From this article:

A dominant theme of the past 50 years has been the growing understanding of how to create computer programs for specific tasks. A central theme of the next 50 will be the systematic exploration of the "computational universe" of all possible programs.

In recent years we have discovered that very small programs can produce immensely rich and complex behaviour. As we explore the computational universe this fact will become crucial to science, art, technology and our whole way of thinking. Today when we create things, we expect to do it by explicit human effort. Fifty years from now, it will more often be done by automatically mining the computational universe. Perhaps we will even find the ultimate model of our universe that way. No doubt many industries will be created from technology discovered in the computational universe - whether for programmable nanostructures, algorithmic drugs, mass-customised art or generative microeconomics.

Just as scientific concepts such as momentum and natural selection are commonplace in our thinking today, so in 50 years will be concepts like computational irreducibility and the principle of computational equivalence. I expect the children of 50 years from now will learn cellular automata before they learn algebra.

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