Number Words and Number Symbols: A Cultural History of Numbers

I had the russian edition. The book consists of several sections and begins with author’s explanation about how numbers had possibly emerged in the languages of different nations. They appeared not at once, but one after another anf often not sequencially but when they were needed. That’s why round numbers (tens, hundreds) emerged earlier then their lower non round neighbours and the names of round numbers affected the names of their neighbours too. In some cases people even didn’t need the actual names for the numbers and used signs or special names connected with the field they were used at. Right now we all count in the decimal system, but much earlier people have used names based on five or on twenty. Even the definition of the number was evolving. Not only zero wasn’t treated as a number, one was also not treated by europeans as a number for a long time.

There are myriads of different facts represented in the book and all they are accompanied with lots of photos and cross references. The density of them sometimes is so high, that it was a bit hard to get through all of them while reading. Also, some examples or descriptions of the calculation techniques and algorythms are not well defined and may contain errors (may be it’s only true for russian edition) that it takes significant time to get it right. For example to really understand how calculations were done by Sumer I just took anothe book (“History of Mathematics” by A. Yushkevich).

The big advantage of this book is that during exmplanations author constantly shows connections with current languages and shows how different words or terms were born like bankrupt, bureau, the names and symbols of currencies etc.

It’s very interesting to read section devoted to calculations and numbers usage in Middle Ages. We are so used to arabic numbers (that are actually form India) that it’s hard to believe that in the middle ages most of european countries used roman numbers for writing and special calculation table for actual calculations, because roman letters do not provide any machanics to use them in the calculations directly. These tables and their analogs were wide spread everywhere from Japan to Western Europe and were used even in the twentieth century.

It may also be a revelation that some nations used non-decimal numbering systems for the calculations, based on twenty or sixty, and it affected the way the calculations were done by them. The consequence for us now is that we have 60 seconds in a minute now.

The last cool thing that I want to mention is how calculations were made when the paper was expensive and not widespread. All sort of counting rods were used in the Europe and one type of them was called Split tally sticks and was used by British exchecquer until 1826. It was used for tax collection or debt recording. Every stick with the number of tax to be paid or debt to be returned was split into to part and by joining them again one could verify that the payment is correct and should be done.

The book has a lot of useful information and it is a drastic difference comparing with most of modern popular science books that usually have the same volume but contain just few facts and just repeat them through the pages again and again in different variations.

I highly recommend this book for all those who are interested to know more about how we ended up with all the numbers and the things around them that we have now. The only advice I can give is not to dig very deep into the sections connected with the representation of numbers in different languages. This section has so many comparisons and crossreferences between different language that it really doesn’t give a lot to the general idea but it really takes a lot of time to understand the whole thing.

As a conclusion I want to say that I was surprised to find very little information about the author in the internet, and there is actually rather small number of references to this book, at the same time it’s quite old. All this raises some suspictions, that this book is not a classic one on the subject, so probably it may differ from “official” points of view and it may be worth to double check any information of any importance in different sources before actually using it anywhere seriously.