A display's resolution is a number everybody quotes. The resolution of the channel in the other direction — you, pressing things — has a number too, and Fitts's law puts it in the same unit: bits. Here they are side by side. The surprise, for me, was which device comes out worst.
The time budget only moves the cursor rows. A fingertip's target width is anatomical — spending longer does not make your finger narrower, which is the whole point below.
| surface | display cells | input cells | display ÷ input | input width |
|---|
Fitts's law gives a slope: spend more time, hit a smaller target. For a cursor that holds until you reach pixel pitch. For a finger it stops meaning anything once the predicted width drops below the finger — the binding constraint changes from control bandwidth to contact area and occlusion. The dashed line is where the model stops describing a hand.
Machine → you: · you → machine:
Ratio . Measured throughputs: mouse 4.5 bits/s (accepted range 3.7–4.9), finger on a phone 6.95 bits/s (MacKenzie, 16 participants), touchpad ~2 bits/s. Keyboard is computed from typing speed, below.
| channel | bits/s | vs mouse | what it measures |
|---|
Two honest numbers for a keyboard, measuring
different things. Which-key is what the machine receives: one of ~50 reachable
keys, log₂(50) ≈ 5.64 bits per keystroke. English entropy is what
you actually conveyed — Shannon's estimate of 1.0–1.5 bits per character. The first is
a channel rate; the second is an information rate. Both are real, and the gap between
them is redundancy.
The thing I didn't expect. The newest surface here is the worst at this. A phone shows ~3 million pixels and offers about places a finger can reliably land — a ratio in the tens of thousands. A twenty-year-old desktop with a mouse does far better, because a cursor's precision is a time budget rather than a body part. Touch didn't make input finer; it made input anatomical, and anatomy doesn't negotiate.
And the one surface where display resolution still equals input resolution, exactly, is the one under your hands. A keyboard is 104 legends and 104 switches at 19.05 mm pitch — the same square doing both jobs, which is what a mosaic mimic panel was. It is also the widest channel we have into a machine. Those two facts are not a coincidence.
Assumptions and limits are in the post. In short: cell counts are naïve floor division and ignore bezels and non-grid keys; "input cells" for a cursor assumes a 2 mm practical pitch at a 1-second budget and moves with the slider; display bandwidth is raw frame bandwidth, which is an upper bound on what the panel pushes and not a claim about what your visual system receives; Fitts throughputs are device-level means from the HCI literature, not properties of any individual.