We are human because we are part of, but not because only part of, communities; and the attempt to understand man's brotherhood in terms only of the individual man is as little likely to describe our world as is the attempt to describe general laws as the summary of their instances. These are indeed two complementary views, neither reducible to the other, no more reducible than is the electron as wave to the electron as particle. And this is the mitigant of our ignorance. It is true that none of us will know very much; and most of us will see the end of our days without understanding in all its detail and beauty the wonders uncovered even in a single branch of a single science. Most of us will not even know, as a member of any intimate circle, anyone who has such knowledge; but it is also true that, although we are sure not to know everything and rather likely not to know very much, we can know anything that is known to man, and may, with luck and sweat, even find out some things that have not before been known to him. This possibility, which, as a universal condition of man's life is new, represents today a high and determined hope, not yet a reality. It is one of the manifestations of our belief in equality, that belief which could perhaps better be described as a commitment to unparalleled diversity and unevenness in the distribution of attainments, knowledge, talent, and power. This open access to knowledge, these unlocked doors and signs of welcome, are a mark of a freedom as fundamental as any. They give a freedom to resolve difference by converse, and, where converse does not unite, to let tolerance compose diversity.

Remember that your soul is in your keeping alone. When you stand before God, you cannot say, but I was told by others to do thus, or that virtue was not convenient at the time. This will not suffice, remember that.

Gödel proved that within any formal system there will always be undecidable statements that cannot be proved true yet cannot be proved false. Turing proved that within any formal system, not only are there functions that cannot be computed, but there is no definite method to distinguish computable from non-computable functions in advance. That’s the bad news. The good news is that, as Leibniz suggested, we appear to live in the best of all possible worlds, where the computable functions make life predictable enough to be survivable, while the non-computable functions make life unpredictable enough to remain interesting, no matter how far computers continue to advance.

When you think all is lost and there is no hope left, remember the lobsters in the tank at the Titanic's restaurant.