Idea Seeds #11 – Problem Solving – Review your Progress
Finding it Ourselves
These articles have been written in keeping with what Galileo Galilei believed and said about teaching: “You cannot teach a person anything, you can only help them to find it for themselves.” Use the following two examples, which require no mathematics, to test your understanding of the basics and more importantly to explain in simple terms to someone else why what happens does so.
The Bicycle Question
A bicycle is shown in the adjacent diagram with a length of red string attached to one of the pedals. Assume that there is someone preventing, very lightly, the bicycle from falling over and that you are standing behind it pulling on the string. Which way will the bicycle be moving?
The Box and the Bee
In the first adjacent picture a sealed box with a bee sitting on the bottom has been placed on the right hand pan of a balance. The box is full of air and the balance has been brought into balance by adding the correct mass to the left hand pan. The second picture, taken a few minutes later, is of the same setup but the bee is now flying around in the box. Is the balance still in balance or has the box gone down and the mass up or has the box gone up and the mass down?
Reflecting on One's Progress
Hopefully by now you will have studied the previous ten ‘Idea Seeds’ articles. If you have then in keeping with good practice, it is now time to reflect on your progress. By doing so, you will be in the good company of many of the ‘Giants’, some long dead, some still going strong. Nobel Lauriat, Richard Feynman is one such giant. His philosophy of keeping detailed written records that he regularly reviewed and refined to keep track of his progress is worth emulating. He did not do this in isolation and regularly tested his understanding in discussions, in particular, with his graduate students. You should do the same with your peers, parents, friends, mentors or whoever else is prepared to join in on the discussions. It was Alex Mautner, a friend curious about physics, however, who stumped him when she asked him to explain the crazy ideas of quantum mechanics. He promised her that someday he would write a series of lectures to explain the theory in layman’s terms. When he had written the lectures, he took sabbatical leave and travelled to New Zealand to try them out. Why New Zealand? Because, he said “New Zealand was far enough away that if they weren’t successful it would be alright!” They were indeed very successful and soon thereafter published by Penguin with the title: ‘QED - The strange theory of light and matter’ to much acclaim. One reviewer wrote: “In these entertaining and witty lectures Feynman uses everyday examples to explain the deepest and most complex mysteries of the world around us, in the definitive introduction to Quantum Electrodynamics.”
A Smart-Lazy Filing System
In ‘Idea Seeds #05 and #06’\ you would have learnt that it was essential to start a ‘smart personal filing system’ from which you can quickly and effortlessly retrieve information, add to it, edit it, update it, sequence it, review it and importantly cross-reference it to other categories. Author and ‘Giant’ Robert Pirsig’s, filing system is impossible to fault in both ‘Return on investment - ROI’ and ‘Least action’, the ‘smart lazy approach’.
Small Chunks of Information
The basic idea of the filing system is to ‘write each bit of information or idea on a slip of paper’ (A good size is 130 x 70 mm as six slips can be cut from an A4 sheet of paper with least waste.) and then to file these it in a tray under a ‘topic category’. “Information organised into small chunks can be accessed and sequenced at random which makes it much more valuable than in any other form.” is what he said made it unique. With all previously collected information and ideas safely filed and cross-referenced and ready for easy retrieval, it allows you to keep your head empty and ready to learn about new things and importantly make connections to what you have already learnt. No ‘Google search’ can do this for you. Pirsig viewed the information stored on the over 10 000 slips in his filing trays as an ‘extension to his mind’. Study #05 and #06 again and start your filing system now if you haven’t already done so. It is the essential first step if you want to get yourself ‘on the road to wisdom.’ Much more on the importance of wisdom in a future article.
How to Work with Slips
If you processed the information in ’italics’ in the first ten articles then your filing system should have slips similar to the following:
- Category slip labeled: ‘Problem Solving Ritual (PSR)’.
- Slip labeled ‘PSR Step One’ with the following information written on it: ‘What has been given?’ ‘What has to be done?’ ‘Have I reflected back that I have understood what is required to be done?’
- Slip labeled ‘PSR Step Two:’ ‘Have I identified all the ‘limits’ and ‘constraints’ that apply, or put another way, have I identified the boundaries within which I have to find a solution?’. 2D, 3D, Time, Money, Properties ……
- Slip labeled ‘PSR Step Three:’ ‘Are there any other starting points I can start from?’
- ‘Have I really looked at the problem from ‘every angle?’
- Slip labeled ‘PSR Step Four:’ ‘What type of problem is it?’ ‘Divergent or Convergent’.
Obviously it’s up to you to add any other information you think makes things clearer to you on the slips. It is after all an ‘an extension of your mind’. Slips with the puzzles that demonstrate how the questions help solve the problems can be made and filed with the questions. Use paper clips to keep all the slips in a category together and properly sequenced.
Category Slips and Cross Referencing
Category slips should have been made for the ’Principle of least action (PLA)’ On it I would have written the quotation in ‘Genius’ by James Glieck: “The universe wills simplicity; Newton’s laws provide the mechanics; the ‘principle of least action’ ensures the grace.” Under that heading I would have made slips with Feynman’s diagrams showing the path a lifesaver takes to save a drowning person and it’s ‘analogy’ with the refraction of light, As a ‘Cross Reference’ I would have made a category slip labeled ‘Light’ and on it made the note ‘See also: Principle of least action’. Slips dealing with the properties of light and other information about it should be filed with the category slip, ‘Light’. In the same way Category Slips should be made for ‘Mass’, ‘Weight’, ‘Gravity’, ‘Density’, ‘Specific Gravity’, ‘Force’, ’Archimedes Principle’ and then very importantly cross referenced to each where relevant to the others. Reread the articles and make slips for information related to these categories in particular ‘benchmark’ stuff like the information on the densities etc.
There is a lot of other information in the articles you should be making slips for and then categorising and cross-referencing them. If you do, you will find the ‘ROI’ will be very worthwhile.