Of all the fairy tales I encountered as a child, Rumpelstiltskin always struck me as the most peculiar. The story revolves around a girl who must spin straw into gold or face death at the hands of the king. A dwarf appears out of nowhere, and spins the straw into gold — for a price. On the first night he takes a necklace, and on the second a ring. On the third night the girl has nothing left to pay him with, and so the dwarf makes her promise to give him her firstborn child. The king’s greed is sated after three days of gold-spinning, and he marries the girl. In due time the new queen gives birth to a child, and sure enough, the dwarf returns to receive his pounds of flesh. But the queen refuses, and tries to offer him some of her newly acquired riches instead. The dwarf agrees to give up his claim on the child, but only if the queen can guess his name within three days. Her guesses on the first two days fail. But then one of her spies returns with a strange tale. He came across a little cottage in the woods, in front of which he saw a dwarf prancing around a fire, singing a song that ended “Little does my lady dream / Rumpelstiltskin is my name!” On the third day the queen initially pretends not to know the dwarf’s name. Finally she says, “Could your name be Rumpelstiltskin?” At this the dwarf flies into a rage, and stomps his foot on the ground so hard that a chasm opens up in the ground, swallowing the dwarf, who was never seen again.
As a child I found the dwarf’s plunge into the subterranean void the most eerie element in the story, but in recent years I’ve been pondering another, perhaps deeper mystery. Why did Rumpelstiltskin’s name have so much power?
Fairy tales notwithstanding, by the time I got to college I had come to think that names were mere conventions that had no intrinsic meaning. For all practical purposes, surely one label was as good as any other? Dismissing a debate on what to call something as “mere semantics” seemed to be an act of hard-nosed skepticism and realism.
But as I gradually discovered, naming involves much more than simply assigning a label to something that has already been identified. The act of naming is one of the central mysteries of human cognition — it is the visible tip of an iceberg whose depth below the surface of conscious thought we have only just begun to plumb. I cannot claim to have solved this mystery, but I’d like to present what I have cobbled together so far: a handful of puzzle pieces which I hope will entice the reader to join in the investigation. I’ve divided up the essay into four parts. Here’s the plan:
- We’ll introduce two key motifs — the named and the nameless — with a little help from the Tao Te Ching.
- We’ll examine a research problem that crops up in cognitive psychology, neuroscience and artificial intelligence, and link it with more Taoist motifs.
- We’ll look at how naming might give us power over animals, other people, and even mathematical objects.
- We’ll explore the power of names in computer science, which will facilitate some wild cosmic speculation.
1. The name that can be named
My change of attitude towards naming started with a book on Chinese philosophy that I found in a second-hand book store. I discovered that most ancient Chinese philosophical schools had a theory of “names and actualities”. In Confucianism the correspondence between names and things took on special ethical importance — ranks, duties and functions needed to be clearly delineated in order for society to be harmonious. I initially put this sort of thing down to the inscrutableness of ancient modes of thought — the same alienness that caused people to impute divinity and power into the names of their deities. Surely it is the things — the objects, forces, people, and processes — that are important, and not what we choose to call them?
At it turned out, not all ancient thinkers thought names and things were the same. Lao Tzu, the founder of Taoism, seemed to go against the Confucian ideal, denying the equation of names with actualities. The very first chapter of Lao Tzu’s Tao Te Ching sets the stage for a more ambivalent attitude towards names.
The Tao that can be expressed
Is not the Tao of the Absolute.
The name that can be named
Is not the name of the Absolute.
The nameless originated Heaven and Earth.
The named is the Mother of All Things.
One way to read this is as saying that the Tao, or the way of nature, goes beyond our expressive capabilities. Whatever we can name, delineate, and define is not enough to encapsulate the way nature works, or the way we should work with nature. This is the usual mystical interpretation. Taoist metaphysics has at least two parallels — one from the West, and one from India. Apophatic theology developed in Europe, and centers on the belief that, because God is ineffable, no positive attributes can be assigned to Him. One can only list all the things that God is not. This often amounts to listing everything that one can think of, and then asserting God is not any of them. A similar approach is taken in the Jnana Yoga and Advaita Vedanta schools of Hindu thought. The supreme reality, Brahman, is “neti neti”, or “not this, not this”. It is the essence of “suchness” for which no other definition applies.
If unnameable forces are so powerful, why then does Lao Tzu bestow upon the named the honor of being the “Mother of All Things”? Why give naming any credit at all? Perhaps there is a clue in the saying “the namer of names is the father of things” 1. The mystery of names seems to lead us to the mystery of creation.
2. Manifest boundaries
The act of naming requires at least two components: the name, and the thing to be named. So in order to understand the process of naming, we have to think about things. The “namer of names” needs raw material for his task. So what are things? How do we decide that a thing is a thing? The question seems so absurd that I suspect most people never think of it. Perhaps more people have pondered the following question: before you are introduced to the name of an emotion, have you really experienced it? When I was a child I didn’t know what “ennui” meant, so maybe I never experienced it. But once I was given the definition, I could discern the outlines of this emotion in my own life. How does this sort of thing happen?
This is where the cognitive and neural sciences come in. Unlike philosophers, cognitive scientists, neural network modelers and artificial intelligence researchers are trying to emulate human cognition, rather than just come up with verbal theories about it. Complex emotions are among the most difficult topics for scientists to address. (Plus, for the time being robots that display signs of ennui are not high on our priority list.) We have a hard enough time grappling with things! For researchers trying to imitate human intelligence, the nature of objects is a matter of practical concern. Brains and artificial systems are not directly presented with objects — what we receive are patterns of energy: photons on our retinas and vibrations on our ear drums. Artificial intelligence researchers learned the hard way that getting separate objects to “pop out” of these undifferentiated sensory fields is an unexpectedly complex ability that most humans take for granted. Objects aren’t completely “out there” in the world — they’re also products of our minds and brains, and therefore of our cultures. So naming an object can be a creative act. (Also, deciding which naming system to adopt can be a political act.) Philosophers have often acknowledged the subjective and creative aspects of naming, but the sheer mechanistic complexity of naming is best appreciated through the attempts to get machines to do what humans find trivially simple.
When presented with a rich visual scene — like a cluttered desk, for instance — how can we pick out separate things: coins, keys, wallet, pen, phone? This is a problem that humans are extraordinarily good at. The process is called visual object segmentation, and it is thought to be a key first step in pattern recognition. Even after decades of research, most advanced algorithms cannot perform object segmentation better than little children. The artificial approaches are improving and will soon overtake humans, partly by taking inspiration from the human brain. Still, the way in which Google and Facebook’s artificial neural networks pick out the faces in our photographs is only a loose approximation of how we do it. There exists the distinct possibility that we will come up with devices that imitate human intelligence without shedding light on how natural, biological intelligence works. Only time will tell, but in the meantime the scientists and engineers will keep probing, coding, and tinkering. Perhaps they’ll need to engage with the philosophers and their verbal theories.
Many artificial object segmentation systems start by trying to discover the boundaries in an image. You can use these boundaries — lines, contours, edges, discontinuities of lighting and texture — to discover the outlines of objects present in the image. This itself is a challenging task for machines. The trick is to find the important boundaries, because there are many contours that don’t mark the outlines of things. Neural networks and other techniques such as Bayesian modeling require considerable training in order to approach the performance that comes naturally to a toddler. The result of this training is a form of expectation. These models learn to sort images into different categories, and then use the categorization system as a guide for what to expect in a new image. In the case of neural networks, this expectation takes the form of connection weights between artificial neurons. In a Bayesian model, the expectation takes the form of probability distributions called priors, which help the model determine how likely it is for a particular object to be found given other information present in the image. If the image has been categorized as a photograph taken in a forest, the probability that the model picks out the outlines of trees should be much higher than the probability that it picks out the shape of a sofa. The model, like a human, should expect to see trees in the image, not sofas. For both humans and machines, prior expectations seem necessary in order to perceive useful boundaries. Without these prior expectations, the sensory world might appear poorly defined — like an impressionistic painting in continuously varying shades of grey, lacking distinct nameable objects.
Characterizing pattern recognition in terms of boundaries and expectation evokes these lines from chapter 1 of the Tao Te Ching, which follow the lines I quoted earlier:
Thus, without expectation,
One will always perceive the subtlety;
And, with expectation,
One will always perceive the boundary.
With the Tao Te Ching, every translation captures different shades of meaning. Consider this version of the four lines I just quoted:
Ever desireless,
One can see the mystery.
Ever desiring,
One can see the manifestations.
Subtlety and mystery are easy to link. A mystery is the absence of a clear dividing line between truth and falsehood, an absence that renders everything subtle, shadowy and indistinct. How about desire and expectation? A desire for food, for instance, is closely linked to the expectation that the reassuring outlines of edible objects will soon appear, perhaps with a little effort. When someone sitting at a restaurant table says they expect prompt service, you can be pretty sure they desire the rapid manifestation of a waiter.
More problematic for me initially was the link between “boundary” and manifestation”. The connection became apparent only after I was exposed to visual object recognition research. If you are unable to see boundaries in the world, you will be unable to perceive objects. In a very real sense boundaries are required for things to become manifest to you.
What do expectation and desire have to do with objects? The typical mystical approach is to downplay them in order to gain a heightened awareness of subtlety. But I like to think that that Lao Tzu was telling us that the two ways of seeing both have their roles to play. He probably didn’t know about expectation values in Bayesian decision theory, but he may have intuited that when you look at the world with desire, or with the expectation of getting something from it, you tend to assess your perceptions in starkly delineated terms: good and bad, useful and useless, dangerous and safe, edible and poisonous. A starving person is not usually interested in subtleties. Acknowledging the importance of both desire and desirelessness is consistent with the dialectical style that characterizes Taoism, a philosophy that emphasizes the interplay of opposing forces: yin and yang. Lao Tzu ends the chapter like this:
The source of these two is identical,
Yet their names are different.
Together they are called profound.
Profound and mysterious, the gateway to the Collective Subtlety.
Floating in a sensory world without boundaries, lacking expectation or desire, nothing would ever become manifest. Being set adrift in a grey sea of subtlety sounds rather depressing. In fact, depression has been described as a “flaw in love“, a disease that attacks the very basis of desire and other strong motivations. Antonio Damasio, in his book Descartes’ Error, documents neurological disorders that reduce emotional expression. The surprising result of such disorders is that they sometimes render the patient incapable of making decisions. Such patients’ cognitive abilities seem untouched — they can solve problems when asked to do so. But when asked to make decisions for themselves, they cannot pick one alternative over any other. All the alternatives seem equally good — shades of grey everywhere, and no way to draw a line between them. There is some preliminary neuroscientific data that suggest that some clinically depressed people have a weakened ability to tell apart different patterns. In other words, their “desireless” condition is correlated with an inability to draw boundaries between perceptual objects, memories, and situations. 2
There is no doubt that the act of naming requires that patterns become manifest to us. In order for things to become manifest, their boundaries must be delineated. But the mystery of naming seems to go deeper. Where does the power of names come from?
3. Naming and Taming the Infinite
When your dog has learned its name, you can exercise a small but useful amount of control over its behavior. When you call it by name, it comes. Perhaps it has been trained to expect a treat when its name is called. Most cats on the other hand are unable or unwilling to react strongly to their own names. Evolutionary biologists inform us that dogs may have been the first animals to be domesticated — perhaps 12000 years ago. Names may have been crucial to the transformation from wild wolves into tame dogs. Cats may have joined the party much later, around 5000 years ago. Maybe we haven’t fully domesticated them yet! Or maybe to gain power over something by naming it requires a degree of consent on the part of the named.
The behavioral control we wield over (some!) named animals even shows up in when we use a human’s name. If you hear your name being spoken you will most likely direct your attention to the source of the sound. In conversation with someone, judiciously slipping in their name can cause them to lower their guard. Salespeople, confidence tricksters and politicians routinely use this to their advantage. Dale Carnegie, in his legendary self-help book How to Win Friends and Influence People, tells us to “Remember that a person’s name is to that person the sweetest and most important sound in any language.” Perhaps the act of naming allowed humans to domesticate each other, completing our transition from wild apes to cultured individuals.
Stories like Rumpelstiltskin might be cultural relics from a time when language was new and strange, and just beginning to reveal its powers. The belief in the power of names may have roots in the prehistoric infancy of our species, but it lives on in many of the world’s religions. The sacred place given to particular names may reflect an appreciation of the civilizing, domesticating role of naming itself. In the Hindu Namakarana ceremony, a child is given two names: one ordinary name, and one secret name that is derived from astrology and known only to the father. The Hebrew scriptures seem to link God’s creative power with the act of naming. In Genesis, “God said, ‘Let there be Light’, and there was light.” The Jewish people came to believe that the name of God — the Tetragrammaton – was too holy to be uttered. Some Christians inverted this belief, and held that the name of God, or of Jesus, was so holy that it ought to be uttered repeatedly. A variant of this belief, known as name-worshiping, emerged in Tsarist Russia, and persists to this day despite condemnation from the Russian Orthodox Church. The name-worshipers believe that “The name of God is God Himself and can produce miracles.” In a twist that brings us closer to the idea that names have power, this strange, heretical belief system may have had an impact on the world of pure mathematics.
Mathematics is distinct from science in that it deals with what appear to be pure forms of thought — entities that seem to have no necessary connection with the natural world, other than the fact that they are produced by human minds. For this reason mathematics departments may be the last bastions of platonism — the belief that there exist objects that are neither material nor mental, but are in essence abstract. Only a subset of mathematics is of relevance to science (though one never knows which arcane branch with prove useful in the future). Mathematicians are often given to wonder about the ontological status of the concepts they work with. What are mathematical “objects”? Do mathematical objects exist? Are the names of mathematical objects important? The celebrated 20th Century Russian-French mathematician Alexander Grothendieck was said to have “a flair for choosing striking evocative names for new concepts; indeed, he saw the act of naming mathematical objects as an integral part of their discovery, as a way to grasp them even before they have been entirely understood.”
In the late 1800s Georg Cantor initiated a seminal phase in the debate on the reality of mathematical objects. Cantor could justifiably be called the Father of Infinity; although he didn’t invent the concept, he forever changing how mathematicians think about it. Before Cantor, most mathematicians followed Aristotle’s approach, holding that infinity was a potentiality rather than an actuality. Cantor broke with this tradition by asserting that infinity was real, not a potentiality, and that there were several different sorts of infinity, each with rigorously provable properties. To cut a long and complex story short, Cantor created a formal system called set theory, which was used to study collections of mathematical objects, such as numbers. He used set theory to show that there were different sorts of infinite sets. So the set of all natural numbers (1,2,3,4, and so on) was infinite yet countable, and the set of real numbers — the collection of all points on a real line — was infinite but uncountable. He then showed in very convincing ways that the set of points on the real line was in a sense “bigger” than the set of natural numbers, despite the fact that both sets are infinite. He also showed that the rational numbers, the numbers that can each be written as a ratio of two integers, were also countable. So the uncountable real numbers vastly outnumber the countable rational numbers. The real numbers that aren’t rational are called, unsurprisingly, irrational numbers, and a tiny handful of them do have names, such as the square root of two, pi, and Euler’s number e. As if the notion of two sort of infinity were not mind-boggling enough, Cantor went on to reveal an infinite number of such infinite sets, each “bigger” than the last.
By naming the properties of new, unheard-of objects, Cantor seemed to be drawing them out of the shadows and into the light of day, where they were forced to obey the rules of pen-and-paper mathematics. The ontological question is this: did Cantor create these dizzying infinities, or simply bestow names on mathematical objects that already existed in some sense? Does something need to exist before you can name it? Or can a concept arise at the very moment it is named? Influential French mathematicians followed Cantor into this strange domain where naming and creation resemble each other, but according to one version of the story, they lost their nerve, and climbed down from the vertiginous precipice of infinity. Perhaps that was the safe thing to do, because some people think Cantor’s attempt to tame infinity drove him to depression and madness.
A handful of Russian mathematicians lead by Dmitri Egorov and Nikolai Luzin had no such failure of nerve. Egorov and Luzin were both name-worshipers. They believed that “if they named God, they assured his existence, and similarly they thought that by naming the new sets they could make them real. God could not be defined, but he could be named.” The concepts that Egorov and Luzin picked up in Paris were hard to visualize, but they could be named, as Cantor had demonstrated. Luzin’s personal papers contain a suggestive account of his attitude to definitions:
Each definition is a piece of secret ripped from Nature by the human spirit. I insist on this: any complicated thing, being illumined by definitions, being laid out in them, being broken up into pieces, will be separated into pieces completely transparent even to a child, excluding foggy and dark parts that our intuition whispers to us while acting; only by separating into logical pieces can we move further, towards new successes due to definition.
This belief may have contributed to Egorov and Luzin’s role in starting up the influential Moscow School of Mathematics. A modern Taoist might say that in desiring to understand Nature, Luzin and his colleagues perceived new mathematical manifestations. But Luzin may also have been aware that this came at a price: perhaps the “foggy and dark parts that our intuition whispers to us” are the subtle mysteries that can only be seen without expectation. 3
4. The Algorithm helps those who help themselves
There is another modern domain that makes use of “name magic”, and it may be the most unexpected of all. Where do you suppose the following quote comes from?
One of the things that every sorcerer will tell you is if you have the name of a spirit you have power over it.
It’s not from a medieval grimoire or a fantasy novel. It’s from an MIT lecture on computer science from 1986 4. As the textbook that accompanied this course explains,
A computational process is indeed much like a sorcerer’s idea of a spirit. It cannot be seen or touched. It is not composed of matter at all. However, it is very real. It can perform intellectual work. It can answer questions. It can affect the world by disbursing money at a bank or by controlling a robot arm in a factory. The programs we use to conjure processes are like a sorcerer’s spells.
Despite the fact that computer programs can only work their magic in the decidedly material world of electronic circuits, there is a sense in which they are like mathematical objects — they seem to reside in a platonic realm of pure forms. After all, a program can move from device to device, but it is still the same program. But why do names crop up in computer science? What is the source of their power? Another line might give us a clue. “To call up a demon, you must learn its name”. (This time it is from a novel: William Gibson’s Neuromancer.)
In computer science, a “daemon” is a program running as a background process that quietly performs system “chores”. It was named after Maxwell’s demon, a creature from a physics thought experiment who works tirelessly to sort molecules into two piles. Maxwell’s demon might trace its roots to the demons of Greek mythology — nature spirits who were believed to be constantly working behind the scenes. So we can draw a genealogical line from the mythical demons of the past to the real daemons operating on your computer or smartphone. The program daemons are working behind the scenes without your explicit permission, so to gain control of them, you need to know what they’re called.
In recent years, some physicists have speculated that the whole universe is a simulation — a labyrinthine algorithm running on some vast alien supercomputer. One can never tell how seriously physicists take concepts like this. But some claim that there are ways to establish this experimentally, implausible as this sounds 5. If this idea takes hold, perhaps history will come full circle, and we will discover our commonality with ancient seers and medieval alchemists, invoking the hidden daemons that keep the Universal Algorithm running smoothly. Like cosmic hackers, some of us might seek to learn the names of these code-spirits in order to gain power over them. The tendency to see our minds and our genetic material as computational codes might turn the daemon quest inwards as well.
Every generation features people who think that they have arrived at a comprehensive rational understanding of how the Universe works. They think they already know the names of all the daemons that keep the Universal Algorithm from crashing. Perhaps these new daemons, instead of being called Abraxas or Gorgon or Pantalaimon (or Rumpelstiltskin?), have names like “Higgs Boson” or “Quark” or “Superstring” or “Selfish Gene”. Let’s call the set of all known concepts the “nameable concepts”. Are the nameable concepts all there is to the universe? An analogy with mathematics is in order. The nameable numbers are infinite, but like the rational numbers, they are countably infinite. We can say the same about the nameable concepts. We can always list them one by one, as entries in a limitless encyclopedia like Wikipedia. But just as there are unnameable numbers, there could be unnameable concepts — a far larger infinite set whose elements we may never fully list, or count, or compute, or even point to. 6
When we take our nameable concepts too seriously and forget about the possibility that there are things we haven’t named, we are confusing the map with the territory. We mistake the finger pointing at the moon with the moon itself, and we forget that there might be other heavenly bodies out there — some that astronomers might one day discern, and some that are so far away that their light will never reach us. But even this analogy doesn’t capture the possibilities outside the reach of our named concepts — things that we can only talk about negatively, apophatically. Perhaps there are things out there that are not galaxies, not stars, not planets, not dark matter, not living, not dead…
Maybe the story of Rumpelstiltskin, in its cryptic way, is trying to tell us two intertwined tales. On the one hand it is telling us that unnamed powers lurk in the shadows: capricious spirits that can both help and harm us. Like stories themselves, these powers may be infinite. Perhaps our rational concepts can never fully account for them. But on the other hand, it seems to be telling us that when malevolent or irrational forces manifest themselves, we can — if we’re lucky — name them and tame them.
But maybe I’m wrong about this. After all,
The Tao that can be expressed
Is not the Tao of the Absolute.
The name that can be named
Is not the name of the Absolute.
Originally published on March 24, 2014 at 3 Quarks Daily.
Rumpelstiltskin image: Helena Meijer
Notes and References
- I’ve been unable to trace the origins of this saying.
- A recent study indicated that people suffering from depression have a weakened pattern separation ability — compared to healthy people, the boundaries between their memories were more blurred. This may have something to do with the loss of the ability to produce new neurons in the hippocampus, as Siddhartha Mukherjee explains in his masterful New York Times article, “Post-Prozac Nation: The Science and History of Treating Depression”. The existence of hippocampal neurogenesis in humans remains controversial, however.
- The mathematical section of the article was inspired by the paper “The Power of Names” by Loren Graham which appeared in the journal Theology and Science. The quotes in this section also come from this paper. Graham and co-author Jean-Michel Kantor expand on the theme of name-worshiping and mathematics in their book Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity.
- No, it is not a Dungeons & Dragons reference either.
- See, for example, recent news items in the New York Times (“Is the Universe a Simulation?”) and Discover Magazine ( “Do We Live in the Matrix?”).
- In the arcane psychoanalytic theories of Jacques Lacan — which I have only encountered via Slavoj Žižek and Wikipedia — experience is divided into three orders: the Imaginary, the Symbolic and the Real. I don’t know whether Lacan or Žižek studied higher mathematics, but the concept of the Real might have something in common with the concept of real numbers, or perhaps with Georg Cantor’s concept of the Absolute Infinite, which he equated with God. The real numbers are uncountably infinite, and therefore always “exceed” the rational numbers. As Cantor demonstrated using his surprisingly intuitive and nontechnical diagonal argument, the rational just can’t keep pace with the real. As far as I can discern, the psychoanalytic Real involves the unnameable, unanticipated aspects of experience that break through our cozy certainties, exposing the inadequacy of our named concepts. Perhaps the Real is the experience — sometimes exciting, sometimes traumatic — of discovering that Nature always has a trick up her sleeve. Perhaps the Real is where black swans come from. The Real eludes our attempts to draw neat boundaries to pick out perceptual and conceptual objects, forever lurking unmanifest in the “foggy and dark parts” of the universe, and of the mind.
