Douglas Hofstadter - I Am a Strange Loop

Page 150 respect for …the most mundane of analogies… See [Hofstadter 2001] and [Sander], as well as Chapter 24 in [Hofstadter 1985] and [Hofstadter and FARG].

Page 159 X’s play is so mega-inconsistent… This should be heard as “X’s play is omega-inconsistent”, which makes a phonetic hat-tip to the metamathematical concepts of omega-inconsistency and omega-incompleteness, discussed in many books in the Bibliography, such as [DeLong], [Nagel and Newman], [Hofstadter 1979], [Smullyan 1992], [Boolos and Jeffrey], and others. For our more modest purposes here, however, it suffices to know that this “o”-containing quip, plus the one two lines below it, is a play on words.

Page 160 Indeed, some years after Gödel, such self-affirming formulas were concocted… See [Smullyan 1992], [Boolos and Jeffrey], and [Wolf].

Page 164 Why would logicians …give such good odds… See [Kneebone], [Wilder], and [Nagel and Newman], for reasons to believe strongly in the consistency of PM- like systems.

Page 165 not only although…but worse, because… For another treatment of the perverse theme of “although” turning into “because”, see Chapter 13 of [Hofstadter 1985].

Page 166 the same Gödelian trap would succeed in catching it… For an amusing interpretation of the infinite repeatability of Gödel’s construction as demonstrating the impossibility of artificial intelligence, see the chapter by J. R. Lucas in [Anderson], which is carefully analyzed (and hopefully refuted) in [DeLong], [Webb], and [Hofstadter 1979].

Page 167 called “the Hilbert Program”… See [DeLong], [Wolf ], [Kneebone], and [Wilder].

Page 170 In that most delightful though most unlikely of scenarios… [DeLong], [Goodstein], and [Chaitin] discuss non-Gödelian formulas that are undecidable for Gödelian 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).