A photograph, mostly deleted.

Start with the whole picture: 768 × 576 dots, 442,368 of them, each an exact color fixed by the recipe. This is the raw material — there is nothing else in the file.

Zoom in, to the lighthouse. The smooth photograph is a grid of squares. There are no curves anywhere — only tiles of solid color, packed edge to edge.

Zoom onto the red band, forty-eight times. One tile of that grid is three numbers: how much red, how much green, how much blue. Values 0–255 — three bytes. That is all a dot ever is.

So the honest size of this picture is 442,368 × 3 = 1,327,104 bytes — about 1.27 MB. That is the number everything below has to beat.

The JPEG file will keep only a slice of it. Five cuts follow, all computed from this exact photo, in your browser, as you scroll.

The first move isn't a cut — it's a change of accounting. Each dot's red-green-blue triple is rewritten as three other numbers: Y, its brightness, and Cb, Cr, its two color offsets.

Look at Y alone: the whole black-and-white photograph is in there, at full resolution. Color television was built on exactly this fact — brightness was the signal everyone already owned.

Now the color planes. They are soft — watercolor washes. Edges live in brightness; color mostly says which wash goes where.

So JPEG keeps every Y sample, and only one Cb and one Cr per 2×2 square — “4:2:0”. Three of every four color samples are never written: 1,327,104 samples become 663,552. Half the photo, already gone.

Recombined: the largest change anywhere is — levels of 255 — on the lighthouse's red edge, where averaging is hardest to hide. The average change is —. Find it by eye. I'll wait.

Each block: 64 numbers. Zoomed here on the lighthouse's foot, where tower, door, rock, and sea meet — the busiest square on the whole photo.

JPEG rewrites those 64 numbers as 64 weights on this fixed dictionary of waves. Every tile is a pure cosine ripple — and any 8×8 block whatsoever is exactly some mix of these 64.

The dictionary runs rough to fine: a flat average in the corner, faster ripples outward. Photographs live at the rough end; the fine tiles hold grain and hard edges.

Rebuild the busiest block from its single flattest weight: a gray smear — but the smear is already the right gray. One number, one guess, and it isn't wrong.

Fifteen weights in: light side, dark side, the shape of the door. The remaining forty-nine weights are mostly grain. Your eye already stopped caring.

Now the whole photo, rebuilt block by block from its first k waves. Scroll and k runs to 64 — the world sharpens into place. At k = 64 the transform is exact: nothing has been lost yet.

The busiest block's 64 weights. The corner value is the block's average; the rest measure ripple at each of the dictionary's frequencies. Still reversible — these numbers rebuild the block exactly.

Now divide each weight by its table entry at quality 75 — the classic mapping — and round to the nearest integer.

— of the 64 weights rounded to zero. Across the entire photo, — of all weights are now zero — before any clever coding has happened. This table is the meaning of “quality.”

Decoding multiplies back by the table. Zeros stay zero. The missing waves do not come back smaller — they do not come back. That rounding is the entire loss in “lossy.”