The way we have understood the reality is to be understood before we understand reality itself. We start learning geometry in our school from a simple straight line starting from a place extending in one direction to certain length. That is very easy to understand. We can see it differentiate and do not require much imagination. Then we extend this line to infinity. And what we comprehend from that it is so long that we cannot find end. This is fine as it is only imaginary concept and on paper i do see line ending with an arrow. I just tell my mind that this goes on and on.
Then we say that join two such lines back to back extending in opposite direction. This is an axis. That is what you see extends in two directions. By that time mind has stopped bothering about infinity.
Same thinking holds in lots of other areas. When we judge people personalities we create dimensions. A basic example is MBTI personality indicator where there are four dimensions and we define by four charaters which quadrant (or say section as this is 4D) the personality is.
In decison theory we create graphs and mark quadrants what they represent and what could be done in those quadrants.
This is fine, but it is also important to keep in my mind that this is a reflection of reality. What should be in the mind when seeing world through linear lenses,
1. The world is basically non-linear, small separation of values could mean big differences and vice versa.
2. Since beyond 4D we cannot hold it in our imagination most of the relfections of higher dimensional reality are on lower dimensional (<=4D) canvas. So we have to know that in a non-linear world we are ignoring dimensions which could change everything we understand.
This doesn't mean that we stop dimensionalizing reality, but we should be ready to savour surprises at rare times when our understanding doesn't hold good.