introductions to ideas that people can then learn more about

[ajschumacher]

like a directory of approaches... just enough to know they exist and sort of how they work?

[ajschumacher]

the idea of broad and deep education: learn about a lot of things at a very surface level, dive into just some in depth...

[ajschumacher]

maybe something like this for math "classes"?

[ajschumacher]

mostly about knowing what there is to know

[ajschumacher]

"Fundamental Theorems" or axioms are interesting but may not be the most instructive/accessible, as in:

https://writings.stephenwolfram.com/2018/11/logic-explainability-and-the-future-of-understanding/

which has a really useless (but very brief) axiom for logic

---

fundamental theorems also came up in Halmos's I want to be a mathematician... seem like good things to know about

[ajschumacher]

see also: Chris Ferrie's "for babies" books

[ajschumacher]

https://planspace.org/20200923-axiomatic_thinking_hilbert_1918/#5

[ajschumacher]

"Unless one can pick out the dominant idea one is going to be dominated by it." (page 123, de Bono in Lateral Thinking)

[ajschumacher]

"map of mathematics" https://www.youtube.com/watch?v=OmJ-4B-mS-Y&ab_channel=DoS-DomainofScience

(and more!)

[ajschumacher]

pantology

[ajschumacher]

maybe this sort of mental models stuff? https://www.wisecharlie.com/blog

Charlie Munger has an idea about “elementary worldly wisdom”

see also: Farnham St books ("great mental models")

[ajschumacher]

this kind of thing too? https://planspace.org/20210131-101_things_to_learn_in_art_school_by_white/

[ajschumacher]

maybe an API guide for the world / science? treat lots of things as functions and just what their input/output is?

[ajschumacher]

https://en.wikipedia.org/wiki/Propaedeutics (as seen in Diamond Age, "Propaedeutic Enchiridion")

a historical term for an introductory course into an art or science

[ajschumacher]

"What I’ve urged is the use of a bigger multidisciplinary bag of tricks, mastered to fluency, to help economics and everything else."

https://fs.blog/great-talks/academic-economics-charlie-munger/

[ajschumacher]

related: https://twitter.com/machinaut/status/1386181247546773512

The more I learn about biological techniques the more I wish there was a central repository with all of the things we know how to do.

Something like a higher-order type system for all of the kinds of stuff, and functions for all the transformations.

[ajschumacher]

this is a neat intro to lots of philosophy, via a quiz: https://programs.clearerthinking.org/philosophical_beliefs.html

[ajschumacher]

Patrick Winston (in How To Speak) distinguishes two purposes for talks: "exposing" (use slides) vs. "teaching" (use chalk).

[ajschumacher]

a good "objective" for a lesson should (?) be unintelligible to someone who hasn't learned the material yet

maybe there's a distinction between understanding what the objective is and satisfying/accomplishing the objective (learning the material) - maybe this is "exposing" vs. "teaching"

sort of the difference between understanding the question and understanding the solution

maybe as an example (connected to fundamental theorems): https://en.wikipedia.org/wiki/Homography#Fundamental_theorem_of_projective_geometry is basically unintelligible

[ajschumacher]

"In other words, exposition is intended to attract and describe more than to explain and instruct." (page 390, Halmos, I want to be a mathematician)

[ajschumacher]

Threshold Concepts and Troublesome Knowledge https://www.etl.tla.ed.ac.uk//docs/ETLreport4.pdf

"Understanding and recognizing the most important conceptual areas of our subjects upon which all else rests might help us to make better decisions about both what and how to teach." (page 164, Didau, What if everything you knew about education was wrong?)

[ajschumacher]

or: Wells's https://en.wikipedia.org/wiki/The_Outline_of_History or Russell's History of Western Philosophy

[ajschumacher]

https://en.wikipedia.org/wiki/Iron_law_of_wages

Goethe's "great, eternal iron laws" in Das Göttliche