I have designed a glyph for the numeral ten to be used in base twelve numeration. Various characters have been used historically for the digit ten in base twelve numbers. One of the earliest used by a dozenal society is the Pitman turned digit two, based on the initial letter t of the word ten. Various conventions have been tried for the letter to be used for the numeral ten. One is the letter A, part of the system of transdecimal extensions to the Indo-Arabic digits used for hexadecimal numbers and called IBM computerese by dozenists. This scheme is considered to emphasise base ten as the ace of bases too much for dozenists by the first letter of the alphabet starting on ten. Another option is the letter J because it is the tenth letter of the alphabet. Yet another proposal is the letter d standing for dec or dek meaning ten. In recent years, some dozenists have begun annotating that numbers are to be read as written in base twelve by suffixing them with a subscript letter of the alphabet. This means that in order for dozenal numbers to remain distinct from decimal numbers, the decimal numbers need to be annotated with a literal suffix. However, these are not standard practice in formal mathematical literature, where bases are annotated when distinction between bases is necessary by digits in decimal format rather than by letters of the alphabet. The most popular numeral for ten among dozenists currently is the Pitman turned two ever since it entered Unicode. As such, this symbol can be interpreted as a numeral and not just a letter, bringing it into line with conventional mathematics.
My design is based on all of these literal characters for ten. Firstly, it is derived from the Pitman turned two by closing the curl in order for the character to have a distinct seven-segment modular element display. This fixed one of the disadvantages of the original unmodified Pitman turned two whereby it looked too similar to other numbers or characters, including the numbers two and seven, and the letter zed. However, closing the loop resulted in a figure that looked too similar to a style of the digit three having a horizontal top bar. To improve this issue, the next stage was to make the numeral look more like the tenth letter J of the alphabet while still resembling the Pitman turned two by a horizontal top bar and closing curve with the end meeting onto the partial stem. The present latest version modifies this further by making the join of the closed curve attach to the partial stem tangentially upwards. The resulting glyph can be written by hand quickly and effortlessly without lifting the implement from the page until the digit is complete. Additional bonuses are that it conveys a lower case letter d and double story letter a. Thus, my design proposal solves most of the conflicting usages of different letters for the digit ten by merging them all into one character. This character remains distinct enough from other alphanumeric symbols and glyphs to retain its unique meaning dedicated to the numeral ten for numeration using base twelve.
Further benefits of my design are that it has cues of the digits five and two that are the prime factors producing the number ten. As well as the turned digit two derived from the Pitman turned two, it contains a reversed digit five. Another effect is that a horizontal line and a closed curve suggest the numerals one and zero of the number ten in decimal format joined together and written vertically. This may increase subliminal identification in a transition from decimal to dozenal notation.
In summary, my design for the numeral ten for dozenal numbers satisfies the following inclusively:
The initial letter t of the word ten from the Pitman turned two;
The initial letter d of the morpheme dec or dek for ten;
The tenth letter J of the alphabet;
The letter a in lower case double story style from IBM “computerese”, often used for the numeral ten in hexadecimal numbers;
The decimal digits 1 and 0 forming the number ten in decimal format joined together and written vertically one under the other; and
The digits for the prime numbers two and five of which the number ten is composed as the product.
There is a certain dozenal forum that currently has forty-three topics and 151 posts.
Posts include the topic of dozenal directions from Monday 21st September 2020 last year, where the main author on that forum proposed a system of dozenal compass directions whereby directions that are a twelfth of a turn from a cardinal direction are indicated by the word “of” between the names of two adjacent cardinal directions, with the direction after the word “of” being the angularly nearer of the cardinal directions. The abbreviation proposed was “XoY”, where X and Y are the initials of the cardinal directions. The system was extended to indication of quarter twelfths of a turn and preserves by incorporation the existing conventional scheme of binary divisions in compass directions.
Another topic in the forum is a proposal for a dozenal metrological system that preserves as much as possible existing units of measurement of the decimal metric international system reframed dozenally. The system allows existing decimal metric measurements and their units to be more easily converted mentally without the aid of calculational devices to dozenal than to any other dozenal system because it is so constructed that the conversions require only shifting decimal points or dozenal fractional points, apart from the conversion of numbers from base ten to base twelve. The most recent post under this topic was on Friday 12th February 2021 this year. The topic was started in the forum on Sunday 15th September 2019, but contains principles which were conceived and published earlier, for example the unit of time and the consequent unit of length leading to area and volume derived from it were communicated on the DozensOnline forum on Saturday 21st January 2017, and stated to have been conceived the previous year and can be read at the webpage address https://www.tapatalk.com/groups/dozensonline/all-your-base-are-belong-to-us-t1615.html#p40005757. The unit of mass was mentioned on Friday 28th April 2017 at https://www.tapatalk.com/groups/dozensonline/requirements-for-implementation-of-uncial-t1591.html#p40009356. The unit of temperature was mentioned on Monday 12th June 2017 at https://www.tapatalk.com/groups/dozensonline/requirements-for-implementation-of-uncial-t1591-s24.html#p40010490. There is a table for conversion from decimal metric to the dozenal system with hundreds of units of measurement.
Another topic on the dozenal forum, from Thursday 8th October 2020 last year, is on how the decimal metric millimetre can be retained as being dozenally incorporated into a system based on the troy weight and including ounces and a carat weight. It is possible for several consistently dozenal metrological systems to be employed to allow retention and peaceful co-existence of contemporary units of measurement. Another example of such a system is that containing the inch and foot, of which the yard is a multiple by a dozenal divisor or snapping point.
From Tuesday 29th September 2020 last year, there is a topic on how Old Irish metrics were apparently consistently dozenal.
In the Mathematics section of the forum, from Monday 13th April 2020 there is a topic on probabilities of prime and composite numbers related to their importance or rank by occurrence or frequency relevant to which of them should be chosen in the formation of a base of numeration. This concept is related to or an elaboration derivable from the post here entitled “The Trouble With Base Thirty” from Saturday 26th January 2019. Soon after this article was published here, several of its concepts or key persuasive arguments appeared by different authors on the DozensOnline forum without attribution. The concept of the importance rank of divisors appeared earlier on Thursday 8th June 2017 at https://www.tapatalk.com/groups/dozensonline/prime-numbers-in-metrology-t1713.html#p40010405.
Also in the Mathematics section of the forum, there is a topic on ratios of decimal and dozenal powers from Sunday 20th October 2019. The concept is relatable to the previous topic on dozenal rounding from Tuesday 30th May 2017 at Rounding, Surrogates, And Auxiliaries – Dozensonlinehttps://www.tapatalk.com/groups/dozensonline/rounding-surrogates-and-auxiliaries-t1748.html. These topics are relevant to implementation of dozenism by conversion of decimal values to dozenal preferred values. They are contrary to the misconception of certain dissenters against dozenal that sizes converted from decimal could not be made to look elegant in dozenal. In fact, as was demonstrated, values converted to convenient dozenal numbers can be organised with excellent memorability and optics. The methods of conversion discussed demonstrated that interconversion between decimal and dozenal could be done mentally. There is some further discussion of roundness under the topic “Ripples and Awayness” in the Mathematics section on the dozenal forum from Monday 12th August 2019.
Another topic, from Thursday 19th Sep 2019, in the Mathematics section proves that fifths can be represented better in dozenal than thirds can be in decimal. This argument and conclusion is contrary to the mistaken beliefs of the antagonists infesting the DozensOnline forum. The argument also implies that octal encoding its square is better than the square of four as a base, again contrary to the sway on the DozensOnline forum. The topic incidentally contains a recurrence relation and summation defining the base of the natural logarithms dated from July 2010. A single function of a running variable there defines the numbers of the continued fraction of the base of the natural logarithms. It looks like original material to me despite lack of a reference for the fairly common knowledge of the continued fraction and associated notation, although continued fractions are not mentioned explicitly in the comment.
There is a topic from Saturday 7th September 2019 outlining a proof of the limitation of the number of regular four-dimensional figures bound by straight figures to six and mention of lack of fivefold symmetries in regular bricks. This is a recurrent theme on the dozenal forum, for example under “Angles in Crystals” in a comment of Friday 6th September 2019 under the topic “Comments on Angle Units” in the Metrology section. It is also stated earlier on Thursday 8th June 2017 at https://www.tapatalk.com/groups/dozensonline/prime-numbers-in-metrology-t1713.html#p40010405. Incidentally, there is a discussion of angles in a dodecahedral crystal in the topic “Pyritohedral crystal” in the Phaenomena section of the dozenal forum. In the Mathematics section of the dozenal forum, there is a topic on how simply angular fractions of a circle may be represented in rectangular co-ordinates. This demonstrates the greater simplicity of twelfths than tenths or even fifths of a circle. Furthermore, twelfths of a circle are not less simple than sixths or eighths, showing dozenal to be not inferior to senary or octal for the purpose of angular measure in the context of Euclidean constructability by straight unmarked ruler and compass. The unusually simple expressions for the double dozenths of a circle appeared earlier in an issue of the Duodecimal Bulletin, which was not cited.
In the Phaenomena section, there are also topics on global atmospheric air current zones and hexadactyly.
As a proposal for common speech dozenal analogies of the decimal terms million, billion, trillion and milliard, billiard, trilliard used for example in finance, the nomenclature based on the suffix -lliad and Greek prefixes was described from Friday 9th August 2019 on the dozenal forum. For a more technical scientific style of nomenclature for powers of twelve to be used for example in units of measurement, from Saturday 28th September 2019 a system with the suffix -on or -ino and Greek prefixes was described. These systems incorporate the advantageous fourth power of twelve as base, as advocated here on Friday 22nd March 2019 in “A Reply to https://www.tapatalk.com/groups/dozensonline/duodecimal-myriad-system-t1970.html#p40018012”. Except the prefix “enkomi” for eleven seeming to be a bit long, in style and for international applicability, these proposals seem better than those on the DozensOnline forum. For example, -on or -ona is better than -qua, and -ino is better than -cia because there ought to be a vowel between the consonants in many languages. Derivation of the suffixes from the Latin word uncia was described to show that this is possible. However, in style it seems inferior to the earlier versions. A compatible version of the nomenclature for every power of twelve was proposed. In the nomenclatures, for example in the naming of geometrical figures, the consonant z rather than ch for twelve the dozen or zero was preferred.
Another section of the forum is on the design of numerals. There is discussed dozenal notation and design of numerals. On Saturday 17th August 2019 under the topic “Co-existing bases” was proposed the reversed semi-colon Unicode 204F as a dozenal fractional point marker. On Saturday 18th April 2020 last year under the topic “Font CSS” in the Forum Management section of the dozenal forum, the reversed comma was proposed for separation of groups of four numerical figures in dozenal numbers to match the reversed semi-colon as dozenal fractional point. These have been implemented on the dozenal forum so that they appear and anyone can type them with dozenal distinct against decimal numerals. On Friday 10th April 2020 last year, a character for the numeral eleven was proposed looking like a Gothic arch.
Lastly, there is a section for references on the forum and in the forum there are links to sites such as DozensOnline and an author of poorly competing schemes, such that if anyone monitors the source of internet traffic or referral webpages for those websites, he would know about the existence of the dozenal forum. Many ideas from here or the dozenal forum have been appearing soon afterwards by other authors on the DozensOnline forum.
Ideas & Observations 