Numbers and calculations are only one out of many tools to uncover imperative hidden objects. They tend to work well when available. But that does not mean that we should refuse exploiting alternative discovering methods, such as intuition, imagination, visions, dreams, trends, internal visualizations, analogies and other irrationally rejected feature discovering methods, which are completely number independent. We should explore these non-data-driven numerically independent methods of variation determinations for directional environmental changes at least as seriously as the numeric ones. Otherwise, we unnecessarily deprive ourselves to keep making progress in feature selection in the absence of numerical data. Of course intuition and data should not contradict one another. But no option should be discarded because it is erroneously believed as being “too hypothetical or speculative”.
I forget where I heard that numbers change someone’s mind and policy, but a story, vision, imagination, and intuition, well written, will change someone’s heart. It seems to me that there is an analogy to your argument of different research methods. Very interesting and worthwhile to further study on this topic. You may also look into information management. I have found a few articles that may interest you:
Mason, R. O., & Mitroff, I. I. (1973). A program for research on management information systems. Management science, 19(5), 475-487.
Ritchie, J., & Spencer, L. (2002). Qualitative data analysis for applied policy research. The qualitative researcher’s companion, 573(2002), 305-29.
King, L., & Appleton, J. V. (1997). Intuition: a critical review of the research and rhetoric. Journal of Advanced Nursing, 26(1), 194-202.
Allinson, C. W., & Hayes, J. (1996). The cognitive style index: A measure of intuition‐analysis for organizational research. Journal of Management studies, 33(1), 119-135.
McAfee, A., Brynjolfsson, E., Davenport, T. H., Patil, D. J., & Barton, D. (2012). Big data: the management revolution. Harvard business review, 90(10), 60-68.
Carlin, W., & Soskice, D. (2005). Macroeconomics: imperfections, institutions, and policies. OUP Catalogue.
Bird, H. R., Gould, M. S., & Staghezza, B. (1992). Aggregating data from multiple informants in child psychiatry epidemiological research. Journal of the American Academy of Child & Adolescent Psychiatry, 31(1), 78-85.
In Science, the first step towards understanding a phenomenon is an intelligent observation, which require intuition and intellect and the second stage involves attempting to explain the phenomenon through known laws of science, and if such do not already exist, there arises a need to come up with new ideas and speculations that answers the questions pertaining to the phenomenon. Role of Mathematics comes into picture wherever we need to establish a quantifiable, numerical relationship among the properties and expressing the laws that govern the phenomenon in language of numbers, equations and so on. But the question we need to address is that whether the mathematics that is already known to us is capable of addressing this phenomenon in numerical terms, as like any other discipline mathematics is progressing in different frontiers everyday and thus a substantial amount of this knowledge we do possess, but every now an then a phenomenon gets discovered which leads to development of an entirely new direction in mathematical research, my opinion as regarding your question is that mathematical language cannot replace the subject intuition and other finer aspects of your subject, but it is essential to establish your hypothesis pertaining to the phenomenon you are studying on a firm, quantitative ground.
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