When Edwin Abbott Abbott set "Flat-land", a satire on Victorian society, in a two-dimensional universe, it was not meant as a compliment. In Abbott Abbott's geometrical romance, enlightenment conies to the hero, Mr Square, from his understanding of the nature of a third dimension. More dimensions, it seems, are better than less. Yet, when it comes to building circuits with light, the failure of photons (the particles of which light is composed) to squeeze into flatness has made them less, not more, useful. Electronic chips are essentially two-dimensional, the electrons being confined to conductive and semiconductive layers laid down on a chip's surface. Engineers would like to be able to build chips in which photons and electrons can have meaningful interactions, since that would permit better ways of handling data.
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