Everything is complex because it contains many changes. If you want to understand the complexity and find a clue from the complexity, you may wish to find the unchanging things in it first.
01.
Go or run?
Let's say it's raining outside and you want to go across the road, but there's no umbrella. If you want to make yourself less rainy, will you choose to walk over or run over?
You may choose to run, after all, the speed is faster, the time spent in the rain is shorter, and naturally there is less rain.
But I ask you to recall a scene where the faster you get in a car or drive on a rainy day, the more rain seems to hit the glass.
So should I go or run?
Let's start with a few assumptions:
First, the raindrops are falling vertically, without wind.
Second, the rate at which raindrops fall is constant.
Third, ignore the rain that hits you on your head and shoulders and only consider what is on the front of your body.
In this case, let's consider what exactly is the unchanging quantity in this question?
What doesn't change is the volume of air your body sweeps through.
Because the distance you travel is constant, the volume of air your body sweeps through is constant. The speed of raindrops is also constant, so the number of raindrops in this air volume is also constant.
This leads to a startling conclusion: whether you are fast or slow, you are drenched by the rain to the same degree, because the volume of air you sweep is the same.
02.
Perfect coverage
Let's look at another example, this time it's a math puzzle:
There is a 10x10 black-and-white chessboard, which looks something like this:
One day, the two diagonals of the board— the small white squares in the upper left and lower right corners—were dropped. Now that there are 2x1 rectangular cards (an unlimited number), can we cover them all on the board? (No vacancies, no overlap)
Maybe you'll try it yourself and come up with the answer. But what if it's a 10,000 x 10,000 chessboard? There are so many changes that it takes a lot of effort to try it out. At this time, you need to find the constant quantity.
What remains unchanged in this process?
Because the rectangular card can only cover one black square and one white square at a time, there is one quantity that is constant, that is, the remaining black square minus the number of remaining white squares, which may be set to K, that is
K = Number of Remaining Black Blocks - The number of remaining white blocks
If it is a complete 10x10 chessboard with 50 black squares and 50 white squares, then at the beginning K=50-50=0.
Now that the board is broken and two white squares are missing, then K=50-48=2.
To completely cover the board, that is, there are no black and white squares left, it means that K=0.
We said before that K is the constant amount, but here K has changed, so this game cannot be completed, and we can never completely cover the entire board.
Find the invariant quantity in the complex, and it is the key to your game breaking.