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Description
One conclusion to be drawn is that, IF a computer can effectively calculate an algorithm THEN so can an equivalent Turing Machine. But the converse is not true: It is NOT true that IF a Turing machine can calculate an algorithm THEN so can a computer; no computer is as computationally powerful as a Turing Machine since a computer does not have the required infinite memory nor infinitely-sized variables.

Thus it is not possible to build a calculation device that is as powerful as the simplest theoretical computing mechanism (a Turing machine). Note that this formulation of power disregards practical factors such as speed or memory capacity; it considers all that is theoretically possible, given unlimited time and memory.

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stock:

original size:
20x35 inches

Description
One conclusion to be drawn is that, IF a computer can effectively calculate an algorithm THEN so can an equivalent Turing Machine. But the converse is not true: It is NOT true that IF a Turing machine can calculate an algorithm THEN so can a computer; no computer is as computationally powerful as a Turing Machine since a computer does not have the required infinite memory nor infinitely-sized variables.

Thus it is not possible to build a calculation device that is as powerful as the simplest theoretical computing mechanism (a Turing machine). Note that this formulation of power disregards practical factors such as speed or memory capacity; it considers all that is theoretically possible, given unlimited time and memory.

----

stock:

original size:
20x35 inches