Steven Weinberg - Four Golden lessons
- My advice is to go for the messes — that’s where the action is.
- If you want to be creative, then you will have to get used to spending most of your time not being creative, to being becalmed on the ocean of scientific knowledge.
- The best antidote to the philosophy of science is a knowledge of the history of science.
- Some good habits
- Write a note in HTML after meeting with the advisor
- Write a report in HTML or Latex every week so that you can see your
progress made. The report describes what the problems are and how
you approach the problems. The report will become a
journal/conference paper later.
- Write down the problems you have encountered. Use the techniques
in the book of "How to solve it" to deal with it.
- Simplifying the problem (solve the simpler problem first, then solve
- Divide and conquer
- Find lower/upper bounds
- Removing dependence between events
- How can you judge your simulation results are correct, instead of results
of buggy programs?
- Use rough analysis to get approximation or lower/upper bound and check your
simulation results are feasible.
- For example, a linear program may not have analytical (close-form) solution.
However, when you remove some constraints, the new linear program may admit a
close-form solution. The objective value corresponding to this
solution can be used as a lower or upper bound for the objective function of the
original linear program.
- Use numerical analysis to get rough results to compare with the simulation
- Simplify the constraints so that you can can rough analytical results to
compare with the simulation results.
- On the other hand, analytical results also need validation by simulations.
- Minimize the critical path by appropriately allocating resources among
nodes. Sometimes, you solve one problem but create another problem.
What is the right tradeoff? A smart design is to shift the burden in
a right way, e.g., shifting the burden from memory to processor so as to
minimize the delay.