  We construct families of trivial $2$-knots $K_i$ in $\mathbb{R}^4$ such that
the maximal complexity of $2$-knots in any isotopy connecting $K_i$ with the
standard unknot grows faster than a tower of exponentials of any fixed height
of the complexity of $K_i$. Here we can either construct $K_i$ as smooth
embeddings and measure their complexity as the ropelength (a.k.a the
crumpledness) or construct PL-knots $K_i$, consider isotopies through PL knots,
and measure the complexity of a PL-knot as the minimal number of flat
$2$-simplices in its triangulation. These results contrast with the situation
of classical knots in $\mathbb{R}^3$, where every unknot can be untied through
knots of complexity that is only polynomially higher than the complexity of the
initial knot.
