maldv/crabcanon · Datasets at Hugging Face

text stringlengths 0 174
...Ant Fugue. An imitation of a musical fugue: each voice enters with the same statement. The
theme-holism versus reductionism-is introduced in a recursive picture composed of words
composed of smaller words, etc. The words which appear on the four levels of this strange picture
are "HOLISM", "REDLCTIONIsM", and "ML". The discussion veers off to a friend of the
Anteater's Aunt Hillary, a conscious ant colony. The various levels of her thought processes are
the topic of discussion. Many fugal tricks are ensconced in the Dialogue. As a hint to the reader,
references are made to parallel tricks occurring in the fugue on the record to which the foursome
is listening. At the end of the Ant Fugue, themes from the Prelude return, transformed
considerably.

Chapter XI: Brains and Thoughts. "How can thoughts he supported by the hardware of the brain is
the topic of the Chapter. An overview of the large scale and small-scale structure of the brain is
first given. Then the relation between concepts and neural activity is speculatively discussed in
some detail.

English French German Suite. An interlude consisting of Lewis Carroll's nonsense poem
"Jabberwocky' 1 together with two translations: one into French and one into German, both done
last century.

Chapter XII: Minds and Thoughts. The preceding poems bring up in a forceful way the question
of whether languages, or indeed minds, can be "mapped" onto each other. How is communication
possible between two separate physical brains: What do all human brains have in common? A
geographical analogy is used to suggest an answer. The question arises, "Can a brain be
understood, in some objective sense, by an outsider?"

Aria with Diverse Variations. A Dialogue whose form is based on Bach's Goldberg Variations, and
whose content is related to number-theoretical problems such as the Goldbach conjecture. This
hybrid has as its main purpose to show how number theory's subtlety stems from the fact that
there are many diverse variations on the theme of searching through an infinite space. Some of
them lead to infinite searches, some of them lead to finite searches, while some others hover in
between.

Chapter XIII: BIooP and FlooP and GIooP. These are the names of three computer languages.
BIooP programs can carry out only predictably finite searches, while FlooP programs can carry
out unpredictable or even infinite searches. The purpose of this Chapter is to give an intuition for
the notions of primitive recursive and general recursive functions in number theory, for they are
essential in Godel’s proof.

Air on G's String. A Dialogue in which Godel’s self-referential construction is mirrored in words.
The idea is due to W. V. O. Quine. This Dialogue serves as a prototype for the next Chapter.

Chapter XIV: On Formally Undeeidable Propositions of TNT and Related Systems. This
Chapter's title is an adaptation of the title of Godel’s 1931 article, in which his Incompleteness
Theorem was first published. The two major parts of Godel’s proof are gone through carefully. It
is shown how the assumption of consistency of TNT forces one to conclude that TNT (or any
similar system) is incomplete. Relations to Euclidean and non-Euclidean geometry are discussed.
Implications for the philosophy of mathematics are gone into with some care.


Overview


XI



Birthday Cantatatata ... In which Achilles cannot convince the wily and skeptical Tortoise that today
is his (Achilles') birthday. His repeated but unsuccessful tries to do so foreshadow the
repeatability of the Godel argument.

Chapter XV: Jumping out of the System. The repeatability of Godel’s argument is shown, with
the implication that TNT is not only incomplete, but "essentially incomplete The fairly notorious
argument by J. R. Lucas, to the effect that Godel’s Theorem demonstrates that human thought
cannot in any sense be "mechanical", is analyzed and found to be wanting.

Edifying Thoughts of a Tobacco Smoker. A Dialogue treating of many topics, with the thrust being
problems connected with self-replication and self-reference. Television cameras filming
television screens, and viruses and other subcellular entities which assemble themselves, are
among the examples used. The title comes from a poem by J. S. Bach himself, which enters in a
peculiar way.

Chapter XVI: Self-Ref and Self-Rep. This Chapter is about the connection between self-reference
in its various guises, and self-reproducing entities e.g., computer programs or DNA molecules).
The relations between a self-reproducing entity and the mechanisms external to it which aid it in
reproducing itself (e.g., a computer or proteins) are discussed-particularly the fuzziness of the
distinction. How information travels between various levels of such systems is the central topic of
this Chapter.

The Magnificrab, Indeed. The title is a pun on Bach's Magnifacat in D. The tale is about the Crab,
who gives the appearance of having a magical power of distinguishing between true and false
statements of number theory by reading them as musical pieces, playing them on his flute, and
determining whether they are "beautiful" or not.

Chapter XVII: Church, Turing, Tarski, and Others. The fictional Crab of the preceding Dialogue
is replaced by various real people with amazing mathematical abilities. The Church-Turing
Thesis, which relates mental activity to computation, is presented in several versions of differing
strengths. All are analyzed, particularly in terms of their implications for simulating human
thought mechanically, or programming into a machine an ability to sense or create beauty. The
connection between brain activity and computation brings up some other topics: the halting
problem of Turing, and Tarski's Truth Theorem.

SHRDLU, Toy of Man's Designing. This Dialogue is lifted out of an article by Terry Winograd on
his program SHRDLU: only a few names have been changed. In it. a program communicates
with a person about the so-called "blocks world" in rather impressive English. The computer
program appears to exhibit some real understanding-in its limited world. The Dialogue's title is
based on Jesu, joy of Mans Desiring , one movement of Bach's Cantata 147.

Chapter XVIII: Artificial Intelligence: Retrospects, This Chapter opens with a discussion of the
famous "Turing test"-a proposal by the computer pioneer Alan Turing for a way to detect the
presence or absence of "thought" in a machine. From there, we go on to an abridged history of

...Ant Fugue. An imitation of a musical fugue: each voice enters with the same statement. The

theme-holism versus reductionism-is introduced in a recursive picture composed of words

composed of smaller words, etc. The words which appear on the four levels of this strange picture

are "HOLISM", "REDLCTIONIsM", and "ML". The discussion veers off to a friend of the

Anteater's Aunt Hillary, a conscious ant colony. The various levels of her thought processes are

the topic of discussion. Many fugal tricks are ensconced in the Dialogue. As a hint to the reader,

references are made to parallel tricks occurring in the fugue on the record to which the foursome

is listening. At the end of the Ant Fugue, themes from the Prelude return, transformed

considerably.

Chapter XI: Brains and Thoughts. "How can thoughts he supported by the hardware of the brain is

the topic of the Chapter. An overview of the large scale and small-scale structure of the brain is

first given. Then the relation between concepts and neural activity is speculatively discussed in

some detail.

English French German Suite. An interlude consisting of Lewis Carroll's nonsense poem

"Jabberwocky' 1 together with two translations: one into French and one into German, both done

last century.

Chapter XII: Minds and Thoughts. The preceding poems bring up in a forceful way the question

of whether languages, or indeed minds, can be "mapped" onto each other. How is communication

possible between two separate physical brains: What do all human brains have in common? A

geographical analogy is used to suggest an answer. The question arises, "Can a brain be

understood, in some objective sense, by an outsider?"

Aria with Diverse Variations. A Dialogue whose form is based on Bach's Goldberg Variations, and

whose content is related to number-theoretical problems such as the Goldbach conjecture. This

hybrid has as its main purpose to show how number theory's subtlety stems from the fact that

there are many diverse variations on the theme of searching through an infinite space. Some of

them lead to infinite searches, some of them lead to finite searches, while some others hover in

between.

Chapter XIII: BIooP and FlooP and GIooP. These are the names of three computer languages.

BIooP programs can carry out only predictably finite searches, while FlooP programs can carry

out unpredictable or even infinite searches. The purpose of this Chapter is to give an intuition for

the notions of primitive recursive and general recursive functions in number theory, for they are

essential in Godel’s proof.

Air on G's String. A Dialogue in which Godel’s self-referential construction is mirrored in words.

The idea is due to W. V. O. Quine. This Dialogue serves as a prototype for the next Chapter.

Chapter XIV: On Formally Undeeidable Propositions of TNT and Related Systems. This

Chapter's title is an adaptation of the title of Godel’s 1931 article, in which his Incompleteness

Theorem was first published. The two major parts of Godel’s proof are gone through carefully. It

is shown how the assumption of consistency of TNT forces one to conclude that TNT (or any

similar system) is incomplete. Relations to Euclidean and non-Euclidean geometry are discussed.

Implications for the philosophy of mathematics are gone into with some care.

Overview

XI

Birthday Cantatatata ... In which Achilles cannot convince the wily and skeptical Tortoise that today

is his (Achilles') birthday. His repeated but unsuccessful tries to do so foreshadow the

repeatability of the Godel argument.

Chapter XV: Jumping out of the System. The repeatability of Godel’s argument is shown, with

the implication that TNT is not only incomplete, but "essentially incomplete The fairly notorious

argument by J. R. Lucas, to the effect that Godel’s Theorem demonstrates that human thought

cannot in any sense be "mechanical", is analyzed and found to be wanting.

Edifying Thoughts of a Tobacco Smoker. A Dialogue treating of many topics, with the thrust being

problems connected with self-replication and self-reference. Television cameras filming

television screens, and viruses and other subcellular entities which assemble themselves, are

among the examples used. The title comes from a poem by J. S. Bach himself, which enters in a

peculiar way.

Chapter XVI: Self-Ref and Self-Rep. This Chapter is about the connection between self-reference

in its various guises, and self-reproducing entities e.g., computer programs or DNA molecules).

The relations between a self-reproducing entity and the mechanisms external to it which aid it in

reproducing itself (e.g., a computer or proteins) are discussed-particularly the fuzziness of the

distinction. How information travels between various levels of such systems is the central topic of

this Chapter.

The Magnificrab, Indeed. The title is a pun on Bach's Magnifacat in D. The tale is about the Crab,

who gives the appearance of having a magical power of distinguishing between true and false

statements of number theory by reading them as musical pieces, playing them on his flute, and

determining whether they are "beautiful" or not.

Chapter XVII: Church, Turing, Tarski, and Others. The fictional Crab of the preceding Dialogue

is replaced by various real people with amazing mathematical abilities. The Church-Turing

Thesis, which relates mental activity to computation, is presented in several versions of differing

strengths. All are analyzed, particularly in terms of their implications for simulating human

thought mechanically, or programming into a machine an ability to sense or create beauty. The

connection between brain activity and computation brings up some other topics: the halting

problem of Turing, and Tarski's Truth Theorem.

SHRDLU, Toy of Man's Designing. This Dialogue is lifted out of an article by Terry Winograd on

his program SHRDLU: only a few names have been changed. In it. a program communicates

with a person about the so-called "blocks world" in rather impressive English. The computer

program appears to exhibit some real understanding-in its limited world. The Dialogue's title is

based on Jesu, joy of Mans Desiring , one movement of Bach's Cantata 147.

Chapter XVIII: Artificial Intelligence: Retrospects, This Chapter opens with a discussion of the

famous "Turing test"-a proposal by the computer pioneer Alan Turing for a way to detect the

presence or absence of "thought" in a machine. From there, we go on to an abridged history of