Dyson's eternal intelligence
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In 1979, Freeman Dyson published a paper in which he argued that in an open universe, it would be possible for an intelligent being to think an infinite number of thoughts. As the universe cooled, the thoughts would be slower and slower, but there would still be an infinite number of them.
Two recent observations have presented problems for Dyson's scenario. The first is that the expansion of the universe appears to be accelerating rather than decelerating due to a positive cosmological constant, meaning some regions of the universe will become permanently separated from one another. The second is that there appears to be a lower bound for the temperature of a vacuum, meaning that the universe would not continue to cool indefinitely.
Also, most of the Grand unification theories predict that protons are unstable particles that will decay in the far future. Thus also the material base for intelligence could go away. However, no evidence for proton decay has been detected as yet.