(Original Review, 1980)

It is true that Gödel numbering by itself is not an information compression technique. Its purpose is merely to represent a message as a number so that the message can be operated on with arithmetic and number theory. Gödel's original use of this device was to enable statements in number theory to talk about statements in number theory, possibly even about themselves, unambiguously. In Pohl's "The Gold at the Starbow's End", some very smart people want to send a very long message with a very small amount of energy. They Gödelized the message, and then converted it to a compact expression (perhaps by magic - these are VERY smart people) which evaluates to the original number:

354 852 2008 47 9606 88
1973 + 331 + 17 + 5 + 3 + 2 - 78

The recipients, although they are unable to compute the number and decrypt the message, are able to estimate the size of the message as "equal to the contents of a standard unabridged dictionary."

However, from the way Pohl described them in "The Gold at the Starbow's End" they do indeed present a way of substantially reducing the information encoded by accumulating powers, i.e. 2^X1 * 3^X2 * 5^X3 * . . . (0 ( )

Comprised of one novella and four short stories, The Gold at the Starbow's End is a somewhat fascinating collection. The title tale regards a group of astronauts on a very long journey to Alpha Centuari and what they do to occupy the time they spend getting there. They have been sent by a very forward-thinking man who may not really have their best interests at heart. This story was hilarious in regards to the kind of antics the astronauts got up to, and the reaction their handler has to their reports are absolutely priceless in more ways than one.
"Sad Solarian Screenwriter Sam" is one of those stories where extra-terrestrials decide to destroy the human race because we suck. Sam is their one and only test subject. He sucks. Quite a bit of this story is cribbed from Burroughs Martian saga. I was not amused.
"Call Me Million" is a 'what-if' kind of story that is uniquely written, but never really goes anywhere. Charley is a soul sucker. He eats people's souls and they die. There are no people left to eat except other people eaters. What now? There. You've read the story. Skip it.
After reading "Shaffery Among the Immortals" I was hoping that the final story would also feature a complete sad sack so I could say I didn't really like or identify with any of the main characters in these stories. Shaffery is a pathetic loser even compared to Sam and Charley. However, the story was worth reading for the ending. Very fitting.
Probably the best story in the book was "The Merchants of Venus." Pohl did a very good job of world-building in regards to the planet, it's atmosphere, it's previous denizens, etc. without bogging the reader down with exposition. I did not disdain the main character. I was rooting for Audee to find what he was looking for. The fact that he was destined to do so was obvious from the first, but the struggle and journey were quite enjoyable to read about.
Final take: Skip stories two and three and you have a 4 star book. ( )