Tom Stuart - 'A lever for the mind' at BathRuby

I’m at Bath Ruby 2015, live blogging some of the talks

Slide photo by @trailsuite

Photo by @trailsuite

  • Brains are just not very good at working with several complex ideas concurrently
  • Abstraction is our solution to this
  • Numbers are a property of sets (?) of things. It doesn’t matter how we arrange the things, or how big they are
  • We build other concepts on top of our idea of number: e.g. successor - a way to generate new numbers. gt/lt can be built from the idea of successors
  • These abstractions allow us to predict what would happen in reality when certain actions occur: we can do the ‘work’ in the ‘abstract world’ rather than doing it in the real world and observing the result.
  • Recognise patterns. Some patterns can be generalised to apply to whole classes of items (e.g. all natural numbers)
  • You don’t need to remember the details of why a particular formula works: it doesn’t matter: you can use it without understanding why it’s true
  • A walk across a graph is a sequence of visits from node to node along their adjacent edges
  • A connected graph is one where there exists a walk between any pair of notes
  • A trail is a walk which doesn’t repeat traversing edges
  • An Euleurian trail is a walk which visits every node and uses every edge
  • Mathematics: “spot patterns, build reusable abstractions”
  • Abstractions help us take complex things from the real world and reconstruct them in our heads so that we cal (?reason about them?)
  • Idea of the honest abstraction - the one which ‘honestly’ models your problem.
  • The minimal abstraction: start from nothing and only add the behaviours/ideas/operations which are strictly necessary
  • “the most exciting thing you can do with your brain is to strap it into the hulking exoskeleton of mathematics”
  • If you can write a program, you’re good at mathematics