I am interested in promoting rationality in my local community. As I don't know anyone who are involved in the movement I'll probably have to do some initial teaching. Which, in your oppinion, are the most essential/fundemental parts of rationality, and of these which are most accessible to newcomers?

While I learned a lot from Yudkowski's 'Rationality: from AI to Zombies', it's my impression that large parts of it would be confusing and discouraging to anyone without technical knowledge and in particular strong math skills.

The Bayesian Conspiracy, Waking up with Sam Harris and Rationality Speaking all provide valueable skills but from what I've experienced they all teach rationality in an indirect way rather than focusing on teaching it directly.

Does any exercises that help teach rationality exist?

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The CFAR Exercise Prize is a good place to start.

Though I'm more interested in how we can test rationality. Compared to many other skills it seems unusually hard to test.

I did one workshop about changing our mind.

The first exercise was to have everybody write down a list of where they changed their mind in the last year for 10 minutes. The next exercise was to discuss the results in groups of 3 people. As a next step this can be build up to discuss together the principles about how we made great belief updates.

This approach is very open and even people who aren't formally interested in "ratioanlity" find it easy to participate.

The easiest thing to do with complete newcomers is to get them to read things. There are plenty of popular psychology books that will help pique peoples' interests - I like the ones by Dan Ariely, you can also find more in the Ravenclaw section of the Rationalist Bookshelf. If they like philosophizing, they might like the Humans' Guide to Words sequence on LessWrong.

For actual exercises, I think one of the most interesting things I've done was try staring into someone's eyes for twenty minutes by the clock. Or trying to actually work out to do, on some things I waqs having trouble deciding on, by estimating probabilities and trying to think about relative utility.

Also, yes, this is sort of the problem CFAR is working on - but I'm not sure what they do for very very introductory material.