← experiments

29 October 2026 · Day 29 · Built with Claude

Between the looks

A note, drawn as a turning arm, plays a slow tune. An observer looks at it now and then, and between its looks it knows nothing. Change how often it looks, and whether it sees the whole plane or only a shadow, and watch smooth motion turn into jumps and phantoms.

The world from above. Three arms turn together, one per harmonic; the tip is the note. The line beneath is its shadow. The dashed arm is where the observer thinks the main arm is.
  • the world, dimmed in the gaps
  • a look
  • what it holds between looks
  • its smoothest guess

 

What it can see
Sound
Sound off

Headphones help: in 2D, one dimension goes to each ear.

Try this

  1. Start the sound, then press "Hear what it gets". At 24 looks per turn the tune is all there, with a grainy edge from the jumps between looks.
  2. Try 2.2. The low notes come through, and the high notes fold back into other notes, so the observer hears a different tune.
  3. Try 1.5 and watch the dashed arm turn backwards, like a wagon wheel in a film. Try 1 and it stands still.
  4. Switch to "Only a shadow". However often it looks, it can no longer tell which way round the arm turns.
  5. Turn "How finely it tells values apart" down to two or three steps. Smooth change becomes jumps between a few allowed states.

The Nyquist rate

To follow a turning thing you have to look at least twice per turn. Look less often and the looks fit a slower turn just as well, or a backwards one, and nothing in the record says which. Harry Nyquist set out the limit for telegraphy in 1928 and Claude Shannon made it general in 1949. Between looks the observer has nothing, so the most it can do is hold the last value it saw, or draw the smoothest curve through its looks. Below the limit, that smooth curve is a phantom.

Dimensions matter as well as rate. A turning arm seen edge-on is a back-and-forth on a line. Turning one way or the other casts the same shadow, so an observer with one dimension can't tell them apart however often it looks. Add the second dimension and the direction comes back.

Where the idea comes from

Mark Burgess's Smart Spacetime (2019) ties what an observer can see to the scale it observes at, through the Nyquist rate, and suggests some quantum strangeness may come from observing at a scale, and in too few dimensions, to see the continuum. In Information and Causality in Promise Theory (2020) he defines a fast enough observer by the Shannon–Nyquist sampling law, and notes that this approximation fails at computational and quantum scales.

This page is a lens, not physics. It shows only that an observer's scale, in rate, in value and in dimensions, decides whether a smooth world looks smooth, jumpy or haunted.