Paradox and pedagogy

When water freezes, it expands. Thus, my latest invention places a weight on a column of water, then freezes the water to lift the weight, doing work. By using a weight heavy enough that the work done is greater than the energy expenditure to freeze the water, I create a perpetual motion machine. The Second […]

Link: On Proof and Progress in Mathematics

William Thurston’s On Proof and Progress in Mathematics (1994) [17-page PDF] is good, unassuming philosophy of science. I think it’s pretty well-known, but given my goals for link posts I’m not worried about being redundant.

A partial taxonomy of aesthetic compressibility

Some art doesn’t need to be experienced to be mostly apprehended.a A good enough description suffices. Maybe the thing follows convention too closely, or the author is in a rut. But less redundant art can still internally have a variety of flavors of compressibility: Signposting: Rather than do the thing, loudly proclaim that you’re doing the thing. Candidates: […]

Exposition and guidance by analogy

[expanded from tumblr post] In the above table (from Mary Hesse, Models and Analogies in Science), we notice that there are a lot of apparent correspondences between water waves, sound, and light. The “horizontal” notion of similarity lets us notice that sound echoes and light reflects, or that these things all have some sort of […]

Exercise #6: Exercise fodder

Keep an eye out for large, ordered collections of bite-sized chunks of similar (but not too similar) intellectual material. This is the kind of thing that I like to use for exercises, like a paper with many proposed engineering techniques, a site with many social science results, the many answers to questions, or news and commentary […]

Thinking on the page

“Thinking on the page” is a handle that I’ve found useful in improving my writing and introspection more generally. When I write, for the most part, I’m trying to put something that I already feel is true into words. But when I think on the page, the words are getting ahead of my internal sense […]

Link: Trial By Mathematics

Since it’s been a while, I’ll reaffirm my pre-hiatus policy on linkposts: I’d like to use your attention responsibly. To that end, I want to avoid spraying links to whatever’s recently hijacked my brain. When I share a link, I’ll do my best to make it a classic: a text I’ve had time to consider and […]

Unfair outcomes from fair tests

[Summary: Say you use a fair test to predict a quality for which other non-tested factors matter, and then you make a decision based on this prediction. Then people who do worse on the test measure (but not necessarily the other factors) are subject to different error rates, even if you estimate their qualities just as well. If that’s […]

The Hedgehog and the Fox, GMU economist edition

Tyler Cowen on Robin Hanson: Robin is very fond on powerful theories which invoke a very small number of basic elements and give those elements great force.  He likes to focus on one very central mechanism in seeking an explanation or developing policy advice.  Modern physics and Darwin hold too strong a sway in his […]