People often ask me: will this game make me understand the fourth dimension?
The thing about this question is that there are multiple ways of understanding something, so we have to define which way we mean.
I think about Miegakure as a toy ball. I mean that in the sense that by playing with a toy ball as a kid you intuitively learn about how gravity works. You can adjust the throwing angle and force and see the different paths the ball takes. You learn about parabolas without even knowing the word for them.
This is very different from knowing the second-order differential equations of motion under the force of gravity. Clearly you don't need to understand them to know how to throw a ball.
In the same way, Miegakure doesn't explain anything explicitly about the fourth dimension, it just lets you be inside of a 4D world. If someone wants to learn the mathematical theory, however, it can be built upon stronger instincts.
I have watched tons of people play Miegakure and I see people fall along a spectrum between two types: intuitive and reasoned.
The intuitive types try something, fail and try something different. They often don't understand how they are able to solve the puzzles or know exactly what they are doing and why. But they gradually build an intuition for the patterns they encounter.
The reasoned types, on the other hand, when put in situation they do not understand, stop and think: what is this system I am interacting with? They formulate theories and test them. They move a little bit, think, press a button and examine the results. Some people go back to previously solved levels in order to test theories. They quickly build a model of how the rules of the game work and it is this model that allows them to solve puzzle effectively.
This is not to say that any type is better. I have seen very smart people in both categories. I have seen someone play for 4 hours, beat almost the whole game, all on intuition. At the end I asked: so can you explain to me what happens when you press the "rotate" button? Their first answer was no, but as they started thinking about it they had an epiphany: oh! I see this is how it works!
I can tell a lot about the way someone thinks from the way they play Miegakure. I am reminded of David Sirlin's great GDC 2012 microtalk [Blog Post] [GDC vault link]. It is about the difference between conscious thought and unconscious thought, and contains this quote from Capcom's Seth Killian :
I can learn more about someone by watching them play 10 seconds of Street Fighter than 10 hours of an RPG