And now something completely different

From Propp, Vladimir. Morphology of the Folktale. 1927. Trans., Laurence Scott. 2nd ed. Austin: University of Texas Press, 1968.

The Functions of the Dramatis Personae (in a true oral folk tale).

Theorems:

1. The functions of characters serve as stable, constant elements in a tale, independent of how and by whom they are fulfilled.
2. The number of functions known to the fairy tale is limited.
3. The sequence of functions is always identical.
4. All fairy tales are of one type in regard to their structure.
http://www-personal.umich.edu/~esrabkin/Propp.htm

It should be possible to express the structure of a true oral folk tale in terms of Category Theory. Per Theorem 4, a distinct structure is a category.

upd. Probably related from "Why Don't Students Like School?"

(no subject)

Завтра буду передавать эстафету в spacetime. Для этого надо придумать какую-то тему и, по-хорошему, что-нибудь написать самому. После чтения книжки про обучение, думаю, что задам тему в виде вопроса. Интересно, что из этого получится.

Quote of the Day

Civilization advances by extending the number of important operations which we can perform without thinking about them.

-- Alfred NorthWhitehead.

In good old days we had to use humans for non–thinking, but in the future, we'll be increasingly using robots and computers for the very same task. Many people are disturbed by the fact that they would have to think for a living.

Dilemma of the day: teaching vs learning

Cognition early in training is fundamentally different from cognition late in training.

...information in an expert’s long-term memory...is organized differently from the information in a novice’s long-term memory. Experts don’t think in terms of surface features, as novices do; they think in terms of functions, or deep structure.

The novices ...[generate]... categories based on the objects in the problems.

...transfer [using known info to apply to new problems] is so difficult because novices tend to focus on surface features and are not very good at seeing the abstract, functional relationships among problems that are key to solving them.

...experts are able to ignore unimportant details and home in on useful information; thinking functionally makes it obvious what’s important.

--- Willingham. Why students don't like school? 2009.

Here's the teaching/learning dilemma:
- On the one hand, you want to teach "objects", i.e surface features, so that novices can learn.
- On the other hand, you want to teach functional relationships, i.e. abstract, deep structures, so that learners acquire useful skills.

In other words, if you are an expert you can't teach novices "the real thing" and must dumb down the material, so that it becomes learnable.

As a side note, Category Theory can be a good teaching/learning tool for experts because it focuses on functional relationships, instead of objects.