I Am a Strange Loop - by Douglas R. Hofstadter

On Souls and Their Sizes

I am among those who reject the notion that a full-fledged human soul comes into being the moment that a human sperm joins a human ovum to form a human zygote. By contrast, I believe that a human soul — and, by the way, it is my aim in this book to make clear what I mean by this slippery, shifting word, often rife with religious connotations, but here not having any — comes slowly into being over the course of years of development. It may sound crass to put it this way, but I would like to suggest, at least metaphorically, a numerical scale of “degrees of souledness”. We can initially imagine it as running from 0 to 100, and the units of this scale can be called, just for the fun of it, “hunekers”.

In short, I would here argue, echoing and generalizing the provocative statement by James Huneker, that “souledness” is by no means an off–on, black-and-white, discrete variable having just two possible states like a bit, a pixel, or a light bulb, but rather is a shaded, blurry numerical variable that ranges continuously across different species and varieties of object, and that also can rise or fall over time as a result of the growth or decay, within the entity in question, of a special kind of subtle pattern (the elucidation of whose nature will keep us busy for much of this book). I would also argue that most people’s largely unconscious prejudices about whether to eat or not to eat this or that food, whether to buy or not to buy this or that article of clothing, whether to swat or not to swat this or that insect, whether to root or not to root for this or that species of robot in a sci-fi film, whether to be sad or not to be sad if a human character in a film or a novel meets with a violent end, whether to claim or not to claim that a particular senescent person “is no longer there”, and so forth, reflect precisely this kind of numerical continuum in their minds, whether they admit it or not.

The central aim of this book is to try to pinpoint the nature of that “special kind of subtle pattern” that I have come to believe underlies, or gives rise to, what I have here been calling a “soul” or an “I”. I could just as well have spoken of “having a light on inside”, “possessing interiority”, or that old standby, “being conscious”.

Do dreads and dreams, hopes and griefs, ideas and beliefs, interests and doubts, infatuations and envies, memories and ambitions, bouts of nostalgia and floods of empathy, flashes of guilt and sparks of genius, play any role in the world of physical objects? Do such pure abstractions have causal powers? Can they shove massive things around, or are they just impotent fictions? Can a blurry, intangible “I” dictate to concrete physical objects such as electrons or muscles (or for that matter, books) what to do? Have religious beliefs caused any wars, or have all wars just been caused by the interactions of quintillions (to underestimate the truth absurdly) of infinitesimal particles according to the laws of physics? Does fire cause smoke? Do cars cause smog? Do drones cause boredom? Do jokes cause laughter? Do smiles cause swoons? Does love cause marriage? Or, in the end, are there just myriads of particles pushing each other around according to the laws of physics — leaving, in the end, no room for selves or souls, dreads or dreams, love or marriage, smiles or swoons, jokes or laughter, drones or boredom, cars or smog, or even smoke or fire?

I grew up with a physicist for a father, and to me it was natural to see physics as underlying every last thing that happened in the universe. Even as a very young boy, I knew from popular science books that chemical reactions were a consequence of the physics of interacting atoms, and when I became more sophisticated, I saw molecular biology as the result of the laws of physics acting on complex molecules. In short, I grew up seeing no room for “extra” forces in the world, over and above the four basic forces that physicists had identified (gravity, electromagnetism, and two types of nuclear force — strong and weak). But how, as I grew older, did I reconcile that rock-solid belief with my additional convictions that evolution caused hearts to evolve, that religious dogmas have caused wars, that nostalgia inspired Chopin to write a certain étude, that intense professional jealousy has caused the writing of many a nasty book review, and so forth and so on? These easily graspable macroscopic causal forces seem radically different from the four ineffable forces of physics that I was sure caused every event in the universe. The answer is simple: I conceived of these “macroscopic forces” as being merely ways of describing complex patterns engendered by basic physical forces, much as physicists came to realize that such macroscopic phenomena as friction, viscosity, translucency, pressure, and temperature could be understood as highly predictable regularities determined by the statistics of astronomical numbers of invisible microscopic constituents careening about in spacetime and colliding with each other, with everything dictated by only the four basic forces of physics. I also realized that this kind of shift in levels of description yielded something very precious to living beings: comprehensibility.

The Causal Potency of Patterns

Deep understanding of causality sometimes requires the understanding of very large patterns and their abstract relationships and interactions, not just the understanding of microscopic objects interacting in microscopic time intervals.

This idea — that the bottom level, though 100 percent responsible for what is happening, is nonetheless irrelevant to what happens — sounds almost paradoxical, and yet it is an everyday truism. Flip a quarter a million times and you’ll very reliably get within one percent of 500,000 heads. Flip a penny the same number of times, and the same statement holds. Use a different coin on every flip — dimes, quarters, new pennies, old pennies, buffalo nickels, silver dollars, you name it — and still you’ll get the same result. Shave your penny so that its outline is hexagonal instead of circular — no difference. Replace the hexagonal outline by an elephant shape. Dip the penny in apple butter before each flip. Bat the penny high into the air with a baseball bat instead of tossing it up. Flip the penny in helium gas instead of air. Do the experiment on Mars instead of Earth. These and countless other variations on the theme will not have any effect on the fact that out of a million tosses, within one percent of 500,000 will wind up heads. That high-level statistical outcome is robust and invariant against the details of the substrate and the microscopic laws governing the flips and bounces; the high-level outcome is insulated and sealed off from the microscopic level. It is a fact in its own right, at its own level. That is what it means to say that although what happens on the lower level is responsible for what happens on the higher level, it is nonetheless irrelevant to the higher level. The higher level can blithely ignore the processes on the lower level.

I am not suggesting that the invisible, swarming, chaotic, microscopic level of the world can be totally swept under the rug and forgotten. Although in many circumstances we rely on the familiar macroworld to be completely predictable to us, there are many other circumstances where we are very aware of not being able to predict what will happen.

Loops, Goals, and Loopholes

We might anthropomorphically describe a flush toilet as a system that is “trying” to make the water reach and stay at a certain level. Of course, it’s easy to bypass such anthropomorphic language since we effortlessly see how the mechanism works, and it’s pretty clear that such a simple system has no desires; even so, when working on a toilet whose tank has sprung a leak, one might be tempted to say the toilet is “trying” get the water up to the mark but “can’t”. One doesn’t truly impute desires or frustrations to the device — it’s just a manner of speaking — but it is a convenient shorthand.

Why does this move to a goal-oriented — that is, teleological — shorthand seem appealing to us for a system endowed with feedback, but not so appealing for a less structured system? It all has to do with the way the system’s “perceptions” feed back (so to speak) into its behavior. When the system always moves towards a certain state, we see that state as the system’s “goal”. It is the self-monitoring, self-controlling nature of such a system that tempts us to use teleological language.

Feedback — making a system turn back or twist back on itself, thus forming some kind of mystically taboo loop — seems to be dangerous, seems to be tempting fate, perhaps even to be intrinsically wrong, whatever that might mean. These are primal, irrational intuitions, and who knows where they come from. One might speculate that fear of any kind of feedback is just a simple, natural generalization from one’s experience with audio feedback, but I somehow doubt that the explanation is that simple. We all know that some tribes are fearful of mirrors, many societies are suspicious of cameras, certain religions prohibit making drawings of people, and so forth. Making representations of one’s own self is seen as suspicious, weird, and perhaps ultimately fatal. This suspicion of loops just runs in our human grain, it would seem.

The mysterious and strangely robust phenomena that emerge out of looping processes such as video feedback will serve from here on out as one of the main metaphors in this book, as I broach the central questions of consciousness and self. From my video voyages I have gained a sense of the immense richness of the phenomenon of video feedback. More specifically, I have learned that very often, wonderfully complex structures and patterns come to exist on the screen whose origins are, to human viewers, utterly opaque. I have been struck by the fact that it is the circularity — the loopiness — of the system that brings these patterns into existence and makes them persist. Once a pattern is on the screen, then all that is needed to justify its staying up there is George Mallory’s classic quip about why he felt compelled to scale Mount Everest: “Because it’s there!” When loops are involved, circular justifications are the name of the game.

To put it another way, feedback gives rise to a new kind of abstract phenomenon that can be called “locking-in”. From just the barest hint (the very first image sent to the TV screen in the first tiny fraction of a second) comes, almost instantly (after perhaps twenty or thirty iterations), the full realization of all the implications of this hint — and this new higher-level structure, this emergent pattern on the screen, this epiphenomenon, is then “locked in”, thanks to the loop. It will not go away because it is forever refreshing itself, feeding on itself, giving rebirth to itself. Otherwise put, the emergent output pattern is a self-stabilizing structure whose origins, despite the simplicity of the feedback loop itself, are nearly impenetrable because the loop is cycled through so many times.

In short, there are surprising new structures that looping gives rise to that constitute a new level of reality that could in principle be deduced from the basic loop and its detailed properties, but that in practice have a different kind of “life of their own” and that demand — at least when it comes to extremely finite, simplicity-seeking, pattern-loving creatures like us — a new vocabulary and a new level of description that transcend the basic level out of which they emerge.

Of Selves and Symbols

I begin with the simple fact that living beings, having been shaped by evolution, have survival as their most fundamental, automatic, and built-in goal. To enhance the chances of its survival, any living being must be able to react flexibly to events that take place in its environment. This means it must develop the ability to sense and to categorize, however rudimentarily, the goings-on in its immediate environment (most earthbound beings can pretty safely ignore comets crashing on Jupiter). Once the ability to sense external goings-on has developed, however, there ensues a curious side effect that will have vital and radical consequences. This is the fact that the living being’s ability to sense certain aspects of its environment flips around and endows the being with the ability to sense certain aspects of itself.

That this flipping-around takes place is not in the least amazing or miraculous; rather, it is a quite unremarkable, indeed trivial, consequence of the being’s ability to perceive. It is no more surprising than the fact that audio feedback can take place or that a TV camera can be pointed at a screen to which its image is being sent. Some people may find the notion of such self-perception peculiar, pointless, or even perverse, but such a prejudice does not make self-perception a complex or subtle idea, let alone paradoxical. After all, in the case of a being struggling to survive, the one thing that is always in its environment is… itself. So why, of all things, should the being be perceptually immune to the most salient item in its world? Now that would seem perverse!

Perception takes as its starting point some kind of input (possibly but not necessarily a two-dimensional image) composed of a vast number of tiny signals, but then it goes much further, eventually winding up in the selective triggering of a small subset of a large repertoire of dormant symbols — discrete structures that have representational quality. That is to say, a symbol inside a cranium, just like a simmball in the hypothetical careenium, should be thought of as a triggerable physical structure that constitutes the brain’s way of implementing a particular category or concept.

I should offer a quick caveat concerning the word “symbol” in this new sense, since the word comes laden with many prior associations, some of which I definitely want to avoid. We often refer to written tokens (letters of the alphabet, numerals, musical notes on paper, Chinese characters, and so forth) as “symbols”. That’s not the meaning I have in mind here. We also sometimes talk of objects in a myth, dream, or allegory (for example, a key, a flame, a ring, a sword, an eagle, a cigar, a tunnel) as being “symbols” standing for something else. This is not the meaning I have in mind, either. The idea I want to convey by the phrase “a symbol in the brain” is that some specific structure inside your cranium (or your careenium, depending on what species you belong to) gets activated whenever you think of, say, the Eiffel Tower. That brain structure, whatever it might be, is what I would call your “Eiffel Tower symbol”. You also have an “Albert Einstein” symbol, an “Antarctica” symbol, and a “penguin” symbol, the latter being some kind of structure inside your brain that gets triggered when you perceive one or more penguins, or even when you are just thinking about penguins without perceiving any.

In the interests of clarity, I have painted too simple a picture of the process of perception, for in reality, there is a great deal of two-way flow. Signals don’t propagate solely from the outside inwards, towards symbols; expectations from past experiences simultaneously give rise to signals propagating outwards from certain symbols. There takes place a kind of negotiation between inward-bound and outward-bound signals, and the result is the locking-in of a pathway connecting raw input to symbolic interpretation. This mixture of directions of flow in the brain makes perception a truly complex process. For the present purposes, though, it suffices to say that perception means that, thanks to a rapid two-way flurry of signal-passing, impinging torrents of input signals wind up triggering a small set of symbols, or in less biological words, activating a few concepts.

Without going into more detail, let me simply say that it makes perfect sense to discuss living animals and self-guiding robots in the same part of this book, for today’s technological achievements are bringing us ever closer to understanding what goes on in living systems that survive in complex environments. Such successes give the lie to the tired dogma endlessly repeated by John Searle that computers are forever doomed to mere “simulation” of the processes of life. If an automaton can drive itself a distance of two hundred miles across a tremendously forbidding desert terrain, how can this feat be called merely a “simulation”? It is certainly as genuine an act of survival in a hostile environment as that of a mosquito flying about a room and avoiding being swatted.

A spectacular evolutionary gulf opened up at some point as human beings were gradually separating from other primates: their category systems became arbitrarily extensible. Into our mental lives there entered a dramatic quality of open-endedness, an essentially unlimited extensibility, as compared with a very palpable limitedness in other species. Concepts in the brains of humans acquired the property that they could get rolled together with other concepts into larger packets, and any such larger packet could then become a new concept in its own right. In other words, concepts could nest inside each other hierarchically, and such nesting could go on to arbitrary degrees.

The depth and complexity of human memory is staggeringly rich. Little wonder, then, that when a human being, possessed of such a rich armamentarium of concepts and memories with which to work, turns its attention to itself, as it inevitably must, it produces a self-model that is extraordinarily deep and tangled. That deep and tangled self-model is what “I”-ness is all about.

The Epi Phenomenon

Thanks to the funneling-down processes of perception, which lead eventually — that is, in a matter of milliseconds — to the activation of certain discrete symbols in its brain, an animal (and let’s not forget robot vehicles!) can relate intimately and reliably to its physical environment. A mature human animal not only does a fine job of not slipping on banana peels and not banging into thorn-bristling rosebushes, it also reacts in a flash to strong odors, strange accents, cute babies, loud crashes, titillating headlines, terrific skiers, garish clothes, and on and on. It even occasionally hits curve balls coming at it at 80 miles an hour. Because an animal’s internal mirroring of the world must be highly reliable (the symbol elephant should not get triggered by the whine of a mosquito, nor should the symbol mosquito get triggered if an elephant ambles into view), its mirroring of the world via its private cache of symbols becomes an unquestioned pillar of stability. The things and patterns it perceives are what define its reality — but not all perceived things and patterns are equally real to it.

Although nobody planned it that way, most of us wind up emerging from adolescence with a deeply nuanced sense of what is real, with shades of gray all over the place. (However, I have known, and probably you have too, reader, a few adults for whom every issue that strikes me as subtle seems to them to be totally black-and-white — no messy shades of gray at all to deal with. That must make life easy!) Actually, to suggest that for most of us life is filled with “shades of gray” is far too simple, because that phrase conjures up the image of a straightforward one-dimensional continuum with many degrees of grayness running between white and black, while in fact the story is much more multidimensional than that. All of this is disturbing, because the word “real”, like so many words, seems to imply a sharp, clear-cut dichotomy. Surely it ought to be the case that some things simply are real while other things simply are not real. Surely there should be nothing that is partly real — that wouldn’t make sense! And yet, though we try very hard to force the world to match this ideal black-and-white dichotomy, things unfortunately get terribly blurry.

Through many types of abstraction and analogy-making and inductive reasoning, and through many long and tortuous chains of citations of all sorts of authorities (which constitute an indispensable pillar supporting every adult’s belief system, despite the insistence of high-school teachers who year after year teach that “arguments by authority” are spurious and are convinced that they ought to be believed because they are, after all, authority figures), we build up an intricate, interlocked set of beliefs as to what exists “out there” — and then, once again, that set of beliefs folds back, inevitably and seamlessly, to apply to our own selves.

We are all egocentric, and what is realest to each of us, in the end, is ourself. The realest things of all are my knee, my nose, my anger, my hunger, my toothache, my sideache, my sadness, my joy, my love for math, my abstraction ceiling, and so forth. What all these things have in common, what binds them together, is the concept of “my”, which comes out of the concept of “I” or “me”, and therefore, although it is less concrete than a nose or even a toothache, this “I” thing is what ultimately seems to each of us to constitute the most solid rock of undeniability of all. Could it possibly be an illusion? Or if not a total illusion, could it possibly be less real and less solid than we think it is? Could an “I” be more like an elusive, receding, shimmering rainbow than like a tangible, heftable, transportable pot of gold?

An epiphenomenon is a collective and unitary-seeming outcome of many small, often invisible or unperceived, quite possibly utterly unsuspected, events. In other words, an epiphenomenon could be said to be a large-scale illusion created by the collusion of many small and indisputably non-illusory events.

Each living being, no matter how simple, has a set of innate goals embedded in it, thanks to the feedback loops that evolved over time and that characterize its species. These feedback loops are the familiar, almost clichéd activities of life, such as seeking certain types of food, seeking a certain temperature range, seeking a mate, and so forth. Some creatures additionally develop their own individual goals, such as playing certain pieces of music or visiting certain museums or owning certain types of cars. Whatever a creature’s goals are, we are used to saying that it pursues those goals, and — at least if it is sufficiently complicated or sophisticated — we often add that it does so because it wants certain things.

“Why did you ride your bike to that building?” “I wanted to practice the piano.” “And why did you want to practice the piano?” “Because I want to learn that piece by Bach.” “And why do you want to learn that piece?” “I don’t know, I just do — it’s beautiful.” “But what is it about this particular piece that is so beautiful?” “I can’t say, exactly — it just hits me in some special way.” This creature ascribes its behavior to things it refers to as its desires or its wants, but it can’t say exactly why it has those desires. At a certain point there is no further possibility of analysis or articulation; those desires simply are there, and to the creature, they seem to be the root causes for its decisions, actions, motions. And always, inside the sentences that express why it does what it does, there is the pronoun “I” (or its cousins “me”, “my”, etc.). It seems that the buck stops there — with the so-called “I”.

Embarking on a Strange-Loop Safari

What I mean by “strange loop” is — here goes a first stab, anyway — not a physical circuit but an abstract loop in which, in the series of stages that constitute the cycling-around, there is a shift from one level of abstraction (or structure) 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. That is, despite one’s sense of departing ever further from one’s origin, one winds up, to one’s shock, exactly where one had started out. In short, a strange loop is a paradoxical level-crossing feedback loop.

Strange loops are shy creatures, and they tend to avoid the light of day. The quintessential example of this phenomenon, in fact, was only discovered in 1930 by Kurt Gödel, and he found it lurking in, of all places, the gloomy, austere, supposedly paradox-proof castle of Bertrand Russell’s theory of types.

Pattern and Provability

In the early twentieth century, Bertrand Russell, spurred by the maxim “Find and study paradoxes; design and build great ramparts to keep them out!” (my words, not his), resolved that in Principia Mathematica, his new barricaded fortress of mathematical reasoning, no set could ever contain itself, and no sentence could ever turn around and talk about itself. These parallel bans were intended to save Principia Mathematica from the trap that more naïve theories had fallen into. But something truly strange turned up when Kurt Gödel looked closely at what I will call PM — that is, the formal system used in Principia Mathematica for reasoning about sets (and about numbers, but they came later, as they were defined in terms of sets).

At this juncture, I feel compelled to point out a distinction not between two classes of numbers, but between two classes of people. There are those who will immediately be drawn to the idea of pattern-seeking, and there are those who will find it of no appeal, perhaps even distasteful. The former are, in essence, those who are mathematically inclined, and the latter are those who are not. Mathematicians are people who at their deepest core are drawn on — indeed, are easily seduced — by the urge to find patterns where initially there would seem to be none. The passionate quest after order in an apparent disorder is what lights their fires and fires their souls.

A mathematician who finds a pattern of this sort will instinctively ask, “Why? What is the reason behind this order?” Not only will all mathematicians wonder what the reason is, but even more importantly, they will all implicitly believe that whether or not anyone ever finds the reason, there must be a reason for it. Nothing happens “by accident” in the world of mathematics. The existence of a perfect pattern, a regularity that goes on forever, reveals — just as smoke reveals a fire — that something is going on behind the scenes. Mathematicians consider it a sacred goal to seek that thing, uncover it, and bring it out into the open. This activity is called, as you well know, “finding a proof ”, or stated otherwise, turning a conjecture into a theorem.

We have just seen up close a lovely example of what I call the “Mathematician’s Credo”, which I will summarize as follows: X is true because there is a proof of X; X is true and so there is a proof of X. Notice that this is a two-way street. The first half of the Credo asserts that proofs are guarantors of truth, and the second half asserts that where there is a regularity, there is a reason. Of course we ourselves may not uncover the hidden reason, but we firmly and unquestioningly believe that it exists and in principle could someday be found by someone. To doubt either half of the Credo would be unthinkable to a mathematician. To doubt the first line would be to imagine that a proved statement could nonetheless be false, which would make a mockery of the notion of “proof ”, while to doubt the second line would be to imagine that within mathematics there could be perfect, exceptionless patterns that go on forever, yet that do so with no rhyme or reason. To mathematicians, this idea of flawless but reasonless structure makes no sense at all. In that regard, mathematicians are all cousins of Albert Einstein, who famously declared, “God does not play dice.” What Einstein meant is that nothing in nature happens without a cause, and for mathematicians, that there is always one unifying, underlying cause is an unshakable article of faith.

This, then, constitutes the flip side of the Mathematician’s Credo: X is false because there is no proof of X; X is false and so there is no proof of X. In a word, just as provability and truth are the same thing for a mathematician, so are nonprovability and falsity. They are synonymous.

Gödel’s Quintessential Strange Loop

I must stress here that each rule of inference in a formal system like PM not only leads from one or more input formulas to an output formula, but it does so by purely typographical means — that is, via purely mechanical symbol-shunting that doesn’t require any thought about the meanings of symbols. From the viewpoint of a person (or machine) following the rules to produce theorems, the symbols might as well be totally devoid of meaning. On the other hand, each rule has to be very carefully designed so that, given input formulas that express truths, the output formula will also express a truth. The rule’s designer (Russell and Whitehead, in this case) therefore has to think about the symbols’ intended meanings in order to be sure that the rule will work exactly right for a manipulator (human or otherwise) who is not thinking about the symbols’ intended meanings.

Gödel did not actually believe that a perfect alignment between truths and PM theorems had been attained, nor indeed that such a thing could ever be attained, and his deep skepticism came from having smelled an extremely strange loop lurking inside the labyrinthine palace of mindless, mechanical, symbol-churning, meaning-lacking mathematical reasoning.

In short, Gödel showed how any visual symbol-pattern whatsoever in the idiosyncratic notation of Principia Mathematica could be assigned a unique number, which could easily be decoded to give back the visual pattern (i.e., sequence of symbols) to which it corresponded. Conceiving of and polishing this precise two-way mapping, now universally called “Gödel numbering”, constituted the first key step of Gödel’s work.

Young Kurt Gödel — he was only 25 in 1931 — had discovered a vast sea of amazingly unsuspected, bizarrely twisty formulas hidden inside the austere, formal, type-theory-protected and therefore supposedly paradoxfree world defined by Russell and Whitehead in their grandiose threevolume œuvre Principia Mathematica, and the many counterintuitive properties of Gödel’s original formula and its countless cousins have occupied mathematicians, logicians, and philosophers ever since.

I wish to point out explicitly that the most concise English translations of Gödel’s formula and its cousins employ the word “I” (“I am not provable in PM ”; “I am not a PM theorem”). This is not a coincidence. Indeed, this informal, almost sloppy-seeming use of the singular first-person pronoun affords us our first glimpse of the profound connection between Gödel’s austere mathematical strange loop and the very human notion of a conscious self.

How Analogy Makes Meaning

In my many years of reflecting about what Gödel did in 1931, it is this insight of his into the roots of meaning — his discovery that, thanks to a mapping, full-fledged meaning can suddenly appear in a spot where it was entirely unsuspected — that has always struck me the most. I find this insight as profound as it is simple.

A remark made with the aim of talking about situation A can also implicitly apply to situation B, even if there was no intention of talking about B, and B was never mentioned at all. All it takes is that there be an easy analogy — an unforced mapping that reveals both situations to have essentially the same central structure or conceptual core — and then the extra meaning is there to be read, whether one chooses to read it or not. In short, a statement about one situation can be heard as if it were about an analogous — or, to use a slightly technical term, isomorphic — situation. An isomorphism is just a formalized and strict analogy — one in which the network of parallelisms between two situations has been spelled out explicitly and precisely — and I’ll use the term freely below.

If two people are romantically involved (or even if they aren’t, but at least one of them feels there’s a potential spark), then almost any conversation between them about any romance whatsoever, no matter who it involves, stands a good chance of being heard by one or both of them as putting a spotlight on their own situation. Such boomeranging-back is almost inevitable because romances, even very good ones, are filled with uncertainty and yearning. We are always on the lookout for clues or insights into our romantic lives, and analogies are among the greatest sources of clues and insights. Therefore, to notice an analogy between ourselves and another couple that is occupying center stage in our conversation is pretty much a piece of cake handed to us on a silver platter. The crucial question is whether it tastes good or not.

It is all too easy to forget that moths, flies, dogs, cats, neonates, television cameras, and other small-souled beings do not perceive a television screen as we do. Although it’s hard for us to imagine, they see the pixels in a raw, uninterpreted fashion, and thus to them a TV screen is as drained of long-ago-and-far-away meanings as is, to you or me, a pile of fall leaves, a Jackson Pollock painting, or a newspaper article in Malagasy (my apologies to you if you speak Malagasy; in that case, please replace it by Icelandic — and don’t tell me that you speak that language, too!). “Reading” a TV screen at the representational level is intellectually far beyond such creatures, even if for most humans it is essentially second nature already by age two or so. A dog gazing vacantly at a television screen, unable to make out any imagery, unaware even that any imagery is intended, is thus not unlike Lord Russell staring blankly at a formula of his beloved system PM and seeing only its “easy” (arithmetical) meaning, while the other meaning, the mapping-mediated meaning due to Gödel, lies intellectually beyond him, utterly inaccessible, utterly undreamt-of.

Indeed, what we might be tempted to call “direct” reference is mediated by a code, too — the code between words and things given to us by our native language (Malagasy, Icelandic, etc.). It’s just that that code is a simpler one (or at least a more familiar one). In sum, the seemingly sharp distinction between “direct” reference and “indirect” reference is only a matter of degree, not a black-and-white distinction. To repeat, analogy has force in proportion to its precision and visibility.

A reader might conclude that a strange loop necessarily involves a self-undermining or self-negating quality (“This formula is not provable”; “This line is not pennable”; “You should not be attending this play”). However, negation plays no essential role in strange loopiness. It’s just that the strangeness becomes more pungent or humorous if the loop enjoys a self-undermining quality. Recall Escher’s Drawing Hands. There is no negation in it — both hands are drawing. Imagine if one were erasing the other! In this book, a loop’s strangeness comes purely from the way in which a system can seem to “engulf itself ” through an unexpected twisting-around, rudely violating what we had taken to be an inviolable hierarchical order.

The preconception that an obviously suspicion-arousing word such as “this” (or “I” or “here” or “now” — “indexicals”, as they are called by philosophers — words that refer explicitly to the speaker or to something closely connected with the speaker or the message itself) is an indispensable ingredient for self-reference to arise in a system is shown by Gödel’s discovery to be a naïve illusion; instead, the strange twisting-back is a simple, natural consequence of an unexpected isomorphism between two different situations (that which is being talked about, on the one hand, and that which is doing the talking, on the other). Bertrand Russell, having made sure that all indexical notions such as “this” were absolutely excluded from his formal system, believed his handiwork to be forever immunized against the scourge of wrapping-around — but Kurt Gödel, with his fateful isomorphism, showed that such a belief was an unjustified article of faith.

Kurt Gödel was the first person to realize and exploit the fact that the positive integers, though they might superficially seem to be very austere and isolated, in fact constitute a profoundly rich representational medium. They can mimic or mirror any kind of pattern. Like any human language, where nouns and verbs (etc.) can engage in unlimitedly complex dancing, the natural numbers too, can engage in unlimitedly complex additive and multiplicative (etc.) dancing, and can thereby “talk”, via code or analogy, about events of any sort, numerical or non-numerical.

On Downward Causality

To my mind, the most unexpected emergent phenomenon to come out of Kurt Gödel’s 1931 work is a bizarre new type of mathematical causality (if I can use that unusual term). I have never seen his discovery cast in this light by other commentators, so what follows is a personal interpretation. To explain my viewpoint, I have to go back to Gödel’s celebrated formula — let’s call it “KG” in his honor — and analyze what its existence implies for PM.

We have just uncovered a very strange anomaly inside PM: here is a statement of arithmetic (or number theory, to be slightly more precise) that we are sure is true, and yet we are equally sure it is unprovable — and to cap it off, these two contradictory-sounding facts are consequences of each other! In other words, KG is unprovable not only although it is true, but worse yet, because it is true. This weird situation is utterly unprecedented and profoundly perverse. It flies in the face of the Mathematician’s Credo, which asserts that truth and provability are just two sides of the same coin — that they always go together, because they entail each other. Instead, we’ve just encountered a case where, astoundingly, truth and unprovability entail each other. Now isn’t that a fine how-do-you-do?

In other words, the hole in PM (and in any other axiomatic system as rich as PM) is not due to some careless oversight by Russell and Whitehead but is simply an inevitable property of any system that is flexible enough to capture the chameleonic quality of whole numbers. PM is rich enough to be able to turn around and point at itself, like a television camera pointing at the screen to which it is sending its image. If you make a good enough TV system, this looping-back ability is inevitable. And the higher the system’s resolution is, the more faithful the image is. As in judo, your opponent’s power is the source of their vulnerability. Kurt Gödel, maneuvering like a black belt, used PM’s power to bring it crashing down. Not as catastrophically as with inconsistency, mind you, but in a wholly unanticipated fashion — crashing down with incompleteness. The fact that you can’t get around Gödel’s black-belt trickery by enriching or enlarging PM in any fashion is called “essential incompleteness”

Kurt Gödel’s bombshell, though just as fantastic, was not a fantasy. It was rigorous and precise. It revealed the stunning fact that a formula’s hidden meaning may have a peculiar kind of “downward” causal power, determining the formula’s truth or falsity (or its derivability or nonderivability inside PM or any other sufficiently rich axiomatic system). Merely from knowing the formula’s meaning, one can infer its truth or falsity without any effort to derive it in the old-fashioned way, which requires one to trudge methodically “upwards” from the axioms. This is not just peculiar; it is astonishing. Normally, one cannot merely look at what a mathematical conjecture says and simply appeal to the content of that statement on its own to deduce whether the statement is true or false (or provable or unprovable).

Gödel revealed to us that there is a profound gulf between truth and provability in PM (indeed, in any formal axiomatic system like PM). That is, there are many true statements that are not provable, alas. So if a formula of PM fails to be a theorem, you can’t take that as a sure sign that it is false (although luckily, whenever a formula is a theorem, that’s a sure sign that it is true).

There is thus a curious upside-downness to our normal human way of perceiving the world: we are built to perceive “big stuff” rather than “small stuff”, even though the domain of the tiny seems to be where the actual motors driving reality reside. The fact that our minds see only the high level while completely ignoring the low level is reminiscent of the possibilities of high-level vision that Gödel revealed to us. He found a way of taking a colossally long PM formula (KG or any cousin) and reading it in a concise, easily comprehensible fashion (“KG has no proof in PM”) instead of reading it as the low-level numerical assertion that a certain gargantuan integer possesses a certain esoteric recursively defined number-theoretical property (non-primness). Whereas the standard low-level reading of a PM string is right there on the surface for anyone to see, it took a genius to imagine that a high-level reading might exist in parallel with it.

By contrast, in the case of a creature that thinks with a brain (or with a careenium), reading its own brain activity at a high level is natural and trivial (for instance, “I remember how terrified I was that time when Grandma took me to see The Wizard of Oz”), whereas the low-level activities that underwrite the high level (numberless neurotransmitters hopping like crazy across synaptic gaps, or simms silently bashing by the billions into each other) are utterly hidden, unsuspected, invisible. A creature that thinks knows next to nothing of the substrate allowing its thinking to happen, but nonetheless it knows all about its symbolic interpretation of the world, and knows very intimately something it calls “I”.

Such mentalistic notions as “belief”, “hope”, “guilt”, “envy”, and so on arose many eons before any human dreamt of trying to ground them as recurrent, recognizable patterns in some physical substrate (the living brain, seen at some fine-grained level). This tendency to proceed slowly from intuitive understanding at a high level to scientific understanding at a low level is reminiscent of the fact that the abstract notion of a gene as the basic unit by which heredity is passed from parent to offspring was boldly postulated and then carefully studied in laboratories for many decades before any “hard” physical grounding was found for it. When microscopic structures were finally found that allowed a physical “picture” to be attached to the abstract notion, they turned out to be wildly unexpected entities: a gene was revealed to be a medium-length stretch of a very long helically twisting cord made of just four kinds of molecules (nucleotides) linked one to the next to form a chain millions of units long.

And then, miraculously, it turned out that the chemistry of these four molecules was in a certain sense incidental — what mattered most of all when one thought about heredity was their newly revealed informational properties, as opposed to their traditional physico-chemical properties. That is, the proper description of how heredity and reproduction worked could in large part be abstracted away from the chemistry, leaving just a high-level picture of information-manipulating processes alone. At the heart of these information-manipulating processes lay a high abstraction called the “genetic code”, which mapped every possible three-nucleotide “word” (or “codon”), of which there are sixty-four, to one of twenty different molecules belonging to a totally unrelated chemical family (the amino acids). In other words, a profound understanding of genes and heredity was possible only if one was intimately familiar with a high-level meaning-mediating mapping. This should sound familiar.

The Elusive Apple of My “I”

As a simple illustration of how profoundly wedded our thinking is to the blurry, hazy categories of the macroworld, consider the curious fact that logicians — people who by profession try to write down ironclad, razor-sharp rules of logical inference that apply with impeccable precision to linguistic expressions — seldom if ever resort to the level of particles and fields for their canonical examples of fundamental, eternal truths. Instead, their most frequent examples of “truth” are typically sentences that use totally out-of-focus categories — sentences such as “Snow is white”, “Water is wet”, “Bachelors are unmarried males”, and “Communism either is or is not in for deep trouble in the next few years in China.” If you think these sentences do express sharp truths, just ponder for a moment… What does “snow” really mean? Is it as sharp a category as “checkmate” or “prime number”? And what does “wet” really mean, exactly? No blur at all there? What about “unmarried” — not to mention “the next few years” and “in for deep trouble”? Ambiguities galore here! And yet such classic philosophers’ sentences, since they reside at the level where we naturally float, seem to most people far realer and (therefore far more reliably true) than sentences such as “Electrons have spin 1/2” or “The laws of electromagnetism are invariant under a mirror reflection.”

The foregoing means that we can best understand our own actions just as we best understand other creatures’ actions — in terms of stable but intangible internal patterns called “hopes” and “beliefs” and so on. But the need for self-understanding goes much further than that. We are powerfully driven to create a term that summarizes the presumed unity, internal coherence, and temporal stability of all the hopes and beliefs and desires that are found inside our own cranium — and that term, as we all learn very early on, is “I”. And pretty soon this high abstraction behind the scenes comes to feel like the maximally real entity in the universe. Just as we are convinced that ideas and emotions, rather than particles, cause wars and love affairs, so we are convinced that our “I” causes our own actions. The Grand Pusher in and of our bodies is our “I”, that marvelous marble whose roundness, solidity, and size we so unmistakably feel inside the murky box of our manifold hopes and desires.

The strange loop making up an “I” is no more a pinpointable, extractable physical object than an audio feedback loop is a tangible object possessing a mass and a diameter. Such a loop may exist “inside” an auditorium, but the fact that it is physically localized doesn’t mean that one can pick it up and heft it, let alone measure such things as its temperature and thickness! An “I” loop, like an audio feedback loop, is an abstraction — but an abstraction that seems immensely real, almost physically palpable, to beings like us, beings that have high readings on the hunekometer.

Since we perceive not particles interacting but macroscopic patterns in which certain things push other things around with a blurry causality, and since the Grand Pusher in and of our bodies is our “I”, and since our bodies push the rest of the world around, we are left with no choice but to conclude that the “I” is where the causality buck stops. The “I” seems to each of us to be the root of all our actions, all our decisions. This is only one side of the truth, of course, since it utterly snubs the viewpoint whereby an impersonal physics of micro-entities is what makes the world go round, but it is a surprisingly reliable and totally indispensable distortion. These two properties of the naïve, non-physics viewpoint — its reliability and its indispensability — lock it ever more tightly into our belief systems as we pass from babyhood through childhood to adulthood.

What would make a human brain a candidate for housing a loop of self-representation? Why would a fly brain or a mosquito brain not be just as valid a candidate? Why, for that matter, not a bacterium, an ovum, a sperm, a virus, a tomato plant, a tomato, or a pencil? The answer should be clear: a human brain is a representational system that knows no bounds in terms of the extensibility or flexibility of its categories. A mosquito brain, by contrast, is a tiny representational system that contains practically no categories at all, never mind being flexible and extensible. Very small representational systems, such as those of bacteria, ova, sperms, plants, thermostats, and so forth, do not enjoy the luxury of self-representation. And a tomato and a pencil are not representational systems at all, so for them, the story ends right there (sorry, little tomato! sorry, little pencil!).

Constantly, relentlessly, day by day, moment by moment, my self-symbol is being shaped and refined — and in turn, it triggers external actions galore, day after day after day. (Or so the causality appears to it, since it is on this level, not on the micro-level, that it perceives the world.) It sees its chosen actions (kicks, tosses, screams, laughs, jokes, jabs, trips, books, pleas, threats, etc.) making all sorts of entities in its environment react in large or small ways, and it internalizes those effects in terms of its coarse-grained categories (as to their graininess, it has no choice). Through endless random explorations like this, my self-symbol slowly acquires concise and valuable insight into its nature as a chooser and launcher of actions, embedded in a vast and multifarious, partially predictable world.

Similarly, my social actions induce reactions on the part of other sentient beings. Those reactions bounce back to me and I perceive them in terms of my repertoire of symbols, and in this way I indirectly perceive myself through my effect on others. I am building up my sense of who I am in others’ eyes. My self-symbol is coalescing out of an initial void.

Let me now summarize the foregoing in slightly more abstract terms. The vast amounts of stuff that we call “I” collectively give rise, at some particular moment, to some external action, much as a stone tossed into a pond gives rise to expanding rings of ripples. Soon, our action’s myriad consequences start bouncing back at us, like the first ripples returning after bouncing off the pond’s banks. What we receive back affords us the chance to perceive what our gradually metamorphosing “I” has wrought. Millions of tiny reflected signals impinge on us from outside, whether visually, sonically, tactilely, or whatever, and when they land, they trigger internal waves of secondary and tertiary signals inside our brain. Finally this flurry of signals is funneled down into just a handful of activated symbols — a tiny set of extremely well-chosen categories constituting a coarse-grained understanding of what we’ve just done

And thus the current “I” — the most up-to-date set of recollections and aspirations and passions and confusions — by tampering with the vast, unpredictable world of objects and other people, has sparked some rapid feedback, which, once absorbed in the form of symbol activations, gives rise to an infinitesimally modified “I”; thus round and round it goes, moment after moment, day after day, year after year. In this fashion, via the loop of symbols sparking actions and repercussions triggering symbols, the abstract structure serving us as our innermost essence evolves slowly but surely, and in so doing it locks itself ever more rigidly into our mind. Indeed, as the years pass, the “I” converges and stabilizes itself just as inevitably as the screech of an audio feedback loop inevitably zeroes in and stabilizes itself at the system’s natural resonance frequency.

Strangeness in the “I” of the Beholder

Why, you might be wondering, do I call the lifelong loop of a human being’s self-representation, as described in the preceding chapter, a strange loop? You make decisions, take actions, affect the world, receive feedback, incorporate it into your self, then the updated “you” makes more decisions, and so forth, round and round. It’s a loop, no doubt — but where’s the paradoxical quality that I’ve been saying is a sine qua non for strange loopiness? Why is this not just an ordinary feedback loop? What does such a loop have in common with the quintessential strange loop that Kurt Gödel discovered unexpectedly lurking inside Principia Mathematica?

Just as something very strange had to be happening inside the stony fortress of Principia Mathematica to allow the outlawed “I” of Gödelian sentences like “I am not provable” to creep in, something very strange must also take place inside a bony cranium stuffed with inanimate molecules if it is to bring about a soul, a “light on”, a unique human identity, an “I”. And keep in mind that an “I” does not magically pop up in all brains inside all crania, courtesy of “the right stuff” (that is, certain “special” kinds of molecules); it happens only if the proper patterns come to be in that medium. Without such patterns, the system is just as it superficially appears to be: a mere lump of spongy matter, soulless, “I”-less, devoid of any inner light.

Some philosophers see our inner lights, our “I” ’s, our humanity, our souls, as emanating from the nature of the substrate itself — that is, from the organic chemistry of carbon. I find that a most peculiar tree on which to hang the bauble of consciousness. Basically, this is a mystical refrain that explains nothing. Why should the chemistry of carbon have some magical property entirely unlike than that of any other substance? And what is that magical property? And how does it make us into conscious beings? Why is it that only brains are conscious, and not kneecaps or kidneys, if all it takes is organic chemistry? Why aren’t our carbon-based cousins the mosquitoes just as conscious as we are? Why aren’t cows just as conscious as we are? Doesn’t organization or pattern play any role here? Surely it does. And if it does, why couldn’t it play the whole role? By focusing on the medium rather than the message, the pottery rather than the pattern, the typeface rather than the tale, philosophers who claim that something ineffable about carbon’s chemistry is indispensable for consciousness miss the boat.

Our own brains are no different from careenia, except, of course, that whereas careenia are just my little fantasy, human brains are not. The symbols in our brains truly do do that voodoo that they do so well, and they do it in the electrochemical soup of neural events. The strange thing, though, is that over the eons that it took for our brains to evolve from the earliest proto-brains, meanings just sneaked ever so quietly into the story, almost unobserved. It’s not as if somebody had devised a grand plan, millions of years in advance, that high-level meaningful structures — physical patterns representing abstract categories — would one day come to inhabit big fancy brains; rather, such patterns (the “symbols” of this book) simply came along as an unplanned by-product of the tremendously effective way that having bigger and bigger brains helped beings to survive better and better in a terribly cutthroat world.

Much as Gödel saw the great potential of shifting attention to a wholly different level of PM strings, so I am suggesting (though I’m certainly far from the first) that we have to shift our attention to a far higher level of brain activity in order to find symbols, concepts, meanings, desires, and, ultimately, our selves. The funny thing is that we humans all are focused on that level without ever having had any choice in the matter. We automatically see our brains’ activity as entirely symbolic. I find something wonderfully strange and upside-down about this,

What makes a strange loop appear in a brain and not in a video feedback system, then, is an ability — the ability to think — which is, in effect, a one-syllable word standing for the possession of a sufficiently large repertoire of triggerable symbols. Just as the richness of whole numbers gave PM the power to represent phenomena of unlimited complexity and thus to twist back and engulf itself via Gödel’s construction, so our extensible repertoires of symbols give our brains the power to represent phenomena of unlimited complexity and thus to twist back and to engulf themselves via a strange loop.

But there is a flip side to all this, a second key ingredient that makes the loop in a human brain qualify as “strange”, makes an “I” come seemingly out of nowhere. This flip side is, ironically, an inability — namely, our Klüdgerotic inability to peer below the level of our symbols. It is our inability to see, feel, or sense in any way the constant, frenetic churning and roiling of micro-stuff, all the unfelt bubbling and boiling that underlies our thinking. This, our innate blindness to the world of the tiny, forces us to hallucinate a profound schism between the goal-lacking material world of balls and sticks and sounds and lights, on the one hand, and a goalpervaded abstract world of hopes and beliefs and joys and fears, on the other, in which radically different sorts of causality seem to reign.

In summary, the combination of these two ingredients — one an ability and the other an inability — gives rise to the strange loop of selfhood, a trap into which we humans all fall, every last one of us, willy-nilly. Although it begins as innocently as a humble toilet’s float-ball mechanism or an audio or video feedback loop, where no counterintuitive type of causality is posited anywhere, human self-perception inevitably ends up positing an emergent entity that exerts an upside-down causality on the world, leading to the intense reinforcement of and the final, invincible, immutable locking-in of this belief. The end result is often the vehement denial of the possibility of any alternative point of view at all.

Entwinement

I declared that there was one strange loop in each human cranium, and that this loop constituted our “I”, but I also mentioned that that was just a crude first stab. Indeed, it is a drastic oversimplification. Since we all perceive and represent hundreds of other human beings at vastly differing levels of detail and fidelity inside our cranium, and since the most important facet of all of those human beings is their own sense of self, we inevitably mirror, and thus house, a large number of other strange loops inside our head. But what exactly does it mean to say that each human head is the locus of a multiplicity of “I” ’s?

Well, I don’t know precisely what it means. I wish I did! And I reckon that if I did, I would be the world’s greatest philosopher and psychologist rolled into one. As best I can guess, from far below such a Parnassus, it means we manufacture an enormously stripped-down version of our own strange loop of selfhood and install it at the core of our symbols for other people, letting that initially crude loopy structure change and grow over time. In the case of the people we know best — our spouse, our parents and siblings, our children, our dearest friends — each of these loops grows over the years to be a very rich structure adorned with many thousands of idiosyncratic ingredients, and each one achieves a great deal of autonomy from the stripped-down “vanilla” strange loop that served as its seed.

For better or for worse, we humans are born with only the tiniest hints of what our perceptual systems will metamorphose into as we interact with the world over the course of decades. At birth, our repertoire of categories is so minimal that I would call it nil for all practical purposes. Deprived of symbols to trigger, a baby cannot make sense of what William James evocatively called the “big, blooming, buzzing confusion” of its sensory input. The building-up of a self-symbol is still far in the future for a baby, and so in babies there exists no strange loop of selfhood, or nearly none. To put it bluntly, since its future symbolic machinery is 99 percent missing, a human neonate, devastatingly cute though it might be, simply has no “I” — or, to be more generous, if it does possess some minimal dollop of “I”-ness, perhaps it is one huneker’s worth or thereabouts — and that’s not much to write home about. So we see that a human head can contain less than one strange loop. What about more than one?

I believe we are drawing slowly closer to an understanding of what genuine human identity is all about. In fact, how could anyone imagine that it would be possible to gain deep insight into the mystery of human identity without eventually running up against some sort of unfamiliar abstract structures? Sigmund Freud posited egos, ids, and superegos, and there may well exist some such abstractions inside the architecture of a human soul (perhaps not exactly those three, but patterns of that ilk). We humans are so different from other natural phenomena, even from most other types of living beings, that we should expect that in order to get a glimpse into what we truly are, we would have to look in very unexpected places. Although my strange loops are obviously very different from Freud’s notions, there is a certain similarity of spirit. Both views of what a self is involve abstract patterns that are extremely remote from the biological substrate they inhabit — so remote, in fact, that the specifics of the substrate would seem mostly irrelevant.

At first I had proposed that a human “I” results from the existence of a very special strange loop in a human brain, but now we see that since we mirror many people inside our crania, there will be many loops of different sizes and degrees of complexity, so we have to refine our understanding. Part of the refinement hinges, as I just stated, on the fact that one of these loops in a given brain is privileged — mediated by a perceptual system that feeds directly into that brain. There is another part of the story, though, which has to do with what a brain controls rather than what it perceives.

Thermostat in my house does not regulate the temperature in your house. Analogously, the decisions made in my brain do not control the body that’s hard-wired to your brain. When you and I play tennis, it’s only my arms that my brain controls! Or so it would seem at first. On second thought, that’s clearly an oversimplification, and this is where things start to get blurry once again. I have partial and indirect control over your arms — after all, wherever I send the ball, that’s where you run, and my shot has a great deal to do with how you will swing your arms. So in some indirect fashion, my brain can control your muscles in a game of tennis, but it is not a very reliable fashion. Likewise, if I hit my brakes while driving down the road, then the person behind me will also hit their brakes. What happens in my brain exerts a little bit of control over that driver’s actions, but it is an unreliable and imprecise control.

The type of external control just described does not create a profound blurring of two people’s identities. Tennis and driving do not give rise to deep interpenetrations of souls. But things get more complicated when language enters the show. It is through language most of all that our brains can exert a fair measure of indirect control over other humans’ bodies — a phenomenon very familiar not only to parents and drill sergeants, but also to advertisers, political “spin doctors”, and whiny, wheedling teen-agers. Through language, other people’s bodies can become flexible extensions of our own bodies. In that sense, then, my brain is attached to your body in somewhat the same way as it is to my body — it’s just that, once again, the connection is not hard-wired. My brain is attached to your body via channels of communication that are much slower and more indirect than those linking it to my body, so the control is much less efficient.

We all possess two cerebral hemispheres (left and right halves), each of which can function pretty well as a brain on its own, in case one side of our brain is damaged. I’ll presume that both of your hemispheres are in good shape, dear reader, in which case what you mean when you say “I” involves a very tight team consisting of your left and right half-brains, each of which is fed directly by just one of your eyes and just one of your ears. The communication between your team’s two members is so strong and rapid, however, that the fused entity — the team itself — seems like just one thing, one absolutely unbreakable self. You know just what this feels like because it’s how you are constructed! And if you’re anything like me, neither of your half-brains goes around calling itself “i” and brazenly proclaiming itself an autonomous soul! Rather, the two of them together make just one capital “I”.

No one has trouble with the idea that “the same gene” can exist in two different cells, in two different organisms. But what is a gene? A gene is not an actual physical object, because if it were, it could only be located in one cell, in one organism. No, a gene is a pattern — a particular sequence of nucleotides (usually encoded on paper by a sequence of letters from the four-letter alphabet “ACGT”). And so a gene is an abstraction, and thus “the very same gene” can exist in different cells, different organisms, even organisms living millions of years apart. No one has trouble with the idea that “the same novel” can exist in two different languages, in two different cultures. But what is a novel? A novel is not a specific sequence of words, because if it were, it could only be written in one language, in one culture. No, a novel is a pattern — a particular collection of characters, events, moods, tones, jokes, allusions, and much more. And so a novel is an abstraction, and thus “the very same novel” can exist in different languages, different cultures, even cultures thriving hundreds of years apart.

And so no one should have trouble with the idea that “the same hopes and dreams” can inhabit two different people’s brains, especially when those two people live together for years and have, as a couple, engendered new entities on which these hopes and dreams are all centered. Perhaps this seems overly romantic, but it is how I felt at the time, and it is how I still feel. The sharing of so much, particularly concerning our two children, aligned our souls in some intangible yet visceral manner, and in some dimensions of life turned us into a single unit that acted as a whole, much as a school of fish acts as a single-minded higher-level entity.

Grappling with the Deepest Mystery

One day, as I gazed at a photograph of Carol taken a couple of months before her death, I looked at her face and I looked so deeply that I felt I was behind her eyes, and all at once, I found myself saying, as tears flowed, “That’s me! That’s me!” And those simple words brought back many thoughts that I had had before, about the fusion of our souls into one higher-level entity, about the fact that at the core of both our souls lay our identical hopes and dreams for our children, about the notion that those hopes were not separate or distinct hopes but were just one hope, one clear thing that defined us both, that welded us together into a unit, the kind of unit I had but dimly imagined before being married and having children. I realized then that although Carol had died, that core piece of her had not died at all, but that it lived on very determinedly in my brain.

The name “Carol” denotes, for me, far more than just a body, which is now gone, but rather a very vast pattern, a style, a set of things including memories, hopes, dreams, beliefs, loves, reactions to music, sense of humor, self-doubt, generosity, compassion, and so on. Those things are to some extent sharable, objective, and multiply instantiatable, a bit like software on a diskette. And my obsessive writing-down of memories, and the many videotapes she is on, and all our collective brain-stored memories of Carol make those pattern-aspects of her still exist, albeit in spread-out form — spread out among different videotapes, among different friends’ and relatives’ brains, among different yellow-sheeted notebooks, and so on. In any case, there is a spread-out pattern of Carolness very clearly discernable in this physical world. And in that sense, Carolness survives.

Just where comes the point of “critical mass”, when having a pattern, perhaps a large set of videotapes, perhaps an extensive diary (like Anne Frank’s), amounts to having a significant percentage of the person — a significant percentage of their self, their soul, their “I”, their consciousness, their interiority? If you concede that a significant percentage of the person would exist at some point along this spectrum, provided that one had a sufficiently large pattern, then it seems to me that you would have to concede that even having a much smaller pattern, such as a photo or my cherished collection of Carol’s “bonner mots”, already gives you a non-zero (even if microscopic) fraction of the actual person — of “the view from inside” — not just of how it was to be with them.

A person is a point of view — not only a physical point of view (looking out of certain eyes in a certain physical place in the universe), but more importantly a psyche’s point of view: a set of hair-trigger associations rooted in a huge bank of memories. The latter can be absorbed, more and more over time, by someone else. Thus it’s like acquiring a foreign language step by step. For a while, one’s speaking is largely “fake” — that is, one is thinking in one’s native language but substituting words quickly enough to give the impression that the thinking is going on in the second language; however, as one’s experience with the second language grows, new grammatical habits form and turn slowly into reflexes, as do thousands of lexical items, and the second language becomes more and more rooted, more and more genuine. One gradually becomes a fluent thinker in and speaker of the other language, and it is no longer “fake”, even if one has an accent in it. So it is with coming to see the world through another person’s soul.

There are shallower aspects of a person and there are deeper aspects, and the deeper aspects are what imbue the shallower ones with genuine meaning. I guess that sounds cryptic. What I mean is that if I believe statement X (for example, “Chopin is a great composer”) and someone else also believes X, then, despite this ostensible agreement between us, our internal feelings when we think X may be unutterably different even though, on the superficial verbal level, our belief is “the same”. On the other hand, if our souls have a deep resemblance, then our two beliefs in X will in fact be very similar, and we will intuitively resonate with each other. Communication (at least on that topic) will be nearly effortless.

What really matters for mutual understanding of two people are such things as having similar responses to music (not just shared likes but also shared dislikes), having similar responses to people (again, I mean both likes and dislikes), having similar degrees of empathy, honesty, patience, sentimentality, audacity, ambition, competitiveness, and so on. These central building blocks of personality, character, and temperament are decisive in mutual understanding. Consider, for instance, the shattering experience of constantly feeling inferior to other people. Some people know this intimately, and some don’t know it at all. A person with huge reserves of self-confidence will simply never be able to feel how it is to be paralyzed by the lack of confidence — they “just don’t get it”. It is these sorts of aspects, these innermost aspects of a soul (as opposed to such relatively objective and transferable items as countries visited, novels read, cuisines mastered, historical facts known, and so forth) that make for soul-uniqueness.

But the key question is, no matter how much you absorb of another person, can you ever have absorbed so much of them that when that primary brain perishes, you can feel that that person did not totally perish from the earth, because they (or at least a significant fraction of them) are still instantiated in your brain, because they still live on in a “second neural home”?

In my opinion, to deal with this question head-on, one really has to focus on this thing I call the “Gödelian swirl of self”. The key question becomes this: When the pointers to “self” — the structures that, through a lifetime of locking-in and self-stabilizing, have given rise to an “I” — are copied in some imperfect, low-resolution fashion in a secondary brain, where exactly do they wind up pointing? My internal model of Carol is certainly “thin” or sparse in comparison to the original self-model (the one that was located inside her own brain), but that sparseness is not the key issue. The crux is this: even if my internal model of Carol were unbelievably rich (e.g., like my Mom’s model of my Dad, say, or even ten times stronger than that), would it nonetheless be the wrong kind of structure to give rise to an “I”? Would it be something other than a strange loop? Would it be a structure pointing not at itself but at something else, and therefore be lacking that essentially swirly, vorticial, self-referential quality that makes an “I”? My guess is that if the model were extremely rich, extremely faithful, then effectively the destinations of all the pointers in it would be fluid — in other words, the pointers inside my model of Carol would be able to slip, to point just as validly to the symbol for her in my brain as to her own self-symbol. If so, then the original swirliness, the original “I”-ness of the structure, would have been successfully transported to a second medium and reconstructed faithfully (though far more coarse-grainedly) in it.

How We Live in Each Other

This, in essence, is what the computer revolution is all about: when a certain well-defined threshold — I’ll call it the “Gödel–Turing threshold” — is surpassed, then a computer can emulate any kind of machine. This is the meaning of the term “universal machine”, introduced in 1936 by the English mathematician and computer pioneer Alan Turing,

Inspired by Gödel’s mapping of PM into itself, Alan Turing realized that the critical threshold for this kind of computational universality comes at exactly that point where a machine is flexible enough to read and correctly interpret a set of data that describe its own structure. At this crucial juncture, a machine can, in principle, explicitly watch how it does any particular task, step by step. Turing realized that a machine that has this critical level of flexibility can imitate any another machine, no matter how complex the latter is. In other words, there is nothing more flexible than a universal machine. Universality is as far as you can go!

We human beings, too, are universal machines of a different sort: our neural hardware can copy arbitrary patterns, even if evolution never had any grand plan for this kind of “representational universality” to come about. Through our senses and then our symbols, we can internalize external phenomena of many sorts.

Representational universality also means that we can import ideas and happenings without having to be direct witnesses to them. For example, as I mentioned in Chapter 11, humans (but not most other animals) can easily process the two-dimensional arrays of pixels on a television screen and can see those ever-changing arrays as coding for distant or fictitious three-dimensional situations evolving over time.

In the world of living things, the magic threshold of representational universality is crossed whenever a system’s repertoire of symbols becomes extensible without any obvious limit. This threshold was crossed on the species level somewhere along the way from earlier primates to ourselves. Systems above this counterpart to the Gödel–Turing threshold — let’s call them “beings”, for short — have the capacity to model inside themselves other beings that they run into — to slap together quick-and-dirty models of beings that they encounter only briefly, to refine such coarse models over time, even to invent imaginary beings from whole cloth. (Beings with a propensity to invent other beings are often informally called “novelists”.) Once beyond the magic threshold, universal beings seem inevitably to become ravenously thirsty for tastes of the interiority of other universal beings. This is why we have movies, soap operas, television news, blogs, webcams, gossip columnists, People magazine, and The Weekly World News, among others. People yearn to get inside other people’s heads, to “see out” from inside other crania, to gobble up other people’s experiences.

Although I have been depicting it somewhat cynically, representational universality and the nearly insatiable hunger that it creates for vicarious experiences is but a stone’s throw away from empathy, which I see as the most admirable quality of humanity. To “be” someone else in a profound way is not merely to see the world intellectually as they see it and to feel rooted in the places and times that molded them as they grew up; it goes much further than that. It is to adopt their values, to take on their desires, to live their hopes, to feel their yearnings, to share their dreams, to shudder at their dreads, to participate in their life, to merge with their soul.

What is really going on when you dream or think more than fleetingly about someone you love (whether that person died many years ago or is right now on the other end of a phone conversation with you)? In the terminology of this book, there is no ambiguity about what is going on. The symbol for that person has been activated inside your skull, lurched out of dormancy, as surely as if it had an icon that someone had double-clicked. And the moment this happens, much as with a game that has opened up on your screen, your mind starts acting differently from how it acts in a “normal” context. You have allowed yourself to be invaded by an “alien universal being”, and to some extent the alien takes charge inside your skull, starts pushing things around in its own fashion, making words, ideas, memories, and associations bubble up inside your brain that ordinarily would not do so. The activation of the symbol for the loved person swivels into action whole sets of coordinated tendencies that represent that person’s cherished style, their idiosyncratic way of being embedded in the world and looking out at it. As a consequence, during this visitation of your cranium, you will surprise yourself by coming out with different jokes from those you would normally make, seeing things in a different emotional light, making different value judgments, and so forth.

If you seriously believe, as I do and have been asserting for most of this book, that concepts are active symbols in a brain, and if furthermore you seriously believe that people, no less than objects, are represented by symbols in the brain (in other words, that each person that one knows is internally mirrored by a concept, albeit a very complicated one, in one’s brain), and if lastly you seriously believe that a self is also a concept, just an even more complicated one (namely, an “I”, a “personal gemma”, a rock-solid “marble”), then it is a necessary and unavoidable consequence of this set of beliefs that your brain is inhabited to varying extents by other I’s, other souls, the extent of each one depending on the degree to which you faithfully represent, and resonate with, the individual in question. I include the proviso “and resonate with” because one can’t just slip into any old soul, no more than one can slip into any old piece of clothing; some souls and some suits simply “fit” better than others do.

Music seems to me to be a direct route to the heart, or between hearts — in fact, the most direct. Across-the-board alignment of musical tastes, including both loves and hates — something extremely rarely run into — is as sure a guide to affinity of souls as I have ever found. And an affinity of souls means that the people concerned can rapidly come to know each other’s essences, have great potential to live inside each other.

We are all curious collages, weird little planetoids that grow by accreting other people’s habits and ideas and styles and tics and jokes and phrases and tunes and hopes and fears as if they were meteorites that came soaring out of the blue, collided with us, and stuck. What at first is an artificial, alien mannerism slowly fuses into the stuff of our self, like wax melting in the sun, and gradually becomes as much a part of us as ever it was of someone else (though that person may very well have borrowed it from someone else to begin with). Although my meteorite metaphor may make it sound as if we are victims of random bombardment, I don’t mean to suggest that we willingly accrete just any old mannerism onto our sphere’s surface — we are very selective, usually borrowing traits that we admire or covet — but even our style of selectivity is itself influenced over the years by what we have turned into as a result of our repeated accretions. And what was once right on the surface gradually becomes buried like a Roman ruin, growing closer and closer to the core of us as our radius keeps increasing.

In the end, what is the difference between actual, personal memories and pseudo-memories? Very little. I recall certain episodes from the novel Catcher in the Rye or the movie David and Lisa as if they had happened to me — and if they didn’t, so what? They are as clear as if they had. The same can be said of many episodes from other works of art. They are parts of my emotional library, stored in dormancy, waiting for the appropriate trigger to come along and snap them to life, just as my “genuine” memories are waiting. There is no absolute and fundamental distinction between what I recall from having lived through it myself and what I recall from others’ tales. And as time passes and the sharpness of one’s memories (and pseudo-memories) fades, the distinction grows ever blurrier.

Even if most readers agree with much that I am saying, perhaps the hardest thing for many of them to understand is how I could believe that the activation of a symbol inside my head, no matter how intricate that symbol might be, could capture any of someone else’s first-person experience of the world, someone else’s consciousness. What craziness could ever have led me to suspect that someone else’s self — my father’s, my wife’s — could experience feelings, given that it was all taking place courtesy of the neurological hardware inside my head, and given that every single cell in the brain of the other person had long since gone the way of all flesh? The key question is thus very simple and very stark: Does the actual hardware matter? Did only Carol’s cells, now all recycled into the vast impersonal ecosystem of our planet, have the potential to support what I could call “Carol feelings” (as if feelings were stamped with a brand that identified them uniquely), or could other cells, even inside me, do that job?

To my mind, there is an unambiguous answer to this question. The cells inside a brain are not the bearers of its consciousness; the bearers of consciousness are patterns. The pattern of organization is what matters, not the substance. It ain’t the meat, it’s the motion! Otherwise, we would have to attribute to the molecules inside our brains special properties that, outside of our brains, they lack. For instance, if I see one last tortilla chip lying in a basket about to be thrown away, I might think, “Oh, you lucky chip! If I eat you, then your lifeless molecules, if they are fortunate enough to be carried by my bloodstream up to my brain and to settle there, will get to enjoy the experience of being me! And so I must devour you, in order not to deprive your inert molecules of the chance to enjoy the experience of being human!” I hope such a thought sounds preposterous to nearly all of my readers. But if the molecules making you up are not the “enjoyers” of your feelings, then what is? All that is left is patterns. And patterns can be copied from one medium to another, even between radically different media. Such an act is called “transplantation” or, for short, “translation”.

A novel can withstand transplanting even though readers in the “guest language” haven’t lived on the soil where the original language is spoken; the key point is, they have experienced essentially the same phenomena on their own soil. Indeed, all novels, whether translated or not, depend on this kind of transplantability, because no two human beings, even if they speak the same language, ever grow up on exactly the same soil. How else could we contemporary Americans relate to a Jane Austen novel? Carol’s soul can withstand transplanting into the soil of my brain because, even though I didn’t grow up in her family and in their various houses, I know, to some degree, all the key elements of her earliest years. In me robustly live and survive her early inner roots, out of which her soul grew. My brain’s fertile soil is a soul-soil not identical to, but very similar to, hers. And so I can “be” Carol albeit with a slight Doug accent,

When the sun is eclipsed, there remains a corona surrounding it, a circumferential glow. When someone dies, they leave a glowing corona behind them, an afterglow in the souls of those who were close to them. Inevitably, as time passes, the afterglow fades and finally goes out, but it takes many years for that to happen. When, eventually, all of those close ones have died as well, then all the embers will have gone cool, and at that point, it’s “ashes to ashes and dust to dust”.

The Blurry Glow of Human Identity

Among the beliefs most universally shared by humanity is the idea “One body, one person”, or equivalently, “One brain, one soul”. I will call this idea the “caged-bird metaphor”, the cage being, of course, the cranium, and the bird being the soul. Such an image is so self-evident and so tacitly built into the way we all think about ourselves that to utter it explicitly would sound as pointless as saying, “One circle, one center” or “One finger, one fingernail”; to question it would be to risk giving the impression that you had more than one bat in your belfry. And yet doing precisely the latter has been the purpose of the past few chapters.

In contrast to the caged-bird metaphor, the idea I am proposing here is that since a normal adult human brain is a representationally universal “machine”, and since humans are social beings, an adult brain is the locus not only of one strange loop constituting the identity of the primary person associated with that brain, but of many strange-loop patterns that are coarse-grained copies of the primary strange loops housed in other brains. Thus, brain 1 contains strange loops 1, 2, 3, and so forth, each with its own level of detail. But since this notion is true of any brain, not just of brain 1, it entails the following flip side: Every normal adult human soul is housed in many brains at varying degrees of fidelity, and therefore every human consciousness or “I” lives at once in a collection of different brains, to different extents.

What one starts to realize, as one explores these disorienting but technologically feasible ideas of virtual presence “elsewhere”, is that as the telepresence technology improves, the “primary” location becomes less and less primary. Indeed, one can imagine a proverbial “brain in the vat” in Bloomington controlling a strolling robot out in California, and totally believing itself to be a physical creature way out west and not believing one word about being a brain in a vat.

To varying degrees, we human beings live inside other human beings already, even in a totally nontechnological world. The interpenetration of souls is an inevitable consequence of the power of the representationally universal machines that our brains are. That is the true meaning of the word “empathy”. I am capable of being other people, even if it is merely an “economy class” version of the act of being, even if it falls quite a bit short of being those people with the full power and depth with which they are themselves. I have the good fortune — at least I usually consider it fortunate, though at times I wonder — of always having the option of falling back and returning to being “just me”, because there is only one primary self housed in my brain. If, however, there were a few high-powered selves in my brain, all competing with each other for primacy, then the meaning of the word “I” would truly be up for grabs.

To put things in somewhat sharper focus, let’s invent a variation on the hammerhead shark. We’ll posit a creature whose eyes are taking in one situation (say in Bloomington) and whose ears are taking in another, unrelated situation (say in Stanford). The same brain is going to process these inputs at the same time. I hope you won’t claim that this is an impossible feat! If that’s your inclination, please first recall that you drive your car while reacting to other cars, scenery, billboards, and roadsigns, and also while talking with a far-off friend on your cell phone (and the topics covered in the conversation may vividly transport you to yet other places), and all during that very same period a recently-heard tune is running through your head, your strained back is bugging you, you smell cow manure wafting through the air, and your stomach is shouting to you, “I am hungry!” You manage to process all those different simultaneous worlds perfectly well — and in that same spirit, nothing is going to prevent a human brain from dealing simultaneously with the two unrelated worlds of Stanford sounds and Bloomington sights, no more than the hammerhead shark’s brain protests, “Does not compute!” So the idea “I cannot be simultaneously here and there” goes down in flames. We are simultaneously here and there all the time, even in our everyday lives.

We’ll posit a creature whose eyes are taking in one situation (say in Bloomington) and whose ears are taking in another, unrelated situation (say in Stanford). The same brain is going to process these inputs at the same time. I hope you won’t claim that this is an impossible feat! If that’s your inclination, please first recall that you drive your car while reacting to other cars, scenery, billboards, and roadsigns, and also while talking with a far-off friend on your cell phone (and the topics covered in the conversation may vividly transport you to yet other places), and all during that very same period a recently-heard tune is running through your head, your strained back is bugging you, you smell cow manure wafting through the air, and your stomach is shouting to you, “I am hungry!” You manage to process all those different simultaneous worlds perfectly well — and in that same spirit, nothing is going to prevent a human brain from dealing simultaneously with the two unrelated worlds of Stanford sounds and Bloomington sights, no more than the hammerhead shark’s brain protests, “Does not compute!” So the idea “I cannot be simultaneously here and there” goes down in flames. We are simultaneously here and there all the time, even in our everyday lives.

That’s all I’m claiming — that there is blur. That some of what happens in other brains gets copied, albeit coarse-grainedly, inside the brain of “Number One”, and that the closer two brains are to each other emotionally, the more stuff gets copied back and forth from one to the other, and the more faithful the copies are. There’s no claim that the act of copying is simultaneous or perfect or total — just that each person lives partially in the brain of the other, and that if the bandwidth were turned up more and more and more and still more, they would come to live more and more inside each other — until, in the limit, the sense of a clear boundary between them would slowly be dissolved,

My point, though, is that the myth of watertight boundaries between souls is something whose falsity we all have slight tastes of all the time, but since it is so convenient and so conventional to associate one body with precisely one soul, since it is so deeply tempting and so deeply ingrained to see a body and a soul as being in perfect alignment, we choose to downplay or totally ignore the implications of the everyday manifestations of the interpenetration of souls.

It seems to me, therefore, that the instinctive although seldom articulated purpose of holding a funeral or memorial service is to reunite the people most intimate with the deceased, and to collectively rekindle in them all, for one last time, the special living flame that represents the essence of that beloved person, profiting directly or indirectly from the presence of one another, feeling the shared presence of that person in the brains that remain, and thus solidifying to the maximal extent possible those secondary personal gemmae that remain aflicker in all these different brains. Though the primary brain has been eclipsed, there is, in those who remain and who are gathered to remember and reactivate the spirit of the departed, a collective corona that still glows. This is what human love means. The word “love” cannot, thus, be separated from the word “I”; the more deeply rooted the symbol for someone inside you, the greater the love, the brighter the light that remains behind.

Consciousness = Thinking

From the very start in this book, I have used a few key terms pretty much interchangeably: “self”, “soul”, “I”, “a light on inside”, and “consciousness”. To me, these are all names for the same phenomenon. To other people, they may not seem to denote one single thing, but that’s how they seem to me.

Consciousness is the dance of symbols inside the cranium. Or, to make it even more pithy, consciousness is thinking. As Descartes said, Cogito ergo sum. Unfortunately, I suspect that this answer is far too compressed for even my most sympathetic readers, so I will try to spell it out a little more explicitly. Most of the time, any given symbol in our brain is dormant, like a book sitting inertly in the remote stacks of a huge library. Every so often, some event will trigger the retrieval of this book from the stacks, and it will be opened and its pages will come alive for some reader. In an analogous way, inside a human brain, perceived external events are continually triggering the highly selective retrieval of symbols from dormancy, and causing them to come alive in all sorts of unanticipated, unprecedented configurations. This dance of symbols in the brain is what consciousness is. (It is also what thinking is.) Note that I say “symbols” and not “neurons”. The dance has to be perceived at that level for it to constitute consciousness. So there you have a slightly more spelled-out version.

My brain (and yours, too, dear reader) is constantly seeking to label, to categorize, to find precedents and analogues — in other words, to simplify while not letting essence slip away. It carries on this activity relentlessly, not only in response to freshly arriving sensory input but also in response to its own internal dance, and there really is not much of a difference between these two cases, for once sensory input has gotten beyond the retina or the tympani or the skin, it enters the realm of the internal, and from that point on, perception is solely an internal affair. In short, and this should please the skeptics, there is a kind of perceiver of the symbols’ activity — but what will not please them is that this “perceiver” is itself just further symbolic activity. There is not some special “consciousness locus” where something magic happens, something other than just more of the same, some locus where the dancing symbols make contact with… well, with what? What would please the skeptics? If the “consciousness locus” turned out to be just a physical part of the brain, how would that satisfy them?

The “I” — yours, mine, everyone’s — is a tremendously effective illusion, and falling for it has fantastic survival value. Our “I” ’s are self-reinforcing illusions that are an inevitable by-product of strange loops, which are themselves an inevitable by-product of symbol-possessing brains that guide bodies through the dangerous straits and treacherous waters of life.

A Brief Brush with Cartesian Egos

It seems that the way in which a science-fiction scenario is related is crucial in determining our intuitions about its credibility. This is a point that my old colleague and friend Dan Dennett has made many times in his discussions of philosophers’ crafty thought experiments. Indeed, Dan calls such carefully crafted fables intuition pumps, and he knows very well whereof he speaks, since he has dreamt up some of the most insight-providing intuition pumps in the field of philosophy of mind.

This issue lies at the very core of Parfit’s book, and the explanation of his position occupies about a hundred pages. The key notion to which he is opposed is what he dubs “Cartesian Pure Ego”, or “Cartesian Ego”, for short. To put it in my words, a Cartesian Ego constitutes one exact quantum of pure soul (also known as “personal identity”), and it is 100 percent indivisible and undilutable. In short, it is what makes you be you and me be me. My Cartesian Ego is mine and no one else’s, has been from birth and will be to death, and that’s that. It’s my very own, completely private, unshared and unsharable, first-person world. It’s the subject of my experiences. It’s my totally unique inner light. You know what I mean!

Parfit staunchly resists the idea that the concept of “personal identity” makes sense. To be sure, it makes sense in the everyday world that we inhabit — a world without telecloning or fanciful cut-andpaste operations on brains and minds. The fact is, we all more or less take for granted this notion of “Cartesian Ego” in our daily lives; it is built into our common sense, into our languages, and into our cultural backgrounds as profoundly, as tacitly, as seamlessly, and as invisibly as is the notion that time passes or the notion that things that move preserve their identity. But Parfit is concerned with investigating how well this primordial notion of Cartesian Egos stands up under extreme and unprecedented pressures. As a careful thinker, he is doing something analogous to what Einstein did when he imagined himself moving at or near the speed of light — he is pushing the limits of classical notions — and, like Einstein, he finds that classical worldviews do not always work in worlds that are very different from those in which they were born and grew.

The essence of his position is that when pushed to its limits, personal identity becomes an indeterminate notion. The new view that Parfit proposes is a radical reperception of what it is to be, and in certain ways it is extremely disturbing. In other ways, it is extremely liberating! Parfit even devotes a page or two to explaining how this radical new view of human existence has freed him up and profoundly changed his attitudes towards his life, his death, his loved ones, and other people in general.

It has often seemed to me that ultimately, when I am thinking about who my closest friends are, it all comes down to how they are — how they smile, how they talk, how they laugh, how they listen, how they suffer, how they share, and so on. I think to myself that the innermost essence of each friend is made up of thousands of such “how” ’s, and that that collection of “how” ’s is the answer — the full answer — to “Who is this person?” It may seem that this is purely a third-person, external perspective, and that it takes away, or even denies, the whole first-person perspective. It may seem to short-change or even to casually dismiss the “I”. I don’t think so, however, for I think that even to itself, that is all an “I” is. The rub is, an “I” is very good at convincing itself that it is a lot more than that — in fact, that is the entire business that the word “I” is in! “I” has a vested interest in continuing this scam (even if it is its own victim)!

A Tango with Zombies and Dualism

The well-known Australian philosopher of mind David Chalmers, which not only is a cherished friend but also is my former doctoral student, has devoted many years to arguing for the provocative idea that there could be both “machines that think” and also “machines who think”. For me, the notion of both types of machine coexisting makes no sense, because, as I declared in Chapter 19, the word “thinking” stands for the dancing of symbols in a cranium or careenium (or some such arena), and this is also what is denoted by the word “consciousness”. Since being conscious merits the use of the pronoun “who” (and also, of course, the pronouns “I”, “me”, and so on), so does thinking — and that settles the question for me. In other words, “machine that thinks” is an incoherent phrase because of its relative pronoun, and if some day there really are machines that think, then by definition they will be machines who think.

Basically, a zombie is an unconscious humanoid who acts — oops, I mean “that acts” — as if it were conscious. There’s no one home inside a zombie, though from the outside one might think so.

In debates about consciousness, one of the most frequently asked questions goes something like this: “What is it about consciousness that helps us survive? Why couldn’t we have had all this cognitive apparatus but simply been machines that don’t feel anything or have any experience?” As I hear it, this question is basically asking, “Why did consciousness get added on to brains that reached a certain level of complexity? Why was consciousness thrown into the bargain as a kind of bonus? What extra evolutionary good does the possession of consciousness contribute, if any?” To ask this question is to make the tacit assumption that there could be brains of any desired level of complexity that are not conscious.

It assumes that consciousness is some kind of orderable “extra feature” that some models, even the fanciest ones, might or might not have, much as a fancy car can be ordered with or without a DVD player or a power moonroof. But consciousness is not a power moonroof (you can quote me on that). Consciousness is not an optional feature that one can order independently of how the brain is built.

Consciousness is nothing but the upper end of a spectrum of self-perception levels that brains automatically possess as a result of their design.

Consciousness is not an add-on option when one has a 100-huneker brain; it is an inevitable emergent consequence of the fact that the system has a sufficiently sophisticated repertoire of categories. Like Gödel’s strange loop, which arises automatically in any sufficiently powerful formal system of number theory, the strange loop of selfhood will automatically arise in any sufficiently sophisticated repertoire of categories, and once you’ve got self, you’ve got consciousness. Élan mental is not needed.

Philosophers who believe that consciousness comes from something over and above physical law are dualists. They believe we inhabit a world like that of magical realism, in which there are two types of entities: magical entities, which possess élan mental, and ordinary entities, which lack it. More specifically, a magical entity has a nonphysical soul, which is to say, it is imbued with exactly one “dollop of consciousness” (a dollop being the standard unit of élan mental), while ordinary entities have no such dollop.

The questions entailed by a Capitalized Essence called “Consciousness” or élan mental abound and multiply with out end. Belief in dualism leads to a hopelessly vast and murky pit of mysteries.

Killing a Couple of Sacred Cows

There’s an idea in the philosophical literature on consciousness that makes me sea-blue, and that is the so-called “problem of the inverted spectrum”. After describing this sacred cow as accurately I can, I shall try to slaughter it as quickly as I can. (It suffers from mad sacred cow disease.) It all comes from the idea that you are supposedly so different from me that there is no way to cross the gap between our interiorities — no way for you to know what I am like inside, or vice versa. In particular, when you look at a bunch of red roses and I look at the same bunch of red roses, we both externalize what we are seeing by making roughly the same noise (“red roses”), but maybe, for all you know, what I am experiencing as redness inside my private, inaccessible cranium is what you, if only you could “step inside” my subjectivity for a moment or two, would actually call “blue”. (By the way, advocates of the inverted-spectrum riddle would spurn any suggestion that you and I actually are already inside each other, even the littlest bit. Their riddle is predicated upon the existence of an Unbridgeable You–Me Chasm — that is, the absolute inaccessibility by one person of any other person’s interiority. In other words, belief in the inverted spectrum is a close cousin to belief in Cartesian Egos — the idea that we are all disjoint islands and that “you can’t get there from here”.)

This hypothetical notion makes our inner experiences of the colors in the rainbow sound like a set of floating pre-existent pure abstractions that are not intimately (in fact, not at all) related to the physics outside our skull, or even to any physics inside it; rather, these inner experiences are arbitrarily mappable onto outside phenomena. As we grow up, the rainbow colors get mapped onto the spectrum of prefabricated feelings with which our brains all come equipped “from the factory”, but this mapping is not mediated by neural wiring; after all, neural wiring is observable from a detached third-person perspective, such as that of a neurosurgeon, so that rules it out.

The inverted-spectrists say it is pure feeling. Since this distinction is completely independent of physics, it amounts to dualism (something we already knew, in effect, since belief in Cartesian Egos is a kind of dualism).

Why is it that those who postulate the inverted spectrum always do so only for experiences that lie along a one-dimensional numerical scale? It seems like a great paucity of imagination to limit oneself to swapping red and blue. If you think it’s coherent to say to someone else, “Maybe your private inner experience of red is the same as my private inner experience of blue”, then why would it not be just as coherent to say, “Maybe your private inner experience of looking at a red rose is the same as my private inner experience of looking at a blue violet”? What is sacrosanct about the idea of shuffling colors inside a spectrum? Why not shuffle all sorts of experiences arbitrarily? Maybe your private inner experience of redness is the same as my private inner experience of hearing very low notes on a piano. Or maybe your private inner experience of going to a baseball game is the same as my private inner experience of going to a football game.

The inverted-spectrum riddle depends on the idea that we are all born with a range of certain “pure experiences” that have no physical basis but that can get attached, as we grow, to certain external stimuli, and thus specific experiences and specific stimuli get married and from then on they are intimately tied together for a lifetime. But these “pure experiences” are supposedly not physical states of the brain. They are, rather, subjective feelings that one simply “has”, without there being any physical explanation for them. Your brain state and mine could look as identical as anyone could ever imagine (using ultra-fine-grained brain-scanning devices), but whereas I would be feeling blueness, you would be feeling redness. The inverted-spectrum fairy tale is a feeble mixture of bravado and timidity. While it boldly denies the physical world’s relevance to what we feel inside, it meekly limits itself to a one-dimensional spectrum, and to the electromagnetic one, to boot. The sonic spectrum is too tied to objective physical events like shaking and vibrating for us to imagine it as being inverted, and if one tries to carry the idea beyond the realm of one-dimensional spectra, it becomes far too absurd to give any credence to.

There’s something else in the philosophical literature on consciousness that gives me the willies, and that is the so-called “problem of free will”. When people decide to do something, they often say, “I did it of my own free will.” I think what they mean by this is usually, in essence, “I did it because I wanted to, not because someone else forced me to do it.” Although I am uncomfortable with the phrase “I did it of my own free will”, the paraphrase I’ve suggested sounds completely unobjectionable to me. We do indeed have wants, and our wants do indeed cause us to do things. What makes no sense is to maintain, over and above that, that our wants are somehow “free” or that our decisions are somehow “free”. They are the outcomes of physical events inside our heads! How is that free?

What, then, is all the fuss about “free will” about? Why do so many people insist on the grandiose adjective, often even finding in it humanity’s crowning glory? What does it gain us, or rather, what would it gain us, if the word “free” were accurate? I honestly do not know. I don’t see any room in this complex world for my will to be “free”. I am pleased to have a will, or at least I’m pleased to have one when it is not too terribly frustrated by the hedge maze I am constrained by, but I don’t know what it would feel like if my will were free. What on earth would that mean? That I didn’t follow my will sometimes?

Yes, certainly, I’ll make a decision, and I’ll do so by conducting a kind of inner vote. The count of votes will yield a result, and by George, one side will come out the winner. But where’s any “freeness” in all this?

In sum, our decisions are made by an analogue to a voting process in a democracy. Our various desires chime in, taking into account the many external factors that act as constraints, or more metaphorically, that play the role of hedges in the vast maze of life in which we are trapped. Much of life is incredibly random, and we have no control over it. We can will away all we want, but much of the time our will is frustrated. Our will, quite the opposite of being free, is steady and stable, like an inner gyroscope, and it is the stability and constancy of our non-free will that makes me me and you you, and that also keeps me me and you you.

On Magnanimity and Friendship

I think that wittingly or unwittingly, we all equate the size of a living being’s soul with the “objective” value of that being’s life, which is to say, the degree of respect that we outsiders pay to that being’s interiority. And we certainly do not place equal values on all beings’ lives! We don’t hesitate for a moment to draw a huge distinction between the values of a human life and an animal life, and between the values of the lives of different “levels” of animals.

Most people I know would rate (either explicitly, in words, or implicitly, through choices made) cat souls as higher than cow souls, cow souls higher than rat souls, rat souls higher than snail souls, snail souls higher than flea souls, and so forth. And so I ask myself, if soul-size distinctions between species are such a commonplace and non-threatening notion, why should we not also be willing to consider some kind of explicit (not just tacit) spectrum of soul-sizes within a single species, and in particular within our own?

I’ll go out on a limb and make a very crude stab at such a distinction. To do so I will merely cite two ends of a wide spectrum, with yourself and myself, dear reader, presumably falling somewhere in the mid-range (but hopefully closer to the “high” end than to the “low” one). At the low end, then, I would place uncontrollably violent psychopaths — adults essentially incapable of internalizing other people’s (or animals’) mental states, and who because of this incapacity routinely commit violent acts against other beings. It may simply be these people’s misfortune to have been born this way, but whatever the reason, I class them at the low end of the spectrum. To put it bluntly, these are people who are not as conscious as normal adults are, which is to say, they have smaller souls.

What about the high end of the spectrum? I suspect it will come as no surprise that I would point to individuals whose behavior is essentially the opposite of that of violent psychopaths. This means gentle people such as Mohandas Gandhi, Eleanor Roosevelt, Raoul Wallenberg, Jean Moulin, Mother Teresa, Martin Luther King, and César Chávez — extraordinary individuals whose deep empathy for those who suffer leads them to devote a large part of their lives to helping others, and to doing so in nonviolent fashions. Such people, I propose, are more conscious than normal adults are, which is to say, they have greater souls.

In any case, having a conscience — a sense of morality and of caring about doing “the right thing” towards other sentient beings — strikes me as the most natural and hopefully also the most reliable sign of consciousness in a being. Perhaps this simply boils down to how much one puts into practice the Golden Rule.

So I would say that those who strike us as self-less are in fact very soul-full — that is, they house many other souls inside their own skulls/brains/minds/souls — and I don’t think this sharing of mind-space diminishes their central core but enlarges and enriches it. As Walt Whitman put it in his poem “Song of Myself ”, “I am large, I contain multitudes.” All this richness is a consequence of the fact that at some point in the dim past, the generic human brain surpassed a critical threshold of flexibility and became quasi-universal, able to internalize the abstract essences of other human brains. It is something to marvel at.

Epilogue: The Quandary

In a nutshell, our quandary is this. Either we believe that our consciousness is something other than an outcome of physical law, or we believe it is an outcome of physical law — but making either choice leads us to disturbing, perhaps even unacceptable, consequences. My purpose in these final pages is to face this dilemma head-on.

I discussed dualism — the idea that over and above physical entities governed by physical law, there is a Capitalized Essence called “Consciousness”, which is an invisible, unmeasurable, undetectable aspect of the universe possessed by certain entities and not others. This notion, very close to the traditional western religious notion of “soul”, is appealing because it conforms with our everyday experience that the world is divided up into two kinds of things — animate and inanimate — and it also gives some kind of explanation for the fact that we experience our own interiority or inner light, something of which we are so intimately aware that to deny its existence would seem absurd if not impossible.

Dualism also holds out the hope of explaining the mysterious division of the animate world into two types of entity: myself and others. Otherwise put, this is the seemingly unbridgeable gap between the subjective, first-person view of the world and an impersonal, third-person view of the world. If what we call “I” is a squirt of some unanalyzable Capitalized Essence magically doled out to each human being at the moment in which it is conceived, with each portion imbued with a unique savor permanently defining the recipient’s identity, then we need look no further for an explanation of what we are (even if it depends on something inexplicable). Furthermore, the idea that each of us is intrinsically defined by a unique incorporeal essence suggests that we have immortal souls; belief in dualism may thus remove some of the sting of death.

If instead one believes that consciousness (now with a small “c”) is an outcome of physical law, then no room remains for anything extra “on top”. This is appealing to a scientific mind because it is far simpler than dualism. It gets rid of a puzzling dichotomy between ordinary physical entities and extraordinary nonphysical essences, and it cancels the long list of questions about the nature of the nonphysical Capitalized Essence. On the other hand, throwing dualism out the window is troubling as well, because, at least on first glance, doing so seems to leave us with no distinction between animate and inanimate entities, and no explanation for our unique experience of our own interiority or inner light, no explanation for the gulf between our self and other selves. A more careful look at this viewpoint, however, shows that there is room in it for such distinctions.

A nondualistic view of the world can thus include animate entities perfectly easily, as long as different levels of description are recognized as valid. Animate entities are those that, at some level of description, manifest a certain type of loopy pattern, which inevitably starts to take form if a system with the inherent capacity of perceptually filtering the world into discrete categories vigorously expands its repertoire of categories ever more towards the abstract. This pattern reaches full bloom when there comes to be a deeply entrenched self-representation — a story told by the entity to itself — in which the entity’s “I” plays the starring role, as a unitary causal agent driven by a set of desires. More precisely, an entity is animate to the degree that such a loopy “I” pattern comes into existence, since this pattern’s presence is by no means an all-or-nothing affair. Thus to the extent that there is an “I” pattern in a given substrate, there is animacy, and where there is no such pattern, the entity is inanimate.

There still remains a sticky question: What would make a loopy abstract pattern, however fancy it might be, constitute a locus of interiority, an inner light, a site of first-person experience? Otherwise put, where does me-ness come from?

And this is our central quandary. Either we believe in a nonmaterial soul that lives outside the laws of physics, which amounts to a nonscientific belief in magic, or we reject that idea, in which case the eternally beckoning question “What could ever make a mere physical pattern be me?” — the question that philosopher David Chalmers has seductively and successfully nicknamed “The Hard Problem” — seems just as far from having an answer today (or, for that matter, at any time in the future) as it was many centuries ago.

Together, you and I have gone through instance after instance of increasingly sophisticated structures having loops, from the ever-darting-off Exploratorium red dot to fine-grained television cameras taking in the screens they fill, then to formulas asserting that they have no PM proof, and winding up with the strange loop that comes about inside the ever-growing repertoire of symbols in each human being’s brain. (Élan mental we have no truck with, for it leads to endless traps.) If there were ever, in our physics-governed world, a kind of magic, it is surely in these self-reflecting, self-defining patterns. Such strange loops, inspired by Gödel’s Trojan horse that sneaked self-consciousness inside the very fortress that was built to keep it out, and recalling Roger Sperry’s tower of forces within forces within forces (found inside each teet’ring bulb of dread and dream), give the only explanation I can fancy for how animate, desire-driven beings can arise from just plain matter, and for how, among the swarm of loops that populate our planet, there is one, and only one, that you call “I” (and I call “you”).

You and I are mirages who perceive themselves, and the sole magical machinery behind the scenes is perception — the triggering, by huge flows of raw data, of a tiny set of symbols that stand for abstract regularities in the world. When perception at arbitrarily high levels of abstraction enters the world of physics and when feedback loops galore come into play, then “which” eventually turns into “who”. What would once have been brusquely labeled “mechanical” and reflexively discarded as a candidate for consciousness has to be reconsidered.

We human beings are macroscopic structures in a universe whose laws reside at a microscopic level. As survival-seeking beings, we are driven to seek efficient explanations that make reference only to entities at our own level. We therefore draw conceptual boundaries around entities that we easily perceive, and in so doing we carve out what seems to us to be reality. The “I” we create for each of us is a quintessential example of such a perceived or invented reality, and it does such a good job of explaining our behavior that it becomes the hub around which the rest of the world seems to rotate. But this “I” notion is just a shorthand for a vast mass of seething and churning of which we are necessarily unaware.