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I am looking for a story about a tiny universe smaller than our Solar System. It has one star and one planet, and the planet's orbit is on the edge of universe. The planet's single face points to its sun at all times. The world has a very tall wall around its twilight circumference.

A civilization grows on the planet. The ruler of the civilization - curious about what is beyond the wall - commissions for a ladder to be built up the wall. He climbs the ladder and walks towards the darkness beyond the twilight atop the wall. He keeps walking and

comes back to his original location. Anything that goes beyond the wall at the edge of the universe is reflected back on itself.

I think it starts with a quote like this: "Many and strange are the universes that exist like bubbles in the foam along the river of time."

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Sounds like Arthur C. Clarke's The Wall of Darkness:

Many and strange are the universes that drift like bubbles in the foam upon the River of Time. Some – a very few – move against or athwart its current; and fewer still are those that lie forever beyond its reach, knowing nothing of the future or the past. Shervane’s tiny cosmos was not one of these: its strangeness was of a different order. It held one world only – the planet of Shervane’s race – and a single star, the great sun Trilorne that brought it life and light. Shervane knew nothing of night, for Trilorne was always high above the horizon, dipping near it only in the long months of winter.


So he walked on: and when presently an icy hand fastened itself upon his heart, he did not pause as a man of lesser courage would have done. Without flinching, he watched that shockingly familiar landscape rise around him, until he could see the plain from which his journey had started, and the great stairway itself, and at last Brayldon’s anxious, waiting face.


For a moment he had a sudden, inexpressibly poignant vision of another stairway, watched by another Shervane, falling in identical ruins on the far side of the Wall. But that, he realised, was a foolish thought: for none knew better than he that the Wall possessed no other side.

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    The Wall of Darkness" is also the second of three stories identified in answer to this question. The story is available at the Internet Archive. – user14111 Apr 6 '17 at 7:57
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    But what if he had run a string behind him? What would it have looked like when he "turned around"? Did he end up as a mirror-image of himself? – Justsalt Apr 6 '17 at 17:53
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This is "The Wall of Darkness" by Arthur C. Clarke, as previously discussed in this question.

A summary from Alex Kasman's Mathematical Fiction site:

In a universe consisting of one star and one planet, there is a mysterious impenetrable wall surrounding the entire planet in the deep freezing southlands. Two men, one with money, the other with building skills, engage in a long-term program to scale the wall and find out what's on the other side. The answer turns out to be mathematical. And rather upsetting.

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