Prediction of the Hualian earthquakes in Taiwan and an extended discussion on the method of commensurability

The method of commensurability was used by the authors to predict the great earthquake of magnitude 7.5 that occurred on March 31,2002 in Taiwan 70 km away from Hualian. Analyzing the earthquakes of magnitude ⩾7.0 which occurred in the Hualian area of Taiwan within the 20th century, the authors discovered that the occurrences of the earthquakes are commensurable. The earthquakes of magnitude 7.6 which occurred in Hualian of Taiwan, on September 20th, 1999 and of magnitude 7.5 which occurred 70 km away from Hualian, on March 31th, 2002 appeared at the commensurable point of K=2 and the period times the golden section, respectively. An extended discussion is carried out on the method of commensurability and its implied physical significance, especially on the contribution of the commensurable periodic extension made by Prof. Weng Wenbo.