Moore’s law says that the number of transistors in a dense integrated circuit do

Question

Moore’s law says that the number of transistors in a dense integrated circuit doubles approximately every two years. Explain how you could test this hypothesis using simple linear regression. Let N = the number of transistors in a circuit and let T = time (in years.) Suppose you have pairs of data of the form (Ti,Ni), i = 1,...,n. Start by writing down the (supposed) relationship between T,N, including all unknown parameters. Then, explain how to turn this into a model for which you can extract the parameters using SLR. Finally, explain how you would test the specific hypothesis that the doubling time is two years. (You don’t need to actually test it.)

Explanation / Answer

Moore's Law, of course, famously suggests that the complexity of computers grows at a rate of double the transistors per circuit every two years, resulting in exponential growth. Looking at the complexity of computers today and working Moore's Law backwards shows that the first microchips came about during the 1960s, which is when they were actually invented. In their paper, Gordon and Sharov take the same approach, only they apply it to biological complexity.

The two researchers acknowledge their ideas are more of a "thought exercise" than a theory proposal, but at the same time suggest their calculations ought to be taken seriously. They start with the idea of genetic complexity doubling every 376 million years—working backwards, they say, means that life first came about almost 10 billion years ago, which of course predates the creation of Earth itself. Most scientists agree the Earth formed just 4.5 billion years ago. Assuming that Moore's Law does apply to biological complexity, this would suggest that life began somewhere other than on Earth and migrated here.

Of course there are other possibilities to explain what happened, as the two acknowledge—life could have evolved following Moore's Law during certain periods but not at others—a deep freeze could have temporarily halted changes in complexity, for example, or cataclysmic events could have periodically killed off the more advanced biotic life forms. There is also the possibility that the development of life had to reach a certain stage of development before it began to conform to Moore's Law. Then of course, there is the very real possibility that the beginnings and evolution of life don't conform to Moore's Law at all.

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