Today I Learnt 6

Thoughts Regarding My RSS Feed

Emotinality as a predictor for cultural success

• Found orignally from marginal revolution.
• Couldn’t access the article 😪
• This sounds very interesting

AdaFruit

• Lately I have been really interested in using more sensors and display for my Raspberry Pi, but everything is so f**ing expensive. I don’t know if I can buy anything.
• One thing I definitely am going to try is make a pir activated night light using Pico and Led matrix. I have got all the ingredients.

Spaced repetition in Mathematics

• I recently started using Anki again. With MathJax support it finally seems worth the effort. But I am still not sure about how to write my cards. To remedy that I am reading a number of articles on using Anki.
• I really like this take on spaced repetition.
• I think that my memory is weak. And there is a definite possibility that improving it can make me a better mathematician.
• The Ankification process 😘 of understanding math.
  1. **Understanding the proof : Requires multiple passes over the proof.
     • Start by picking out single elements of the proof and converting them to Anki cards.
     • Then restate the idea in multiple ways. One way to do this is by simplifying both questions and answers.
     • Move to all the different ideas in the proof. Stay on an idea until it feels like it’s yours. You should feel comfortable in these spaces. That means understanding it in as many ways as possible and making as many connections as possible.¹
     • The problem with this step is that it is undirected, and you never know when to stop.
     • Have the following aim in mind: How do I describe the proof in one line.
     • You should have enough chunks to prove the statement in one line.
     • Think of this as the boundary condition for proof-learning optimization.
     • Make both questions and answers as atomic as possible.
     • This process can feel very wasteful, but over time this completely changes the understanding of the proof. In fact some older cards may start to seem bad and should be replaced by newer better ones. This is a long-term process; wait for it to run its course.
  2. Variations, pushing the boundaries: One way of deepening your understanding further is to find ways of pushing the boundaries of the proof and of the theorem. Ask yourself a few questions.
     • Is every hypothesis necessary? What if I remove one? What if I change one? Why not?
     • Can you get more out of the proof? Can you take the argument further? Try to apply it elsewhere!
     • This phase really is open ended!