// instruments · the jitter
the jitter
A trace that looks like thermal noise, and whose variance reads its temperature. The catch: this jiggle is not random. It is a fixed sum of 128 hidden oscillators, deterministic and reproducible. Reseed it and it comes back byte-identical; step the clock backward and it retraces. Yet turn the temperature up and the spread widens exactly in proportion — while the mean stays pinned at zero. The signal carries no temperature. The spread does.
mean V
0.000
std dev
0.00
measured variance
0.0
temperature from variance
0 K
slider T
500 K
clock t
0.00 s
Move T and watch the two readouts diverge in behaviour: the mean hovers at zero for every setting, while the measured variance — and the temperature recovered from it — tracks the slider. You read the temperature off the spread alone. The mean gives you nothing.
reseed — identical every time. the jiggle is fixed, not random. temperature still reads off the spread. Freeze, then step back and forward: the trace retraces exactly, because the clock is the only state and the signal is a pure function of it.
The reveal draws five of the 128 fixed sines that add up to the trace. Each is a clean, periodic oscillator with a fixed frequency and phase. Their sum is what looks like noise. Determinism is underneath the whole way down — “random” here is a description of the aggregate, not a fact about the mechanism.
// the point
temperature is in the fluctuation, not the signal. the mean tells you nothing; the variance tells you T.
This is the idea behind Johnson–Nyquist noise thermometry: a resistor at temperature T carries a fluctuating voltage whose variance is set by T, and you can read the temperature off that variance with no other probe. Here the fluctuation is manufactured — a fixed sum of hidden oscillators — yet the same reading works: variance ∝ T, mean ≈ 0, and the temperature comes back out of the spread.
// what this is, and isn't
This illustrates Johnson–Nyquist thermal-noise thermometry — the observation that a conductor's equilibrium voltage noise has a variance proportional to temperature (Johnson 1928; Nyquist 1928). It also makes a narrower point about the word “random”: the noise on this page is a deterministic sum of hidden oscillators, reproducible on reseed and reversible in the clock, and the temperature still reads cleanly off its variance. “Random” is a description of the aggregate, not a claim about the mechanism underneath — that is a proposal about the word, offered plainly, not a physics result.
It is a simulation, not a measurement. Real Johnson–Nyquist noise follows the fluctuation–dissipation relation, with mean-square voltage 4 k_B T R Δf over a bandwidth Δf, and quantum corrections at high frequency or low temperature. The numbers here are arbitrary units: amplitudes are set so the variance equals the slider T in the long-time average, which is a convenience, not a calibration — over the finite window the measured variance scatters a few percent around T, the same reason real noise thermometry averages for a long time. This trace is also band-limited and built from 128 discrete tones, so its spectrum is neither white nor continuous, unlike thermal noise; the point being shown — variance carries T, the mean does not — does not depend on the spectrum. What is faithful is the shape of the claim — that temperature lives in the spread and the mean carries none of it. Cites: Johnson 1928; Nyquist 1928; kin does entropy exist.
// kin
electric thermometer — temperature from a voltage, written up · does entropy exist — the ontological question · the grain — the site's other reversible instrument, where the reading is read off a grain