With a marketing image (which I have learned from Smashwords not to call a book cover) of two pairs of shoes ensconced in a shallow box of red bricks and a title page photograph of a swamp with hundreds of dead trees, I can say Fathoming Gödel lives up to these aspects of its innovative promotion.
Is Gödel’s mathematical logic like picking up sticks in a forest? The forest is littered with sticks, but you convince yourself that you can pick up enough sticks to create a park that you and other people can enjoy. Then you lower your expectations and hope to create a small clearing that you alone might enjoy. Time passes, tinged with madness, and all that remains is the forest and sticks.
Is Gödel’s mathematical logic like The Beatles’ album "Sargent Pepper’s Lonely Hearts Club Band"? It’s not actually a concept album, but since so many people claim that it is one, and not only that, but the first concept album in rock and roll, then in a way it is a concept album notwithstanding that it is not a concept album.
If you read "I Am a Strange Loop" by Douglas Hofstadter, he seems to admit that Gödel’s first incompleteness proof is invalid, but then he seems to go on to say that it is true by analogy. And, perhaps, he makes the further claim that all truth comes from analogy. This neatly sidesteps the claim that I believe was made by Aristotle that analogy is the weakness form of argument.
Perhaps, the explanation of a lesser mystery will shed light on the greater mystery of Gödel and his proofs. For years, I wondered why the rock and roll group The Band had managed to accrue such overwhelming accolades from their peers as well as from the critics in the music press. The Band put out a few fine albums, but I think the actual reason they were so lauded is that they were too obscure to be appreciated by the average rock music fan. It is difficult to believe that being too obscure for the average fan would be of paramount importance to the elite, but it seems it is. So it is with Gödel. It is the impenetrable obscurity of his proofs that by far makes the greatest contribution to his mystique. Those who claim to understand his work and can convince others of this fact have an automatic elevation in their status. And, to rise in the pecking order is the most sublime achievement society can offer. I recently learned that snapping turtles spend the winter months buried in mud at the bottom of ponds. This act would seem to rival Gödel in the obscurity competition.
It seems no one ever bothers to ask of Gödel and his proofs and other creators of obscure theories why wouldn’t friendly individuals produce at least one and perhaps several straightforward explanations of their complex ideas. Sometimes it seems that in the past, famous people were little more than gimmicks. If we ever achieve the world depicted in the "Star Trek" universe, the question will not be why was there a book probing Gödel’s proofs, but instead the question will be why weren’t there many books written suspecting his proofs.
(review of free book)