Diversification in the Cosmos

The last of the five philosophical problems is the problem of final aims. The problem here is to try to formulate some {298} statement of the ultimate purpose of the universe. In other words, the problem is to read God's mind. Previous attempts to read God's mind have not been notably successful. One of the more penetrating of such attempts is recorded in the Book of Job. God's answer to Job out of the whirlwind was not encouraging. Nevertheless I stand in good company when I ask again the ...

 Von Neuman and Predicting the Weather

I remember a talk that Von Neumann gave at Princeton around 1950, describing the glorious future which he then saw for his computers. Most of the people that he hired for his computer project in the early days were meteorologists. Meteorology was the big thing on his horizon. He said, as soon as we have good computers, we shall be able to divide the phenomena of meteorology cleanly into two categories, the stable and the unstable. The unstable phenomena are those which are upset by small dist...

 The Flat Universe Problem

The next obvious feature of the universe in which we live is that it is old, very old. It took intelligent life about 3.5 billion years to develop on Earth. Hence, our existence requires a universe that accommodated our arrival by lasting billions of years. The current best estimate for the age of our universe is between about 10 billion and 20 billion years, which is plenty long enough. It turns out, however, that it is not so easy a priori to design a universe that expands, as our universe ...

 Uniformity, Non-Uniformity, and Irreversibility

We must make the following remark: a proof, that after a certain time t1, the spheres must necessarily be mixed uniformly, whatever may be the initial distribution of states, cannot be given. This is in fact a consequence of probability theory, for any non-uniform distribution of states, no matter how improbable it may be, is still not absolutely impossible. Indeed it is clear that any individual uniform distribution, which might arise after a certain time from some particular initial state, ...