\Delta

Delta (change / difference)

Notation: structural shorthand

In plain English

"The change in." $\Delta x = x_{\text{after}} - x_{\text{before}}$ . Unlike $dx$ , which is an infinitesimal nudge, $\Delta x$ is a finite, measurable change. Average velocity is $\Delta x / \Delta t$ . Caution: in advanced physics $\Delta$ alone (e.g. $\Delta f$ ) can also mean the Laplacian operator, and lowercase $\delta$ has several other jobs (a small variation, the Kronecker or Dirac delta).

As code

const before = 12.0, after = 15.5;
const delta = after - before;   // Δ = 3.5

See it

Position xx=0.00 · slope -0.45

\Delta

is a finite change.

\Delta y/\Delta x

is the slope of the chord between two points. Shrink

\Delta x

to zero and it becomes the derivative.

What it means, field by field

Physics

Finite change (ΔE, Δt); the uncertainty principle Δx·Δp ≥ ħ/2 (where Δ means spread); the Laplacian in PDEs.

Biology

Change in a trait between generations; ΔG for free-energy change in biochemistry.

AI / ML

Change in loss or in weights between steps (Δθ); "delta" between a fine-tuned and a base model.

Epistemics

Effect sizes are Δs. Always ask "Δ relative to what baseline?"

In a research paper

Gibbs free energy in chemistry and biochemistry; whether a reaction proceeds spontaneously.

\Delta G = \Delta H - T\,\Delta S

The change in free energy equals the change in enthalpy minus temperature times the change in entropy.

Common misreadings

Treating Δx as Δ multiplied by x. It is a single symbol: "change in x".
Conflating Δ (finite change) with d or ∂ (infinitesimal change).
Missing that Δ can mean the Laplacian or a spread, depending on the paper.

Connected symbols

\frac{d}{dx}

Derivative

\nabla

Gradient operator (nabla, del)

\approx

Approximately equal

Where it appears on this site

§ 1. Learning to Read Equations § 2. The Physics of Systems § 3. Biology as an Information System § 5. Complexity and Systems Thinking