I Am a Strange Loop - Douglas R. Hofstadter [226]
Page 41 Deep understanding of causality… See [Pattee], [Holland 1995], [Holland 1997], [Andersen], [Simon], and Chapter 26 of [Hofstadter 1985].
Page 45 The Careenium… Chapter 25 of [Hofstadter 1985] is a lengthy Achilles–Tortoise dialogue spelling out the careenium metaphor in detail.
Page 49 The effect…was explained…by Albert Einstein… See [Hoffmann] and [Pais 1986].
Page 49 From this perspective, there are no simmballs, no symbols… This view approaches the extreme reductionist philosophy expressed in [Unger 1979] and also in [Unger 1979].
Page 52 Why does this move to a goal-oriented — that is, teleological — shorthand… See [Monod], [Cordeschi], [Haugeland 1981], and [Dupuy 2000].
Page 53 In the video called “Virtual Creatures” by Karl Sims… This is found easily on the Web.
Page 53 a strong pressure to shift …to the goal-oriented level of cybernetics… See [Dupuy 2000], [Monod], [Cordeschi], [Simon], [Andersen], and Chapter 11 in [Hofstadter and Dennett], which discusses a trio of related “isms” — holism, goalism, and soulism.
Page 54 the story of a sultan who commanded… Found in the charming old book [Gamow].
Page 55 contains the seeds of its own destruction… Compare this scenario of self-breaking to the story recounted in the dialogue “Contracrostipunctus” in [Hofstadter 1979].
Page 57 I stumbled upon …a little paperback… Of course this was [Nagel and Newman].
Page 57 I’m sure I didn’t think “he or she”… See Chapters 7 and 8 of [Hofstadter 1985].
Page 60 pushed my luck and invented the more threeful phrase… Although I didn’t know it, I was dimly sensing the infinite hierarchy of arithmetical operations and what I would later come to know as “Ackermann’s function”. See [Boolos and Jeffrey] and [Hennie].
Page 61 a pathological retreat from common sense… I cannot resist pointing out that Principia Mathematica opens with a grand flourish of self-reference, its first sentence unabashedly declaring: “The mathematical treatment of the principles of mathematics, which is the subject of the present work, has arisen from the conjunction of two different studies, both in the main very modern.” Principia Mathematica thus points at itself through the proud phrase “the present work” — exactly the kind of self-pointer that, in more formal contexts, its authors were at such pains to forbid categorically. Perhaps more weirdly, the chapter in which the self-reference–banning theory of types is presented also opens self-referentially: “The theory of logical types, to be explained in the present Chapter, recommended itself to us in the first instance by its ability to solve certain contradictions…” Note finally that the pronoun “us” is yet another self-pointer that Russell and Whitehead have no qualms using. Were they not aware of these ironies?
Page 62 the topic of self-reference in language… See Chapters 1–4 of [Hofstadter 1985].
Page 62 This pangram tallies… This perfectly self-tallying or self-inventorying “pangram” was discovered by Lee Sallows using an elaborate analog computer that he built.
I have often mused about a large community of sentences somewhat like Sallows’, each one inventorying not only itself (i.e., giving 26 letter-counts as above), but in addition some or perhaps all of the others. Thus each sentence would be far, far longer than Sallows’ pangram. However, in my fantasy, these “individuals”, unlike Sallows’ remarkable sentence, do not all give accurate reports. Some of what they say is dead wrong. In the self-inventorying department, I imagine most of them as being fairly accurate (most of their 26 “first-person” counts would be precisely right, with just a few perhaps being a little bit off). On the other hand, each sentence’s inventory of other sentences would vary in accuracy, from being somewhat close to being wildly far off.
Needless to say, this is a metaphor for a society of interacting human beings, each of whom has a fairly accurate self-image and less accurate images of others, often based on very quick