LYING WORDS AND PAIRS OF DUCKS Matthew Jordan (@mattyj612)
“You are currently reading these words.”
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entences like the one above are always unsettling. You get a sinking feeling when you realize that you’ve fallen prey to the words, unable to escape from their prophetic claims. You simply can’t win! That particular sentence is so bamboozling because it’s self-referential, and we’re not used to seeing words talk about themselves. In fact, it’s a tough task to conceptualize most instances of self-reference in nature. This is especially true of cognitive functions; I get a little woozy when reminded that my brain can generate thoughts about its own neural structure. Before I continue, I should provide the following disclaimer: This is a very brain-intensive article. Do some cerebral stretches, work those cranial kegles, and massage that medulla because this is about to be a sanity-testing mental workout. Leggo. Probably the most famous self-referential sentence is the liar paradox, which has been around since ancient Greek times. Here’s the simplest version:
“This sentence is false.” Whoa. What is this saying? Well, let’s assume the sentence is true. Then we have
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to believe the assertion it’s making, namely that it’s false. So if it’s true, it’s false. And what if it’s false? Then we have to believe its negation, namely that it’s true. So if it’s false, it’s true. Once again, you simply can’t win! The liar paradox is, for lack of a better phrase, trippy as balls. Every time you try to pin it down, it flips back on itself, making it impossible to ever actually understand what it means. A paradox of this type is called a Strange Loop. A perfect visual representation of this Strange Loop is M.C. Escher’s work Drawing Hands in the bottom-left corner, which, like the liar paradox, seems to defy logic. Let’s take a look at another Strange Loop. This is a variation of Bertrand Russell’s paradox, which dates back to 1901. Suppose, as you likely do every day, that you are an overworked librarian. You’re tasked with creating a multi-volume encyclopaedic guide to the library’s archive. You decide on a whim to start by cataloguing ‘Biographical Works’, which is simply a list of all biographies on the shelves. Nothing too tough there! But notice that in doing so you’ve actually written a new book called Biographical Works. Hmmm. Next, maybe you go with ‘Books with Titles Beginning with “B”’. You would certainly put Beowulf, Brave New World, and the Book of Mormon on that list. You also just wrote the comprehensive Biographical Works, so that should go on the list, too. But wait, what about the book you’re currently writing? Doesn’t that start with ‘B’ as well? It most definitely does! So it should go on the list. Stated another way, Books with Titles Beginning with ‘B’ contains itself. This is different from Biographical Works, which certainly
did not contain itself. Feeling ambitious, you decide to try to catalogue ‘Books that do not Contain Themselves’. Well, Biographical Works clearly goes on this list. So do Books with Japanese Titles and Works Compiled by Amateur Ventriloquists (since you’re probably an expert ventriloquist). All is well and good there. But what of the book you’re now in the process of compiling, Books that do not Contain Themselves? Well, if you decide to leave it out, then Books that do not Contain Themselves does not contain itself, and therefore ought to be included on the list. But if you add it to the list, then it has suddenly become a book that contains itself, so you have to take it out. Uh-oh. Oh no. You’re stuck in a Strange Loop! Russell’s Paradox is a fickle beast and a foundational modern philosophical conundrum. It’s also the progenitor of one of the most cringe-worthy math jokes of all time:
What goes ‘quack-quack’ and contradicts itself? Russell’s pair o’ ducks. These days, Strange Loops are most prominent in artificial intelligence research. The idea is that, if a sufficiently rich neural structure is able to produce human consciousness, artificial neural networks programmed into a computer will give rise to sentient, thinking machines. Though it seems far-fetched at first, it’s not all that implausible when you consider the role of self-reference in humans. Our most basic building block is inherently self-referential; the magic of DNA is its ability to reproduce itself. More impressively, DNA can synthesize proteins whose sole task is to manipulate – and in some cases, destroy – the very DNA that created them. Strange Loops are all around us. Given our recursively defined DNA, we ourselves are strange loops. For the ultimate example of self-reference, consider the following sentence, which makes a claim about both itself and its author: I am a Strange Loop. Most ideas in this article were inspired by Douglas Hofstadter’s exceptional works Gödel, Escher, Bach and I Am A Strange Loop. INCITE MAGAZINE, NOVEMBER 2014