I Am a Strange Loop

Page 68 If dogs were a bit more like robots… As I was putting the finishing touches on these notes, my children and I flew out to California for Christmas break. We were gliding low, approaching the San Jose airport at night, when Danny, who was peering out the window, said to me, “You know what I just saw?” “What?” I replied, having not the foggiest idea. He said, “A parking lot packed with cars whose headlights and taillights were all flashing on and off at random!” “Why were they all doing that?” I asked, a bit densely. Danny instantly supplied the answer: “Their alarm systems were all triggering each other. I know that’s what it was, because I’ve seen fireworks set car alarms off.” Seeing this in my mind’s eye, I grinned from ear to ear with delight and amazement, all the more so since Danny hadn’t read any of my manuscript and had no idea how relevant his sighting of reverberant honking and flashing was to my book — in fact to the chapter that I was writing notes for just then (Chapter 5). Danny’s reverberant parking lot truly put reverberant barking to shame, and what an infernal racket it must have been for people down on the ground! And yet, as observed from above by chance voyeurs in the plane, it was a totally silent, surrealistic vision of robots who had gotten one another all excited, and who certainly weren’t about to calm down, as dogs will. What a stupendous last-minute addition to my book!

Page 69 the amazing visual universe discovered around 1980… See [Peitgen and Richter].

Page 76 winds up triggering a small set… See [Kanerva] and [Hofstadter and FARG].

Page 77 Suppose we begin with a humble mosquito… See [Griffin] and [Wynne]. The latter contains a remarkable account of analogy-making by bees, of all creatures!

Page 80 cars that drive themselves down …highways or across rocky deserts… See [Davis 2006].

Page 82 structure that represents itself (i.e., the dog itself, not the symbol itself !)… This sounds like a joke, but not entirely. When it comes to the self-symbols of humans — their “I” ’s — much of the structure of the “I” involves pointers that point right back at the abstraction “I”, and not just at the body. This is discussed in Chapters 13 and 16.

Page 83 their category systems became arbitrarily extensible… I defend this point of view in [Hofstadter 2001]. For more on human categories, see [Sander], [Margolis], [Minsky 1986], [Schank], [Aitchison], [Fauconnier], [Hofstadter 1997], and [Gentner et al.].

Page 85 memories of episodes can be triggered… See [Kanerva], [Schank], and [Sander].

Page 86 That deep and tangled self-model is what “I”-ness is all about… See [Dennett 1991], [Metzinger], [Horney 1942], [Horney 1945], [Wheelis], [Nørretranders], and [Kent].

Page 89 Abstraction piled on abstraction… Should anyone care to get a taste of this, try reading [Ash and Gross] all the way to the end. It’s a bit like ordering “Indian hot” in an authentic Indian restaurant — you’ll wonder why you ever did.

Page 91 radicals, such as Évariste Galois… The great Galois was indeed a young radical, which led to his absurdly tragic death in a duel on his twenty-first birthday, but the phrase “solution by radicals” really refers to the taking of nth roots, called “radicals”. For a shallow, a medium, and a deep dip into Galois’ immortal, radical insights into hidden mathematical structures, see [Livio], [Bewersdorff ], and [Stewart], respectively.

Page 95 there is a special type of abstract structure or pattern… “Real Patterns” in [Dennett 1998] argues powerfully for the reality of abstract patterns, based on John Conway’s cellular automaton known as the “Game of Life”. The Game of Life itself is presented ideally in [Gardner], and its relevance to biological life is spelled out in [Poundstone].

Page 102 I am sorry to say, now hackneyed… I have long loved Escher’s art, but as time has passed, I have found myself drawn ever more to his early non-paradoxical landscapes, in which I see hints everywhere of his sense of the magic residing in ordinary scenes. See [Hofstadter 2002], an article written for a celebration of Escher’s 100th birthday.

Page 103 Is there, then, any genuine strange loop — a paradoxical structure that… Three excellent books on paradoxes are [Falletta], [Hughes and Brecht], and [Casati and Varzi 2006].