Analyze the data. Gather all the information available and look at all the clues. Eliminate as many variables as possible -- such as those that cannot be changed (or can they?). Reduce the problem to its most basic elements. Build a picture of the how and why so that it makes sense. Then you can begin to formulate a solution.
When I studied art in school, one of the things I learned is to look at the negative space -- the part that isn't the subject or other objects in a drawing or image -- as a shape unto itself. It has form and depth. This is particularly useful when attempting to attach something to another object. I have on many occasions added peripherals to the front of an engine -- peripherals being: alternator, power steering pump, air-conditioning compressor etc. where a bracket did not exist. The solution is to hold the unit in the desired position -- using blocks of wood, bits of scrap metal and clamps -- so that the shape of the bracket reveals itself in the negative space.
As a child I was fascinated by the space programs and I have continued to study them -- especially the moon missions. The Apollo program has two excellent examples of working a problem backward.
The first dealt with how to accomplish such a mission. In the early stages of planning it was assumed that a capsule launched from Earth would land on the moon and return, but this presents a major problem -- mass. A spacecraft capable of carrying three astronauts, all the supplies necessary to keep them alive for the duration of the mission, a massive heat shield to protect them during reentry, and enough fuel to land and then take off from the moon would be comparatively big. So large that it would take an impossibly huge rocket to get the payload off the ground and to the moon. An alternative would be to launch two manageably large rockets -- one for the spacecraft and the other for the fuel. By "manageably large" I mean the biggest rockets ever built -- the Saturn 5.
From the very beginning a handful of visionary engineers championed another approach. They started at the other end and worked backward asking the question what does it take to get astronauts and moon rocks off the moon. Then, what does it take to get such a craft down to the moon's surface. This line of thinking ultimately led to LOR (lunar orbit rendezvous) -- having a second small disposable spacecraft to land and then return to a mother ship in orbit thus eliminating the need to land the mother ship itself. The system had an additional advantage in that it provided a redundant spacecraft that could be used as a lifeboat in the event of a problem with the mother ship. It was a life-saving advantage for the crew of Apollo 13 -- the mission that brings us to the second example of working a problem backward.
If you've seen the film, when the ground control personnel are discussing what to do, one individual steps forward and says "We have to turn everything off." He was John Aaron, at the time widely regarded as the best engineer at NASA. His argument was simply that without enough battery power to open the parachutes after reentry there would be no point in doing anything else. They continued working from this direction to solve the lack of power problem.
This strategy can also be
helpful when taking an exam. You might be surprised at how many answers can
be found later in a test to questions posed earlier.
In traditional ground warfare the adversaries seek a weak point in their opponents' lines, then weaken their own lines to mass troops at that point. This creates an area of locally overwhelming force.
For those of us who are not Generals, applying force still requires strategy. That pesky jar of pickles will yield its treasures to those smart enough to outmaneuver its adult proof lid. Yes there are many tricks to defeat this particular foe, but we who prize brute force can gain a mechanical advantage by grasping said lid with the left hand instead of the right. Pulling with the fingers tightens the grip -- as opposed to pushing with them. This tactic can be applied in many situations. Of course if you are left-handed you already have the advantage over a jar of pickles, but what if you are trying to tighten the lid so that no one else can get to them?
A similar situation to that above is opening a beer bottle with the bottom of the cigarette lighter. Here again the counterintuitive opposite hand strategy applies. By holding the bottle with the stronger dominant hand and using the first finger as the fulcrum, the non-dominant hand can easily use the leverage provided to pop the top.
Other examples are: the end
of a chisel, the edge of a knife, the point of an awl, the knuckle of a martial
artist breaking a board, and the reduction of an argument to a single irrefutable
point.
Possibly my favorite approach to solving a problem, though seldom used it can produce an answer to a seemingly impossible situation. Once again space travel is the setting for this example -- but this time it's science fiction.
In the real universe light is the fastest thing that exists. But even its unattainably high speed is hopelessly slow in the immensity of the cosmos. With our current technology it would take about 92,000,000 years to get to the nearest star outside our solar system. If we could travel at the speed of light the same trip would still take almost 4 1/2 years. We won't be going interstellar anytime soon.
And in science fiction, bending or breaking the laws of physics is usually a requirement for a good story -- but there are some theories based in real science that might make it possible to change some of those laws. Even if you're not a fan you have probably heard of warp drive. Space can be bent, stretched and compressed by mass -- gravity. That's the reason the earth goes around the sun, the moon goes around the earth and we stay firmly stuck to the ground. So if a spaceship could bend space around it the right way without mass, not only would the distance be compressed but the space itself would move past the ship -- as opposed to the ship moving through space. It is, of course, changing the rules of physics. While this is a theoretical possibility, unfortunately there is no theoretical way to accomplish such a thing.
Perhaps a more down to earth,
hence better but less interesting, example is the intake tube on my old car.
It was made of rubber, but over the years it dried out, became brittle and
eventually broke. Unfortunately that particular part is not available. It
consisted of two components -- one of which I could make and the other I can
buy, although not in the correct size. I bought the latter and made an adapter
so it would fit, but it was longer than the original so the part I made had
to be shorter than the original to compensate. Here in lay the problem. Two
hoses were connected to the side of the original part but my shorter replacement
only had room for one. I used a single hose and tee to connect to the two
hoses. The single hose and tee had to be oversized to compensate for the demands
of two hoses connected at a single point -- but it works, and well.
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