Fitts's Law¶

Predict how long an aimed reach takes as a logarithmic function of target distance over target width — MT = a + b·log₂(2D/W) — treating the movement as transmission across a finite-throughput motor channel.

Core Idea¶

Fitts's law (Paul Fitts, 1954) is the empirical regularity that the time required for a person to move an effector to acquire a target is a logarithmic function of the ratio of target distance to target width: MT = a + b · log₂(2D/W), where D is centre-to-centre distance from start to target, W is the width of the target (the spatial tolerance for acquisition), a is an empirically fit intercept capturing response-initiation overhead, and b is the slope capturing the inverse throughput of the movement channel in bits per second. The quantity log₂(2D/W) is the index of difficulty (ID); the inverse 1/b is the index of performance — the information-theoretic throughput of the targeting channel.

The structural commitment is that the speed-accuracy trade-off in aimed movement is logarithmic, not linear: doubling distance adds a constant increment of time rather than a proportional one, and doubling target width reduces movement time by a constant amount rather than halving it. This shape, and its derivation from Shannon channel-capacity theory treating the movement as a transmission of spatial information across a noisy motor channel, provide both the predictive law and the theoretical grounding. The law has been validated across effectors (finger, hand, arm, head, foot, eye), modalities (mouse, touchscreen, stylus, VR controller, eye tracker), and populations with small adjustments to a and b. In human-computer interaction it underwrites design rules such as placing high-frequency targets at screen edges (infinite effective width under cursor-stop behaviour), enlarging small targets before increasing proximity, and comparing input devices by their Fitts throughput in bits per second.

Structural Signature¶

Sig role-phrases:

the effector — the finger, hand, arm, head, foot, or eye that moves from a start position to acquire the target
the distance D — the centre-to-centre separation between start and target
the target width W — the spatial tolerance allowed for acquisition
the index of difficulty — ID = log₂(2D/W), the single scalar that fuses distance and tolerance into one difficulty axis
the movement-time law — MT = a + b·ID, with intercept a (response-initiation overhead) and slope b (inverse channel throughput) fit per effector/modality
the logarithmic shape — the engineered guarantee that the speed-accuracy trade-off is logarithmic, not linear: each doubling of distance adds, and of width subtracts, a constant time (diminishing returns to enlargement; edge-parking → infinite effective width)
the channel-capacity grounding — derivation from Shannon throughput treating the reach as transmission across a noisy motor channel, yielding 1/b as a bits-per-second comparison currency
the aimed-movement regime boundary — the form holds only for a single ballistic-plus-corrective reach to one tolerance-bounded target; choosing among many options is a different law (Hick/Pirolli), and the logarithmic floor is not trainable away

What It Is Not¶

Not a linear speed-accuracy trade-off. The relation is logarithmic in distance over width: doubling distance adds a constant time and doubling width subtracts a constant, not a proportion. A button twice as wide is not twice as easy, and the returns to enlargement diminish — which is exactly why parking a target against a screen edge (effective width → infinity) beats any finite enlargement.
Not a law of choosing among options. Fitts's law governs a single aimed reach to one tolerance-bounded target; a task whose difficulty comes from selecting among many options scales with the number of choices (Hick's law) or information-foraging structure (Pirolli), a different functional form. Applying the index of difficulty to search or menu choice is a category error, not a generalization.
Not a causal mechanism. It is a measured empirical regularity — a functional form with two fitted constants — not a causal account of how movement is generated. The Shannon channel-capacity derivation explains why the logarithm holds but the law itself predicts time; it does not name a cause to intervene on beyond the geometry and the constants.
Not a ceiling that practice removes. Training lowers the slope b somewhat but the logarithmic floor remains: no amount of skill makes a far, small target as fast as a near, large one. The trade-off is a physical-informational limit on aimed movement, not a learnable-away inefficiency.
Not a pair of universal constants. The intercept a (response-initiation overhead) and slope b (inverse channel throughput) are fit per effector and modality — a mouse, a stylus, an eye tracker each have their own. A Fitts fit characterizes one device-and-effector channel; the constants are not a fixed property of the law transportable across modalities.
Not a general throughput figure. The index of performance 1/b is a comparison currency only among targeting channels; read as generic "bits per second" detached from aimed movement it loses the precondition that gives it meaning. It ranks pointing devices, not arbitrary information-processing rates.

Scope of Application¶

Because Fitts's law is a measured functional law rather than a causal mechanism, it applies wherever its one precondition holds — a single aimed effector-to-target movement, a ballistic-plus-corrective reach to acquire a tolerance-bounded spatial target — and the fields below are real uses of the identical law, the constants a and b re-fit but the logarithmic form intact, not analogies; it ceases to apply (to Hick/Pirolli choice-and-search laws) when difficulty comes from selecting among many options rather than acquiring one located target.

Human-computer interaction — the home of its design use: predicting pointing time for mice, trackpads, touchscreens, styli, VR controllers, and eye trackers, underwriting button sizing, menu design, and edge-target placement.
Motor-control psychology — the founding quantitative model of the speed-accuracy trade-off in voluntary aimed movement, validated across effectors (finger, hand, arm, head, foot, eye).
Robotics and teleoperation — end-effector positioning and haptic-interface design, where the same throughput law governs aimed reaches.
Sport science — aiming and reaching tasks showing the identical logarithmic trade-off with practitioner-specific constants.
Accessibility engineering — a motor impairment surfacing as an elevated slope b, with the corrective inflating target width W to hold b·ID within tolerance.
Augmentative and alternative communication — scanning-and-selection methods optimized against Fitts-style movement-time predictions.

Clarity¶

Before Fitts's law the speed-accuracy trade-off in aimed movement was a qualitative observation — small far targets are "harder" to hit — with no way to say how much harder, or to compare one design against another. Naming the law makes the difficulty measurable and collapses the two relevant variables into a single index: distance and tolerance stop being separate knobs and become one quantity, log₂(2D/W), so two very different layouts that share an index of difficulty are predicted to cost the same movement time. That lets a designer ask the sharp question — what is this target's ID, and which term is driving it? — and reason about the trade-off the geometry actually imposes rather than guessing.

The law's most clarifying move is fixing the shape of the trade-off as logarithmic, not linear, which corrects an intuition that quietly misleads interface design: that a button twice as wide is twice as easy, or a target twice as far is twice as slow. Because doubling distance adds a constant time and doubling width subtracts a constant time, the gains from enlarging a target diminish, and the largest gain of all comes from pushing effective width to infinity by parking a target against a screen edge — a consequence that is invisible without the logarithm but obvious once it is named. By recasting the movement as transmission across a channel of finite throughput, the law also supplies a common currency: the index of performance, 1/b in bits per second, lets a mouse, a touchscreen, a stylus, and an eye tracker be compared on one scale, separating the device's channel capacity (the slope b) from fixed response-initiation overhead (the intercept a) — two things a raw movement time silently confounds.

Manages Complexity¶

The space a motor-control researcher or interface designer must reason about is, on its face, enormous: every combination of target distance and target width is a distinct pointing task, every effector (finger, hand, arm, head, foot, eye) a distinct motor system, every modality (mouse, touchscreen, stylus, VR controller, eye tracker) a distinct channel, and every population a distinct profile — a high-dimensional grid of conditions, each of which could in principle demand its own measurement of how long acquisition takes. Fitts's law collapses that grid along three axes at once. First, it collapses the two geometric variables: distance and width stop being independent knobs and fuse into a single scalar, the index of difficulty log₂(2D/W), so the infinite plane of (D, W) pairs is reduced to a one-dimensional difficulty axis along which movement time rises by a fixed functional form. Two layouts that look nothing alike but share an ID are predicted to cost the same time, so the designer reads cost off the index rather than re-measuring each layout. Second, it collapses the effector-and-modality axis onto two physically interpretable scalars: once a device's intercept a (response-initiation overhead) and slope b (inverse channel throughput) are fit, the whole device is characterized — its entire performance across all distances and widths is read off MT = a + b·ID, and a brand-new layout's movement time is computed, not measured. Third, by recasting the movement as transmission across a channel of finite capacity, it puts every effector and every modality on a single comparison currency, the index of performance 1/b in bits per second, so a mouse, a stylus, and an eye tracker — which share no obvious common scale — are ranked on one number, with the fixed overhead a held cleanly apart from the throughput b that a raw movement time would silently confound. What the analyst tracks shrinks to three things: the index of difficulty the geometry imposes, the device's two constants, and which of the two terms — fixed overhead or per-bit slope — dominates a given case. From those, the qualitative design conclusions follow without further data: because the trade-off is logarithmic rather than linear, the returns to enlarging a target diminish (each doubling of width subtracts the same constant, not a proportion), so the branch structure tells the designer that enlarging a small target buys more than enlarging an already-large one, that shortening distance and widening tolerance are substitutable along the same ID axis, and that the limiting move — parking a target against a screen edge so its effective width goes to infinity and its ID contribution collapses — yields the largest gain available. A sprawling per-condition timing problem is thus reduced to: compute the index of difficulty, read movement time off two constants, and locate the case on the logarithmic curve to know where the leverage lies.

Abstract Reasoning¶

Fitts's law licenses a tight family of quantitative inferences about aimed movement, each running through the index of difficulty and the two device constants.

The predictive move is the most direct: given a layout's geometry (distance D, width W) and a device's fitted intercept a and slope b, the analyst computes the expected movement time before anyone moves — MT = a + b·log₂(2D/W) — and can rank two unbuilt layouts by computing their indices of difficulty. Because the relation is an equation with physically interpretable constants, the reasoning is forward and exact rather than heuristic: a 50-pixel target at 500 pixels and a 100-pixel target at 1000 pixels share an ID and are predicted to cost the same time, a prediction that holds across layouts that look nothing alike. The order-of-magnitude prediction is also qualitative and reliable: enlarging an already-large target buys little, because each doubling of width removes the same constant, so the marginal return to width is decreasing along the difficulty axis.

The interventionist move reads the leverage point off which term dominates the index. To make a target faster the designer can shorten distance, widen tolerance, or — the limiting and most powerful intervention — drive effective width to infinity by parking the target against a screen edge so the cursor stops there regardless of overshoot, collapsing that target's ID contribution entirely. The law predicts the size of each intervention's payoff, not just its sign: it says the edge placement beats any finite enlargement, that distance and width are substitutable along the same ID axis (so a given time saving can be bought either way), and that once a target is large the cheaper remaining gains lie in cutting travel, not in further enlargement. Each design change is thus a prediction about the resulting movement time, falsifiable by measurement.

The diagnostic move runs from observed timing data back to the two constants, and from the constants to the state of the channel. By fitting a and b to a person's or device's pointing data, the analyst separates two things a raw movement time confounds: fixed response-initiation overhead (the intercept a) and per-bit channel throughput (the slope b). An elevated b is read as a lower-capacity targeting channel — the inference that underwrites accessibility engineering, where a motor impairment manifests as a steeper slope, and the corrective is to inflate W to keep the product b·ID within tolerable bounds rather than to attack the overhead. A device with low b but high a is diagnosed as fast-per-bit but slow-to-start, pointing the fix at initiation latency, not at the movement itself. The index of performance 1/b becomes a comparison currency: a mouse, a stylus, and an eye tracker are ranked on one number, and a claim that one device is "better" is decomposed into whether it has higher throughput or merely lower fixed overhead.

The boundary-drawing move keeps these inferences inside the regime where the logarithmic form holds. The law governs aimed effector-to-target movement — a single ballistic-plus-corrective reach to acquire a spatial target of defined tolerance — and the reasoning collapses outside it: a task whose difficulty comes from choosing among many options rather than acquiring one located target is not a Fitts task (its time scales with the number of choices, a different functional form), and reaching for the index of difficulty there is a category error. The boundary also bounds the training inference: practice lowers b somewhat but the logarithmic ceiling remains, so the law predicts that no amount of skill makes a far, small target as fast as a near, large one — the trade-off is a physical-informational floor on aimed movement, not a learnable-away inefficiency.

Knowledge Transfer¶

Fitts's law is a quantitative law — a measured functional form with two physically interpretable constants — rather than a causal mechanism, so the usual "mechanism within, metaphor beyond" framing does not apply to it. The right question is instead instrument-reach versus over-reading: the construct transfers literally wherever its precondition holds — a single aimed effector-to-target movement, a ballistic-plus-corrective reach to acquire a spatial target of defined tolerance — and ceases to apply, not by weakening into analogy, but by the functional form simply changing when that precondition fails. Within that precondition its reach is exceptionally clean and genuinely cross-substrate, because the substrate is always the same kind of thing: an effector traversing distance to a tolerance-bounded target. In human-computer interaction it predicts pointing time for mice, trackpads, touchscreens, styli, VR controllers, and eye trackers, and underwrites menu design, button sizing, and edge-target placement. In motor-control psychology it is the founding model of the speed-accuracy trade-off in voluntary aimed movement. In robotics and teleoperation it governs end-effector positioning and haptic-interface design. In sport science aiming and reaching tasks show the same logarithmic trade-off with practitioner-specific constants. In accessibility engineering a motor impairment shows up as an elevated slope b, and the corrective inflates W to hold b·ID in tolerance. In augmentative communication scanning-and-selection methods are optimized against Fitts-style time predictions. Crucially, these are not three structurally distinct domains but one substrate type — aimed movement and its digital extensions — across which the same equation holds with only a and b re-fit, which is exactly why the transfer is literal rather than analogical: the units change, the logarithm does not.

The boundary to mark, then, is over-reading in two forms. The first is applying the law outside aimed movement. A task whose difficulty comes from choosing among many options rather than acquiring one located target is not a Fitts task — its time scales with the number of choices (Hick's law) or with information-foraging structure (Pirolli), a different functional form — so reaching for the index of difficulty there is a category error, not a generalization; proposed extensions to "search difficulty" quietly replace the distance-tolerance logarithm with a different shape and are no longer Fitts's law. The second form of over-reading is mistaking the index of performance for an unbounded figure of merit: 1/b is a comparison currency only among targeting channels, and reading it as general "throughput" detached from aimed movement strips the precondition that gives it meaning. Where a genuinely cross-domain principle is present, it is not Fitts's law itself but the more general pattern it instantiates: the information-theoretic ceiling on a noisy channel, information_theory_channel_capacity, of which aimed motor movement is one beautiful instance, and the abstract power_law/log-scaling family of which this is one specific log relation. The honest division is therefore: the law transfers literally across every aimed-movement substrate, constants re-fit and form intact; the channel-capacity logic that explains why it holds is the general prime's to carry; and invoking "Fitts's law" for choice, search, or generic difficulty is over-reading a targeting law past the precondition that makes it true (see Structural Core vs. Domain Accent).

Examples¶

Canonical¶

Work a concrete prediction through the equation. A user must move a cursor to a target 500 pixels away that is 50 pixels wide. The index of difficulty is ID = log₂(2D/W) = log₂(2·500/50) = log₂(20) ≈ 4.32 bits. If the device has been fitted with intercept a = 200 ms and slope b = 100 ms/bit, the predicted movement time is MT = a + b·ID = 200 + 100 × 4.32 ≈ 632 ms. Now take a completely different layout — a 100-pixel target at 1000 pixels: 2D/W = 2·1000/100 = 20 again, so ID ≈ 4.32 and the predicted time is the same 632 ms, even though the two layouts look nothing alike. Doubling the distance to 1000 with the original 50-pixel target instead raises ID to log₂(40) ≈ 5.32, adding exactly one bit — 100 ms — not doubling the time.

Mapped back: The 500 px and 50 px are the distance D and the target width W; fusing them into log₂(20) ≈ 4.32 is the index of difficulty. Computing 632 ms is the movement-time law MT = a + b·ID with its two constants. That doubling distance adds a fixed 100 ms rather than doubling the time is the logarithmic shape — the constant-increment trade-off the law guarantees.

Applied / In Practice¶

Fitts's law directly shapes real interface design. The classic application is edge and corner placement: because a screen edge stops the cursor regardless of overshoot, a target parked against it has effectively infinite width, collapsing its ID contribution and making it maximally fast to hit. This is why the macOS global menu bar sits flush against the top edge of the screen (you can fling the cursor upward without overshooting), and why screen corners — infinitely wide in two directions at once — are prime real estate for high-value controls like the Start button or hot corners. Designers also apply the diminishing-returns lesson: enlarging a tiny button yields a large speed gain, while enlarging an already-large one yields little, so effort goes to the small, frequently-used targets and to shortening travel distance rather than inflating big targets further.

Mapped back: The cursor-stopping screen edge driving effective width to infinity is the logarithmic shape taken to its limit — the edge-parking move that collapses a target's ID. Putting the menu bar and corner controls there exploits exactly that. Prioritizing enlargement of small over large targets applies the diminishing-returns consequence of the index of difficulty: each doubling of the target width W subtracts the same constant, so the marginal payoff shrinks as targets grow.

Structural Tensions¶

T1: Two variables fused into one index versus the mechanism the fusion hides (equal ID is not equal in all respects). Collapsing distance and tolerance into a single scalar, log₂(2D/W), is the law's master compression: two layouts sharing an ID are predicted to cost the same movement time, so cost is read off one number rather than re-measured. But the fusion treats a far-large target and a near-small target as interchangeable when they can differ in what actually happens — error type (overshoot versus fine-correction), fatigue, submovement structure, and the kind of accuracy demand. The tension is that the index's predictive economy comes from discarding the distinct physical situations behind a given difficulty, so equal-ID does not mean equal-in-every-way, and a designer optimizing purely on ID can miss differences (error cost, effort) the scalar was built to suppress. Diagnostic: Is movement time the only quantity that matters here, or do two equal-ID layouts differ in error type, fatigue, or accuracy demand that the fused index hides?

T2: A sharp regime boundary versus the pull to over-extend (index of difficulty as category error). Fitts's law is exact within a well-defined regime — a single aimed, ballistic-plus-corrective reach to one tolerance-bounded target — and that sharp precondition is a strength: it says precisely where the logarithm holds. But the same crispness makes misapplication easy, because "difficulty" feels general and search, menu choice, and decision tasks look like difficulty too. Applying the index of difficulty to a task whose cost comes from choosing among many options is a category error — its time follows Hick's law or information-foraging structure, a different functional form — yet the law's success invites exactly that over-reach. The tension is that the boundary which guarantees the law's validity is the boundary practitioners are most tempted to cross, and proposed "search difficulty" extensions quietly swap the distance-tolerance logarithm for another shape while keeping the name. Diagnostic: Does the difficulty here come from acquiring one located target (Fitts) or from selecting among many options (Hick/Pirolli) — and is the index of difficulty being applied across that line?

T3: An informational floor versus what practice can move (the ceiling that skill cannot remove but does lower). The law frames the speed-accuracy trade-off as a physical-informational floor: no amount of skill makes a far, small target as fast as a near, large one. That is a genuine and useful invariant — it forecloses the fantasy that training away the trade-off is possible. But practice does lower the slope b, so the channel's throughput is partly learnable even though the logarithmic form is not, and treating the whole trade-off as immovable can under-credit the real gains skill and device improvement buy. The tension is that the law is simultaneously a hard floor (the shape is fixed) and a movable target (the constants are not), so "it's a fundamental limit" and "it can be improved" are both true of different parts of the equation, and conflating them either romanticizes practice or dismisses it. Diagnostic: Is the concern here the fixed logarithmic floor (not trainable away) or the fitted slope b (which practice and better devices genuinely lower) — and is the invariant being read onto the part that is actually movable?

T4: The channel-capacity grounding versus alternative accounts of why it holds (one interpretation, not the mechanism). The Shannon channel-capacity derivation gives Fitts's law a satisfying theoretical grounding — the reach as transmission across a noisy motor channel — and yields the bits-per-second currency 1/b. But the derivation is one interpretation among several that fit the same data: optimized-submovement models and stochastic optimal-control accounts reproduce the logarithmic form without invoking information transmission. The tension is that the elegant channel-capacity story explains why the law holds only if one adopts a particular theoretical frame, so the information-theoretic reading is a chosen lens, not an established mechanism, and treating 1/b as literal "channel throughput" imports a commitment the bare empirical regularity does not require. Diagnostic: Is the information-channel interpretation being used as a convenient framing for the fitted constants, or asserted as the mechanism — when submovement and optimal-control models explain the same logarithm differently?

T5: Forward exactness versus the empirical calibration it presupposes (compute-don't-measure only after measuring). The law's headline power is prediction: given geometry and a device's a and b, compute a novel layout's movement time without testing it. But that forward exactness is purchased by a prior empirical step — a and b must be fit per effector, modality, and population, since they are not universal constants — so "compute, don't measure" holds only once the constants have been measured for the specific channel. The tension is that the law presents as a predictive equation while depending on calibration data that a new device, effector, or user group does not yet have, so its exactness is conditional on a fitting exercise the equation's clean form conceals. Diagnostic: Are the a and b in this prediction actually fit for the specific device, effector, and population, or is the equation being applied with borrowed constants that may not characterize this channel?

T6: Autonomy versus reduction (a measured targeting law or an instance of channel capacity and log-scaling). Fitts's law is a specific, calibrated functional form that transfers literally — constants re-fit, logarithm intact — across every aimed-movement substrate (mice, styli, eye trackers, robotic effectors, impaired motor systems), which is one substrate type, not many domains. But the genuinely cross-domain content is not the law itself: it is the more general pattern it instantiates — the information-theoretic ceiling on a noisy channel, information_theory_channel_capacity, of which aimed movement is one beautiful instance, within the broader power_law/log-scaling family. The channel-capacity logic that explains why the law holds is the prime's to carry; invoking "Fitts's law" for choice, search, or generic difficulty over-reads a targeting law past its precondition. Diagnostic: Resolve toward information_theory_channel_capacity / log-scaling when carrying the noisy-channel-ceiling idea beyond aimed movement; toward Fitts's law when a single effector-to-target reach with a defined tolerance is what is being timed.

Structural–Framed Character¶

Fitts's law sits at mixed-structural on the structural–framed spectrum: a genuine, evaluatively neutral empirical law about a natural regularity of the human motor system, transferring literally across its substrate, held off the pole only by being pinned to the aimed-movement precondition and its geometry-and-constants vocabulary. Four criteria point structural, and strongly. Its evaluative weight is nil: MT = a + b·log₂(2D/W) predicts a time; it praises and blames nothing, and even a "high index of difficulty" is a neutral geometric fact, not a defect. Its institutional origin is none: it is an empirical regularity of aimed movement discovered by Fitts, not an artifact of any agency, survey, or convention — the logarithm holds because of how the noisy motor channel behaves, whether or not anyone fits its constants. And it is not human-practice-bound in the constituting sense: while it concerns human effectors (and their digital extensions), the trade-off is a physical-informational property of the motor channel that obtains in any aimed reach, observer-free, not a norm or a designed practice that dissolves when withdrawn. Within its precondition cross-domain reuse is the strongest form of recognition there is — literal identity: the same equation, constants merely re-fit, holds across HCI, motor psychology, robotics, sport science, accessibility, and AAC, which the entry stresses are "one substrate type, not many domains."

What holds it off the structural pole is vocab-travels and the sharp precondition boundary. The operative vocabulary — index of difficulty, effector-to-target reach, target width/tolerance, ballistic-plus-corrective movement, index of performance — presupposes a single aimed movement to one tolerance-bounded target, and the law does not weaken into analogy so much as simply stop being true off that precondition (choice and search obey Hick/Pirolli, a different functional form); reaching for the index of difficulty there is a category error, not a generalization. So on import-vs-recognize the honest reading is instrument-reach within aimed movement and over-reading beyond it.

The portable structural skeleton is genuinely a related pair, and the entry distinguishes them: the information-theoretic ceiling on a noisy channel (information_theory_channel_capacity), which grounds why the logarithm holds and supplies the bits-per-second currency, together with the broader log-scaling / power_law family that names the functional shape. Those are what carry beyond aimed movement, not "Fitts's law": aimed motor movement is "one beautiful instance" of channel capacity, and the cross-domain reach belongs to that prime and the log-scaling family, while the effector geometry, the index of difficulty, the device constants, and the edge-parking design corollaries stay home as motor-control accent. Its character: an evaluatively neutral, institution-free empirical law about a natural motor-channel regularity whose structural credentials are strong and whose within-substrate transfer is literal, but whose content is welded to the aimed-movement precondition, so it travels beyond that substrate only as the channel-capacity and log-scaling patterns it instantiates — mixed-structural, a canonical worked instance rather than a free-floating cross-domain prime.

Structural Core vs. Domain Accent¶

This section decides why Fitts's law is a domain-specific abstraction and not a prime — and the skeleton here is genuinely a related pair, so being exact about the two portable parts matters.

What is skeletal (could lift toward a cross-domain prime). Strip the motor geometry and two related portable structures survive. The first and grounding one is the information-theoretic ceiling on a noisy channel: a system that transmits information across a capacity-limited, noisy channel pays a throughput cost that grows with the precision demanded, so time-to-transmit scales with the log of the signal-to-tolerance ratio. That is information_theory_channel_capacity, of which aimed motor movement is one beautiful instance, and it supplies the bits-per-second comparison currency. The second is the functional shape — a power_law / log-scaling relation in which each doubling of a ratio adds a constant increment rather than a proportion. Both are genuinely substrate-portable, and both are what Fitts's law instantiates from above. That channel-capacity-plus-log-scaling pair is the core Fitts's law shares, not what makes it distinctive.

What is domain-bound. What makes this specifically Fitts's law is aimed-movement furniture and none of it survives extraction. Its worked content requires a single ballistic-plus-corrective reach: the effector (finger, hand, eye, robotic end-effector) traversing a distance D to a tolerance-bounded target of width W, the index of difficulty log₂(2D/W), the movement-time law MT = a + b·ID with its per-effector/per-modality constants, the index of performance 1/b, and the design corollaries (edge-parking to infinite effective width, diminishing returns to enlargement). The empirical cases (the 632 ms cursor prediction, the macOS menu bar and screen corners) are drawn from it. The decisive test is unusually sharp: the law does not weaken into analogy off its precondition — it simply stops being true. A task whose difficulty comes from choosing among many options rather than acquiring one located target obeys Hick's or Pirolli's law, a different functional form, so reaching for the index of difficulty there is a category error, not a generalization; and reading 1/b as generic "throughput" detached from targeting strips the precondition that gives it meaning. The effector geometry, the index of difficulty, and the device constants are the accent, and they stay home.

Why this does not clear the prime bar. A prime is a relational structure whose vocabulary travels and whose cross-domain transfer is recognition of the same mechanism, not analogy — and Fitts's law is a rare entry whose within-substrate transfer is literal identity rather than mechanism-recognition-across-different-substrates. Within aimed movement it moves as the same equation, constants merely re-fit, across HCI, motor-control psychology, robotics and teleoperation, sport science, accessibility engineering, and AAC — which are one substrate type (aimed movement and its digital extensions), not many domains. Beyond that substrate the law does not travel at all: choice and search obey different laws, and invoking "Fitts's law" for generic difficulty is over-reading. What does travel is not the law but the more general patterns it instantiates — information_theory_channel_capacity (carrying the why, the noisy-channel ceiling) and the power_law/log-scaling family (carrying the shape). So when the bare structural lesson is needed elsewhere — a noisy capacity-limited channel imposes a logarithmic cost for precision — it is already carried, in general form, by those parents. The cross-domain reach belongs to them; Fitts's law is the canonical aimed-movement worked instance, whose geometry-and-constants apparatus should stay home rather than a free-floating prime.

Relationships to Other Abstractions¶

Current abstraction Fitts's Law Domain-specific

Parents (1) — more general patterns this builds on

Fitts's Law is a decomposition of Channel Capacity Prime

Fitts's Law is Channel Capacity applied to aimed movement, treating target acquisition as transmission of spatial information through a noisy finite-throughput motor channel.

Hierarchy path (1) — routes to 1 parentless root

Fitts's Law → Channel Capacity

Not to Be Confused With¶

Hick–Hyman law. Hick's law predicts choice-reaction time as a logarithmic function of the number of alternatives one must select among; Fitts's law predicts movement time for acquiring one located target of known distance and tolerance. Both are logarithmic, which invites the conflation, but the index of difficulty log₂(2D/W) is defined on target geometry, not on option count — applying it to menu or choice tasks is a category error, not a generalization. Tell: does the difficulty come from where a single target sits (Fitts) or from how many options must be chosen between (Hick)?
Information-foraging / Pirolli search laws. These govern the time and cost of searching through structured information to locate something, scaling with foraging structure (scent, patch layout) rather than with a distance-to-tolerance ratio. Like Hick's law they concern finding-among-many, not reaching-to-one, and carry a different functional form. Tell: is the effector already aimed at a known target and merely traversing to it (Fitts), or is the task to find the target amid alternatives first (foraging/search)?
The steering law (movement along a constrained path). This governs the time to move an effector through a bounded path or tunnel — a continuous accuracy constraint held over the whole trajectory — whereas Fitts's law governs a single ballistic-plus-corrective reach to a target constrained only at its endpoint. The precondition differs: pointing to one tolerance-bounded location versus tracing a tolerance-bounded corridor. Tell: is tolerance enforced only where the movement ends (Fitts) or continuously along the way (steering)?
information_theory_channel_capacity (the parent). The substrate-neutral ceiling on a noisy, capacity-limited channel — the logic that explains why Fitts's logarithm holds and supplies the bits-per-second currency 1/b — not a peer. Aimed motor movement is one instance of it, and the channel-capacity idea is what actually travels beyond aimed movement. Tell: if the claim is about a noisy channel's throughput cost for precision in the abstract (any substrate), it belongs to the parent; if it is about an effector timed reaching a target, it is Fitts's instantiation. (Treated fully in the sections above.)
The power_law / log-scaling family (the shape parent). The general family of relations in which each doubling of a ratio adds a constant increment — the functional shape Fitts's law wears — as against Fitts's specific, calibrated claim that aimed-movement time takes that shape in target distance over width. Tell: are you naming the bare log/power form that recurs across countless unrelated quantities (the family), or the specific motor law with fitted a and b that instantiates it for reaching (Fitts)?

Neighborhood in Abstraction Space¶

Fitts's Law sits in a sparse region of the domain-specific corpus (68^th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.

Family — Psychophysical Laws of Perception (10 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-07-12