Dozenal Notation

Numbers can be written in which the positions of digits represent powers of the base twelve instead of ten.

In the official journals and publications of the Dozenal Societies of America and Britain, there were various methods of specifying that numbers were dozenal.

The simplest was to assume that all numbers were dozenal unless otherwise indicated. This would only work in a context where this interpretation had been declared sufficiently obviously, such as by a statement at the beginning of the publication, because throughout the world people usually assume that numbers written with the Indo-Arabic digits are decimal. Decimal numbers were therefore marked for difference, such as by being placed in brackets.

Another method employed was to have special formatting for dozenal numbers, such as by them being in italics. The effectiveness of this has limitations in general contexts where italic formatting is often used for other purposes.

Yet another form of presentation was to place a symbol or annotation next to the dozenal number. An example of a symbol that has been used in this way is a prefixing asterisk *. A disadvantage of this procedure is that the addition of a symbol makes the dozenal notation more complex than the ordinary unannotated decimal numbers, thus subordinating dozenal relative to decimal, which is unacceptable to steadfast dozenalists who would rather have the number twelve as the default base.

Some who wrote numbers to be read dozenally have appended after the numerals as a suffix a letter standing for the base. Often this letter is an abbreviation of a word for the dozen, such as z. Sometimes then decimal numbers can be annotated with a different letter to show that they are not dozenal. However, dozenalists would have a hard time convincing decimalists to annotate all their decimal numbers with a letter, so this still subordinates dozenal notation. Another problem is that the letters that different people have been using to stand for the same base have been different, with the same letter standing for different bases to different people. This ambiguity cannot be remedied without decree and enforcement of an official style to be obeyed. Also, there is a limit to the number of letters available.

A preferable method that has been used in the Dozenal Societies is to change the fractional point from a decimal dot "." to a semicolon ";". The semicolon does not take up much width and merely replaces a character that often would have been included in the number anyway, so this notation does not subordinate dozenal much at all. The character is readily available for typing from a keyboard. An objection is that it could be confused with punctuation. Suggested remedies include other punctuation symbols.

The comma, which the French use in decimal numbers instead of a decimal point and which they call a virgule, is not to recommended for the fractional point, because of its use to group digits. In decimal numbers, digits are grouped by threes, as in a million written as 1,000,000. For dozenal numbers, the comma can be used to group numeral characters by fours instead of threes. This permits yet another distinction by which to contrast dozenal numbers from decimal numbers.

For dozenalists, only a solution for the base twelve is desired that enables base twelve to be the default base and not subordinate to unannotated decimal. Specially designed annotations for other bases, such as powers of binary, are not desired. Any other base than dozenal that might arise can be written using the dozenal numerals followed by a subscript number written dozenally and equal to the base the powers of which are to be interpreted as those at the positions of the numeral characters in the preceding number. This is analogous to how numbers in bases other than decimal are indicated in academic mathematics.