Full Cycle of Scientific Inquiry:
A good scientific research has three indispensable tasks:
An observation is objective if it can be confirmed by independent observations. A formal system is consistent if it cannot be falsified by logic; it is simple if it has short description length. A one-to-one mapping between the physical and formal world goes both directions: abstraction is the map from the physical world to the formal world; interpretation is the map from the formal world to the physical world.
Every scientific theory is a candidate dual representation of (certain aspects of) the physical world. When a duality is properly established, a formal theory can help us understand the world with parsimony: outcomes that hold in the formal system should also hold in the physical system; when the outcome is observed in the physical world, it is called explanation; when not yet observed, it is called prediction.
Concepts are often created to distinguish something from the “background noise”, either the unspecified “Universe” or a subspace which has been previously assigned to a concept and treated as homogeneous within.
Abstract thinking, i.e. manipulating vague concepts in mind, helps one to do rewarding research. This is because once concepts get well defined and problems clearly formulated, pioneering work must have been done. According to convexity of cost function, the remaining reward in this research area is limited, while the cost is prohibitively high. More often, latecomers cannot see the direction/intention which guided pioneers through the theoretic research; they are lost in the jungle of technicalities.
Grouping/categorization using human-understandable names is kind of difficult and low efficient. Now we can use learning algorithms to automatically group statistically distinguishable behavior clusters, the so-called behaviotypes. Many areas & people have been using this new technique (Prof. Ram Rajagopal, Neural-behavioral maps of larvae.)
Closure of a scientific problem
A proper scientific problem is closed in the sense that:
Maybe the reason that most real world problems don’t seem to be readily solvable by scientific methods is that the problems are not in closed form, i.e. the problems are not proposed in a scientific way. When we are students, instructors give us well defined problems; when we are practicing researchers, instructors provide us roughly defined problems, training us in facing research problems.
Develop the right level of abstraction (modeling).
Simplification: Complex system calls for simple analysis.
Causal inference for practical applications should be immune from mathematical exactness.
I’m not interested in research efforts that try to build theory where [these’re deemed to be trash papers.]
The characteristics of a research is largely determined by: (Don’t let your ideas restricted by these limitations.)
[Empirical Science; 实验党] Empirical science is not dauntingly difficult; it can be mind-provokingly simple and fun. For us who are so used to mathematics and formal sciences, research that involves experiments and data seems so intriguing, out of the legend that empirical research is expensive and time-consuming. Current research in physics do require super expensive instruments because of the advanced nature of their research, but in other fields measurements can be made quite inexpensively, as long as you have smart idea. Data can be acquired by measurement, survey, or access to documented data (from the library or someone else). Time spent in collecting data also drastically depend on what smart idea you have. The ultimate lesson for theorists who shun scientific empiricism is to be confident, to know the real world, and to practice the essence of science.
[Method Validation] 在没有可信赖的解（理论解、实验数据、数值解）存在的时候，评价新的方法的有效性其实可以通过与已有解法的解作细致比较得出。
[否定性结论] 我猜是不是怀疑一个理论并最终得出负面结论，比建立一个经得起检验的理论要容易得多，所以我才疯狂的沉迷于反驳既有理论却不知道什么算是合理的理论。 大家最不喜欢听到的恐怕也就是否定性的结论了，比如混沌理论否定了中长期天气预报，哥德尔不完备性定理否定了完备公理体系。
[抽象问题与具体问题] 我有一个思想的误区需要改正：卷入到过度抽象而难于描述的问题中，长时间无法得到任何结论。 正确的做法是，一旦发现自己处于这种状态，立即放弃考虑这个问题，转入到解决具体的问题中去。 按照唐少强的说法就是，“心里装着大问题，手上算着小问题”。 按儒家的说法就是，“吾尝终日而思矣，不如须臾之所学也”。 因为过度抽象的问题不是靠“顿悟”、“冥想”能解决的，它需要许多具体的小问题一点点拼起来以得到一个完整的认识。 我们需要分解，这就是为什么analytical writing是我们获得新认识的方式。
[ceteris paribus] Should the traditional "all else being equal" be replaced by a more practical "all else left unknown", conclusions can become much more useful. This symbolizes a transition from deterministic differential viewpoint to statistical presentation.