Abstract: A magnetic holding device uses an array of switchable magnets. A carrier holds the array of switchable magnets to form a working surface. Each switchable magnet has a coil of wire surrounding a magnetizable core element. The array is arranged in groups of magnets. A circuit is coupled to the coils to selectively magnetize and demagnetize each group of switchable magnets to selectively independently place each group into one of these states: an ON state that configures the selected group to have a first magnetic polarity at the working surface, an ON state that configures the selected group to have an opposite magnetic polarity at the working surface, and an OFF state that configures the magnets in the selected group to have no magnetism at the working surface. This abstract is not to be considered limiting, since other embodiments may deviate from the features described in this abstract.