Page 170 In that most delightful though most unlikely of scenarios… [DeLong], [Goodstein], and [Chaitin] discuss non-Godelian formulas that are undecidable for Godelian reasons.
Page 172 No reliable prim/saucy distinguisher can exist… See [DeLong], [Boolos and Jeffrey] , [Jeffrey], [Goodstein], [Hennie], [Wolf ], and [Hofstadter 1979] for discussions of many limitative results such as this one (which is Church’s theorem).
Page 172 It was logician Alfred Tarski who put one of the last nails… See [Smullyan 1992] and [Hofstadter 1979] for discussions of Tarski’s deep result. In the latter, there is a novel approach to the classical liar paradox (“This sentence is not true”) using Tarski’s ideas, with the substrate taken to be the human brain instead of an axiomatic system.
Page 172 what appears to be a kind of upside-down causality… See [Andersen] for a detailed technical discussion of downward causality. Less technical discussions are found in [Pattee] and [Simon]. See also Chapters 11 and 20 in [Hofstadter and Dennett], and especially the Reflections. [Laughlin] gives fascinating arguments for the thesis that in physics, the macroscopic arena is more fundamental or “deeper” than the microscopic.
Page 174 leaving just a high-level picture of information-manipulating processes… See [Monod], [Berg and Singer], [Judson], and Chapter 27 of [Hofstadter 1985].
Page 177 symbols in our respective brains… See [Hofstadter 1979], especially the dialogue “Prelude… Ant Fugue” and Chapters 11 and 12, for a careful discussion of this notion.
Page 178 the forbidding and inaccessible level of quarks and gluons… See [Weinberg 1992] and [Pais 1986] for attempts at explanations of these incredibly abstruse notions.
Page 178 the only slightly more accessible level of genes… See [Monod], [Berg and Singer], [Judson], and Chapter 27 (“The Genetic Code: Arbitrary?”) in [Hofstadter 1985].
Page 179 we…best understand our own actions as… See [Dennett 1987] and [Dennett 1998].
Page 181 embellished by a fantastic folio of alternative versions… [Steiner 1975] has a rich and provocative discussion of “alternity”, and the dialogue “Contrafactus” in [Hofstadter 1979] features an amusing scenario involving “subjunctive instant replays”. See also [Kahneman and Miller] and Chapter 12 of [Hofstadter 1985] for further musings on the incessantly flickering presence of counterfactuals in the subconscious human mind. [Hofstadter and FARG] describes a family of computational models of human thought processes in which making constant forays into alternity is a key architectural feature.
Page 182 housing a loop of self-representation… See [Morden], [Kent], and [Metzinger].
Page 186 as the years pass, the “I” converges and stabilizes itself… See [Dennett 1992].
Page 188 we cannot help attributing reality to our “I” and to those of other people… See [Kent], [Dennett 1992], [Brinck], [Metzinger], [Perry], and [Hofstadter and Dennett].
Page 189 I was most impressed when I read about “Stanley”, a robot vehicle… See [Davis 2006].
Page 193 just a big spongy bulb of inanimate molecules… I suppose almost any book on the brain will convince one of this, but [Penfield and Roberts] did it to me as a teen-ager.
Page 194 pioneering roboticist and provocative writer Hans Moravec… For some of Moravec’s more provocative speculations about the near-term future of humanity, see [Moravec].
Page 194 from the organic chemistry of carbon… See Chapter 22 in [Hofstadter and Dennett], in which John Searle talks about “the right stuff”, which underwrites what he terms “the semantic causal powers of the brain”, a rather nice-sounding but murky term by which Searle means that when a human brain, such as his own or, say, that of poet Dylan Thomas, makes its owner come out with words, those words don’t just seem to stand for something, they really do stand for something. Unfortunately, in the case of poet Thomas, most of his output, though it sounds rather nice, is so full of murk that one has to wonder what sort of “stuff” could possibly make up the brain behind it.
Page 199 its symbol-count might well exceed “Graham’s constant”… See [Wells 1986].
Page 208 For those who enjoy the taboo thrills of non-wellfounded sets… See [Barwise and Moss].
Page 209 the deeper and richer an organism’s categorization equipment is… See [Hofstadter 2001].
Page 233 a devilishly clever bon mot by David Moser… One evening not long after we were married, Carol and I invited some friends over for an Indian dinner at our house in Ann Arbor. Melanie Mitchell and David Moser, well aware of Carol’s terrific Indian cooking, were delighted to come. It turned out, however, that at the last minute, our oldest guests, in their eighties, called up to tell us that they couldn’t handle very spicy foods, which unfortunately torpedoed Carol’s cooking plans. Somehow, though, she turned around on a dime and prepared a completely different yet truly delicious repast. A couple of hours after dinner was over, after a very lively discussion, most of our guests took off, leaving just David, Melanie, Carol, and me. We chatted on for a while, and finally, as they were about to hit the road, Carol casually reminded them of what she had originally intended to fix and told them why she hadn’t been able to follow through on her promise. Quick as a wink, David, feigning great indignation, burst out, “Why, you Indian-dinner givers, you!”
Page 233 her personal gemma (to borrow Stanislaw Lem’s term …)… See “Non Serviam” in [Hofstadter and Dennett], which is a virtuosic philosophical fantasy masquerading as a book review (of a book that, needless to say, is merely a figment of Lem’s imagination).
Page 239 someone trying to grapple with quantum-mechanical reality… [Pais 1986], [Pais 1992], and [Pullman] portray the transition period between the Bohr atom and quantum mechanics, while [Jauch] and [Greenstein and Zajonc] chart remaining mysteries.
Page 239 it might be tempting for some readers to conclude that in the wake of Carol’s death… See Chapter 15 of [Hofstadter 1997], another place where I discuss many of these ideas.
Page 242 meaning of the term “universal machine”… See [Hennie] and [Boolos and Jeffrey].
Page 248 concepts are active symbols in a brain… See Chapter 11 of [Hofstadter 1979].
Page 252 a marvelous pen-and-ink “parquet deformation” drawn in 1964… For a dozen-plus examples of this subtle Escher-inspired art form, see Chapter 10 of [Hofstadter 1985].
Page 260 It is not easy to find a strong, vivid metaphor to put up against the caged-bird metaphor… The idea of a soul distributed over many brains brought to my mind an image from solid- state physics, the field in which I did my doctoral work. A solid is a crystal, meaning a periodic lattice of atoms in space, like the trees in an orchard but in three dimensions instead of two. In some solids (those that do not conduct electricity), the electrons “hovering” around each atomic nucleus are so tightly bound that they never stray far from that nucleus. They are like butterflies that hover around just one tree in the orchard, never daring to venture as far as the next tree. In metals, by contrast, which are excellent conductors, the electrons are not timid stay-at-homes stuck to one tree, but boldly float around the entire lattice. This is why metals conduct so well.
Actually, the proper image of an electron in a metal is not that of a butterfly fickly fluttering from one tree to another, never caring where it winds up, but of an intensity pattern distributed over the entire crystal at once — in some places more intense, in other places less so, and changing over time. One electron might better be likened to an entire swarm of orange butterflies, another electron to a swarm of red butterflies, another to a swarm of blue butterflies, and so on, with each swarm spread about the whole orchard, intermingling with all the others. Electrons in metals, in short, are anything but tightly bound dots; they are floating patterns without any home at all.
But let’s not lose track of the purpose of all this imagery, which is to suggest helpful ways of imagining what a human soul’s essence is. If we map each tree (or nucleus) in the crystal lattice onto a particular human brain, then in the tight-binding model (which corresponds to the caged-bird metaphor), each brain would possess a unique soul, represented by the cloud of timid butterflies that hover around it and it alone. By contrast, if we think of a metal, then the cloud is spread out across the whole lattice — which is to say, shared equally among all the trees
