Start here?

This blog is kind of hard to navigate. Partly because there’s no obvious theme, I just write about whatever I’m interested in. And partly because there’s a lot of variance in post quality. I stick everything here, from tricky physics explanations that take weeks to write to dumb notebook posts that take half an hour.

This works well for me. I find I produce more and better writing overall if I don’t get too precious about standards. And also it seems appropriate for a blog called Drossbucket, which started life as a tumblr full of low-effort shitposts.

Still, it would be nice if people could find my better stuff without having to slop through the dross. I’ve tried to make it a bit easier to follow by pointing out some of my favourite posts here. Although there’s no set theme, there are a few topics that I keep coming back to. These tend to centre around the following areas:

  • ‘Mathematical intuition’. Whatever that means exactly.
  • Attempts at understanding various ideas, often connected to some kind of continental or postmodern philosophy
  • Physics, especially quantum foundations
  • Reflections on attempting independent work outside academia

Here are my favourite posts from these categories:

Mathematical intuition

> You have doubtless seen those delicate assemblages of silicious needles which form the skeleton of certain sponges. When the organic matter has disappeared, there remains only a frail and elegant lace-work. True, nothing is there except silica, but what is interesting is the form this silica has taken, and we could not understand it if we did not know the living sponge which has given it precisely this form. Thus it is that the old intuitive notions of our fathers, even when we have abandoned them, still imprint their form upon the logical constructions we have put in their place.

— Henri Poincaré, Intuition and Logic in Mathematics

I’m interested in what we actually do when we do mathematics. We manipulate symbols according to formal rules, yes, but on its own this only gives us Poincaré’s ‘frail and elegant lace-work’. To figure out what to calculate, we ground this in the ‘living sponge’ of human experience – vision, kinesthetic sense, language, aesthetics…

This all gets lumped under the term ‘mathematical intuition’ but seems poorly understood. I want to know what’s going on!

I used to write about this quite a lot under my mathbucket tag back when this was a tumblr, in a scrappy example-based way. One representative one is this short post on Seymour Papert’s Mindstorms, which contrasts formal and intuitive approaches to proofs of the irrationality of the square root of two. Since then I’ve done a lot of reading and would like to write some more coherent synthesis posts, but I haven’t really got to that yet.

Still, there are a few more recent posts that touch on this:

  • Two types of mathematician reference list. There’s this weird tiny sub-genre of mathematicians writing essays where they divide mathematicians into two types. I’ve tried to collect as many examples as I can. Not sure what I’m planning to do with this, but it’s fascinating to me that this is such a common impulse.

  • More than you ever wanted to know about the bat and ball problem from the Cognitive Reflection Test. This puzzle question is used as a prototype of a situation where an obvious wrong answer distracts from an unintuitive correct answer that requires effortful thought. I had some suspicions that the story was more complicated than that, so I dug through the internet to find examples of how people solve it in practice. The comments on this one are also well worth reading!

  • This ability to separate out the formal core of a problem from distracting ‘intuitive’ background context is known as cognitive decoupling, a term introduced by Keith Stanovich. I wrote some personal reflections on my own difficulty with decoupling in The cognitive decoupling elite, and an exploration of the history of the idea in Cognitive decoupling and banana phones.

‘Philosophy’

Scare quotes on this one because it isn’t quite right, but I’m not sure what else to call it… maybe ‘reading some stuff and attempting to make sense of it’ would be better.

  • Metarationality: a messy introduction. I wrote this when I was trying to understand what the hell David Chapman was going on about on his Meaningness site. The pieces were just starting to come together for me and I wrote this sort of excitable crash through the material. I wouldn’t do it exactly like this now I know a bit more, but it holds up better than I expected.

  • The middle distance. This is a followup to the bananaphone post, explaining a single related idea from Brian Cantwell Smith’s On the Origin of Objects. Another one where the comments are very good.

  • A braindump on Derrida and close reading. I found the text of an unusually comprehensible talk about Derrida by Christopher Norris online and was inspired to write… whatever this is. Long, rambling, extremely niche post about Empson, Derrida, Rousseau and baroque music that was surprisingly popular.

  • A review of Matthew Crawford’s The World Beyond Your Head. This looks like a standard pop book about avoiding distractions but turns out to have an impressively deep treatment of exactly why working with your hands with real objects is so satisfying.

Physics

Some explorations of various bits of physics. This is actually my main weird interest, but for various reasons it’s taken me longer to start writing about it here. More coming soon hopefully…

  • A pair of posts trying to make some sense out of the idea of negative probability and how it appears in quantum physics, one without equations and one with.

  • Bell’s theorem and Mermin’s machine. Starting from Mermin’s wonderful pop explanation of Bell’s theorem in Quantum Mechanics for Anyone, and linking it back to the standard textbook version.

Working outside academia

I’m interested in independent research outside of academic institutions. Both documenting my own blundering efforts to get there, and speculating on ways to make it easier.

The whole archive

Finally, if you just want to wade through the archive, here it is. Good luck!