Gödel, Escher, Bach: When logic flies out of the window
Sandipan Deb
http://www.livemint.com/Sundayapp/umPh3ARDU4D1XzsobuUQ4J/Gdel-Escher-Bach-When-logic-flies-out-of-the-window.html
Ever since its publication in 1979, Douglas Hofstadter’s Gödel, Escher, Bach: An Eternal Golden Braid (GEB) has been a cult book like hardly any other. For my generation, the one that grew up in the 1980s, it was an endless source of intellectual stimulation—you could dip into it whenever and wherever you liked, and it was like a drug trip. If you were actually on drugs when you opened the book, it was possibly even better.
Hofstadter is an American professor of cognitive science—a discipline that spans many fields, from psychology to neurology to the fine arts to gaming to artificial intelligence. And GEB cuts across all these areas to study human consciousness, in a vastly entertaining and intriguing way, for the layman.
I used the word “intriguing”, because GEB is itself structured as a giant puzzle, with many smaller puzzles cocooned inside it. There are entire chapters which are mind-bending puzzles in their structure, and most of them have no answers, because our brains are not capable of answering them.
GEB deals with the limitations of the mind and logic. Take this old unsolvable riddle: “All Cretans are liars. I am a Cretan.” So, are all Cretans liars? Or consider a card, on both sides of which is printed this sentence: “The statement on the other side of this card is false.” Or change the lines. On one side of the card is printed: “The statement on the other side of this card is false.” And on the flip side: “The statement on the other side of this card is true.” So, what is true? And what is false?
But what they indicate are the limits of our mind/logic/cognitive skills. So, Hofstadter turns to the Austrian mathematician Kurt Gödel, and his Incompleteness Theorem, which, for nearly a century, has defined the boundaries of both our minds and our logic.
Very simply put, this is what it says: “A system cannot know itself fully.”
What is a “system”? I am taking this definition from dictionary.com: “an assemblage or combination of things or parts forming a complex or unitary whole”. It could be a fully visible network like a railway system, an intranet or the bureaucracy in a particular department of a government. But GEB is concerned with the mind as a system.
The mind cannot know itself fully. And all the structure of logic that we have built fails when taken to the ultimate test: the Cretans.
The Dutch graphic artist M.C. Escher spent his life creating works of art that defy our cognitive senses. You do not know whether cascades are falling down or up, whether people are walking up stairs or down or left or right.
Johann Sebastian Bach composed fugues that defy the mathematics that form the bedrock of Western classical music.
How did Escher and Bach accomplish—consistently—what they did? They knew the limits of what human minds can conceive, and then they stepped across the lines. So, the human mind is capable of twisting the three dimensions which define our cognition, and the rule of the octave (in the case of music) and doing something that we cannot explain in the universe that our perceptions reveal to us.
What we see, experience, take as truth, are based on axioms. Gödel said that a system cannot ever prove its axioms (and he wrote a mathematical paper that you and I can’t even begin to read without getting a migraine). But if you remember your Euclidean geometry, it is built on axioms. Quantum physics has clearly proved that most of these axioms are pathetically invalid, at least in the sub-atomic world.
Geometric axioms don’t work when you dig a bit deeper and your maths get somewhat stronger and your particle accelerators become more well-funded and powerful.
Hofstadter, at his core, is a computer scientist, though his interests and work extend to music, the visual arts and the very essence of human creativity. He wants to crack that puzzle. How do we create? And break barriers that are immutably defined by Gödel (and in a way, cannot ever be disproved)?
But our minds keep thinking up new ideas, meta-ideas, that raise an eyebrow to the system, mathematically proved beyond doubt and never challenged.
There is no better book written on human consciousness, based on science and the visceral drive of humanity to know how their mind works and whether they can be made better, and can computers ever supplement them so that we can all chill? But will that ever be an occasion for chilling? For those who have watched 2001 A Space Odyssey, there could be food for thought. HAL the supercomputer.
To those with a spiritual bent of mind, and who have found a way out,GEB is not for you. Or maybe it is.
But GEB is perhaps also a dangerous book. A friend read the book obsessively,for months, and committed suicide. I have found no reason why he did that. I think it is an invigorating book. Rest in peace, VV.
Sandipan Deb is the editorial director of swarajyamag.com.
The Bookmark is a series on ‘interesting’ books—intelligent and thought-provoking, but also enjoyable.
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