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06/19/2008
Memory Capacity and Processing Speed
The more memory capacity any computer has (be it a human or a machine), the less processing speed it needs: this is so because it can then simply remember a calculation, rather than repeat it.
An example is factorials. If a computer needs to calculate very large factorials over and over, it will take longer for it than to simply recall them. This is so because recalling what 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 is (that is, what 12 x 11 is, 132, what 132 x 10 is, 1320, what 1320 x 9 is, 11880, and so on), is considerably more demanding than recalling the cipher 479001600.
Therefore, memory capacity can reduce the need for processing speed, so that even when the latter would reach a limit, the speed of computation could still grow as the former does. As many computations are repeated, making use of otherwise unused memory space to store their results increases computational speed. If all unused memory space were used, computational speed could be furthered enormously. Almost all calculations could then be based on more basic calculations which could then be remembered rather than reiterated.
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