Strange loops can be many things, including musical tones, mathematical problems, and linguistic riddles. They also can be biological fact, and this fact might be translated into computer code or silicon chips. Here's why a philosophical theory might show true artificial intelligence is possible.

What Are Strange Loops?

When following a simple loop, you know you will go on a single trip that takes you back to where you started. There's one journey, and one destination. Strange loops are a bit more complicated — they form a kind of set of instructions, an ordered hierarchy, that brings you higher and higher, until you're back at the beginning where you started.


Strange Loops were the brainchild of Douglas Hofstadter, a philosopher and scientist who wrote I Am a Strange Loop. They can be simple or complex, but they depend on what Hofstadter called "tangled hierarchies." Instead of a linear progression, these hierarchies balance on each other. Together they encompass a set of instructions that set out two equally valid ways of looking at a situation. The situation cannot be resolved without elevating one view and one part of the set of instructions over the other, but there is no objective way to do that.

Examples of Strange Loops

Hofstadter proposes the Mona Lisa, or any painting, as an example of a strange loop. It's a group of pigments that are spackled onto a canvas, and it's a smiling woman. Obviously one is literally true and one is only figuratively true, but one would have to be deliberately obtuse to talk of the painting as only a grouping of colors under varnish. Examples of strange loops within paintings are the famous impossible object images of M. C. Escher and others — the endlessly descending stairs and rigid cages with bars that cross each other. If we could pin down which part of the object was real we could decide which part violated the laws of that painting's universe, but there's no objective basis to declare one part of the image real rather than any other part.

The Shepard Tones comprise a musical strange loop. They are a group of tones that seem to continually rise (or fall) but never actually change. Our attention focuses on certain notes that seem to rise, but the lower notes never drop out. We keep waiting for an impossibly high dog whistle that never comes.

There are also linguistic strange loops that require us to make impossible distinctions. There's the famous two-sentence problem: "The following sentence is a lie. The previous sentence is true." And then there's the Berry Paradox, a famous mathematical definition that invalidates itself. It is meant to describe "the smallest positive integer not definable in under 11 words." Of course, whatever integer that is, it is now definable in under 11 words. Meaning there can't possibly be a smallest possible integer definable in under 11 words, except there has to be so that phrase can define it.


Strange Loops and Artificial Intelligence

What does any of this word play have to do artificial intelligence? Hofstadter meant the title of his book literally. When he said, "I am a strange loop," what he meant was the idea of "I," the concept of the self, was a result of this weird duality of tangled hierarchies. Ask people if their brains, the actual electrically lit-up matter that sits in their head cases, are what what make them themselves, and they'll probably say yes. We are our brains. Ask them if they are simply a mechanical thing, programmed to respond to stimulus, like a complex adding machine, and they would say no. We have a sense of self. To take the strictly literalist view that we do not have selves, that we are mechanical, would be as obtuse as saying the Mona Lisa is a group of colors or a difference engine is a proto-human. Our electrified protein has constructed a more numinous identity, and both the meat and the idea are valid.


So what? So that means that the sense of self will arise organically, from enough data input on sufficiently complex machinery. It doesn't matter if that machinery is made of flesh or anything else. Some people say that computers may imitate intelligent human life very well, but they'll never actually be the equivalent to humans. Others say that a calculator isn't much different from a human brain. The idea of strange loops, as they apply to life and machinery, asserts that calculators are not brains, because they do not construct an identity the way that brains do. However, they can become brains, or more accurately, they can become minds. Minds made of silicon, or anything else, are, when taken as strange loops, in no way distinguishable from human minds. "We" are both physical objects and incorporeal identities constructed from physical objects — and we are constructed so well that no one can say that the physical is more valid than the theoretical.


Top Image: Brett Jordan David Macdonald. Impossible Arch Image: Till Krech.

[Via I Am a Strange Loop, Wolfram Math World, Philosophy Now, Strange Loops In Biology]


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