Imagine a map of a place so exact, that the visual representation supersedes reality. In his famous short story On Exactitude in Science, Jorge Luis Borges describes an Empire whose cartographers, aspiring for scientific perfection, create a map so precise, that it coincides point for point with the territory it is surveying. Generations later, the inhabitants question the usefulness of such a ridiculous creation, and to rid themselves of it, leave its fate to the skies. For centuries, fragments of this map were to be found, scattered across the western desert, inhabited by outcasts and strays.
The self-destruction of the Empire that occurs in this story is fascinating and perplexing. Not only does the representation reflexively replace the real, but the future inhabitants of the map, realising the futility of the copy, appear to step outside it, in order to once again, reveal the real.
When describing The Human Condition – a painting of a garden landscape nested inside a painting of the landscape it depicts – the artist René Magritte says “we see [the world] as being outside ourselves, although it is only a mental representation of what we experience inside ourselves.” This, along with Borges story, relates to the central question behind Douglas Hofstadter’s book Gödel, Escher, Bach: An Eternal Golden Braid. In G.E.B. Hofstadter asks, “What is a self?” His answer, put simply, is the title to his follow-up book: I Am a Strange Loop. A strange loop, however, is a pretty complex concept!
In the introduction to I Am a Strange Loop, Hofstadter describes a strange loop as “a shift from one level of abstraction to another, which feels like an upwards movement in a hierarchy, and yet somehow the successive ‘upward’ shifts turn out to give rise to a closed cycle.”
Similar to ascending an endless staircase, a strange loop moves further and further away from a starting point, yet ultimately ends up exactly where it began due to a tangled hierarchy of levels. A common reference Hofstadter uses to depict this theme is M.C Escher’s Drawing Hands. The lithograph consists of a left hand drawing a right hand, and in an infinite paradoxical loop, the right hand being drawn also draws the left hand.
Philosophers have grappled with the nature of self and consciousness since Plato, but Hofstadter knew he was on to something when he discovered that, at the core of Kurt Gödel’s Incompleteness Theorem lies a strange loop of mathematical logic.
Gödel’s theorem originates from the ancient Epimenides paradox. The paradox involves the philosopher Epimenides, a Cretan, who states, “All Cretans are liars,” inadvertently uttering a self-referring statement. A similar logical contradiction is the statement “this sentence is false.” If the sentence is false, it must be true, but if it’s true, then the sentence is false, and so the argument goes, ad infinitum. By applying this logic to mathematics, Gödel discovered a code that contradicted the very notion of proofs. He had figured out a self-referential, mathematical statement that, against all logic, could not be proved. It was incomplete.
In G.E.B. and I Am a Strange Loop, Hofstadter imaginatively applies Gödel’s theorem to a philosophy of the mind, creating a body of work on the self and consciousness. His journey on strange loops is a bit like falling into a bottomless rabbit hole. At times you feel disorientation, while at others, you feel like you are floating or even, not moving at all. But as you plummet, all of your pre-determined notions of the self will twist, shatter and fold. Just keep in mind Hofstadter’s own law – “It always takes longer than you expect, even when you take into account Hofstadter’s Law.”
START HERE:
Radiolab episode, Loops
This radio episode on loops is as varied as they come, filled with stories on “loops that hurt us, heal us, make us laugh, and, sometimes, leave us wanting more.” The section called “(In)completely Loopy” introduces paradoxes and the work of Gödel in an accessible way.
Douglas Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid
Hofstadter weaves in and out of the lives and works of Kurt Gödel, M.C. Escher and Johann Sebastian Bach, exploring various examples of strange loops in maths, art, music and language, and unlocking the mysteries of the mind in the process.
Douglas Hofstadter, I Am a Strange Loop
Hofstadter returns with a companion book to *G.E.D* in order to re-address and re-emphasise the central theme of the self, something he felt was lost to many in his first attempt.
Words: Sharon Phelan
