Calculus conundrum

I hope by now that the name of the Chinese jester Shi Dongtong 石動筩 (Moving Bucket) is lodging permanently in your brain, as we share several accounts of his making a mockery of leading lights in Chinese philosophy and religion.   Serving emperor Gaozu of the Northern Qi 北齊高祖 (r. 550-59), his boss seems to have enjoyed and even encouraged these irreverent interventions.   Here, Moving Bucket makes mathematical mincemeat of a serious discussion point: 

Quote - Hou Bai - Qiyan Lu

Erudites from the national university could be seen debating a difficult point during which the number of Confucius’ enlightened disciples was given as seventy-two.  Moving Bucket made a joke of this, asking how many of the enlightened disciples were adults and how many were not, to which the scholar replied that the classics did not say.  Moving Bucket was not convinced:

 

‘Since you have studied, can there be anything you would not understand?  Thirty of his disciples were adults and those who were not numbered forty-two.’  The scholar said, `On what writings do you base your argument?’  Moving Bucket explained, `The Analects say “There are five [or] six adults”, five sixes are thirty; “There are six [or] seven children”, six sevens are forty-two, how can that not add up to seventy-two?’  All the guests were delighted, and the scholar had no answer.

 

又嘗於國學中,看博士論難云:「孔子弟子,達者有七十二人。」動筩因問曰:「達者七十二人,幾人已着冠?幾人未着冠?」博士曰:「經傳無文。」動筩曰:「先生讀書,豈合不解! 孔子弟子着冠有三十人,未着冠者有四十二人。」博士曰:「據何文以辨之?」動筩曰:「《論語》云『冠者五六人』,五六三十人也;『童子六七人』,六七四十二人也:豈非七十二人?」坐中皆大悅,博士無以復之。

The joke works better in Chinese which does not need ‘or’ and does not use plurals.

Source: Qiyan lu 啓顏錄, by Hou Bai 侯白 (fl. ca. 581), in Taiping Guangji 太平廣記, comp. Li Fang 李昉 (925-96), fol. 247, in Lidai xiaohua ji歷代笑話集, Wang Liqi 王利器, ed. (Hong Kong: Xinyue Chubanshe, c. 1958), p. 11.

Image credit: One panel of Confucius and His Disciples Yanzi and Huizi at the Apricot Alter, depiction of Huizi, Kano Tan’yû (1602–1674); Museum of Fine Arts, Boston, Fenollosa-Weld Collection, public domain.

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