I once heard a joke (not a great one I'll admit...) about higher dimensional thinking that went as follows- An engineer, a physicist, and a mathematician are discussing how to visualise four dimensions: Engineer: I never really get it Physicist: Oh it's really easy, just imagine three dimensional space over a time- that adds your fourth dimension. Mathematician: No, it's way easier than that; just
![Intuitive crutches for higher dimensional thinking](https://cdn-ak-scissors.b.st-hatena.com/image/square/10df5a86e3137a3cd7bea6fd8ae7e36216ff6c05/height=288;version=1;width=512/https%3A%2F%2Fcdn.sstatic.net%2FSites%2Fmathoverflow%2FImg%2Fapple-touch-icon%402.png%3Fv%3Df1c9606b77ff)