Posted by: Alexandre Borovik | July 31, 2008

How did Classic Greeks understand natural numbers?

A commentary to Plato’s Charmaides by unknown scholar describes a clear distinction between ideal natural numbers and numbers used for mundane everyday counting:

Logistic is the science that treats of numbered objects, not of numbers; it does not consider number in the true sense, but it works with 1 as unit and the numbered object as number, e.g. it regards 3 as a triad and 10 as a decad, and applies the theorems of arithmetic to such cases. It is, then, logistic which treats on the one hand the problem called by Archimedes the cattle-problem, and on the other hand melite and phialite numbers, the latter appertaining to bowls, the former to flocks; in other types of problem too it has regard to the number of sensible bodies, treating them as absolute. Its subject-matter is everything that is numbered; its branches include the so-called Greek and Egyptian methods in multiplications and divisions, as well as the addition and splitting up of fractions, whereby it explores the secrets lurking in the subject-matter of the problems by means of the theory of triangular and polygonal numbers. Its aim is to provide a common ground in the relations of life and to be useful in making contracts, but it appears to regard sensible objects as though they were absolute.

Quoted from

I. Thomas, Selections illustrating the history of Greek mathematics with an inglish translation by Ivor Thomas. Vol. 1: From Thales to Euclid. Harward University Press, Cambridge, Ma. 1938 (reprinted 1980). ISBN 0-674-99369-1.

pp. 17–19, with thanks to David Pierce who brought this quotation to me.

About these ads

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Categories

Follow

Get every new post delivered to your Inbox.

Join 81 other followers

%d bloggers like this: