Hi
Very new to this discussion, i actually found this site randomly.
Ok, well since this isn't an introduction thread ill spare you my life story. As for imagining how a 4 dimentional object looks, or shape which i believe is a better term, i think borders on extremely hard to impossible.
Over the last few days I've been thinking about how one could imagine such a shape, weather it be based from our 2 dimentional square or circle in some way. I think the furthest ive got is understanding the requirements to picture one and I think thats as far as most people will get, myself included.
Alot of the diagrams shown on this site are very helpful, and the explaination on them has pretty well given me these following thoughts, (i was going to say conclusions, but this topic is far from that).
A 4 dimentional shape, requires you to picture a 3 dimentional one, as one of its "sides". Its important to know in our world or realm we can see the entire side of a 3D object just looking at it. IE. I may view the entire side of my desk, it has a wooden finish, i know this because i can see all of it, it is 2D.
Now to picture a 4D desk, you must somehow imagine this same "side" as a 3D object, with the same capabilities. This time i know more about my desk, i can see behind the 3D side to the back of it by looking at its front.
Im sorry I used front and back, they are big no nos when it comes to explaining how to view a 4D object considering their extreme variations, or existance at all.
Anyways simply put, the side of a 4D object is a 3D object, and that same 3D object inverted at the same time. Something both inside out and not inside out at the same time. Also, if your able to picture this, you are only looking at one side of a 4D object, and one side alone. Looking at multipul sides to a 4D object as you can probably already tell gets much more complex. I havent figured out how edges work, or exist.
Id also like to add that trying to illustrate such an object, i think the closest example i can think of is the impossible triangle prehaps. Even then its only half way there.
Please feel free to cut me up for writing this as if im some professor on the subject, to that i am not of course. I am definatly no expert on this, although i might have acted like a know-it-all in this post. Sorry for any offense taken, and welcome all critism and objections to what i have said.
Thank you for reading my post.