“This sentence is a lie.”
That sentence is a famous philosophical paradox. If the sentence is true, that means it’s a lie. But if it’s a lie, then it can’t be true. And if it’s false, that means it’s not a lie. But that means it’s telling the truth. It’s impossible to make sense of it.
Okay, so it’s a weird sentence, sure. But it’s more than a neat party trick. In his 1979 Pulitzer Prize–winning book, Gödel, Escher, Bach,—often called GEB—cognitive scientist Douglas Hofstadter explains that the paradox it contains is something much more.
Let’s start with the three famous thinkers named in the book’s title.
Kurt Gödel was a philosopher best known for his famous incompleteness theorems, first delivered in 1930. Gödel showed that logical systems, no matter how well thought out, will always contain statements that can’t be proven true or false, and that those systems can’t prove that they are consistent with themselves. In other words, you’ll always have paradoxes like the one above.
Escher refers to M. C. Escher, a Dutch artist from the twentieth century known for his paradoxical prints like Relativity—the famous, perspective-shifting image of a staircase with no beginning and no end.
Bach is, of course, the famous composer from the early 1700s, Johann Sebastien Bach. But what you may not know, unless you’re a student of music, is that Bach composed by making paradoxical patterns like those Gödel and Escher worked with. As Brian Hayes wrote in a review of Hofstadter’s book:
The well-known combinatorial trickery of Bach’s canons and fugues gives rise to another rich pattern of ambiguous perceptions. A theme enters, then appears again, inverted or reversed or in a different key or a different tempo; the transformed melody then blends with its original. Figure and ground may unexpectedly change roles. Even though each of the notes is heard distinctly—and in Bach the notes have a logic only slightly less formal than [the one Gödel examined]—the ear cannot always resolve their relationship.
What’s the point of all this? In GEB, Hofstadter was exploring artificial intelligence in its early stages. He was trying to understand how all these systems work. “A large but mechanistic, rule-following system, when it grows complex enough, develops the capacity for self-reference, which in this context is called consciousness,” Hayes explained in his review.
But this isn’t quite the approach AI has taken since then. Now, it’s about getting machines to perform specific actions. Hoftsadter was more theoretical. “In GEB, Hofstadter was calling for an approach to AI concerned less with solving human problems intelligently than with understanding human intelligence,” James Somers wrote in The Atlantic.
This is a book that explores that patterns governing all our lives, from music and physical particles to DNA. By exploring the limits and complexities of our logical systems, Gödel, Escher, Bach tells us something about how we think at all.
Leave a Reply