A short story based on an interesting premise that at some point in the (near) future, mankind will stop making interesting, fundamental discoveries because we have too much knowledge and too much apparatus around us. In the story, the Americans launch eight astronauts in a spaceship on a ten-year journey to Alpha Centauri to land on its habitable planet called “Alpha-Aleph”. The trouble is, the planet does not exist and the spaceship has only sufficient fuel to reach the star system. More damningly, the American President and a very small circle of science and political advisors have sanctioned this one-way suicide mission, fully aware that the planet does not exist.
The rationale for proceeding with this 40-billion dollar hoax is the strong desire to advance fundamental knowledge, backed by the theory that if you throw together a small group of very intelligent people in extended isolation, they will learn to use the meagre tools at their disposal along with raw brain power to make new discoveries in fundamental sciences, especially if such thought process is not aimed at making specific discoveries. So the astronauts are taught basic number theory and elements of human communication and told to think about these as “recreational puzzles” during the long voyage. A multi-billion dollar ivory tower in action.
The rag-tag bunch predictably starts tinkering around with basic number theory (“Ann has taken to binary arithmetic like fish to water”, “Ann has taken to some sort of statistical experimentation with flipping coins”, etc). They play with Fermat’s Last Theorem, Goldbach Conjecture and Godel’s theorems, in addition to chess problems and the structures of modes of communications we employ in order to come up with more efficient ways of conveying ideas and thoughts. In the process, they re-invent “Godelization”, an efficient way of coding up messages using prime numbers for transmission to earth, and use it to send back the proof of Goldbach, the secret of nuclear fusion, etc. (the message is:, “1973354 + 331852 + 172008 + 547 + 39606 + 288 minus 78”)
The story contains a standard paragraph on Goldbach’s Conjecture and nice one on Godelian statements. Pohl also explains the dilemma the scientists on Earth face, since decoding a gigantic Godelian number is nearly impossible for their existing technology (“The practical difficulties! You could not get even the first letter until you had the whole number, and IBM had refused even to bid on constructing a bank of computers to write that number out unless the development time was stretched to 25 years”)
The story ends up with the twist that the US starts going up in flames while the astronauts develop god-like powers to come back for the rescue.
I really liked the concept itself but the execution is completely far-fetched on multiple fronts. A focus on the process of discovery itself would have made for a far better story.