Category: General

Flag for a United Ireland

On the front page of the Business Post of November 28th to 29th 2021, the main headline article was on the results of a survey on what proportion of people would be willing to admit some changes such as to the national flag or anthem in order to accommodate a united Ireland. The question of the flag seemed to me to be an unexpected one. The Irish tricolour flag already is supposed to represent a united Ireland. It was created before the partition of Ireland into the Republic and Northern Ireland. The colours of the flag already include representation of both the predominantly Catholic people of the Republic of Ireland by green and the Protestant majority at the time in Northern Ireland by orange. The white represents peace between these two groups. Does this not represent the outcome that is sought through a united Ireland?

Any problem then with the Irish tricolour flag for a united Ireland does not arise from any lack of appropriateness in its intention for fulfilling that purpose of unity but rather because there are some who see the Irish tricolour flag as a representation of separation of the whole of Ireland from the United Kingdom. In essence, the Tricolour does not seem British enough to Ulster Unionists. The tricolour carries the idea of revolution on the model of the French, appealing to Europe and the notion of a secular state the functions of which are inclusive of freedom of belief but separated from religious control. In the designing principles of the Irish tricolour or the adoption of a national flag by the Irish state, there was probably a motive to avoid an emblem having an overly religious connotation. Instead, the chosen tricolour is based solely on a simple geometrical combination of contrasting colours. For the Loyalists of Ulster on the other hand, there is preferred allegiance to the British crown, which may have its legitimacy conceived as proceeding from the divine right of monarchs. The emblems of the Unionists may for this reason be more likely to allude to religious symbols such as the Christian cross, to be found in the flags of nations in the United Kingdom and others like those of the Northwestern European Scandinavian neighbours. If a new flag is to be designed for a united Ireland to the satisfaction of Ulster Unionists, a model on a cross may be considered.

While Northern Ireland lacks an official national flag different from the Union Jack, there have been flags used for Northern Ireland alongside those of England, Scotland and Wales. The red saltire on a white background has long been used to represent Ireland. Despite being called the Cross of Saint Patrick, the patron saint of Ireland, it is derived from the heraldry that now belongs to the Duke of Leinster, the premier peer of Ireland. It entered the Union Jack where it represented Ireland, and now Northern Ireland. Irish institutions, such as universities in Ireland, have been using this heraldry in their insignia.

Another flag used for Northern Ireland is the Ulster Banner, which has a red cross on a white field. The red cross on a yellow field is contained in the traditional heraldry derived from the shield of Burgh for the Province of Ulster, not quite the same as Northern Ireland. Both of these flags contain the hand of Ulster emblem.

What we are contemplating here is the design of a new flag for a united Ireland, appealing to all, not a new flag for Northern Ireland. When thinking of a flag for Ireland, I first considered what the simplest available heraldry would be. The flag should be as simple as possible, with two or three colours only and no complicated drawings or emblems. As the colour most associated with Ireland is green, this colour should appear prominently. The heraldric pattern in line with Northwestern European nations would be a cross. A green cross on a white field or a green field with either a white or yellow cross seem to be the simplest approaches. The white cross on a green field in a flag for an independent Ireland by the United Irishmen appeared historically, so there is a precedent here. A yellow cross would be a simplification of an orange cross in a white cross. A yellow emblem on a green field appears in the flag of the province of Leinster and the Confederacy of Ireland, so these two colours are quite well associated with Ireland. However, these proposals seem inordinately suggestive of the Republic of Ireland and Catholicism only.

It would seem better therefore to include an orange cross or saltire of some kind to represent the inclusion of Ulster. The saltire because of the Cross of Saint Patrick seems a more fitting choice than a erect cross associated with England. A saltire is also on the flag of Scotland, where a Gaelic language is spoken too. Some have suggested a Celtic cross, but I think the Celtic cross would not represent inclusion of Ulster as well as the saltire would. A red saltire does not seem Irish enough to someone from the Republic of Ireland. Therefore, its colour ought to be changed from red to orange in emulation of the Irish tricolour flag.

The saltire can be modified in shape to a cross of Saint Brigid, which is a symbol heavily connected to Ireland, and probably more characteristically and recognisably Irish than a saltire. The cross of Brigid also happens to resemble the way the cross of Patrick is counterchanged in the Union Jack, so there is the added benefit of this appeasing Unionists. The orange figure must be surrounded by either white fimbriation or a white field, as that is the only available colour of traditional heraldry and suitable for a flag producing a sufficient contrast against orange. To have a green field or background, the contrasting white may intervene between the hues as a saltire.

Here is a depiction of this solution for the flag of a United Free State of the Republic and Northern Ireland:

After designing this flag, I searched Google with the terms “Brigid cross flag” and found that a similar concept had been proposed before, just ten months ago, of which I was previously unaware. In my opinion, the juxtaposition of green and orange there without intervening white fimbriation created an ugly effect. The similarity of the proposals shows how readily an orange cross of Brigid aligned with a saltire is likely to be thought of as representing a unification of the cultures of the Republic and Northern Ireland.

References

https://en.wikipedia.org/wiki/List_of_flags_used_in_Northern_Ireland

https://en.wikipedia.org/wiki/List_of_flags_of_Ireland

I fixed u/Reddinator64’s Ireland Celtic Cross design, giving orange and green equal area from vexillology

https://www.independent.ie/opinion/analysis/rethinking-our-national-emblem-what-could-a-united-ireland-flag-look-like-40395785.html

A saltire flag for the island of Éire, keeping in tradition of other flags in the British Isles by using Brigid’s Cross from vexillology

Dozenal Forum

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 – Dozensonline https://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.

Pyritohedral crystal Empty

In the Phaenomena section, there are also topics on global atmospheric air current zones and hexadactyly.

Another section of the Dozenal Forum is on Nomenclature. From Thursday 3rd October 2019 there is a topic on mnemonics which builds on the earlier post here from Tuesday 9th July 2019, “A Reply to Dozensonline, Number Bases, Dozenal, Request for Help with mnemonics for Dozenal”. From Monday 30th September 2019 on the dozenal forum there is a topic on Proto-Indo-European names for numerals. This is related to the earlier topic at https://www.tapatalk.com/groups/dozensonline/uncial-nomenclature-t1570.html on DozensOnline. The mnemonic solution and Proto-Indo-European nomenclature proposed are related.

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.

Musical Pipe Instrument Pitch Fingering Notation

Notes on a musical pipe instrument are selected by covering or uncovering combinations of holes. The proposed notation for the notes of a pipe instrument displays the fingerings to be used to play the notes. Each of eight holes is represented in the proposed notation by a vertex. If the numbered hole is to be used in playing a note, then its representative vertex is to be joined by a line to the centre of the diagram for that note. The vertices for the covered holes by the same hand are joined to each other in the diagram for the note, but the vertices for holes played by different hands are not to be joined to each other except incidentally.

In the proposed notation, the vertices for the four holes played by the left hand are at the corners of a square oriented with its edges oblique like a diamond. The following picture diagram illustrates the notation for the left hand:

The vertices for the positions played by the right hand on the pipe are the corners of a square with its edges horizontal and vertical. Holes played by the right hand that are half covered can be indicated by writing a short line perpendicular to the diagonal of the square at the relevant vertex. The following diagram shows the notation for the right hand:

The notation for a single note combines both hands as shown in the following diagram:

The fingerings for a selection of scale notes by this notation are exemplified on a treble stave in the following image:

There should be a ledger line for the note middle C. The diagrams for the notes can be written at least twice as big relative to the stave. It is possible to combine the note head diagrams with stems indicating note durations. A distinction between a filled, as of a crochet, or unfilled, as of a minim, note head could be achieved by a cartouche around the note head. Another way to specify the note durations is by writing a mathematical fraction immediately to the right of the diagrammatic note head. For example, a crotchet would be followed by the fraction 1/4. A dotted minim would be 3/4. Metric durations of tuplets can also be specified by this proposal.

The author of this article is the inventor of this proposed notation, is not reporting on the work of someone else, and has not seen anything like it elsewhere.

Base Twelve Calligraphic Numerals

Here is an image of rationally designed featural numerals for base twelve in a calligraphic pen style that was made yesterday well before six o’clock in the evening, based on principles worked out last year. It is possible to use versions of these numerals with a liquid crystal type of modular display containing twelve segments. There are references to Indo-Arabic numerals, Chinese numerals, and Roman numerals in these designs.

This is not a serious proposal for replacement of decimal numerals, for which a better distinguishable against decimal set more similar to the usual Indo-Arabic numerals and based on the normal seven segment modular display such as is used in pocket calculators was proposed earlier.

Dozenification of Contemporary Weights

Previously (Jan 21 2017, 09:21 PM, DozensOnline, Applications, “All Your Base Are Belong To Us”; Apr 28 2017, 08:47 PM, “Requirements For Implementation Of Uncial”) was proposed how using division of the day by a power of the dozen, the gravity of the Earth, and the density of water can produce a unit of mass equal to the metric gram. All metric weights can thereby be converted into a coherent dozenal metrology by moving the decimal point to write the weight in grams, followed by changing the notation of the number from decimal to base twelve.

In choosing units of measurement for a dozenal metrological system, for minimum change and least disruption it is preferable to retain existing units wherever it is possible to incorporate these into a dozenal framework. Retention of the maximum number of existing units while allowing dozenal scales of magnitude would suggest that existing units of measurement still in use that already have dozenal ratios of their magnitudes should be chosen. Retention of existing measures acts as a celebration of the people’s choice of dozenal in the history of measurement and evidence for the benefits of twelve as a division. For this reason, I suggested retention of the inch as a unit of length, which is multiplied by twelve to produce the foot, and has been divided dozenally to the pica and point in typography or graphical design.

As mentioned previously (“Base Twelve in Measurement”, Knew’n’Tell, Ideas & Observations, Thought Views, WordPress, 17th Dec 2018), there are “for weight twelve ounces to a pound troy”. The troy system of weights was used in Britain for weighing of pharmaceuticals of medical prescriptions until it was made illegal since the year 1976 for such use as part of decimal metrication. The troy ounce is, however, still legal for use in the trade of investment precious metal bullion. Another pre-metric system of weights still used is the avoirdupois, which forms part of the American Customary and British Imperial systems of measurement. The troy and avoirdupois systems share as a common unit the weight called a grain, which is about 0.0648 grams, but differ in the multiples of this unit in the formation of larger named units. In the troy system, 480 grains form an ounce troy, so 480 * 12 = 5760 grains form a pound troy, 5760 * ~0.0648 g = ~373.25 g. In the avoirdupois system, on the other hand, seven thousand grains form a pound avoirdupois, 7000 * ~0.0648 g = ~453.6 g. But the avoirdupois pound has sixteen ounces avoirdupois rather than twelve, so the avoirdupois ounce is about 453.6 g / 16 = ~28.35 grams, nearly the same as an ounce troy of about ~373.25 g / 12 = ~31.1 grams.

For unification and dozenification of these current and related systems of weight, I propose that their ounces be dozenalised by being rounded to the same thirty grams, which dozenally is two-and-a-half dozen grams. This is the same as a metric ounce that already exists, so it is not a new unit. Additionally, I suggest that the multiples and divisions of this ounce to form the other named units of weight in the systems should as much as possible be the same as or similar to the ratios of units in the troy and avoirdupois systems, but should be changed only where such ratios involve awkward prime numbers in their factorisations, such as the prime number seven seen in the 7000 grains avoirdupois per pound avoirdupois, or where multiples or divisions are overly decimal (Conversion of decimally rounded numbers to dozenally rounded numbers was described earlier at DozensOnline, Number Bases, Dozenal, “Rounding, Surrogates, And Auxiliaries”, May-June 2017). This procedure allows the adjusted units to resemble in magnitude and relations the existing units, and is thereby along the lines of minimum change while at the same time being dozenalised. After conversion of the sizes of the units, it remains only for the numbers to be written dozenally using dozenal numerical notation of twelve phalangeal numerals.

The dozenified troy, which I call the trade weight system, would then be
0.0625 grams = 1 trade grain
1.5 grams = 1 trade pennyweight = 24 trade grains
30 grams = 1 trade ounce = 20 trade pennyweights = 480 trade grains
360 grams = 1 trade pound weight = 12 trade ounces = 240 trade pennyweights = 5760 trade grains

The dozenalised avoirdupois system or unified American Customary and British Imperial weight systems, which I call the system of civil weights, would become
0.0625 grams = 1 trade grain
1.875 grams = 1 civil dram = 30 trade grains
30 grams = 1 trade ounce = 16 civil drams = 480 trade grains
480 grams = 1 civil pound weight = 16 trade ounces = 256 civil drams = 7680 trade grains
5760 grams = 1 civil stone = 12 civil pounds weight
11520 grams = 1 civil quarter weight = 24 civil pounds weight
46080 grams = 1 civil “hundredweight” = 4 civil quarters weight = 96 civil pounds weight
829440 grams = 1 civil ton = 18 civil “hundredweights” = 144 civil stone = 1728 civil pounds weight

Common to both these trade and civil systems are the thirty gram metric ounce and the trade grain of a sixteenth of a gram. Sixteenths and other binary powers are very convenient for weights and are much simpler in dozenal than decimal, as mentioned before (“The Trouble With Base Thirty”, Knew’n’Tell, Ideas & Observations, Thought Views, WordPress, 26th Jan 2019). At first it might have seemed that the old grain being common to both the troy and avoirdupois systems should have been maintained unchanged. However, in effect that would be no change or no dozenalisation, as the value of the old grain would not be a convenient fraction of the dozenal basic unit of weight, and, with the old grain, only one unit would be common to both the troy and avoirdupois, whereas the sixteenth of a gram allows both the grain and ounce to be the same in both systems dozenalised.

Notice too that in the civil weight scheme, the number of civil pounds weight per civil ton is a cubic dozen, which is near the two thousand pounds per ton of the American Customary and is at the same time the dozenal analogue of the thousand or ten cubed of kilograms per tonne of the metric system.

A weight currently used for gemstones is the carat, which was formerly metricated to 0.205 grams and latterly downgraded to the more decimalised 0.200 grams. The carat is said to be derived from a 24th part of a solidus, where a solidus was a 72nd part of a Roman pound weight. Unifying the Roman pound weight or libra with the trade pound of 360 grams, this would lead to 360 g / 72 = 5 grams for the gem solidus, and 360 g / (24 * 72) = 360/12^3 = ~0.2083 grams for the gem carat weight. I therefore propose replacement of the metric carat by this dozenalised carat of 5/24 grams. However, in earlier times, the number of the gold solidus making up a Roman pound was sixty rather than 72, which would produce a gold solidus weight of 360 / 60 = 6 grams, and 360 g / (24 * 60) = 0.25 g or a convenient quarter of a gram for the gold carat weight. This value for the carat is necessary if the number of trade grains making up a carat weight is to be four. However, since the quarter gram value differs so much from the metric carat, I propose that the quarter gram carat be limited to being a unit of the trade system for precious metals, while the 5/24 gram carat would replace the metric carat used for gemstones.

Hence, the system of trade weights can be supplemented with these further weights, where:
5/24 grams = ~0.2083 grams = 1 gem carat = 1 square dozenth trade ounce = 1 cubic dozenth trade pound
0.25 grams = 1 gold carat weight = 1.2 gem carats = 4 trade grains
1.25 grams = 1 trade scruple = 5 gold carats weight = 6 gem carats = 20 trade grains = 1/4 gem solidus
5 grams = 1 gem solidus = 24 gem carats = 1/72 trade pounds weight
6 grams = 1 gold solidus = 24 gold carats weight = 96 trade grains
360 grams = 1 libra = 60 gold solidi = 1440 gold carats weight = 1728 gem carats

The Latin word siliqua can be used for a carat. The Greek word nomisma can be used for a solidus.

References:
https://en.wikipedia.org/wiki/Troy_weight
https://en.wikipedia.org/wiki/Apothecaries%27_system
https://en.wikipedia.org/wiki/Avoirdupois_system
https://en.wikipedia.org/wiki/Ounce
https://en.wikipedia.org/wiki/Carat_(mass)
https://en.wikipedia.org/wiki/Solidus_(coin)

A Reply to Dozensonline, Number Bases, Dozenal, Request for Help with mnemonics for Dozenal

Replying here in WordPress because Dissenter is not working right now: “500: Failed To Dissent
No workers available to handle the requested job.” 

To “SenaryThe12th 2:54 PM – 1 day ago#1”, at

https://www.tapatalk.com/groups/dozensonline/request-for-help-with-mnemonics-for-dozenal-t2020.html

The simplest option would probably be to split apart from each other the voiced and unvoiced consonants. Eight groups could then be: P, F; B, V; T, Th, Ch; D, Dh, J or Jh; S, Sh; Z, Zh; K, Q, X, H; G. The four remaining groups could be chosen from N and Ng, M, L, R. Y and W or Wh might be considered. The sounds of the letters are to be understood as from “Appendix B: Consonants and Phones” at “SenaryThe12th 6:04 AM – Apr 25#1”, Dozensonline, Number Bases, Non-Dozenal bases, Senary and {2, 3} Bases, Mnemonics for Senary, at https://www.tapatalk.com/groups/dozensonline/mnemonics-for-senary-t1991.html.

A Reply to https://www.tapatalk.com/groups/dozensonline/duodecimal-myriad-system-t1970.html#p40018012

Dozensonline > Tools > Number Names > Duodecimal Myriad System
https://www.tapatalk.com/groups/dozensonline/duodecimal-myriad-system-t1970.html#p40018012
“sunny
8:48 PM – Mar 01 #3″:

“I always liked groupings in fours, replacing a bit unwanted terms like ‘great gross’ or ‘grand’ or any such others by the simple word ‘dozen gross’ that seems straightforward and more helpful. Why should we bother to say in decimal, ‘one thousand five hundred’ when we could do it with the more simpler ‘fifteen hundred’?”

I also rejected the terms “great” and “grand”. Grand means a thousand in decimal. I would go further and discourage “gross” because I have never seen it used for a dozen dozen by anyone other than dozenists and it is not likely to be understood by others. Nevertheless, I do use gross sometimes for brevity.

For grouping of dozenal digits,

[Citation reference:
Dozensonline > Tools > Number Names > Uncial Nomenclature
https://www.tapatalk.com/groups/dozensonline/uncial-nomenclature-t1570.html#p40009563
“DavidKennedy
May 08, 2017 #14″
“Five or six digits are too many to subitise. There is decimal notation that groups digits into threes by commas. From the point of view of visual subitisation of numerical symbols alone, figures could be grouped in threes or fours, but by twos would probably be too frequent. However, from the language point of view, grouping in twos is probably better,”]

I also preferred grouping of dozenal digits by fours, as demonstrated in the tables at

Dozensonline > Number Bases > Dozenal > Rounding, Surrogates, And Auxiliaries
https://www.tapatalk.com/groups/dozensonline/rounding-surrogates-and-auxiliaries-t1748.html

In some browsers the tables may not display anymore. If so, right click on the table and select “inspect element” and read through the pane for the table cell entries.

A Reply to https://www.tapatalk.com/groups/dozensonline/hexcalibur-date-time-and-angles-part-2-t1969.html#p40018104

Dozensonline > Applications > Calendar Reform > Hexcalibur: Date, Time and Angles | Part 2

https://www.tapatalk.com/groups/dozensonline/hexcalibur-date-time-and-angles-part-2-t1969.html#p40018104

Kodegadulo: “11:28 PM – 1 day ago #8

Silvano wrote:
http://www.intuitor.com/hex/hexclock.html

Who ever heard of any kind of “minute” that is only broken up into sixteen of any kind of “second”? Really, can anyone get any more desperate trying to shoehorn a system into the old and moldy sexagesimal pattern? Leave the “hour”, “minute”, and “second” alone. Reserve those terms just for the sexagesimal units we all know and love, uh tolerate.”

To subdivide the period of a hand of a clock into so small a number of tick marks as twelve or forezeen which is sixteen decimally wastes energy through such a large movement in the clockwork mechanism. Currently, my opinion is that the most efficient system for a clock would be to have as many ticks marks as are possible while being still readily distinguishable. The square of forezeen is too many tick marks for the face of a wrist watch because of the difficulty of distinguishing them as a result of parallax [Citation reference: Dozensonline > Number Bases > Non-Dozenal bases > All Your Base Are Belong To Us “:
https://www.tapatalk.com/groups/dozensonline/all-your-base-are-belong-to-us-t1615.html#p40005801
” DavidKennedy
Jan 22, 2017 #17″:
“With as many tick marks as for hexadecimal, parallax would be a huge problem in reading which mark the hand points to.”].

Hence, for a dozenal clock, the number of tick marks should not be as few as twelve, but rather should be as many as the square of twelve which is perhaps just about not too many for a clock or even the face of a wrist watch as long as there is a ticking mechanism which improves distinguishability. However, the most useful number of tick marks for small watch faces is likely to be fewer, which is a reason for preferring half a gross or six dozen in civil analogue clocks. The clock is only a measurement device and does not constrain the consistently dozenal notation and divisions for time for scientific purposes [Citation reference: Dozensonline > Tools > Applications and appliances > Requirements For Implementation Of Uncial
https://www.tapatalk.com/groups/dozensonline/requirements-for-implementation-of-uncial-t1591.html#p40009356
“DavidKennedy
Apr 28, 2017 #2″:
“Time
Hours should be converted to semi nullry semiduors. Minutes should be converted to quick primry units of fifty seconds. Seconds should be converted to quick bisecondry units of the square of five sixths of a second. (Multibase clock)”].

The system of subdivisions for scientific purposes, as opposed to that for civil purposes which is so closely related, thereby becomes one not of base twelve but rather of twelve squared, and consistently so, yet encoded dozenally by pairing of dozenal figures, which is a natural way to group the “digits” linguistically [Citation reference: Dozensonline > Tools > Number Names > Uncial Nomenclature
https://www.tapatalk.com/groups/dozensonline/uncial-nomenclature-t1570.html#p40009563
“DavidKennedy
May 08, 2017 #14″:
“from the language point of view, grouping in twos is probably better, and this also makes sense from the viewpoint of the hands necessary for a clock with tick marks, as I have already explained.”].

I point out and emphasize that this scheme of subdivisions or series of magnitudes in the scale is consistently of the square dozen base, by choosing a period of twelve days and subdividing this into successive levels of subdivisions or ordinately. It is not a mixture of different bases at various subdivisional levels as the sexagesimal system is because of the number of hours per day differing from the number of minutes per hour or seconds per minute. Thus, the number of *secondries per *primery or minette is a square dozen, the number of minettes per *nullry or duor or double hour is a square dozen, and the number of duors per twelve days is a square dozen.

However, in the civil scheme, the divisions of the day become hemiduors, the *primeries are minettes as for the scientific scheme, and then *dysecondries from the viewpoint of the scientific scheme. The *dysecondry can be abbreviated to *dyse. The *trisecondry may be abbreviated to *tryse which is near to a conventional sexagesimal second in duration.

Base Twelve in Measurement

With the age of Enlightenment, dogmas that had persisted for millenia were being questioned and replaced; as was the astronomy of Ptolemy modelled on epicycles and the philosophy of Aristotle held and enforced as doctrine by the Christian Roman Church. The theory of Copernicus and the discoveries of Galileo through testing and verifying theory against reality with construction of instruments revised the knowledge of the heavens. Whereas the opinions of Aristotle were supported mainly by thought alone and persisted by the insistence of belief under authority, the enhanced understanding that was being developed arose through experimentation.

In France at this time, there was an accompanying redistribution of the ruling structure, where monarchy and aristocracy were threatened by the oppressed. While in the past, autocrats had endorsed official units of measurement for consistency in trade and commerce, now a society governed with the insight of thinkers and scientists bore the responsibility once restricted to royalty and endeavoured to design a system of measures suitable not just for the longstanding accounting and exchange of resources, but also for the greater precision and cross-national applicability required for scientific measurement and dissemination for reproduceability of experimental findings.

Whereas before, we hear that the ancient Egyptian unit of length the cubit was decided upon by a distance between the tip of the nose and outstretched arm of a Pharaoh, and the imperial foot was named for its length being that of the anatomical part of some king, with the revision of units of measurement, the basis for them was sought not in the divinity of a hereditary ruler, but rather in some more universal and global phenomenon or condition shared by all humanity.

Furthermore, this opportunity was used to attempt to unify the units of measurement for different kinds of quantity, so that those for lengths, areas, volumes, weight, and time could be related to each other and replicated anywhere in the world without reference to an arbitrary artifact. Originally, therefore, the unit of length was defined as a precise division of the distance between the pole and equator of the common Earth, just as the unit of time had been specified by an agreed division of the day the span of which was likewise the same for all dwelling on this planet. The unit of weight was defined by a reproduceable volume of standard water.

However, during this process of designing a unified system of measurement or metrology, the scheme of division chosen was based on the decimal system of numeration, which then was mainly how numbers were recorded and calculations conducted, as by the digits derived from the positional Indian or Arabic figures and before them the Roman numerals. Even earlier, numbers were written using a decimally encoded sexagesimal system preserved from the ancient civilisations of Sumeria and Babylonia through the Greeks. The Greeks and Hebrews too had a further non-positional decimal system of notation which likewise for Roman numerals in calculation has been superseded by the positional kind not requiring the aid of an abacus. Nevertheless, the sexagesimal notation persisted in the tabulation of astronomical data relating to co-ordinates of the sky around the Earth and division of the circle into angles, and in division of time from the daily global rotation. The strictly decimal metrology never managed to eradicate the use of the sexagesimal system in division of cycles. Consequently, the resulting and still current metrological system combines a mixture of divisions to units by more than one numerical base.

While people can manage or struggle with using this mixture of disparate bases in metrology, such that with our astronomy it is still possible to deliver astronauts into space, there are problems or difficulties that could be resolved if a single base could be selected and used for all metrological divisions leading to units of measure. The failure of the complete decimalisation of metrology could be attributed to the weakness of decimal as a base for practical purposes, particularly for division of quantities into fractions, in contrast to the strength for such purposes of the sexagesimal base, which is of a class of numbers called by mathematicians highly composite. A highly composite number, say the mathematicians, is a number containing more factors than any smaller number than itself. The number sixty, of which the sexagemsimal system is based, has as factors or divisors all of the smallest whole numbers 1, 2, 3, 4, 5, 6, as well as the larger 60, 30, 20, 15, 12, and 10. Thus, all of the simplest unit fractions, the whole, half, third, fourth, fifth, and sixth, can be easily written and used in calculation by sexagesimal. Sexagesimal is in fact the smallest base containing all of the first five or six factors, because sixty is the lowest common multiple of the first five or six counting or cardinal numbers. However, sixty as a base is still rather larger than would be convenient for easily learnt arithmetic. It is very likely that people would find a smaller number as base much more manageable for calculations.

Decimal evidently has a functional size, but lacks divisibility by the number three. The numbers dividing evenly into ten are the unit one, the base ten, its half five, and two. On the other hand, the number twelve is divisible likewise by the unit one, itself twelve, its half six, as well as two. Additionally, however, twelve is divisible by three and four, which decimal does not have as factors. Clearly therefore, if we were to use twelve as the base of our numeration, we would have these extra factors. Twelve, like sexagesimal, is one of the numbers called highly composite, but unlike sexagesimal is considerably closer to the size of ten with which we have been familiar as base.

While ten for the base is more familiar, the use of twelve as a division is quite known to us in metrology. There are for length twelve inches to the foot, for time twelve hours twice a day, and twelve months in a year, and for weight twelve ounces to a pound troy. The metrological uses are in conjunction with the practice in the marketplace of packaging goods by twelves, such as eggs by the dozen or half dozen. The utility of twelve as a factor in actual measures undoubtedly arises from its practicality by high divisibility.

Not only does twelve have extra factors, but these are more important factors for metrology than the factor five in decimal that twelve lacks. The most important factors are those that are smaller, so the most important factor is two, the next most important is three, and so on. Factors of two or three are especially important in metrology because of how easily their divisions can be cut. Furthermore, halves and thirds produce optimum divisions in terms of efficiency of information in certain metrological applications such as scales of weights and accounting where there is a subtractive component to the specification of values. Larger prime numbers such five, seven, or eleven have little value for metrology in themselves.