| Contributed by
Vijay Fafat
Prof. Thorn Jarvis, the Einstein-figure of the story, has built a ship called Infiniterra to undertake “possibly the greatest scientific expedition of history.”
This uranium-powered ship increases in size over and over till it reaches the limits of the visible universe, breaks through the “barrier of infinity”... and surprise!.... finds itself back to the point where Infiniterra took off for the journey, thus forming a consistent time-loop even if anti-spatial. Why? As the prof explains:
| (quoted from The Galactic Circle)
“The infinity paradox,” said Thorn, adjusting dials and keys as they mounted into the weirdly changing sky. “Einstein came at the key to it long ago, with his concept of curved space. Go far enough in a straight line—in any direction—and you find yourself back at the starting point. “We should have deduced the rest of it from that ; it’s simply so obvious that we overlooked it.” [...] the identity of time as an actual fourth dimension is well recognized. There is no real, absolute distinction between time and any spatial dimension. That means that time is only another direction. Go far enough in time, then, and you return to where you were. “To-morrow is the first day of the past ; yesterday lies in the future—infinitely remote around the circle of time.”
“The relativity paradox applies also to extent. Size is relative. The infinitely large is also the minutely small ; the macrocosm and the microcosm are identical. When we became too large to exist longer in our universe, as we thought, we became the smallest particle in it. “Infinity ever brings us back to the starting point. [...] In space, we went around the universe. We completed the circle of time. We went through the cycle of size.”
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The idea of going through infinity to arrive back at something finite is quite reminiscent of clock-like modular arithmetic (modulo infinity :-) ), of a straight line being a giant circle so that positive infinity connects to negative infinity, a Pac-man computer-screen world.
The parallel with Rudy Rucker’s story, “Spacetime Donuts” cannot be missed. In Rucker’s story, the journey goes in the reverse direction, going smaller and smaller till you come out from the large side.
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A few remarks:
- First, I'd like to emphasize that this story does make it clear that the scientists in it are using mathematics. For example:
| (quoted from The Galactic Circle)
"Science, of course, often disproves common sense. I have examined Thorn's mathematical work very carefully -- and I am compelled to admit II see no flaw in it.... I can find no flaw in his mathematics. However, on the grounds of my own unpublished research, I must question his whole system of mathematics."
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| (quoted from The Galactic Circle)
"You think," he asked quickly, "that Starbuck might be right?"
"He may be," Thorn admitted. "My mathematics is correct -- so far as it goes. So, I must admit, is Starbuck's."
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| (quoted from The Galactic Circle)
"A new factor has upset my calculations -- Starbuck's arguments seem to be getting the better of mine..."
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- There is much more going on in this story than what this summary has mentioned. There are lots of emotions and developments in the relationships among the crew of the Infiniterra. But, we are focusing here on just the mathematical aspects.
- I would like to emphasize: Despite the repeated claims in many pulp science fiction stories, the Theory of Relativity does not say that if you go straight far enough in any direction then you will return to the same point. General Relativity does give the universe non-trivial geometry and so going straight and ending up back at your starting point is possible. We do not (currently at least) know the global geometry or topology of the universe, but I must say that it is very unlikely that going in any direction would necessarily bring you back to your starting point.
- There really is a mathematical object that is
"modular arithmetic (modulo infinity :-)" (as Vijay Fafat put it in his contribution above). That would be a projective line.
This story was published in the August 1935 issue of Astounding Stories. |
