about Dozenals...
the site of

It′s Counting, Jim
but not as we know it!

Introduction to Base Twelve

Many people nowadays know that there are counting systems other than the usual decimal one; they will have heard of base two (binary) and base sixteen (hexadecimal) because the computer uses the former and colour codings are usually expressed in the latter. Neither is used in everyday calculations. The computer accepts data in base ten and churns it out again in base ten; how the computer does its work interests few of its users and what numbers it uses in its innards even fewer. The computer is quite happy with base two and people use base ten because they are used to it and know of no alternative.

There are people who think base sixteen might be a good substitute for base ten to bring humans more in line with their computers, but base sixteen, which brings in several new symbols and few arithmetical benefits for humans, is not necessarily the best for humans.

Best for humans… rather begs the question. Is any one number base intrinsically better than another and more suitable for human calculations and daily work?

There are, and have been for many years, people who maintain that base ten is not the best choice for humans.
Long before either hexadecimal or binary became familiar words, and before and ever since the French invented the metre and the decimal metric system, decimal notation and base ten have had a rival: base twelve.

Base twelve (also known as dozenal and originally as duodecimal) has long been singled out as a possible replacement for base ten. It offers many advantages over base ten.

Which begs another question: could a change of number base really bring benefits to man?
We believe it will. You will find arguments and ideas in favour of base twelve in the pages on this site.

A fact or two:

Any and every type of calculation which can be carried out in base ten can be carried out in base twelve or in any other base one might choose. "Points", "logs", slide-rules and even push-button calculators are not peculiar to base ten, but are employed also by other bases, though admittedly not as extensively.

The merits of base twelve are due to the great factorability of the number twelve, the next really useful number being sixty, but this latter number is rather too large to be chosen as an every-day number base. Ten is unsatisfactory because its factors 2 and 5 include the prime 5 which in turn is not as useful as the prime 3 (though one professor of mathematics complained that I was not being really fair to the number 5 when I said this ... ). The dozen, and the dozen dozen, or gross, have shown their usefulness in packing and packaging over many, many years.

And will Mankind be interested enough to listen? or kind enough? We live in hope…

Aye, it′s counting, Jim, but not as we know it…

But just consider, for a moment ... What would happen, if ...?

Now there's a thought to boggle the mind... Suppose we changed the number base, just like that, what would tomorrow be like? For the implications, have a look at "Splash!", (see Contents page).

Your comments and arguments, for or against, are welcomed.

So it′s nothing but base twelve here?

No, there's more, all mathematical, - other bases, number puzzles, units of measure (including historical), important essays, some metric-bashing, - but much more to come as we develop different areas.

New Dozenal Forum !

now anyone can post their ideas and comments and discuss dozenals, decimals and what have you. Extracts with ideas from the Forum will be added to this site.

Magazine: our Dozenal Journal is now available for download: Journal

Please also download the covering letter about this issue

New: some cartoons taken from one of our workbooks at percents

Please click here for list of CONTENTS of this site

Pages updated Monday 1st April 2008

In Memoriam - an obituary for Arthur Whillock

Our Information Secretary, Arthur Whillock, died on Saturday 27th May 2006.
His obituary, written by his son-in-law, Roger Parsons, is at Arthur

Most recent changes: Working Clock by Joshua Harkey; Comments on 487 question; In Defence of Sacred Measures (see metric section); Aims and Principles (under leaflets); In Memoriam: Arthur Whillock. Byraz Colour pdf; Dozenal Journal added. Extracts from the Forum. More anti-metric bits; Table of powers; Book Review (history section); more number work (probabilities); more suggestions for words; other dozenal sites: Dozenal Forum (Owen); TGM pdf booklet added

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a few words about us...

The DSGB, The Dozenal Society of Great Britain (founded 1959) and the DSA, The Dozenal Society of America (founded 1944) are separate organisations with a common aim: to draw attention to the advantages of the Dozen (or twelve-based) system for numeration and measurement. We consider that the decimal system is inadequate and of limited competence in many aspects of numeration. Decimals handicap the teaching of arithmetic and so inhibit understanding of the physical world and the decimal system is unable to express in simple terms the common proportions by which we order our practical and economic activities.

We want to replace decimal numeration by dozenal.

Membership of the Societies is open to all who have an interest in the development of arithmetic and measuring systems as vital tools for our everyday affairs and in promoting a clearer understanding of the ways in which the physical world is defined and ordered. By advocating the adoption of a more flexible numbering system for both scientific and general use we are also supporting the opinions of many philosophers and mathematicians, both past and present.

More at About Us a PDF file introducing the DSGB and see below for details of the DSA.

to contact us:

• DSGB email
• DSAemail
• DSA website: Dozenal Society of America