Because of this substrate independence, shrewd engineers have been able to repeatedly replace the technologies inside our computers with dramatically better ones, without changing the software. The results have been every bit as spectacular as those for memory devices. As illustrated in figure 2.8, computation keeps getting half as expensive roughly every couple of years, and this trend has now persisted for over a century, cutting the computer cost a whopping million million million (1018) times since my grandmothers were born. If everything got a million million million times cheaper, then a
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