# Soft question about imagine the fourth dimension

If I see a circumference like the 2-d "collapse" of a function $\Bbb R^2 \to \Bbb R$ (whose graph is usually a 3-d image) I can also see the sphere like a 3-d collapse of a 4-d graph. So the "grade of diversity" between the graph of a $\Bbb R^2 \to \Bbb R$ function and the graph of a circumference can be the same as the one between a $\Bbb R^3 \to \Bbb R$ function and a sphere? With "grade of diversity" I mean the difference between the two representations as images. May this help me somehow in imagining the fourth dimension? In which way? Is there someone of you that is able to imagine the fourth dimension?

I'm neglecting the "temporal vision" of the fourth dimension because it seems to me that is possible to imagine it even in non-temporal terms. This is only a pastime, I'm not saying that I'm right in any way.

• the human mind really can't perceive past dimension 3 Commented Jul 27, 2017 at 18:43
• How do you obtain a sphere from a function $\mathbb{R} \to \mathbb{R}^3$? Don't we need $\mathbb{R}^2 \to \mathbb{R}^3$? Commented Jul 27, 2017 at 18:44
• Oh, you are right. I was reasoning with implicite function, so the sphere is $\Bbb R^3\to \Bbb R$ also for the circumference with $\Bbb R^2 \to \Bbb R$ Commented Jul 27, 2017 at 19:00
• @SakethMalyala That's wrong. Most skilled differential geometers/algebraic topologists can easily visualize $\mathbb{R}^{4}$ at least. Commented Jul 27, 2017 at 19:16
• @MathematicsStudent1122 I don't believe that, although perhaps the disagreement is over the meaning of the word "visualize". Intuitive crutches for higher dimensional thinking have been discussed here. Note for example Scott Aaronson's comments about visualizing $\mathbb R^4$. While various techniques are available, nobody can directly visualize $\mathbb R^4$ the same way that we can visualize $\mathbb R^3$. Commented Jul 27, 2017 at 19:25