I think it would become intuitive if there was some way to plug 4th dimension in our senses. Have you read stories about people who implant magnets? After a wh

I think it would become intuitive if there was some way to plug 4th dimension in our senses. Have you read stories about people who implant magnets? After a while they develop a sense of direction. Brain adapts to new signals and starts to interpret them. Different example, I remember reading about experiment where people had to wear glasses that flip the picture upside down. After not too long time they adapted and saw things normally. And everything would be upside down when taking the glasses off. Yet another example is asking blind people what they see. They don't see black or grey, the sense of vision simply isn't there. Like our sense of 4th dimension isn't there. So, one thing to try would be to give us sense of rotation and acceleration in 4th dimension and see how it goes. Next, maybe, a new "color channel" for our vision, and let the brain figure out how to represent it "internally".