maldv/crabcanon · Datasets at Hugging Face

text stringlengths 0 174
Dialogue's title is a cross between the word "acrostic" and the word "contrapunctus", a Latin word
which Bach used to denote the many fugues and canons making up his Art of the Fugue. Some
explicit references to the Art of the Fugue are made. The Dialogue itself conceals some acrostic
tricks.

Chapter IV: Consistency, Completeness, and Geometry. The preceding Dialogue is explicated to
the extent it is possible at this stage. This leads back to the question of how and when symbols in
a formal system acquire meaning. The history of Euclidean and non-Euclidean geometry is given,
as an illustration of the elusive notion of "undefined terms". This leads to ideas about the
consistency of different and possibly "rival" geometries. Through this discussion the notion of
undefined terms is clarified, and the relation of undefined terms to perception and thought
processes is considered.

Little Harmonic Labyrinth. This is based on the Bach organ piece by the same name. It is a playful
introduction to the notion of recursive-i.e., nested structures. It contains stories within stories. The
frame story, instead of finishing as expected, is left open, so the reader is left dangling without
resolution. One nested story concerns modulation in music-particularly an organ piece which
ends in the wrong key, leaving the listener dangling without resolution.

Chapter V: Recursive Structures and Processes. The idea of recursion is presented in many
different contexts: musical patterns, linguistic patterns, geometric structures, mathematical
functions, physical theories, computer programs, and others.

Canon by Intervallic Augmentation. Achilles and the Tortoise try to resolve the question, "Which
contains more information-a record, or the phonograph which plays it This odd question arises
when the Tortoise describes a single record which, when played on a set of different
phonographs, produces two quite different melodies: B-A-C-H and C-A-G-E. It turns out,
however, that these melodies are "the same", in a peculiar sense.

Chapter VI: The Location of Meaning. A broad discussion of how meaning is split among coded
message, decoder, and receiver. Examples presented include strands of DNA, undeciphered
inscriptions on ancient tablets, and phonograph records sailing out in space. The relationship of
intelligence to "absolute" meaning is postulated.

Chromatic Fantasy, And Feud. A short Dialogue bearing hardly any resemblance, except in title, to
Bach's Chromatic Fantasy and Fugue. It concerns the proper way to manipulate sentences so as
to preserve truth-and in particular the question


Overview


IX



of whether there exist rules for the usage of the word "arid". This Dialogue has much in common
with the Dialogue by Lewis Carroll.

Chapter VII: The Propositional Calculus. It is suggested how words such as ,,and" can be
governed by formal rules. Once again, the ideas of isomorphism and automatic acquisition of
meaning by symbols in such a system are brought up. All the examples in this Chapter,
incidentally, are "Zentences"-sentences taken from Zen koans. This is purposefully done,
somewhat tongue-in-cheek, since Zen koans are deliberately illogical stories.

Crab Canon. A Dialogue based on a piece by the same name from the Musical Offering. Both are so
named because crabs (supposedly) walk backwards. The Crab makes his first appearance in this
Dialogue. It is perhaps the densest Dialogue in the book in terms of formal trickery and level-
play. Godel, Escher, and Bach are deeply intertwined in this very short Dialogue.

Chapter VIII: Typographical Number Theory. An extension of the Propositional Calculus called
"TNT" is presented. In TNT, number-theoretical reasoning can be done by rigid symbol
manipulation. Differences between formal reasoning and human thought are considered.

A Mu Offering. This Dialogue foreshadows several new topics in the book. Ostensibly concerned
with Zen Buddhism and koans, it is actually a thinly veiled discussion of theoremhood and
nontheoremhood, truth and falsity, of strings in number theory. There are fleeting references to
molecular biology-particular) the Genetic Code. There is no close affinity to the Musical
Offering, other than in the title and the playing of self-referential games.

Chapter IX: Mumon and Godel. An attempt is made to talk about the strange ideas of Zen
Buddhism. The Zen monk Mumon, who gave well known commentaries on many koans, is a
central figure. In a way, Zen ideas bear a metaphorical resemblance to some contemporary ideas
in the philosophy of mathematics. After this "Zennery", Godel’s fundamental idea of Godel-
numbering is introduced, and a first pass through Godel’s Theorem is made.

Part II: EGB

Prelude ... This Dialogue attaches to the next one. They are based on preludes and fugues from
Bach's Well-Tempered Clavier. Achilles and the Tortoise bring a present to the Crab, who has a
guest: the Anteater. The present turns out to be a recording of the W.T.C.; it is immediately put
on. As they listen to a prelude, they discuss the structure of preludes and fugues, which leads
Achilles to ask how to hear a fugue: as a whole, or as a sum of parts? This is the debate between
holism and reductionism, which is soon taken up in the Ant Fugue.

Chapter X: Levels of Description, and Computer Systems. Various levels of seeing pictures,
chessboards, and computer systems are discussed. The last of these is then examined in detail.
This involves describing machine languages, assembly languages, compiler languages, operating
systems, and so forth. Then the discussion turns to composite systems of other types, such as
sports teams, nuclei, atoms, the weather, and so forth. The question arises as to how man
intermediate levels exist-or indeed whether any exist.


Overview


X

Dialogue's title is a cross between the word "acrostic" and the word "contrapunctus", a Latin word

which Bach used to denote the many fugues and canons making up his Art of the Fugue. Some

explicit references to the Art of the Fugue are made. The Dialogue itself conceals some acrostic

tricks.

Chapter IV: Consistency, Completeness, and Geometry. The preceding Dialogue is explicated to

the extent it is possible at this stage. This leads back to the question of how and when symbols in

a formal system acquire meaning. The history of Euclidean and non-Euclidean geometry is given,

as an illustration of the elusive notion of "undefined terms". This leads to ideas about the

consistency of different and possibly "rival" geometries. Through this discussion the notion of

undefined terms is clarified, and the relation of undefined terms to perception and thought

processes is considered.

Little Harmonic Labyrinth. This is based on the Bach organ piece by the same name. It is a playful

introduction to the notion of recursive-i.e., nested structures. It contains stories within stories. The

frame story, instead of finishing as expected, is left open, so the reader is left dangling without

resolution. One nested story concerns modulation in music-particularly an organ piece which

ends in the wrong key, leaving the listener dangling without resolution.

Chapter V: Recursive Structures and Processes. The idea of recursion is presented in many

different contexts: musical patterns, linguistic patterns, geometric structures, mathematical

functions, physical theories, computer programs, and others.

Canon by Intervallic Augmentation. Achilles and the Tortoise try to resolve the question, "Which

contains more information-a record, or the phonograph which plays it This odd question arises

when the Tortoise describes a single record which, when played on a set of different

phonographs, produces two quite different melodies: B-A-C-H and C-A-G-E. It turns out,

however, that these melodies are "the same", in a peculiar sense.

Chapter VI: The Location of Meaning. A broad discussion of how meaning is split among coded

message, decoder, and receiver. Examples presented include strands of DNA, undeciphered

inscriptions on ancient tablets, and phonograph records sailing out in space. The relationship of

intelligence to "absolute" meaning is postulated.

Chromatic Fantasy, And Feud. A short Dialogue bearing hardly any resemblance, except in title, to

Bach's Chromatic Fantasy and Fugue. It concerns the proper way to manipulate sentences so as

to preserve truth-and in particular the question

Overview

IX

of whether there exist rules for the usage of the word "arid". This Dialogue has much in common

with the Dialogue by Lewis Carroll.

Chapter VII: The Propositional Calculus. It is suggested how words such as ,,and" can be

governed by formal rules. Once again, the ideas of isomorphism and automatic acquisition of

meaning by symbols in such a system are brought up. All the examples in this Chapter,

incidentally, are "Zentences"-sentences taken from Zen koans. This is purposefully done,

somewhat tongue-in-cheek, since Zen koans are deliberately illogical stories.

Crab Canon. A Dialogue based on a piece by the same name from the Musical Offering. Both are so

named because crabs (supposedly) walk backwards. The Crab makes his first appearance in this

Dialogue. It is perhaps the densest Dialogue in the book in terms of formal trickery and level-

play. Godel, Escher, and Bach are deeply intertwined in this very short Dialogue.

Chapter VIII: Typographical Number Theory. An extension of the Propositional Calculus called

"TNT" is presented. In TNT, number-theoretical reasoning can be done by rigid symbol

manipulation. Differences between formal reasoning and human thought are considered.

A Mu Offering. This Dialogue foreshadows several new topics in the book. Ostensibly concerned

with Zen Buddhism and koans, it is actually a thinly veiled discussion of theoremhood and

nontheoremhood, truth and falsity, of strings in number theory. There are fleeting references to

molecular biology-particular) the Genetic Code. There is no close affinity to the Musical

Offering, other than in the title and the playing of self-referential games.

Chapter IX: Mumon and Godel. An attempt is made to talk about the strange ideas of Zen

Buddhism. The Zen monk Mumon, who gave well known commentaries on many koans, is a

central figure. In a way, Zen ideas bear a metaphorical resemblance to some contemporary ideas

in the philosophy of mathematics. After this "Zennery", Godel’s fundamental idea of Godel-

numbering is introduced, and a first pass through Godel’s Theorem is made.

Part II: EGB

Prelude ... This Dialogue attaches to the next one. They are based on preludes and fugues from

Bach's Well-Tempered Clavier. Achilles and the Tortoise bring a present to the Crab, who has a

guest: the Anteater. The present turns out to be a recording of the W.T.C.; it is immediately put

on. As they listen to a prelude, they discuss the structure of preludes and fugues, which leads

Achilles to ask how to hear a fugue: as a whole, or as a sum of parts? This is the debate between

holism and reductionism, which is soon taken up in the Ant Fugue.

Chapter X: Levels of Description, and Computer Systems. Various levels of seeing pictures,

chessboards, and computer systems are discussed. The last of these is then examined in detail.

This involves describing machine languages, assembly languages, compiler languages, operating

systems, and so forth. Then the discussion turns to composite systems of other types, such as

sports teams, nuclei, atoms, the weather, and so forth. The question arises as to how man

intermediate levels exist-or indeed whether any exist.

Overview

X