The importance of information is directly proportional to its improbability.
Nobody has any conscience about adding to the improbabilities of a marvelous tale.
Each step is not too improbable for us to countenance, but when you add them up cumulatively over millions of years, you get these monsters of improbability, like the human brain and the rain forest. It should warn us against ever again assuming that because something is complicated, God must have done it.
The more improbable the message, the less "compressible" it is, and the more bandwidth it requires. This is Shannon's point: the essence is its improbability.
The argument from improbability, properly deployed, comes close to proving that God does not exist.
It’s the combination of improbability with an independently given pattern that discredits chance.
The miracle of man is not how far he has sunk but how magnificently he has risen. We are known among the stars by our poems, not our corpses. No creature who began as a mathematical improbability, who was selected through millions of years of unprecedented environmental hardship and change for ruggedness, ruthlessness, cunning, and adaptability, and who in the short ten thousand years of what we may call civilization has achieved such wonders as we find about us, may be regarded as a creature without promise.
The issue, as correctly emphasized by Carl Sagan, is the probability of the evolution of high intelligence and an electronic civilization on an inhabited world. Once we have life (and almost surely it will be very different from life on Earth), what is the probability of its developing a lineage with high intelligence? On Earth, among millions of lineages of organisms and perhaps 50 billion speciation events, only one led to high intelligence; this makes me believe in its utter improbability.
Natural selection is a mechanism for generating an exceedingly high degree of improbability.
