7. THINKING CAN BECOME A WAY OF LIFE
Introduction Hannah Arendt wrote, ‘our most basic thought should be, do we know what we are doing and why we are doing it.’ I discovered that the way in which I would be capable of thinking would be vitally important to me. This was not only to generate new ideas but to help compensate for being, in my own view, a relatively ‘slow’ person. Nothing which required speed appealed to me and certainly not fast reading, which, in the past, was recommended to every one wishing to find success, making it possible to assimilate vast amounts of information in a short time. To some extent the internet has now reduced this need. I looked for ways to make up for my lack of speed, which I felt demanded an improvement in the quality of my thinking. Thinking for me first came alive when trying to find solutions for mathematical problems at school. What was relevant here was that not any old solution would do. It had to be the neatest (most attractive) solution which could be found. This was particularly important given that there was no computer to stamp out mindless calculations. At this time I came across the wonderful concept of Q.E.D. (short for the Latin – Quad Erect Demonstrandum), or proving that a theorem was right by first assuming that it was wrong, which would hopefully lead to a tautology. The magic was that there were always at least two ways to the goal, one of which was always quicker and more elegant than the other. You can see this in use when solving the most complicated Sudoku puzzles. If you have exhausted all the more normal methods then you need Q.E.D. Take a remaining unsolved square where there are only two possibilities, choose one of them and then continue as before. It will either lead to a complete solution which will show you had made the right choice, or a tautology will emerge, such as the same number appearing twice in a line. It is then clear that you must return to where you were and select the other number. If you haven't made a mistake the Sudoku is always solvable. This helped to lead me to realise that there were many different ways to look at the thinking process. Some consideration of the right approach before starting could therefore be profitable. I will mention a few which I find useful. The difference between vertical and lateral thinking Vertical thinking assumes that you start from where you are and proceed logically, step by step. Lateral thinking works back from where you want to get to. And you need both. The idea of lateral thinking was introduced by Edward de Bono who believed that there was always a better method than proceeding logically from where you were. This way you might never get to your desired destination. De Bono has written many books but it was his first that was the most shattering. His later books were more concerned with how lateral thinking could be introduced into organisations and schools. I will quote two examples which illustrate the method. The first one I have used on countless occasions. It demonstrates that however you look to tackle a problem there is nearly always a better way to proceed. Problem: how many matches in a (tennis) tournament are required before a winner can be found from 101 participants? Solution: In the first round there are 37 matches involving 74 players, 27 players are given a bye. This reduces the field to the largest multiple of 2 (64 in this case). There follow 32 + 16 + 8 + 4 + 2 + 1 = 63 matches. This is in total 100. But this is vertical thinking, starting from the beginning with the first round. But suppose you approach the problem laterally, starting with the winner. He never loses. The rest lose, but only once, each in a different match. There must be therefore be 100 matches which are needed. Or in the more general case, always one fewer than the number of participants. Problem: suppose that lilies in a lily pond expand the area which they occupy will double every day. If it takes 17 days to reach 50% of the pond surface in total, when will 100% be reached. Vertical thinking means starting at the beginning trying to determine how large the lily patch was originally. Lateral thinking starts at the end realising that one day would be sufficient (100% of 50% is another 50%). The difference between inductive and deductive thinking Deductive thinking is possible when we know the general case and try to draw conclusions as to the status of an individual situation. For example, all mammals suckle their young. The human animal is a mammal, therefore humans must suckle their young. Thinking the other way around (inductive thinking) the conclusion can be speculative. Is the conclusion drawn from an individual case capable of more general application, and perhaps is worthy of some research and will, in any event, generate new ideas. Famously, are all swans white? The aim is to move from the general case to the specific case, and vice versa, to get another take on the situation. What would happen if this took place more frequently? Or suppose that this is just an isolated occurrence! It is this sort of thinking which can determine whether investment is appropriate or not. We now know that not all swans are white. But what we are beginning to realise is that 'black swans' now have a tendency to turn up more regularly. In terms of risk management you need even to be tuned to imagining what could appear suddenly as a black swan. These could be your main risks. Creative thinking by using parallel mindmaps In an earlier note I talked about mindmaps, thought up by Tony Buzan. This is a way of picturing brainstorming. A very powerful way of using mindmaps is to start one for every project/task which you need to think about and carry out. By dealing with each of them from an elementary start (one word, probably the name of the project, in the centre of an otherwise clean sheet of paper) simultaneously instant progress will be made. Although the structure of each mindmap is likely to be similar there is a mutual triggering. An idea which is added to one mindmap often leads to its inclusion in another (crossfertilisation). Just the exposure to many projects at the same time also increases the chance that external triggering will take place. Things which you see around you now appear relevant. While paying close attention to one project we are unconsciously processing another. Assimilation and accommodation. Whilst accumulating ideas as a result of thinking with a positive mindset you will first be concerned in expanding existing records which you hold in your memory. This is called assimilation. You are working within your existing frame of reference and just trying to expand it. But if you are looking for a real breakthrough then a new frame of reference will be required, a parallel mindmap if you like. But under the same ‘umbrella’. This is because the ideas which you are starting to have no longer fit into the same framework. This is called accommodation. This greatly increases your possibilities. Continuing with assimilation will ultimately brake your progress. The various frames of reference will ultimately ‘challenge’ each other. Every time a new frame is created the door is automatically opened to adding quickly to the first entries. At some stage some form of rationalisation (is there an optimal number of reference frames perhaps?) may be necessary as you examine what you really think. Conclusion The various methods I have mentioned are actually not dissimilar. They all have to do with using instruments to expand your existing way of thinking which may be necessary to deal with new experiences and new problems. This is made easier by there being a direct contrast within each pair of thought directions. Once you get used to what it actually means to think for yourself (writing is an important aid here) and not only recording the thoughts of others (which also has its place of course) then you will become conscious of your use of such instruments and perhaps others which you pick up as you go along. At least you will be trying to avoid an immediate request for digital help before you know what you are trying to achieve. As we have already noted there is only sufficient room for thinking if 80% of all thought processes are automatic (the result of training). Perhaps you would like to reflect on how you think. Which different ways have you discovered and how do you support these? Which ways do you use most often and why? RAD 19.5.2017
1 Comment
Peter Davies
4/7/2017 16:51:42
Enjoyed reading this,Bob. My only quibble is that QED, or 'quod erat demonstrandum' ,is just a phrase to put at the end of a proof to say the required result has been proved. The method you describe is 'proof by contradiction'.
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October 2017
