A dirty trick that is used all the time but goes unnoticed is concretizing abstract thoughts. The entirety of abstract maths is just that. Let me provide an exa

A dirty trick that is used all the time but goes unnoticed is concretizing abstract thoughts. The entirety of abstract maths is just that. Let me provide an example: You've got some abstract concepts of relationships. How do you go around thinking about relationships? You make them concrete. You do so by first representing them as perhaps, two points on a piece of paper and then drawing an arrow between them. This act of representation is an act of concretizing an abstract thought. Now you start adding rules to your concrete representation. If you are rigorous about following your rules you almost inevitably end up when Saunders MacLane ended up with Category Theory. Another example: Think about computers and what they do. Now try to represent them on paper. Depending on how your mind works, you might end up with something that looks like a Turing Machine or cellular automata. I've not come across anyone who thought long enough and came up with something like lambda calculus, so I suppose Church was an alien. I didn't use any mathematical logic examples because those examples typically involve historical battles over symbols.