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Say goodbye to 1s and 0s and hello to a plethora of values. Analog computers here we come. Wahoo!
There is nothing new or revolutionary here. Bulk resistance versus incremental resistance is well known. Nonlinear resistances are well known. Resistance which varies depending upon the history of the device are well known. The claim that a fundamentally new circuit element has been found is overblown.
HP Labs maintains that because of this property, massive memristor arrays could enable brain-like learning. In the brain, a synapse is strengthened whenever current flows through it, similar to the way resistance is lowered by flowing current through a memristor. Such neural networks could learn to adapt by allowing current to flow in either direction as needed.