In general, the key for developing solutions lies in heuristic competence, heuristics being the art of developing solutions. (Note that psychology and related fields sadly habitually abuse this term to refer to cognitive processes that are all but heuristic in the actual sense.) Recommended books to read: “How to Solve It: Modern Heuristics” by Z. Michalewicz and D. Fogel, “Strategies for Creative Problem Solving” by H. Fogler, S. LeBlanc and B. Rizzo, and “Probleme lösen. In komplexen Zusammenhängen denken” (German) by R. Sell and R. Schimweg.
Beyond general heuristic competence, projects may require specific competence for their domain, their system. The ideal problem-solver thus is able to quickly learn the basics of any new field, and then combine its specific idiosyncracies with their heuristic expertise to develop the best solution to the problem. With the meta-competence of quickly learning anything, you can use this resource to acquire any new competence needed to solve the problem you’re currently working on. Your autodidactic skills are your most valuable tool.
As a first step in the solution development process (which could also be done in Step 2), it is often necessary to get past how the problem is usually looked at, to transcend its facade. The way the problem is usually perceived and described is often part of the problem itself. Ignore the aura, the narrative that may come with the problem, and see it plainly as it really is — which is best done with a broad interdisciplinary background.
Be pragmatic in developing the solution, as also the desired solution implied or explicitely envisioned may actually be part of the problem, why it never has been solved, as it may be simply impossible in the real world as such — but one can surely meet the desire behind the dream-solution. Find creative ways to solve seemingly impossible-to-solve problems. Think of how the dream of man flying can never be fulfilled as such, as man simply is no bird or bat, but people with a lot of competence and expertise have enabled people to fly by many different means so far, using aircraft, and some computer games and virtual reality experiences address and fulfill other aspects of that dream.
In developing solutions, be careful though to not get lost in the worlds of abstraction or fantasy, always come down back to Earth, and bring back to it real solutions.
Practice eclectic interdisciplinariness, that is learn from a range of very different fields with an open mindset, focusing on their best bits, and apply those freely across fields, which will often have powerful synergetic effects, that is be more powerful than the mere sum of the individual parts.
Fields most useful for general heuristics for instance include all engineering branches, computer programming and software development, logic, mathematics, and linguistics.
Specific fields particularly relevant for the BWTT are for instance sociology, psychology, psychotherapy, economy, and jurisprudence, and also medicine, survival, and security can prove quite useful fields here. Also, learn from “enemy studies”, looking at how the other side works that creates many of the problems we solve. This should include at least management, marketing, and public relations, but can also go beyond that.
Establish and employ methods for effectively and efficiently working with notes, and then use sketches and visualizations as much as it helps you to develop the best solutions. You may also use or even develop simulations to evaluate your ideas.
One of the most important tools is working with the concept of Finite State Machines, which can be done for instance using SDL (Specification and Description Language). This ensures that the solution will cover any possible event and variable value and their effects, leaving no uncertainties or loopholes. Think of it as a complete if-this-then-that network with no loose, unconsidered ends.
Also, you may employ various creativity techniques in developing solutions, such as the Mind Maps by Tony Buzan, the Six Thinking Hats by Edward de Bono, or the Asian Godai Elements (Earth, Water, Fire, Wind, Void), or Gogyo Elements (Earth, Water, Fire, Metal, Wood) as for instance described by Stephen K. Hayes, or other techniques.
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