science

Metamagical Themas

Metamagical Themas is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Metamagical Themas rather than just read about it. In short: Metamagical Themas is an eclectic collection of articles that Douglas Hofstadter wrote for the popular science magazine Scientific American during the early 1980s. The anthology was published in 1985 by Basic Books.

Key takeaways

Metamagical Themas belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Metamagical Themas to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Metamagical Themas from memory before moving on to harder problems.

Reference excerpt

Metamagical Themas is an eclectic collection of articles that Douglas Hofstadter wrote for the popular science magazine Scientific American during the early 1980s. The anthology was published in 1985 by Basic Books. The volume is substantial in size and contains extensive notes concerning responses to the articles and other information relevant to their content. (One of the notes—page 65—suggested memetics for the study of memes.)

Contents Major themes of the columns include self-reference in memes, language, art and logic; discussions of philosophical issues important in cognitive science/AI; analogies and what makes something similar to something else (specifically what makes, for example, an uppercase letter 'A' recognizable as such); and lengthy discussions of the work of Robert Axelrod on the prisoner's dilemma, as well as the idea of superrationality. The concept of superrationality, and its relevance to the Cold War, environmental issues and such, is accompanied by notes on experiments conducted by the author at the time. Another notable feature is the inclusion of two dialogues in the style of those appearing in Gödel, Escher, Bach. Ambigrams are mentioned. There are three articles centered on the Lisp programming language, in which Hofstadter first details the language itself, and then shows how it relates to Gödel's incompleteness theorem. Two articles are devoted to Rubik's Cube and similar puzzles. Many chapters open with an illustration of an extremely abstract alphabet, yet one which is still gestaltly recognizable as such. The game of Nomic was first introduced to the public in this column, in June 1982, when excerpts from a book (still unpublished at the time) by the game's creator Peter Suber were printed and discussed. The index of the book mentions Hofstadter's recurring alter ego, Egbert B. Gebstadter.

List of Hofstadter's "Metamagical Themas" columns From January 1957 through December 1980, Martin Gardner's "Mathematical Games" column was a monthly feature in Scientific American magazine. In 1981, Gardner's column alternated with a new column by Hofstadter called "Metamagical Themas" (an anagram of "Mathematical Games"). Then Hofstadter's column appeared monthly from January 1982 through July 1983.

French edition

Metamagical Themas was also published in French, under the title Ma Thémagie (InterEditions, 1988), the translators being Jean-Baptiste Berthelin, Jean-Luc Bonnetain, and Lise Rosenbaum. The wordplay was lost in the French title, and replaced with another one (ma Thémagie would translate to "my themagy", where "themagy" is a neologism, but could also be read as maths et magie, which translates to "maths and magic"). The translators had contemplated Le matin des métamagiciens, which would have been a play on Hofstadter's title plus Le Matin des Magiciens and Jeux malins des mathématiciens (respectively, The Dawn of the Magicians and Clever Tricks of Mathematicians); however, the publisher found that suggestion to be too elaborate.

Reception Dave Langford reviewed Metamagical Themas for White Dwarf #88, and stated that "a heady mixture of computers, art, mathematics, philosophy, jokes and above all games."

References

External links Metamagical Themas at Google Books "A Person Paper on Purity in Language", one of the included essays, first published in September 1983

Worked examples

Example 1 — a first encounter with Metamagical Themas

Start with the simplest possible case. Write down what Metamagical Themas claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Metamagical Themas before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Metamagical Themas ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Metamagical Themas

In research: Metamagical Themas appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Metamagical Themas in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Metamagical Themas is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1985 books, Basic Books books, Books by Douglas Hofstadter, so understanding it makes those chapters shorter.
In everyday life: Look for Metamagical Themas outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Metamagical Themas in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Metamagical Themas means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Metamagical Themas out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Metamagical Themas in simple terms?

Why does Metamagical Themas matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Metamagical Themas?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Metamagical Themas.