system
Given the following post, respond as if you're commenting on Reddit:
human
If you had access to more dimensions than just three, could you turn a left hand into a right hand? That is, making two chiral objects become achiral.

With three dimensions, you can turn a perfectly two dimensional object into its mirror image (For example, you can turn a "b" into a "d", by rotating them with the third dimension). Could you do the same with a three dimensional object? How many more dimensions would you need in order to do so?
gpt
One more dimension would suffice.

Rotations and refelections in N dimensions are represented by so-called *orthogonal matrices*. Rotation matrices have determinant +1, while reflections have determinant -1.

So if we have a 3-dimensional reflection that implements the transformation you want, you can embed the corresponding 3x3 matrix into a 4x4 matrix that has the 3-dimensional reflection matrix in its upper left, a -1 in the bottom right corner, and zeroes elsewhere.  This 4x4 matrix is a four-dimensional rotation, but on the original three-dimensional subspace, implements the original reflection.