When we work on problems or projects, others often encourage us to think outside the box. Unfortunately, this is one of the most inside-the-box pieces of advice anyone can give. When offered, the usual meaning is to not limit our thinking. In my view, it is often more useful to think about the box, rather than outside it.
What Is "The Box"?
The box is often used as a metaphor, but when applied to our thinking it is very real if not physical. When we start to think about anything, our assumptions and beliefs define the boundaries of what we consider. We don't usually think about them as much as within them. By staying within them, we define a box for ourselves.
Real world constraints can also be a wall of this box, but more often our beliefs are more limiting than the constraint. A baby elephant that learns it cannot pull free from a tied rope won't even attempt to pull free when it grows to an adult strong enough to do so. The rope is a constraint to a baby elephant, but the adult it becomes is limited by old beliefs based on facts no longer true
Why We Want To Think Outside The Box
The vast majority of problems can be solved with tools immediately at hand. The tools are there because they have solved problems in the past. If a problem seems difficult, one approach to a solution is to look for a tool you don't know about.
For example, try to calculate the sum of all integers from 1 to 2000 (1+2+3...+2000=). This can be solved by grade school addition over a period of several minutes if you're careful enough not to make even one error over the many additions required, or it can be solved in a moment in your head with a change in perspective. 1+2000=2001, 2+1999=2001 ... 1000+1001=2001. That means there are 1000 pairs of numbers, each totaling 2001, so 1000*2001=2,001,000. Pair wise addition and multiplication provide tools to greatly simplify the problem.
For some problems, nobody has a tool to offer a solution. In those cases, looking for solutions outside the box can be either useful or necessary. Even in those cases, however, it is often more useful to think about the box rather than outside it.
If you look casually, Newton's three Laws of Motion seem like a perfect example of thinking outside the box. Instead of limiting his thinking to things he could touch, Newton pushed out from the box to imagine planets in orbit to offer universal laws which hold even today. If anyone was capable of out of the box thinking, it was Newton. While he may have been capable of it, that wasn't what he chose to do.
Newton invented and validated calculus, a whole new branch of mathematics to calculate objects in motion. By doing so, he created a new tool built on the set of tools his peers commonly accepted. This allowed him to see the space outside the existing box by using the box itself as a frame of reference. The result was a bigger box with a better set of tools.
Thinking About The Box
Since the box was made up of assumptions and beliefs, Newton was able to solve a previously unsolvable problem by testing each and seeing if another could take its place. If we cannot solve a problem by thinking within our assumptions and beliefs, the time has come to think about them.
One approach which can work is to present your problem and your thinking to a colleague. Ask the colleague to question anything that isn't either proved or nearly so. You shouldn't have to prove that 2+2=4, but you may want to note it as an assumption. I shared a problem once, meticulously defending each step of my thinking until I stopped in mid sentence, staring at the answer. She didn't see it, but I did.
Another strategy is to explicitly write down every assumption and belief that may touch on the problem you are addressing. Then you walk through them one at a time until something gives. This approach is almost guaranteed to be labor intensive. It is not guaranteed to produce a result.
Every once in a while, ideas pop into existence as if from nowhere. These eureka moments typically occur when one thing connects with another, but even then they aren't useful until they can be connected back to known ideas, methods, and tools.
In the early 1600s, Johannes Kepler noticed a similarity between properties of geometric solids and the number and relative distances of planets in the heavens. He was elated that this showed geometry underlying the Solar System. Given this relationship and his inspiration, he looked meticulously at the data and found nothing. His eureka moment died because he could not connect his out of the box idea back to the box.
The idea that continents drift was first suggested in 1596 by Abraham Ortelius, but it wasn't until plate tectonics offered an explanation in the 1960's that the idea was commonly accepted.
Eureka moments -- out of the box thinking with no connection to the box itself -- do happen, but they only become significant when they can be grounded by recognizing their connection to the existing body of knowledge represented by the box itself. Therefore, it is frequently more useful to think about the beliefs and assumptions which act as the boundaries of our thinking to see if the box can be made bigger.
In his book Getting Things Done, The Art of Stress Free Productivity, David Allen develops a five step model for project planning he calls the Natural Planning Model. Step one includes identifying beliefs, assumptions and constraints so you can think within them. I talk about this on a radio broadcast you can listen to on YouTube. Find it here http://www.youtube.com/watch?v=RC56niTb9vM&feature=email