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. Strange loops 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.
A strange loop is a phenomenon in which, whenever movement is made upwards or downwards through the levels of some hierarchical system, the system unexpectedly arrives back where it started. Hofstadter (1989) uses the strange loop as a paradigm in which to interpret paradoxes in logic (such as Grelling’s paradox, the liar’s paradox, and Russell’s antinomy) and calls a system in which a strange loop appears a tangled hierarchy.
Canon 5 from Bach’s Musical Offering (sometimes known as Bach’s endlessly rising canon) is a musical piece that continues to rise in key, modulating through the entire chromatic scale until it ends in the same key in which it began. This is the first example cited by Hofstadter (1989) as a strange loop.
“… the Gödelian strange loop that arises in formal systems in mathematics … is a loop that allows such a system to perceive itself, to talk about itself, to become self-aware, and in a sense it would not be going too far to say that by virtue of having such a loop, a formal system acquires a self.” —Douglas Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid
The greatest strange loop in biology is the one where DNA is used to make proteins which in turn is used to make more DNA. In general self-replication of a system can be characterised by tangled hierarchies or Strange Loops and emergent/complex behaviour when a network is created between the individual components of the system within the confines of a selective environment.
One cool strange loop has to do with cellular influence on protein folding. Proteins (in the environment) require proteins (in the environment) to fold up. For example, chaperones are proteins that help fold up other proteins. Is there a chaperon in that requires another chaperon in to fold? Now that would be a beautiful Meta strange loop!
One of the strange loops involves the independent/early folding unit (IFU) stabilisation, where these IFUs flicker in and out of an ensemble of conformations and in order to form a stable structure need to interact with each other. Likewise for larger sub-structures.
Beta-strand pairing can also be thought of as a strange loop, much like DNA base pairing is a strange loop. Beta-strand formation is similar to IFU formation in that the hydrogen bonding is required for overall stability.
If a chain folds upon itself sequentially starting from end to end (which we know is not the case) then the entire folding process would be a beautifully recursive strange loop, where to fold a protein of length n, you would fold a protein of length n-1 and then fold the last residue.
All of the above can be generalised. Strange loopiness arises because of context-sensitivity in proteins (as illustrated by the IFU and beta-strand pairing example). So to fold a protein of length n:
f(n) = f(n-1) + c(R_n)
f(n-1) = f(n-1-1) + c(R_n-1) = f(n-2) + c(R_n-1)
f(n-2) = f(n-2-1) + c(R_n-2) = f(n-3) + c(R_n-2)
f(3) = f(3-1) + c(R_3)
f(2) = f(2-1) + c(R_2)
f(1) = c(R_1)
Where c(R_1) is some arbitrary starting point. You can use methods like this to build up protein structures—in fact such a process was used in my CASP3 ab initio prediction method for assigning secondary structure to rough models. The concept is known as recursion.
Note that the recursive call need not be made to a sequence of length n-1. It could be of any size that represents a substructure. So you can view the process as putting together a bunch of independent sub-units.
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 fewer than 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 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.
“You would not find the boundaries of the soul no matter how many paths you traveled, so deep is its measure.” Today, more than two thousand years after Heraclitus wrote those words, science has shrunk the boundaries of the soul considerably. A soul that can transcend space and time, survive death, and even possess others, is considered intellectually passé. In its place we have the brain – “a teetering bulb of dread and dream” as the poet Russell Edson described the grey matter which makes us who we are – which is the indispensable substrate of our personal identity and consciousness. As the brain goes, so goes the mind, they say.
The philosophical question is as to whether mathematics constitutes a part of nature or not. Is math real or constructed?
Learn more by reading the book: I am a strange loop by Douglas R. Hofstadter (you find this on Amazon)
Provided by ESTHER INGLIS-ARKELL