When I was a kid, I used to love a certain kind of pointless mental test, because it was fun to do. These kinds of tests would frequently appear on worksheets handed out to kids at various milestones, and involved a two-dimensional, segmented image and several renditions of a three-dimensional image (obviously rendered in two dimensions, but you get it), with a little quiz: “Which of the following 3D images can unfold into the 2D image presented?” Like this:
Now, you can solve this in a couple different ways. My way was always to just lift the 2D image into the air in front of me and fold it into three dimensions with my mind and then hold the resulting image and look at it. (Yes, really.) But you don’t need any particular ability to visualize things in three dimensions to solve this – simple logic will get you through it. (Based on the 2D image, the single dot and the triple-dot cannot be adjacent to each other, so B and C are eliminated. The single square and double square likewise can’t be adjacent, eliminating A. Only D is possible.)
But either way you do it, you have to think through it. You have to think through it, because the information you have can’t be meddled with. There are no objects to examine, just representations.
In real life, outside of worksheets, that is almost never the case. In real life, if you can’t figure something out – kick it.
My oldest daughter was trying to arrange some furniture in her art studio, and after examining the furniture for a few minutes she wasn’t sure if it was going to work how she wanted it. So she kicked one of the objects (not destructively, just enough to move it around). I laughed and asked if she expected it to fit better now, and she said “No, that was just to look at it differently. I don’t know how it’s going to work yet, but if you do something, then something will happen.”
How true! A change of angle brings new information, information you didn’t have before. Real life isn’t a worksheet. You don’t have to solve everything with theory – you’re allowed to just kick stuff and gather more information. Change your perspective with brute force if you have to. Understanding the theory, the reasoning – these things are great mental exercise, wonderful to sharpen your mind. But when you’re actually trying to get something done, you need not be beholden to the pure methods.
Sometimes it’s even effective to trade one problem for another. Even if the second problem is objectively “worse,” it can be better if you know how to solve it. One time a snake got under our house, and my father just reached his hand in to grab it and pull it out. Later, I asked him “isn’t it much worse to be bitten by a snake than to have a snake living under the house?” He said: “Maybe, but I know how to fix a snake bite. I don’t know any other way to get a snake out from under the house.”
If you do something, something will happen. If you’re stuck on this problem, move to the next one. And if there isn’t a next one – make one.