This book by Douglas Hofstadter
is subtitled "Questing For The
Essence Of Mind
". It consists of a collection of his
columns from Scientific American
which were written under the same
title, alternating with postscript
s which expand on the columns and
link them together. Hofstadter chose the title "Metamagical Themas"
for his column because it is an anagram of "Mathematical Games
's column which Hofstadter's column replaced.
Metamagical Themas covers the following topics, among others:
- Self-referential sentences - simple ones like "This sentence
contains five words", paradoxical ones like "This sentence is false",
self-documenting sentences which tally how many of each letter of the
alphabet they contain, and a story composed entirely of
- Innumeracy - how people often don't have any kind of feel for
large numbers, and how to acquire this feel by getting into the habit
of estimating quantities that you're interested in. The higher the
numbers get, the further out the estimates can be. For example,
conceptually 10100 and 10103 are almost the same
even though they differ by a factor of 1000.
- Fonts - What is it about all capital A's that makes them the
same? If you look at a collection of capital A's from different
display faces, you'll see that they're not all open at the bottom and
closed at the top, but just the same, they are all A's. Also, what do
all the letters in a particular font have in common? How can we
program a computer to design new fonts?
- Nomic - a game which is all about modifying its own rules and
can serve as a model for laws which describe under what circumstances
the law can be changed.
- LISP - short for LISt Processing, this is a programming language
in which programs and data are both represented as lists. Since this
makes it easy to write self-modifying code, some people think that
LISP is the best language to use for A.I.
- Artificial Intelligence - when you're communicating over
computer terminals, what can you tell about the being on the other
end? Some people treat a simple Eliza program as an intelligent
being, but others are willing to view anything on a computer screen as
mechanical. Hofstadter describes how he failed a reverse Turing
Test in which some of his friends pretended to be a new A.I. program.
- Analogies - most Americans would probably define the
term "First Lady" as "wife of the president", but who is the First
Lady of Britain? (This column was written when Margaret Thatcher was
Prime Minister.) In a much simpler domain, if abc goes to
abd, what does xyz go to?
- Game theory - Number games like mediocrity, a game for three
players in which the object is to be mediocre at choosing the middle
number (to be the ones who chooses it the middle number of times over
several rounds). Also, the Prisoner's Dilemma and why a
super-rational player will co-operate even in a one-shot game.
- Nuclear war - Hofstadter relates the proliferation of nuclear
weapons to the Prisoner's Dilemma, and also to the earlier section on
innumeracy by observing that the total nuclear arsenal of the world is
already many times more than enough to kill and ionise every single