Phlegon's Stem-and-Leaf Display

ABSTRACT

The Greek writer Phlegon (80–140 AD) from Tralles in Asia Minor wrote a book entitled On Long-lived Persons that contains a long list of people over a hundred years old. He collected data from the Roman censuses. With respect to the history of statistics, Phlegon's book is the earliest surviving text to use the Stem-and-Leaf display of collected data.

KEYWORDS:

• Data display
• Data visualization
• Exploratory data analysis
• History of statistics

Acknowledgment

The author is grateful to Don Mathews for his comments that improved the quality of the article.

Notes

1 Due to Aristotle's persistence in data gathering, later Greek authors, such as Atticus, nicknamed him as “the nature's secretary.”

2 To quote a few: David (1995), Kafadar (2006), Bucevska (2011), and Larson and Farber (2015).

3 Although there are numerous Internet sites stating that stem-and-leaf “evolved from Arthur Bowley's work in the early 1900s,” I found no scientific reference except Bucevska's (2011) to support this statement. Even Dale and Kotz (2010), in their Bowley's biography, did not state or hint something relevant.

4 The age of this person is missing from Phlegon's original Greek text. I am reporting the value of 117 in order to construct figures and tables. The choice of 117 is absolutely arbitrary. It has been chosen in order to be consistent with all other reported numerical values.

5 Long Lives has been attributed to Lucian, although it is generally agreed that he was not the author.

6 “All these statements, however, have originated in a want of acquaintance with the accurate measurement of time. For some nations reckon the summer as one year, and the winter as another; others again, consider each of the four seasons a year; the Arcadians, for instance, whose years were of three months each. Others, such as the Egyptians, calculate by the moon, and hence it is that some individuals among them are said to have lived as many as one thousand years”. Pliny, The Natural History, VII 49.

7 “Almost entirely” because Phlegon uses the Sibyl's claims, and the mere hear-say report of Herodotus and Anakreon.

8 The Greek phrase Phlegon used is «Οἱ ἑκατὸν ἔτη ζήσαντϵς Ἰταλῶν, ὡς ἐξ αὐτῶν τῶν ἀποτιμήσϵων ἀναζητήσαντϵς οὐ παρέργως ἐμάθομϵν».

9 The Greek word Phlegon used is «ἀπογραψάμϵνοι».

10 It is interesting to note that although Phlegon writes in Greek he follows the Latin alphabetical order. This is understandable since his primary sources, the Roman censuses, were in Latin.

11 My limited knowledge of ancient languages forced me to investigate only the Greek and the Latin ancient texts.