Dr. Eric Li's Blog

The mainstream media and belief is that alternative medicine such as Traditional Chinese Medicine, most of them thousands of years old, are not based on sciences, rather they are based on trial and error without rigorous scientific experiments to verify the validity.

I submit here that time proven medicines are indeed sciences if they can survive for thousands of years.

In applied mathematics and statistics, as I studied in Harvard, there're two types of statistical averages, the ensemble average and the time average.  Both can be statistically significant. 

Ensemble average is to observe an phenomena (e.g., an experiment) over many times (or objects) - the very base of scientific research.  For example, if you want to proven the effecacy of a drug, you design an experiment, and apply the drug to a number of rats or human (e.g., 300) for a few months, calculate the average results and draw conclusion. 

On the other hand, time average is to apply this drug only on a single person at a time.  When this person is not availabe, apply to another (again only one person).  If you do this over many many years, you will get identical results as the ensemble average, if both experiments are designed correctly.

In mathematical terms, if a1, a2, ..., an are the measurements for the n rats or people during a fixed period, then the ensemble average EA = (a₁ + a₂ + ...+a_n)/n.  If b(t₁), b(t₂), b(t₃), ..., b(t_n) are the measurements oberserved sequentially during a long period time, t₁<t₂<t₃<...<t_n, then, time average TA = [b(t₁)+b(t₂)+...+b(t_n)]/t_n.  As n goes to infinity, EA = TA.

This means

1. If over thousands of years, a drug survived as a effective treatment, even if there's no "scientific experiment" done, it is still as scientific as if there were an "scientific study" done.

2. Even if there's a scientific study performed, there's still no guarantee that the results is reliable, partially due to the limited sample size, partially due to poor design of the experiment.  That's why many drugs approved by FDA, only to later find severe side effects which were previously unknown.  On this respect, a time proven remedy could be safer.

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