- Find a duality. Play duels against each other. What if unstoppable force meet immovable object?
- Try adding a new dimension and look at the problem from that dimension
- Think of locality of reference. How to / what does it mean to approach the problem from either spatial / temporal locality ? Is there any other locality (i.e different dimension) that can be used?
- Reduce to first principles by applying Socratic methods or Five whys
- Inverse thinking --> analyze backwards
- Solve a special case / solve a generalized case
- Max >= average, min <= average (any more general implications?)
- Second-order thinking -> try to think ahead more than 1 step
- Think about energy: nature flows in the most optimal way (water from high to low places etc..) --> implications ?
- Think about entropy: in closed systems entropy always increase --> disorder always increase
- The heavier the object, the harder to increase its velocity
- Heisenberg's Uncertainty principle --> implications
- Paradoxes: Russell's, Godel's etc...
- Ideas from quantum physics, meta math, decision / game / control / theory...
- Network effect: Power of network ~ (# of participants)^2
- Nature tries to balance itself. Force has counter force. Equal exchanges --> fair trade. Ask what is the counter force of this action ? What is the constraint ? What is the best trade-off depending on current context ?
- Self-referencing / recursion appears everywhere. Seems to be the way to infinity --> what happens if self-reference happens ?
- Bootstrapping problem -> chicken and egg
- Symmetry vs asymmetry
- Think probabilistically
- Think about topology: tree vs list, linear vs non-linear --> morphism --> category theory / knot theory etc
- Human hierarchy of needs
- Law of large numbers
- https://plato.stanford.edu/index.html
- Choose the notation wisely. Good notations reduce mental loads and might lead to new insights. Make use of other heuristics like symmetry etc to simplify them... (see Tao's "Solving mathematical problems - A personal perspective")
- Try to find the invariant, or push problem to the extreme
- See whether two items can be dimensionally decoupled - be careful not to overgeneralize
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