Scientific concepts must be measurable, unless irreducibly useful.
A good scientific research has three indispensable tasks:
An observation is objective if it can be confirmed by independent observations.
A formal system is simple if it has a short description length; it is consistent if it cannot be falsified by logic.
A bijective mapping between the physical and formal world goes both directions: abstraction is the mapping from the physical world to the formal world; interpretation is the mapping 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.
Full Cycle of Scientific Inquiry:
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.
Measurement. A major difference between natural and social sciences is that, while many concepts in natural sciences and their instrumentation are simultaneously defined (e.g. length, mass, time, electric charge, temperature, amount, luminosity), concepts in social sciences typically have long been in conversational use without unified measurable definitions. Operationalized social science concepts thus have to compete with the preexisting meanings and knowledge of the term, and often serves as proxies to the colloquial concept.
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.
Categorization/Grouping using human-understandable names is kind of difficult and inefficient. Now we can use learning algorithms to automatically group statistically distinguishable behavior clusters, the so-called behaviotypes [@Vogelstein2014]. Many areas and people have been using this new technique, e.g. Ram Rajagopal.
A scientific problem is closed/proper in the sense that: (1) the validity of the problem is not vulnerable to unknown real-world factors; (2) no extra assumption or data is needed to solve the problem. 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.
做研究的时候需要一些假设，但是这并不意味着不可以判断假设靠不靠谱。 我们可以直接否定一些假设。 比如我们绝对不可以假设彩票是有规律性的，或者说历次中奖票号的序列可以做模式分析，又或者说中奖票号是有后效性的。 人工天气预报也是一样，不可以指望从历史气象数据找出匹配模式，基于这种错误假设的经验是不靠谱的。 当我们知道天气系统是个混沌系统后，我们可以直接宣告这种假设是错误的。
Interpretation should be immune from mathematical exactness: perturbation (inputs), bifurcation (parameters), “robustness” of models, “generalization”/extrapolation, use of intuition.
Causal inference must begin with the effects of given causes rather than vice versa (causes of given effects). [@Holland1986] Think of chaotic dynamical systems, where “every initial/boundary condition is relevant”, and the dynamical system is also hold blameful. Nonlinear systems cannot be globally attributed.
經濟學的主要用場是解釋世事，而世事的實情調查是很花時間的工作... 另一方面，如果同學沉迷于某些原理或技術上的發展，驚覺到不管用時，可能已經老了。 --张五常
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: disciplinary paradigm; academic background of the researcher; technologies available at the time. Don’t let your ideas restricted by these limitations.
[Empirical Science] 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, deceived by the myth 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.
[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.
[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。
一篇论文中可能有很多你想探究其合理性的地方，但并不是每个地方都值得花功夫研究，因为不是所有疑点都有内在的价值。 就好像世界上有很多山洞，但只有少部分的山洞里藏有宝藏。 研究中会有很多不够明确的地方，但很多情况下不去追究那些模模糊糊的地方也能达到原先的要求。 做研究时，只需要记录下那些存有模糊的地方，方便有需要时检查就足够了。