  We show that mere observation of a quantum system can turn its dynamics from
a very simple one into a universal quantum computation. This effect, which
occurs if the system is regularly observed at short time intervals, can be
rephrased as a modern version of Plato's Cave allegory. More precisely, while
in the original version of the myth, the reality perceived within the Cave is
described by the projected shadows of some more fundamental dynamics which is
intrinsically more complex, we found that in the quantum world the situation
changes drastically as the "projected" reality perceived through sequences of
measurements can be more complex than the one that originated it. After
discussing examples we go on to show that this effect is generally to be
expected: almost any quantum dynamics will become universal once "observed" as
outlined above. Conversely, we show that any complex quantum dynamics can be
"purified" into a simpler one in larger dimensions.
