A weaving together of minds, machines, and mathematics
Reviewed by Stephen Cass
Douglas R. Hofstadter says his brain runs a copy of his late wife’s mind.
In 1979, Douglas R. Hofstadter became the philosophers’ version of a rock star, and a smashing success with computer scientists, with the publication of the Pulitzer Prizewinning Gödel, Escher, Bach: An Eternal Golden Braid . A hefty tome that tied together the esoteric theorems of Kurt Gödel, the paradoxical drawings of M.C. Escher, and the multilayered compositions of J.S. Bach, Hofstadter’s intellectual tour de force was filled with insights into the nature of mathematics, music, consciousness, and the possibility of creating artificially intelligent selfâ''aware machines.
Now, almost 30 years later, in a much shorter work, Hofstadter has returned to one of the themes of his 1979 opus, believing it to have been somewhat overshadowed by the rest of the book. What is this overlooked gem? That we owe our self-awareness to the existence of ”strange loops.”
In I Am a Strange Loop , Hofstadter develops the implications of this idea, including such questions as the kind of consciousness animals might have, the emergence of a shared identity between life partners, and what remains of people after they die.
I am a strange loop
Douglas R. Hofstadter
Basic Books, New York
Strange loops are notable in several respects. One characteristic is that they operate simultaneously on different levels of abstraction. A mathematical version of a strange loop, for example, can be considered at the microlevel of shunting individual numbers and operators around or at the macrolevel of entire theorems and proofs.
Another key characteristic is that with a strange loop, it is entirely appropriate to consider a chain of events as a consequence of what is happening at either the micro- or the macrolevel. For example, consider what happens when a computer stores a number. On one level, the event could be described in terms of the electronic relations of all the transistors, capacitors, resistors, and wires in the computer. Most of us, however, would find it much more natural to say that the number was placed in memory because a particular software subroutine instructed the CPU to store the number there.
An additional characteristic of a strange loop is that, at some level of abstraction, it can be considered as an infinitely extensible repertoire of symbols representing arbitrary objects and concepts. This extensibility is important, because it means the strange loop can ultimately support a symbol representing the loop itself. This creates a feedback mechanism, where it is pointless to try to decide whether the behavior of the loop is ultimately determined by the microlevel activity that the loop is built out of or by macrolevel symbolic abstractions. Hofstadter argues that this type of feedback is the origin of consciousness, of our sense of ”I.”
He further argues that any system capable of representing a sufficiently rich suite of symbols could develop self-awareness: it doesn’t matter if the microlevel of the strange loop is composed of neurons or transistors. When this idea was expressed in Gödel, Escher, Bach , most people latched onto it for its strong support of the possibility of true artificial intelligence.
In this book, however, Hofstadter probes some of the other implications of his model of the mind. One is that not every brain (or computer!) is capable of supporting the rich symbology required for true sapience, although it may be capable of some degree of self-awareness. Without the brainpower to support a symbolic representation of the world, for instance, a mosquito probably has no self-awareness. A dog, though, has some self-awareness, but it’s still far below the threshold of human consciousness; a dog’s inability to add arbitrary concepts and symbols to its mental world fundamentally limits its sentience.
And, in what’s sure to strike a chord of controversy, Hofstadter argues that this lack of consciousness also applies to newborn babies. Although children are born with the basic apparatus to host a strange loop, it takes time for a self-representing feedback loop to form from the whirl of their experiences. In fact, Hofstadter argues that it takes several years for a child to develop full-fledged human consciousness.
In possibly the most significant extension of the strange loop idea, Hofstadter contends that our brains are not limited to supporting one strange loop—although one, containing the individual’s ”I,” will always be dominant. This means that it is possible for your brain to host a low-fidelity version of another person’s mind. When two people are very close, such as a couple who have known each other intimately for some time, Hofstadter argues that they in effect begin running rough copies of each other’s consciousness in their brains. While both partners retain their individuality, a gestalt entity eventually emerges. In this view of the mind, there is a literal meaning to the romantic notion of a ”you, me, and us” in a close relationship.
And when someone dies, it is possible for rough copies of that person’s consciousness to live on in others. In an extraordinarily personal section of the book that markedly distinguishes I Am a Strange Loop from the more detached tone of Gödel, Escher, Bach , Hofstadter discusses this concept in the context of the sudden death of his own wife, Carol. When he brings his late wife strongly to mind—say, at an important moment for one of their children—he says his copy of her self-aware strange loop is activated.
In other words, Hofstadter is not just experiencing memories of her or imagining what she might have thought of the moment, but enabling a living echo of Carol herself to look through his eyes at their child. Although Hofstadter is aware that he thus risks being accused of wish fulfillment, this line of thinking does follow naturally from the rest of his argument.
If there’s a weakness in Hofstadter’s reasoning, it lies in his claims that the mind can be considered as an abstraction and that we can ignore the details of the brain or whatever other substrate the mind may be running on.
Hofstadter supports this claim with an analogy drawn from thermodynamics. He notes that the Ideal Gas Law can be studied purely by reference to a gas’s temperature and its pressure, concepts meaningless on the level of the individual molecules composing the gas. The precise microscopic arrangement of the molecules and the type of molecules they are do not matter.
But thermodynamic phenomena like the Ideal Gas Law operate in the domain of very large numbers of molecules indeed. Human brains, on the other hand, even with their 100 billion or so neurons, operate with 12 orders of magnitude fewer components than can be found in a whiff of gas. As many engineers have found out the hard way, you can use abstractions and ignore the substrate for most of the time, but every now and then you get caught badly when a handy assumption breaks down.
In recent years, for example, digital chip designers, who had long operated comfortably in the abstract world of gates and Boolean logic, have found themselves confronted by the full messiness of materials science and electromagnetic effects as they try to squeeze devices closer together. Even MEMS developers, although working with components vastly larger than atoms, find that familiar mechanical laws about how gears and levers move cannot always be trusted in the in-between world of the mesoscale.
Because it is precisely in this mesoscale world that our brains operate, this is where I have the most doubt about Hofstadter’s argument. Is there some fundamental element of our physical biology that is responsible for our consciousness? This is the thesis of a number of writers, notably the English mathematical physicist Roger Penrose. However, even if the thesis proves true, it would merely rule out the possibility of creating strange loops outside brains.
Hofstadter’s model for how self-aware beings can arise out of inanimate atoms still deserves to be taken seriously. I recommend the book both to those who have read his earlier work and to those who have not yet become acquainted with this great thinker.