashes.

A second sweep plots the ring against margin ÷ lag. Linear theory puts every lag's boundary at 2.08, so the curves should collapse onto one another if the nonlinear ring keeps the ratio.

Speed spread and contacts against margin ÷ lag for five lags

The collapse is partial. Contacts fall to zero at 1.9, 2.0, 1.8 and 2.0 × lag for lags of 0.4, 0.6, 0.8 and 1.0 s; at 1.2 s they fall to one to three per run by 1.4 × lag and stay there. The waves end sharply near 2 × lag for lags of 0.4 and 0.6 s, at 1.8 for 0.8 s, and gradually for longer lags. On this dense ring a long lag at twice its margin means crawling: 1.65 m/s at a lag of 1.2 s. Noise and the floor at zero speed then blur the edge.

Calm drivers switched in at minute 10: speed spread and mean speed, with uniform-flow speeds

Calm drivers help in proportion to their number. Each one costs uniform-flow speed, since the ring's gaps are shared, and each one removes more of the jam's cost than it adds. With four, the ring runs within 1% of its uniform-flow speed. The all-human ring runs 26% below its own.

Checkpoint

Question	Answer for this piece
What did the subject force to change?	The ring could not be described without seconds of lag, gains per second and seconds of margin. That is control vocabulary, which the question set out to avoid. The subject's own terms (headway, stopping zone, looming) arrived before relation or becoming. The ring's density also forced a correction to the measurement: margin is paid for in speed, which broke the stop criterion.
What does the compelling result leave unestablished?	The 2.06 × law is a theorem about linear drivers with gains matched to their lag. The simulation supports it for lags up to about 0.8 s, and for collisions up to 1 s. Nothing here measures real drivers or a city with intersections. The model humans collide; real ones rarely do.
Can a stranger enter without background?	The page shows cars on a circle; tapping one brakes it, and a jam appears and travels backward. No background is needed. It has not yet been shown to a stranger.
Can a participant change the terms?	On the page: lag, margin, number of cars, which cars are calm, ACC or human, and where to brake. A viewer cannot yet write their own driver law.
Achieved, failed and open, at one scale	Achieved: the linear law and its independent symbolic check, validation of the simulation against theory, P1, P4 and P7, and the page. Failed: P2 (stop durations), P3, P5 and P6 (the stop criterion at low speed), and P8 (the model humans collide). Open: an anticipating human, intersections, a fair re-test of P3, and reception.

Sources

Sugiyama, Y. et al. (2008). Traffic jams without bottlenecks. New Journal of Physics 10, 033001.
Stern, R. E. et al. (2018). Dissipation of stop-and-go waves via control of autonomous vehicles: field experiments. Transportation Research Part C 89, 205–221.
Gunter, G. et al. (2021). Are commercially implemented adaptive cruise control systems string stable? IEEE Transactions on Intelligent Transportation Systems 22(11), 6992–7003.
Milanés, V. and Shladover, S. E. (2014). Modeling cooperative and autonomous adaptive cruise control dynamic responses using experimental data. Transportation Research Part C 48, 285–300.
Gibson, J. J. and Crooks, L. E. (1938). A theoretical field-analysis of automobile-driving. American Journal of Psychology 51, 453–471.
Lee, D. N. (1976). A theory of visual control of braking based on information about time-to-collision. Perception 5, 437–459.
Treiber, M., Kesting, A. and Helbing, D. (2006). Delays, inaccuracies and anticipation in microscopic traffic models. Physica A 360, 71–88.
Bando, M. et al. (1995). Dynamical model of traffic congestion and numerical simulation. Physical Review E 51, 1035.
Aschenbrenner, M. and Biehl, B. (1994). Improved safety through improved technical measures? In Trimpop and Wilde (eds.), Challenges to Accident Prevention.
SAE J3016 (2021), section 7.1.1, "Autonomous".
Aristotle, Physics II.6, trans. Hardie and Gaye.
Merleau-Ponty, M. (1945). Phenomenology of Perception, Part One, chapter 3: a habitual driver "can 'get through' without comparing the width of the opening with that of the wings".
Wiener, N. (1948). Cybernetics.
EPA, basic tire information.

Margin?

The question?

What is actually in the car?

What automation is?

Where the automation is in this ride?

The proposal: margin?

Rejected: autonomy?

The ring?

The consequence?

Limit?

What this says about "what is a computer"?

Checkpoint?

Sources?

Margin

The question

What is actually in the car

What automation is

Where the automation is in this ride

The proposal: margin

Rejected: autonomy

The ring

The consequence

Limit

What this says about "what is a computer"

Checkpoint

Sources