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In scientific and professional fields that utilize computational modeling, the Turing Number is defined as the ratio of the time required for a computation to time interval being simulated. Models that are very intricate and contain more equations (see for instance, Leibniz class problems, Leibniz (unit)) may more accurately predict reality, but the time required to solve the model equations may exceed the time interval of the natural phenomena being modeled - in some cases by many orders of magnitude, on a computer of a given size and speed.

For instance, a model of 10 seconds of fibrillation in the heart may require days of computation time to solve. Or, a 30 second graphical simulation of an ocean scene may require many hours to render. Both examples would have Turing Numbers much larger than unity.

Mathematical models or simulators that are intended to interact with natural or living systems may require Turing numbers on the order of unity or less in order not to introduce an unnatural delay in the dynamics of the entire system. A real time Turing Test of an artificial intelligence with Turing Number much greater than unity may fail due to computational delays producing unnatural pauses that enable the AI system to be distinguished from real live human beings - even if the actual answers are sufficiently human-like.