55. The Memory Map

It was a clear evening, and the window stood wide open. On the table lay Liri’s star map – complete, entered point by point. Beside it lay Erklärus’s notebook: 54 pages, closely written with numbers, sketches and key points. Liri glowed on the windowsill, golden with a blue shimmer.

A night in November. Erklärus couldn’t sleep because he had too many questions – and suddenly a star knocked at his skylight, about the size of an apricot. “I’m lost. Can you help me?” On the first page of his notebook he wrote: Goal: find the way home. Tool: mathematics.

They counted seven stars. They learned that the crocodile always eats the bigger number. They added glow-stones together, made meteorites vanish into a drawn black hole, discovered circles and triangles in everything – and found a tin full of coins under the bed.

Then the numbers got bigger. They bundled a star cluster of 63 stars into bundles of ten, hopped on the number line from stop to stop, shared twelve glow-stones fairly between three friends and learned to read the clock – so that Liri knew when a jump would end: from 14:00 to 17:00, three hours.

Liri’s star map got a grid of squares. 356 plus 274 squares past a nebula. “About 400” was enough to keep the direction. 732 minus 456: still 276 squares to go. They measured lengths, weights, litres, time and money – and with the set square crooked lines became straight.

384,400 kilometres to the Moon. The order of operations decided whether 5 + 3 × 4 is 17 or 32. 243 times 25. The “heaviest crown” of primary school, long division: 848 divided by 4 – every jump 212 squares long. A field on the map, measured with perimeter and area. And the scale 1 : 10 million.

The number of stars in her home galaxy: 400 billion. Then the radio signal: two, three, five, seven, eleven – prime numbers, the beacon from home. With the zeros trick Liri worked out 340 times 100 in her head. With coordinates every point got an address. A box full of stardust – and finally the bar chart: above her home there were far more blue stars than reddish ones.

She folded the map into quarters, added fractions and wrote distances with decimal places: 4.25 light-years to the nearest star. Every change of course got a name – acute, right, obtuse, straight, reflex. And then the old photo of a satellite aerial, built entirely of triangles.

The solar-sail panel, getting narrower towards the top – a trapezium. The slanting shadow of the solar panel – a parallelogram, just like the struts at home. And the icy cold of a moon: minus 15 degrees. Below zero there are numbers too, and +7 and −7 cancel out to zero – like the energy balance of a starship.

Fuel for the journey home, supplies for the crew, the percentage cross, an x that hid itself, the balance kept level – just like the engines were aligned at Liri’s home. With compasses and a set square they constructed positions without measuring once. And Liri wrote down the distance home as a power.

The square search area, worked out with the binomial formulas. A single straight line, y = mx + b, for the whole flight path. The square root of 2, a number that never ends – like the natural constants at Liri’s home. And two courses that meet at exactly one point.

The ring of Saturn – an edge that is the same distance from the centre everywhere, like her round window. The crystal that spread out the light – a prism. The fuel tank – a cylinder. The landing module – a pyramid.

And then Pythagoras’ theorem: the technicians at Liri’s home used three squares to check whether an angle was exactly 90°. With three numbers Erklärus found the right angle on the map – and in the sky, in the Summer Triangle, at Vega.

54 chapters, 54 memories, 54 clues. On Liri’s star map every point, every distance, every shape now stood.

Erklärus laid the pencil on the map.

Liri stood up on the windowsill. Her light grew brighter and brighter, and she didn’t have to fly at all – she only had to shine. A fine thread of light stretched from the window to the sky, as straight as if someone had drawn it with a ruler.

The thread of light carried her up to the right angle of the Summer Triangle – and there the brightest star of all shone a tiny bit brighter than before.

That same night Vega twinkled: twice, three times, five times, seven times, eleven times. Erklärus smiled and whispered: “Goodnight, Liri.”

But the thread of light had not disappeared. It had grown thinner, almost invisible – yet it still stretched from the windowsill up to the sky. And there, where Liri had sat, lay a tiny golden spark, no bigger than a grain of rice.

Erklärus laid it carefully next to his notebook. The spark pulsed – but not in prime numbers. It grew brighter, then darker, then brighter again, quite gently and evenly, like a breath.

He opened a fresh page and wrote down the first values: bright – dark – bright. He couldn’t describe it with his formula for the straight line. But one thing he knew: a pattern that keeps repeating can be worked out. You only need the right tools.

In the silence he thought he heard a voice from far away – soft, warm, a little golden:

And in the summer nights after that he often sat at the open window, looked for the Summer Triangle – and every time, at the right angle, he found her. Beside him the little spark pulsed.