not necessarily deeply familiar with quantum field theory. (One should compare this with the didactic problems related to the “mesomeric effect” in chemistry.)

In this article, we will focus mostly on the second item in the list above, which is elucidated in detail in Section \[sec:autodiff\]. The key insight is that a deformable object, such as a beam bending under the influence of Casimir forces as shown in figure \[fig:beam\], when discretized into $N$ elements (blocks) that are partially restricted in their relative motion, may require a certain computational effort, $T$ processor-seconds, for a reasonable estimate of the Casimir energy of a given configuration, but will then always allow the simultaneous computation of Casimir forces (and moments) on *all* $N$ elements in a way that requires at most $5T$ processor-seconds, *irrespective of the number of bodies $N$*.

\[fig:beam\]

![image](beam){width="8cm"}

[Beam bending under the influence of external forces and moments, a standard problem in Engineering, may be regarded as an energy minimization problem. Geometries such as the one shown above that involve bending beams at tens-of-nanometers length scales are presently being discussed as nanoelectromechanical memory devices [@4160125]. Here, the beam also serves as a floating gate that allows electronic read-out of 