Reality is perception... 

Perception is subjective...

These two sentences are the opening intro to the game I just bought last week. The game whose genre is puzzle, is highly recommended by nintendo life on their youtube channel. In fact, they gave this indie game score 9 of 10, which is amazing!


I like this game, titled FEZ, for two reasons. First, the game's character has infinite lifes, which means that I can progess through the game without worrying about restarting game level when the character died. Yep, just like other games, our hero in this game can also die when they, intentionally or not, free fall from very high places. And fortunately that is the only reason for dying since the game doesn't provide enemies to catch you. The good news is that no matter how many times you die, you can play again from the exact last point before you fell which makes this game not so stressful.

Another reason for loving this game is that because it reminds me alot of my latest course about high dimensional data analysis! Well, I can say that the first two sentences of the intro are able to summarize whole lecture I took this semester.

In high dimensional data, in order to take into account many variables (these give the term "high dimension") we need to involve orthogonal rotation matrix that can not only preserve the distance of variables (and observations) but at the same time give us a helicopter view of these many variables. The only thing the orthogonal rotation does to give us the helicopter view is by changing direction!


I don't want to confuse you with any calculus thingy behind the rotation (since I am still confused about it too), but here I just want to emphasize that indeed the rotation has a pretty important function in the high dimensional data analysis techniques, i.e. principal component analysis (PCA) or correspondence analysis.  

Simply to say, the rotation can help us in summarizing (reducing) so many data dimensions (which is quite impossible to do without rotating) as well as understanding the relations between the variables (and observations) without need to modify too much the original variables (and the observations). This is exactly what the game try to explain us that we actually can go further in the game (or even in our real world) by doing any rotations neccessary to make something improbable to be possible. In other words, if our perceived reality doesn't hold, we need to change our perception on the reality!