by Greg Egan



When Yalda was almost three years old, she was entrusted with the task of bearing her grandfather into the forest to convalesce.

Dario had been weak and listless for days, refusing to move from the flower bed where the family slept. Yalda had seen him this way before, but it had never lasted so long. Her father had sent word to the village, and when Doctor Livia came to the farm to examine Dario, Yalda and two of her cousins, Claudia and Claudio, stayed close to watch the proceedings.

After squeezing and prodding the old man all over with more hands than most people used in a day, Doctor Livia announced her diagnosis. “You’re suffering from a serious light deficiency. The crops here are virtually monochromatic; your body needs a broader spectrum of illumination.”

“Ever heard of sunlight?” Dario replied caustically.

“Sunlight is far too blue,” Doctor Livia countered, “too fast for the body to catch. And the light from the fields is all sluggish red. What you’re lacking lies between those extremes; a man of your age needs umber and gamboge, saffron and goldenrod, jade and viridian.”

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Watch the trailers on Vimeo (higher quality, #1, #2)
or YouTube (less bandwidth, #1, #2).

In Yalda’s universe, light has no universal speed and its creation generates energy.

On Yalda’s world, plants make food by emitting their own light into the dark night sky.

As a child Yalda witnesses one of a series of strange meteors, the Hurtlers, that are entering the planetary system at an immense, unprecedented speed. It becomes apparent that her world is in imminent danger — and that the task of dealing with the Hurtlers will require knowledge and technology far beyond anything her civilisation has yet achieved.

Only one solution seems tenable: if a spacecraft can be sent on a journey at sufficiently high speed, its trip will last many generations for those on board, but it will return after just a few years have passed at home. The travellers will have a chance to discover the science their planet urgently needs, and bring it back in time to avert disaster.

Orthogonal is the story of Yalda and her descendants, trying to survive the perils of their long mission and carve out meaningful lives for themselves, while the threat of annihilation hangs over the world they left behind. It comprises three volumes:

Publication history

Information and illustrations


Many of the pages linked below contain “conceptual” spoilers: although they make no reference to the plot of Orthogonal, they cover scientific matters that are only revealed gradually in the novel.

Main pages

These notes cover a multitude of topics in the physics of the Orthogonal universe. The main exposition, listed here, requires only high school mathematics: trigonometry, algebra and a little calculus. If you’re interested in reading about the subject in more detail, see the complete contents.

World Lines of Constant Acceleration
Sum of slightly different plane waves

All pages

These links include the complete set of notes: more than 80,000 words of text and over a hundred illustrations. The pages marked “[Extra]” go into considerably more detail than the main exposition, and are targeted at readers who have studied some physics and mathematics at an undergraduate level.

Non-contractible loops in SO(3)
Electric Flux Around A Point Charge
Riemannian Cavity Radiation Spectrum
Riemannian gravitational scattering
SO(4)-invariant propagator

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