Tuesday, October 18, 2011

The P-Values Of The Gods

Most ancient cultures seem to have participated in some sort of "lot casting" as a way of communicating with the gods, something similar to asking a god if you should invade Babylon, and if you rolled a pair of dice and the sum was greater than six, that meant you should invade.  In these instances, there is no such thing as chance.  Every event that occurs is a direct manifestation of god's will, and if his will seems confusing, then it must be you who is in error.

I find that fascinating, because it describes a world so different than my own, yet still inhabited by the exact same species of people.  Consequently, I was enthralled to learn of a culture where god's will was discovered by a mix of determinism and chancegod's will was discovered by p-values (a statistical term communicating the probability a hypothesis is wrong).

The Shang dynasty in China existed around 1500 B.C., and in their pursuit of the gods used the shoulder blades of cattle or the shells of turtles as "oracle bones."  Questions would be carved into the bonesquestions asked of ancestors of the present king, who were the gods of interest.  The bones would then be cracked such that the cracks either pointed up or down, constituting a yes or no answer.

But there is more.  Questions were asked sometimes on a daily basis, and many of the questions had answers which could be later verified (e.g., is the harvest going to be good this year?), and the bones would be stored so that future generations could assess the accuracy of a certain king's ancestor.  Yes, the people did verify to determine whether the oracle bones gave accurate answers—what audacity!

But there is more.  Rather than asking a question once, they may ask the question 5, 10 times to determine whether the answer is clear or ambiguous.  If roughly half the answers were yes and half were no, then the gods essentially did not answer.  If there were eight yes answers and two no answers, then the gods' answers were an official yes.  After all if 80% of the time an answer is yes, it is more likely that the gods' true answer is indeed yes.

But there is more.  Today we know (or, I believe) the outcome of the oracle bones is random, and thus the answers are random.  If the gods consistently gave accurate answers, the present king has a true and authentic heavenly mandate because his ancestors are powerful gods.  If the gods seem to know nothing about the future, the present king is a farce, his ancestors are no gods, and the king must be replaced.

The laws of probability asserts that as time goes by, there will be some rulers whose ancestors happen to predict the future well.  And consequently, the rule of a king depended on chancethe rolling of the dieas much as his quality as a ruler. Kings ruled by the power of the p-value.

Note: One might initially think that a modern statistician, if transplanted to the days before Christ, could use the power of mathematics to prove the existence or non-existence of gods. This would be wrong. The statistician might prove that only X% of the time will the oracle bones give correct answers, but the ancient Chinese would simple say this means only X% of the time communication with the gods was possible. As a rule of thumb, it is impossible to have an intelligent conversation about the existence of free-will or god. The same goes for this case.

Dr. Kenneth J. Hammond
From Yao to Mao: 5000 Years of Chinese History
Lecture 2: The First Dynasties
The Teaching Company

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