Ancient Computers, Part I - Rediscovery, Edition 2

People, especially historians, have long struggled to appreciate and understand how Ancient Romans, Greeks, Egyptians, and Babylonians, et al, were able to do their arithmetic calculations. Many say the Ancients "probably" used line abacuses or abaci, a.k.a. counting boards. But most then trivialize the possible impact that use would have on the Ancient cultures because they really don't think those abaci would be very powerful and would be extremely hard to use.

The (re-)discovery Ancient Computers documents and explores materialized from the author's experiences in engineering, with a knowledge that design compromises often have to be made; computer programming, especially the different number bases used; the hobby use of a Japanese abacus called the Soroban; and study of the Ancients' numbers and culture.

The bottom line is that the Ancients had a powerful and lightning fast computer; powerful and fast compared to any other calculation method available to them in their time. Features included:

• multi-base number modes: e.g., sexagesimal, decimal, duodecimal, or nonary;
• operating on those numbers in two parts: a signed fraction of the base and a signed exponent of the base, equivalent to scientific notation;
• easy and low-cost expandability; and
• built-in error checking!

On the "standard" Ancient line abacus doing base-10 calculations, the fraction could have 10 significant digits and the exponent 4. Certainly enough for most modern engineering or scientific problems. If you need more, though, just scribe a few more lines on the abacus and add a few more pebbles to your pouch! By the way, 178 small pebbles will suffice for any problem on the "standard" line abacus. They fit in a pouch that can be easily and comfortably carried in a man's trouser pocket.

I hope you find Ancient Computers interesting and useful.

-Steve Stephenson, July 15, 2010
M.Eng.(Elect.), M.Ed.
Math Teacher (Calculus & Precalculus)
Lowell High, MA

Edition 2 changes some formatting and adds two appendices:
N: Nonary Base (candidate for electronic implementations); and
V: Visualizing Abacus Arithmetic.

Edition 2 is now available as a printed book in addition to the Kindle eBook.

Two DVDs containing the Stephenson Videos are also available on Amazon.com as
Ancient Computers: Part II - Video Users Manual:

1. How to Use a Counting Board Abacus (1 of 2); and
2. How the Romans Used a Counting Board Abacus (2 of 2).

-Steve Stephenson, July 15, 2013
Math Teacher (Retired 6/30/2013)