I am watching this video on topology:
One of the claims is in an earlier video:
https://youtu.be/CZqeAC07_UE?t=1037
Suppose we have manifolds with dimensions $L$ and $K$ in ambient with a dimension $M$. If $K + L - M = -1$, then the manifolds must cross to "change sides". If $K + L - M < -1$, then the crossing can be avoided. The meaning of "changing sides" is left somewhat undefined in the video.
Consequently, in one of his later examples, the lecturer says that to untie the Trefoil knot, you need the ambient space $\mathbb{R}^6$ (one of the students also gives the answer 6).
However, it seems to me that it is possible to untie a Trefoil knot in $\mathbb{R}^4$. If you pull out one part of the knot into the direction of the 4-th dimension, then you can obviously circumvent the adjacent part without crossing it. In fact, this is observed in one of the comments below the video too.
Is this intuition correct? Can you untie the Trefoil knot in 4 dimensions?
If it is, then according to this definition, the Trefoil knot is isotopic to the unknot in $\mathbb{R}^4$.
EDIT:
When I said "Trefoil knot", I actually meant the following 2-dimensional surface:
Yes, all (1-dimensional) knots can be unknotted in $\mathbb{R}^4$, exactly as you argue. A nice visualization is to let the fourth dimension be color-then you can accomplish the necessary crossings by turning, say, the lower strand red and the upper blue. This actually agrees with the inequality given in your lectures.