While the human brain is one of the most fascinating evolutionary products of Earth’s history, it has its limits. Our brains allow us to observe and comprehend an incredible variety of information that we receive, but the brain also has difficulty understanding data that isn’t linear or bounded. Because of this, we can often miss ideas that are hidden in plain sight.
A perfect example of this was all the rage in the 1990s: the Magic Eye puzzles. These puzzles were first used by researchers, who called them stereograms, to better understand how our brain and eyes work together to create depth perception. Although Magic Eye puzzles are two dimensional, looking at them from the correct distance will give the illusion of a 3D image hidden inside. According to the Magic Eye website, the puzzles “are built to be viewed by allowing your eyes to diverge, as if you’re focused on an object more distant than the printed page.”
Our ability to work with long sets of numbers, too, depends on seeing the whole picture properly. In the spirit of the Magic Eye, let’s look at a number problem that looks pretty simple.
Depending on what you did with the zero, you might end up with different figures, maybe 12 or 1. But in fact, there’s something you missed. If you look at the end of each line of numbers, what do you see? If you wrote out the equation on one line it probably looked like this: 1 + 1 + 1 + 1 + 1 + (0 x 1) + 1 + 1 + 1 + 1 + 1. With 5 + 0 + 5, this would give you a result of 10.
But hold on just a minute! While your brain may have assumed that the addition kept going from line to line, look again. The fact that there are no plus signs in between the lines means that rather than counting the final number as 1, it should be read as 11. You probably just kept adding without thinking, as your brain saw a pattern and followed it to what appeared to be its logical conclusion. If you take into account the hidden 11s, you end up with the following equation: 1+1+1+11+(0x1)+11+1+1+1. If you do the math again, you realize that the correct answer is 28!
Beginning in the 1960s, scientists started to experiment with these kinds of problems as a way of describing “lateral thinking,” what we commonly know as thinking outside of the box. Rather than simply following the vertical logic we have been taught, this kind of problem solving gets us to consider all kinds of solutions that might not come to mind at first. To test yourself on your ability to think in a different way, try this classic problem, called the “Nine Dots” problem, which goes back to the early 20th century. Your goal is to connect all the dots with straight lines, without lifting your pen off the paper. Give it a try and see if you can figure it out!