You'll have a whole eternity to think inside the box

"We can't solve problems by using the same kind of thinking we used when we created them."

Albert Einstein

The term "Outside the Box" (or "Outside the Square") intuitively suggests a free from of thinking that breaks out of constraining boundaries, and has parallels with Lateral Thinking.  There is also a literal connection to thinking outside the box, as illustrated by the following example.  Before reading any further, think of ways in which you can connect all the dots with a series of connected straight lines,  in Figure 1, below.  In particular, what is the minimum number of lines you can use?

9 dots


Conventional Thinking

There is a natural tendency to look for answers that use lines that are constrained within the box, and within this paradigm it is easy to see that there are several solutions, but the minimum numbers of lines in each case is 5 (Figure 2):

9 dots conventional

Figure 2.

Outside the Box Thinking

If, however, we free ourselves from having to think inside the box, we can discover an elegant solution that requires only 4 lines (Figure 3):

Figure 3.

Even further Outside the Box

If we start to question other assumptions, eg about the dimension of the dots, and the thickness of the lines, then we can solve the problem with 3 lines, as shown in Figure 4:

Figure 4.

Reductio ad absurdum

Of course, having opened up these possibilities, we can see that by taking things to extremes (eg expanding the dots so that they all overlap, or making the linewidth sufficient to encompass all the dots), then the problem can be "solved" with a single line.  Here, of course, we see the importance of maintaining a connection between free thinking and testing ideas at an appropriate stage for their capacity to provide meaningful solutions to real problems.

Noughts and Crosses

Another illustration of Thinking Outside the Box is putting an extra "O" or "X" literally outside the box to achiev a line of three symbols, and this is the logo we have designed for otbSolutions:

Of course, many will say "That's cheating", in the same way Alexander the Great was criticised for his solution to the Gordian knot - he cut it with his sword!